whisper.cpp/ggml.c

#include "ggml.h"

#if defined(_MSC_VER) || defined(__MINGW32__)
#include <malloc.h> // using malloc.h with MSC/MINGW
#elif !defined(__FreeBSD__)
#include <alloca.h>
#endif

#include <assert.h>
#include <time.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
#include <stdio.h>

// if C99 - static_assert is noop
// ref: https://stackoverflow.com/a/53923785/4039976
#ifndef static_assert
#define static_assert(cond, msg) struct global_scope_noop_trick
#endif

#if defined _MSC_VER || defined(__MINGW32__)

#if !defined(__MINGW32__)
#include <Windows.h>
#else
// ref: https://github.com/ggerganov/whisper.cpp/issues/168
#include <windows.h>
#include <errno.h>
#endif

typedef volatile LONG atomic_int;
typedef atomic_int atomic_bool;

static void atomic_store(atomic_int* ptr, LONG val) {
    InterlockedExchange(ptr, val);
}
static LONG atomic_load(atomic_int* ptr) {
    return InterlockedCompareExchange(ptr, 0, 0);
}
static LONG atomic_fetch_add(atomic_int* ptr, LONG inc) {
    return InterlockedExchangeAdd(ptr, inc);
}
static LONG atomic_fetch_sub(atomic_int* ptr, LONG dec) {
    return atomic_fetch_add(ptr, -(dec));
}

typedef HANDLE pthread_t;

typedef DWORD thread_ret_t;
static int pthread_create(pthread_t* out, void* unused, thread_ret_t(*func)(void*), void* arg) {
    HANDLE handle = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, arg, 0, NULL);
    if (handle == NULL)
    {
        return EAGAIN;
    }

    *out = handle;
    return 0;
}

static int pthread_join(pthread_t thread, void* unused) {
    return (int) WaitForSingleObject(thread, INFINITE);
}

static int sched_yield (void) {
    Sleep (0);
    return 0;
}
#else
#include <pthread.h>
#include <stdatomic.h>

typedef void* thread_ret_t;
#endif

#ifdef __HAIKU__
#define static_assert(cond, msg) _Static_assert(cond, msg)
#endif

#define GGML_DEBUG 0
#define GGML_GELU_FP16

#if UINTPTR_MAX == 0xFFFFFFFF
    #define GGML_MEM_ALIGN 4
#else
    #define GGML_MEM_ALIGN 16
#endif

#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define MIN(a, b) ((a) < (b) ? (a) : (b))

#define UNUSED(x) (void)(x)
#define SWAP(x, y, T) do { T SWAP = x; x = y; y = SWAP; } while (0)

#define GGML_ASSERT(x) \
    do { \
        if (!(x)) { \
            fprintf(stderr, "GGML_ASSERT: %s:%d: %s\n", __FILE__, __LINE__, #x); \
            abort(); \
        } \
    } while (0)

#ifdef GGML_USE_ACCELERATE
#include <Accelerate/Accelerate.h>
#elif GGML_USE_OPENBLAS
#include <cblas.h>
#endif

// floating point type used to accumulate sums
typedef double ggml_float;

// 16-bit float
// on Arm, we use __fp16
// on x86, we use uint16_t
#ifdef __ARM_NEON

// if YCM cannot find <arm_neon.h>, make a symbolic link to it, for example:
//
//   $ ln -sfn /Library/Developer/CommandLineTools/usr/lib/clang/13.1.6/include/arm_neon.h ./src/
//
#include <arm_neon.h>

float ggml_fp16_to_fp32(ggml_fp16_t x) {
    return x;
}

ggml_fp16_t ggml_fp32_to_fp16(float x) {
    return x;
}

#define GGML_FP16_TO_FP32(x) (x)
#define GGML_FP32_TO_FP16(x) (x)

#else

#ifdef __wasm_simd128__
#include <wasm_simd128.h>
#else
#include <immintrin.h>
#endif

#ifdef __F16C__
float ggml_fp16_to_fp32(ggml_fp16_t h) {
    return _cvtsh_ss(h);
}
ggml_fp16_t ggml_fp32_to_fp16(float f) {
    return _cvtss_sh(f, 0);
}

#define GGML_FP16_TO_FP32(x) _cvtsh_ss(x)
#define GGML_FP32_TO_FP16(x) _cvtss_sh(x, 0)

#else

// FP16 <-> FP32
// ref: https://github.com/Maratyszcza/FP16

static inline float fp32_from_bits(uint32_t w) {
    union {
        uint32_t as_bits;
        float as_value;
    } fp32;
    fp32.as_bits = w;
    return fp32.as_value;
}

static inline uint32_t fp32_to_bits(float f) {
	union {
		float as_value;
		uint32_t as_bits;
	} fp32;
	fp32.as_value = f;
	return fp32.as_bits;
}

float ggml_fp16_to_fp32(ggml_fp16_t h) {
    const uint32_t w = (uint32_t) h << 16;
    const uint32_t sign = w & UINT32_C(0x80000000);
    const uint32_t two_w = w + w;

    const uint32_t exp_offset = UINT32_C(0xE0) << 23;
#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) || defined(__GNUC__) && !defined(__STRICT_ANSI__)
    const float exp_scale = 0x1.0p-112f;
#else
    const float exp_scale = fp32_from_bits(UINT32_C(0x7800000));
#endif
    const float normalized_value = fp32_from_bits((two_w >> 4) + exp_offset) * exp_scale;

    const uint32_t magic_mask = UINT32_C(126) << 23;
    const float magic_bias = 0.5f;
    const float denormalized_value = fp32_from_bits((two_w >> 17) | magic_mask) - magic_bias;

    const uint32_t denormalized_cutoff = UINT32_C(1) << 27;
    const uint32_t result = sign |
        (two_w < denormalized_cutoff ? fp32_to_bits(denormalized_value) : fp32_to_bits(normalized_value));
    return fp32_from_bits(result);
}

ggml_fp16_t ggml_fp32_to_fp16(float f) {
#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) || defined(__GNUC__) && !defined(__STRICT_ANSI__)
    const float scale_to_inf = 0x1.0p+112f;
    const float scale_to_zero = 0x1.0p-110f;
#else
    const float scale_to_inf = fp32_from_bits(UINT32_C(0x77800000));
    const float scale_to_zero = fp32_from_bits(UINT32_C(0x08800000));
#endif
    float base = (fabsf(f) * scale_to_inf) * scale_to_zero;

    const uint32_t w = fp32_to_bits(f);
    const uint32_t shl1_w = w + w;
    const uint32_t sign = w & UINT32_C(0x80000000);
    uint32_t bias = shl1_w & UINT32_C(0xFF000000);
    if (bias < UINT32_C(0x71000000)) {
        bias = UINT32_C(0x71000000);
    }

    base = fp32_from_bits((bias >> 1) + UINT32_C(0x07800000)) + base;
    const uint32_t bits = fp32_to_bits(base);
    const uint32_t exp_bits = (bits >> 13) & UINT32_C(0x00007C00);
    const uint32_t mantissa_bits = bits & UINT32_C(0x00000FFF);
    const uint32_t nonsign = exp_bits + mantissa_bits;
    return (sign >> 16) | (shl1_w > UINT32_C(0xFF000000) ? UINT16_C(0x7E00) : nonsign);
}

#define GGML_FP16_TO_FP32(x) ggml_fp16_to_fp32(x)
#define GGML_FP32_TO_FP16(x) ggml_fp32_to_fp16(x)

#endif // __F16C__

#endif // __ARM_NEON

//
// global data
//

// precomputed gelu table for f16 (128 KB)
static ggml_fp16_t table_gelu_f16[1 << 16];

// precomputed exp table for f16 (128 KB)
static ggml_fp16_t table_exp_f16[1 << 16];

//
// timing
//

#if defined(_MSC_VER) || defined(__MINGW32__)
static int64_t timer_freq;
void ggml_time_init(void) {
    LARGE_INTEGER frequency;
    QueryPerformanceFrequency(&frequency);
    timer_freq = frequency.QuadPart;
}
int64_t ggml_time_ms(void) {
    LARGE_INTEGER t;
    QueryPerformanceCounter(&t);
    return (t.QuadPart * 1000) / timer_freq;
}
int64_t ggml_time_us(void) {
    LARGE_INTEGER t;
    QueryPerformanceCounter(&t);
    return (t.QuadPart * 1000000) / timer_freq;
}
#else
void ggml_time_init(void) {}
int64_t ggml_time_ms(void) {
    struct timespec ts;
    clock_gettime(CLOCK_MONOTONIC, &ts);
    return (int64_t)ts.tv_sec*1000 + (int64_t)ts.tv_nsec/1000000;
}

int64_t ggml_time_us(void) {
    struct timespec ts;
    clock_gettime(CLOCK_MONOTONIC, &ts);
    return (int64_t)ts.tv_sec*1000000 + (int64_t)ts.tv_nsec/1000;
}
#endif

int64_t ggml_cycles(void) {
    return clock();
}

int64_t ggml_cycles_per_ms(void) {
    return CLOCKS_PER_SEC/1000;
}

#ifdef GGML_PERF
#define ggml_perf_time_ms()       ggml_time_ms()
#define ggml_perf_time_us()       ggml_time_us()
#define ggml_perf_cycles()        ggml_cycles()
#define ggml_perf_cycles_per_ms() ggml_cycles_per_ms()
#else
#define ggml_perf_time_ms()       0
#define ggml_perf_time_us()       0
#define ggml_perf_cycles()        0
#define ggml_perf_cycles_per_ms() 0
#endif

//
// cache line
//

#if defined(__cpp_lib_hardware_interference_size)
#define CACHE_LINE_SIZE hardware_destructive_interference_size
#else
#define CACHE_LINE_SIZE 64
#endif

const size_t CACHE_LINE_SIZE_F32 = CACHE_LINE_SIZE/sizeof(float);

//
// fundamental operations
//

inline static void ggml_vec_set_i8(const int n, int8_t * x, const int8_t v) { for (int i = 0; i < n; ++i) x[i] = v; }

inline static void ggml_vec_set_i16(const int n, int16_t * x, const int16_t v) { for (int i = 0; i < n; ++i) x[i] = v; }

inline static void ggml_vec_set_i32(const int n, int32_t * x, const int32_t v) { for (int i = 0; i < n; ++i) x[i] = v; }

inline static void ggml_vec_set_f16(const int n, ggml_fp16_t * x, const int32_t v) { for (int i = 0; i < n; ++i) x[i] = v; }

inline static void ggml_vec_add_f32 (const int n, float * z, const float * x, const float * y) { for (int i = 0; i < n; ++i) z[i]  = x[i] + y[i]; }
inline static void ggml_vec_acc_f32 (const int n, float * y, const float * x)                  { for (int i = 0; i < n; ++i) y[i] += x[i];        }
inline static void ggml_vec_acc1_f32(const int n, float * y, const float   v)                  { for (int i = 0; i < n; ++i) y[i] += v;           }
inline static void ggml_vec_sub_f32 (const int n, float * z, const float * x, const float * y) { for (int i = 0; i < n; ++i) z[i]  = x[i] - y[i]; }
inline static void ggml_vec_set_f32 (const int n, float * x, const float   v)                  { for (int i = 0; i < n; ++i) x[i]  = v;           }
inline static void ggml_vec_cpy_f32 (const int n, float * y, const float * x)                  { for (int i = 0; i < n; ++i) y[i]  = x[i];        }
inline static void ggml_vec_neg_f32 (const int n, float * y, const float * x)                  { for (int i = 0; i < n; ++i) y[i]  = -x[i];       }
inline static void ggml_vec_mul_f32 (const int n, float * z, const float * x, const float * y) { for (int i = 0; i < n; ++i) z[i]  = x[i]*y[i];   }
inline static void ggml_vec_div_f32 (const int n, float * z, const float * x, const float * y) { for (int i = 0; i < n; ++i) z[i]  = x[i]/y[i];   }

inline static void ggml_vec_dot_f32(const int n, float * restrict s, const float * restrict x, const float * restrict y) {
    ggml_float sumf = 0.0;
#ifdef __ARM_NEON
    // NEON 128-bit
    const int n16 = (n & ~15);

    float32x4_t sum0 = vdupq_n_f32(0);
    float32x4_t sum1 = vdupq_n_f32(0);
    float32x4_t sum2 = vdupq_n_f32(0);
    float32x4_t sum3 = vdupq_n_f32(0);

    float32x4_t x0, x1, x2, x3;
    float32x4_t y0, y1, y2, y3;

    for (int i = 0; i < n16; i += 16) {
        x0 = vld1q_f32(x + i + 0);
        x1 = vld1q_f32(x + i + 4);
        x2 = vld1q_f32(x + i + 8);
        x3 = vld1q_f32(x + i + 12);

        y0 = vld1q_f32(y + i + 0);
        y1 = vld1q_f32(y + i + 4);
        y2 = vld1q_f32(y + i + 8);
        y3 = vld1q_f32(y + i + 12);

        sum0 = vfmaq_f32(sum0, x0, y0);
        sum1 = vfmaq_f32(sum1, x1, y1);
        sum2 = vfmaq_f32(sum2, x2, y2);
        sum3 = vfmaq_f32(sum3, x3, y3);
    }

    // reduce sum0..sum3 to sum0
    sum0 = vaddq_f32(sum0, sum1);
    sum2 = vaddq_f32(sum2, sum3);
    sum0 = vaddq_f32(sum0, sum2);

    float32x2_t sumf32 = vadd_f32(vget_low_f32(sum0), vget_high_f32(sum0));
    sumf = vget_lane_f32(sumf32, 0) + vget_lane_f32(sumf32, 1);

    // leftovers
    for (int i = n16; i < n; ++i) {
        sumf += x[i]*y[i];
    }
#elif defined(__AVX2__)
    // AVX 256-bit
    const int n32 = (n & ~31);

    __m256 sum0 = _mm256_setzero_ps();
    __m256 sum1 = _mm256_setzero_ps();
    __m256 sum2 = _mm256_setzero_ps();
    __m256 sum3 = _mm256_setzero_ps();

    __m256 x0, x1, x2, x3;
    __m256 y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        x0 = _mm256_loadu_ps(x + i + 0);
        x1 = _mm256_loadu_ps(x + i + 8);
        x2 = _mm256_loadu_ps(x + i + 16);
        x3 = _mm256_loadu_ps(x + i + 24);

        y0 = _mm256_loadu_ps(y + i + 0);
        y1 = _mm256_loadu_ps(y + i + 8);
        y2 = _mm256_loadu_ps(y + i + 16);
        y3 = _mm256_loadu_ps(y + i + 24);

        sum0 = _mm256_fmadd_ps(x0, y0, sum0);
        sum1 = _mm256_fmadd_ps(x1, y1, sum1);
        sum2 = _mm256_fmadd_ps(x2, y2, sum2);
        sum3 = _mm256_fmadd_ps(x3, y3, sum3);
    }

    sum0 = _mm256_add_ps(sum0, sum1);
    sum2 = _mm256_add_ps(sum2, sum3);
    sum0 = _mm256_add_ps(sum0, sum2);

    const __m128 r4 = _mm_add_ps(_mm256_castps256_ps128(sum0), _mm256_extractf128_ps(sum0, 1));
    const __m128 r2 = _mm_add_ps(r4, _mm_movehl_ps(r4, r4));
    const __m128 r1 = _mm_add_ss(r2, _mm_movehdup_ps(r2));

    sumf = _mm_cvtss_f32(r1);

    // leftovers
    for (int i = n32; i < n; ++i) {
        sumf += x[i]*y[i];
    }
#elif defined(__AVX__)
    // AVX 256-bit
    const int n32 = (n & ~31);

    __m256 sum0 = _mm256_setzero_ps();
    __m256 sum1 = _mm256_setzero_ps();
    __m256 sum2 = _mm256_setzero_ps();
    __m256 sum3 = _mm256_setzero_ps();

    __m256 x0, x1, x2, x3;
    __m256 y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        x0 = _mm256_loadu_ps(x + i + 0);
        x1 = _mm256_loadu_ps(x + i + 8);
        x2 = _mm256_loadu_ps(x + i + 16);
        x3 = _mm256_loadu_ps(x + i + 24);

        y0 = _mm256_loadu_ps(y + i + 0);
        y1 = _mm256_loadu_ps(y + i + 8);
        y2 = _mm256_loadu_ps(y + i + 16);
        y3 = _mm256_loadu_ps(y + i + 24);

        sum0 = _mm256_add_ps(_mm256_mul_ps(x0, y0), sum0);
        sum1 = _mm256_add_ps(_mm256_mul_ps(x1, y1), sum1);
        sum2 = _mm256_add_ps(_mm256_mul_ps(x2, y2), sum2);
        sum3 = _mm256_add_ps(_mm256_mul_ps(x3, y3), sum3);
    }

    sum0 = _mm256_add_ps(sum0, sum1);
    sum2 = _mm256_add_ps(sum2, sum3);
    sum0 = _mm256_add_ps(sum0, sum2);

    const __m128 r4 = _mm_add_ps(_mm256_castps256_ps128(sum0), _mm256_extractf128_ps(sum0, 1));
    const __m128 r2 = _mm_add_ps(r4, _mm_movehl_ps(r4, r4));
    const __m128 r1 = _mm_add_ss(r2, _mm_movehdup_ps(r2));

    sumf = _mm_cvtss_f32(r1);

    // leftovers
    for (int i = n32; i < n; ++i) {
        sumf += x[i]*y[i];
    }
#elif defined(__wasm_simd128__)
    // WASM 128-bit
    const int n16 = (n & ~15);

    v128_t sum0 = wasm_f32x4_splat(0);
    v128_t sum1 = wasm_f32x4_splat(0);
    v128_t sum2 = wasm_f32x4_splat(0);
    v128_t sum3 = wasm_f32x4_splat(0);

    v128_t x0, x1, x2, x3;
    v128_t y0, y1, y2, y3;

    for (int i = 0; i < n16; i += 16) {
        x0 = wasm_v128_load(x + i + 0);
        x1 = wasm_v128_load(x + i + 4);
        x2 = wasm_v128_load(x + i + 8);
        x3 = wasm_v128_load(x + i + 12);

        y0 = wasm_v128_load(y + i + 0);
        y1 = wasm_v128_load(y + i + 4);
        y2 = wasm_v128_load(y + i + 8);
        y3 = wasm_v128_load(y + i + 12);

        sum0 = wasm_f32x4_add(sum0, wasm_f32x4_mul(x0, y0));
        sum1 = wasm_f32x4_add(sum1, wasm_f32x4_mul(x1, y1));
        sum2 = wasm_f32x4_add(sum2, wasm_f32x4_mul(x2, y2));
        sum3 = wasm_f32x4_add(sum3, wasm_f32x4_mul(x3, y3));
    }

    sum0 = wasm_f32x4_add(sum0, sum1);
    sum2 = wasm_f32x4_add(sum2, sum3);
    sum0 = wasm_f32x4_add(sum0, sum2);

    sumf = wasm_f32x4_extract_lane(sum0, 0) + wasm_f32x4_extract_lane(sum0, 1) + wasm_f32x4_extract_lane(sum0, 2) + wasm_f32x4_extract_lane(sum0, 3);

    // leftovers
    for (int i = n16; i < n; ++i) {
        sumf += x[i]*y[i];
    }
#else
    // scalar
    for (int i = 0; i < n; ++i) {
        sumf += x[i]*y[i];
    }
#endif

    *s = sumf;
}

inline static void ggml_vec_dot_f16(const int n, float * restrict s, ggml_fp16_t * restrict x, ggml_fp16_t * restrict y) {
    ggml_float sumf = 0.0;
#ifdef __ARM_NEON
    const int n32 = (n & ~31);

#if defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC)
    float16x8_t sum0 = vdupq_n_f16(0);
    float16x8_t sum1 = vdupq_n_f16(0);
    float16x8_t sum2 = vdupq_n_f16(0);
    float16x8_t sum3 = vdupq_n_f16(0);

    float16x8_t x0, x1, x2, x3;
    float16x8_t y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        x0 = vld1q_f16(x + i + 0 );
        x1 = vld1q_f16(x + i + 8 );
        x2 = vld1q_f16(x + i + 16);
        x3 = vld1q_f16(x + i + 24);

        y0 = vld1q_f16(y + i + 0 );
        y1 = vld1q_f16(y + i + 8 );
        y2 = vld1q_f16(y + i + 16);
        y3 = vld1q_f16(y + i + 24);

        sum0 = vfmaq_f16(sum0, x0, y0);
        sum1 = vfmaq_f16(sum1, x1, y1);
        sum2 = vfmaq_f16(sum2, x2, y2);
        sum3 = vfmaq_f16(sum3, x3, y3);
    }

    // reduce sum0..sum3 to sum0
    sum0 = vaddq_f16(sum0, sum1);
    sum2 = vaddq_f16(sum2, sum3);
    sum0 = vaddq_f16(sum0, sum2);

    // load sum0 into 2 float32x4_t
    float32x4_t sum0f32 = vcvt_f32_f16(vget_low_f16(sum0));
    float32x4_t sum1f32 = vcvt_f32_f16(vget_high_f16(sum0));

    // reduce sum0f32 and sum1f32 to sumf
    sum0f32 = vaddq_f32(sum0f32, sum1f32);

    float32x2_t sumf32 = vadd_f32(vget_low_f32(sum0f32), vget_high_f32(sum0f32));
    sumf = vget_lane_f32(sumf32, 0) + vget_lane_f32(sumf32, 1);
#else
    float32x4_t sum0 = vdupq_n_f32(0);
    float32x4_t sum1 = vdupq_n_f32(0);
    float32x4_t sum2 = vdupq_n_f32(0);
    float32x4_t sum3 = vdupq_n_f32(0);
    float32x4_t sum4 = vdupq_n_f32(0);
    float32x4_t sum5 = vdupq_n_f32(0);
    float32x4_t sum6 = vdupq_n_f32(0);
    float32x4_t sum7 = vdupq_n_f32(0);

    float32x4_t x0, x1, x2, x3, x4, x5, x6, x7;
    float32x4_t y0, y1, y2, y3, y4, y5, y6, y7;

    for (int i = 0; i < n32; i += 32) {
        x0 = vcvt_f32_f16(vld1_f16(x + i + 0 ));
        x1 = vcvt_f32_f16(vld1_f16(x + i + 4 ));
        x2 = vcvt_f32_f16(vld1_f16(x + i + 8 ));
        x3 = vcvt_f32_f16(vld1_f16(x + i + 12));
        x4 = vcvt_f32_f16(vld1_f16(x + i + 16));
        x5 = vcvt_f32_f16(vld1_f16(x + i + 20));
        x6 = vcvt_f32_f16(vld1_f16(x + i + 24));
        x7 = vcvt_f32_f16(vld1_f16(x + i + 28));

        y0 = vcvt_f32_f16(vld1_f16(y + i + 0 ));
        y1 = vcvt_f32_f16(vld1_f16(y + i + 4 ));
        y2 = vcvt_f32_f16(vld1_f16(y + i + 8 ));
        y3 = vcvt_f32_f16(vld1_f16(y + i + 12));
        y4 = vcvt_f32_f16(vld1_f16(y + i + 16));
        y5 = vcvt_f32_f16(vld1_f16(y + i + 20));
        y6 = vcvt_f32_f16(vld1_f16(y + i + 24));
        y7 = vcvt_f32_f16(vld1_f16(y + i + 28));

        sum0 = vfmaq_f32(sum0, x0, y0);
        sum1 = vfmaq_f32(sum1, x1, y1);
        sum2 = vfmaq_f32(sum2, x2, y2);
        sum3 = vfmaq_f32(sum3, x3, y3);
        sum4 = vfmaq_f32(sum4, x4, y4);
        sum5 = vfmaq_f32(sum5, x5, y5);
        sum6 = vfmaq_f32(sum6, x6, y6);
        sum7 = vfmaq_f32(sum7, x7, y7);
    }

    // reduce sum0..sum7 to sum0
    sum0 = vaddq_f32(sum0, sum1);
    sum2 = vaddq_f32(sum2, sum3);
    sum4 = vaddq_f32(sum4, sum5);
    sum6 = vaddq_f32(sum6, sum7);
    sum0 = vaddq_f32(sum0, sum2);
    sum4 = vaddq_f32(sum4, sum6);
    sum0 = vaddq_f32(sum0, sum4);

    // reduce sum0 to sumf
    float32x2_t sumf32 = vadd_f32(vget_low_f32(sum0), vget_high_f32(sum0));
    sumf = vget_lane_f32(sumf32, 0) + vget_lane_f32(sumf32, 1);
#endif

    // leftovers
    for (int i = n32; i < n; ++i) {
        sumf += GGML_FP16_TO_FP32(x[i])*GGML_FP16_TO_FP32(y[i]);
    }
#elif defined(__AVX2__)
    // AVX 256-bit
    const int n32 = (n & ~31);

    __m256 sum0 = _mm256_setzero_ps();
    __m256 sum1 = _mm256_setzero_ps();
    __m256 sum2 = _mm256_setzero_ps();
    __m256 sum3 = _mm256_setzero_ps();

    __m256 x0, x1, x2, x3;
    __m256 y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        x0 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 0 )));
        x1 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 8 )));
        x2 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 16)));
        x3 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 24)));

        y0 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 0 )));
        y1 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 8 )));
        y2 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 16)));
        y3 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 24)));

        sum0 = _mm256_fmadd_ps(x0, y0, sum0);
        sum1 = _mm256_fmadd_ps(x1, y1, sum1);
        sum2 = _mm256_fmadd_ps(x2, y2, sum2);
        sum3 = _mm256_fmadd_ps(x3, y3, sum3);
    }

    const __m256 sum01 = _mm256_add_ps(sum0, sum1);
    const __m256 sum23 = _mm256_add_ps(sum2, sum3);
    const __m256 sum0123 = _mm256_add_ps(sum01, sum23);

    const __m128 r4 = _mm_add_ps(_mm256_castps256_ps128(sum0123), _mm256_extractf128_ps(sum0123, 1));
    const __m128 r2 = _mm_add_ps(r4, _mm_movehl_ps(r4, r4));
    const __m128 r1 = _mm_add_ss(r2, _mm_movehdup_ps(r2));

    sumf = _mm_cvtss_f32(r1);

    // leftovers
    for (int i = n32; i < n; ++i) {
        //GGML_ASSERT(false);
        sumf += GGML_FP16_TO_FP32(x[i])*GGML_FP16_TO_FP32(y[i]);
    }
#elif defined(__AVX__)
    // AVX 256-bit
    const int n32 = (n & ~31);

    __m256 sum0 = _mm256_setzero_ps();
    __m256 sum1 = _mm256_setzero_ps();
    __m256 sum2 = _mm256_setzero_ps();
    __m256 sum3 = _mm256_setzero_ps();

    __m256 x0, x1, x2, x3;
    __m256 y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        x0 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 0 )));
        x1 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 8 )));
        x2 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 16)));
        x3 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 24)));

        y0 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 0 )));
        y1 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 8 )));
        y2 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 16)));
        y3 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 24)));

        sum0 = _mm256_add_ps(_mm256_mul_ps(x0, y0), sum0);
        sum1 = _mm256_add_ps(_mm256_mul_ps(x1, y1), sum1);
        sum2 = _mm256_add_ps(_mm256_mul_ps(x2, y2), sum2);
        sum3 = _mm256_add_ps(_mm256_mul_ps(x3, y3), sum3);
    }

    const __m256 sum01 = _mm256_add_ps(sum0, sum1);
    const __m256 sum23 = _mm256_add_ps(sum2, sum3);
    const __m256 sum0123 = _mm256_add_ps(sum01, sum23);

    const __m128 r4 = _mm_add_ps(_mm256_castps256_ps128(sum0123), _mm256_extractf128_ps(sum0123, 1));
    const __m128 r2 = _mm_add_ps(r4, _mm_movehl_ps(r4, r4));
    const __m128 r1 = _mm_add_ss(r2, _mm_movehdup_ps(r2));

    sumf = _mm_cvtss_f32(r1);

    // leftovers
    for (int i = n32; i < n; ++i) {
        //GGML_ASSERT(false);
        sumf += GGML_FP16_TO_FP32(x[i])*GGML_FP16_TO_FP32(y[i]);
    }
#elif defined(__wasm_simd128__)
    // WASM 128-bit
    const int n16 = (n & ~15);

    v128_t sum0 = wasm_f32x4_splat(0.0f);
    v128_t sum1 = wasm_f32x4_splat(0.0f);
    v128_t sum2 = wasm_f32x4_splat(0.0f);
    v128_t sum3 = wasm_f32x4_splat(0.0f);

    v128_t x0, x1, x2, x3;
    v128_t y0, y1, y2, y3;

    float tx[16];
    float ty[16];

    for (int i = 0; i < n16; i += 16) {
        for (int k = 0; k < 16; ++k) {
            tx[k] = GGML_FP16_TO_FP32(x[i + k]);
            ty[k] = GGML_FP16_TO_FP32(y[i + k]);
        }

        x0 = wasm_v128_load(tx + 0);
        x1 = wasm_v128_load(tx + 4);
        x2 = wasm_v128_load(tx + 8);
        x3 = wasm_v128_load(tx + 12);

        y0 = wasm_v128_load(ty + 0);
        y1 = wasm_v128_load(ty + 4);
        y2 = wasm_v128_load(ty + 8);
        y3 = wasm_v128_load(ty + 12);

        sum0 = wasm_f32x4_add(sum0, wasm_f32x4_mul(x0, y0));
        sum1 = wasm_f32x4_add(sum1, wasm_f32x4_mul(x1, y1));
        sum2 = wasm_f32x4_add(sum2, wasm_f32x4_mul(x2, y2));
        sum3 = wasm_f32x4_add(sum3, wasm_f32x4_mul(x3, y3));
    }

    sum0 = wasm_f32x4_add(sum0, sum1);
    sum2 = wasm_f32x4_add(sum2, sum3);
    sum0 = wasm_f32x4_add(sum0, sum2);

    sumf = wasm_f32x4_extract_lane(sum0, 0) + wasm_f32x4_extract_lane(sum0, 1) + wasm_f32x4_extract_lane(sum0, 2) + wasm_f32x4_extract_lane(sum0, 3);

    // leftovers
    for (int i = n16; i < n; ++i) {
        //GGML_ASSERT(false);
        sumf += GGML_FP16_TO_FP32(x[i])*GGML_FP16_TO_FP32(y[i]);
    }
#else
    for (int i = 0; i < n; ++i) {
        sumf += GGML_FP16_TO_FP32(x[i])*GGML_FP16_TO_FP32(y[i]);
    }
#endif

    *s = sumf;
}

inline static void ggml_vec_mad_f32(const int n, float * restrict y, const float * restrict x, const float v) {
#ifdef __ARM_NEON
    // NEON 128-bit
    const int n16 = (n & ~15);

    const float32x4_t v4 = vdupq_n_f32(v);

    float32x4_t x0, x1, x2, x3;
    float32x4_t y0, y1, y2, y3;

    for (int i = 0; i < n16; i += 16) {
        x0 = vld1q_f32(x + i + 0);
        x1 = vld1q_f32(x + i + 4);
        x2 = vld1q_f32(x + i + 8);
        x3 = vld1q_f32(x + i + 12);

        y0 = vld1q_f32(y + i + 0);
        y1 = vld1q_f32(y + i + 4);
        y2 = vld1q_f32(y + i + 8);
        y3 = vld1q_f32(y + i + 12);

        y0 = vfmaq_f32(y0, x0, v4);
        y1 = vfmaq_f32(y1, x1, v4);
        y2 = vfmaq_f32(y2, x2, v4);
        y3 = vfmaq_f32(y3, x3, v4);

        vst1q_f32(y + i + 0, y0);
        vst1q_f32(y + i + 4, y1);
        vst1q_f32(y + i + 8, y2);
        vst1q_f32(y + i + 12, y3);
    }

    // leftovers
    for (int i = n16; i < n; ++i) {
        y[i] += x[i]*v;
    }
#elif defined(__AVX2__)
    // AVX 256-bit
    const int n32 = (n & ~31);

    const __m256 v4 = _mm256_set1_ps(v);

    __m256 x0, x1, x2, x3;
    __m256 y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        x0 = _mm256_loadu_ps(x + i + 0);
        x1 = _mm256_loadu_ps(x + i + 8);
        x2 = _mm256_loadu_ps(x + i + 16);
        x3 = _mm256_loadu_ps(x + i + 24);

        y0 = _mm256_loadu_ps(y + i + 0);
        y1 = _mm256_loadu_ps(y + i + 8);
        y2 = _mm256_loadu_ps(y + i + 16);
        y3 = _mm256_loadu_ps(y + i + 24);

        y0 = _mm256_fmadd_ps(x0, v4, y0);
        y1 = _mm256_fmadd_ps(x1, v4, y1);
        y2 = _mm256_fmadd_ps(x2, v4, y2);
        y3 = _mm256_fmadd_ps(x3, v4, y3);

        _mm256_storeu_ps(y + i + 0, y0);
        _mm256_storeu_ps(y + i + 8, y1);
        _mm256_storeu_ps(y + i + 16, y2);
        _mm256_storeu_ps(y + i + 24, y3);
    }

    // leftovers
    for (int i = n32; i < n; ++i) {
        y[i] += x[i]*v;
    }
#elif defined(__AVX__)
    // AVX 256-bit
    const int n32 = (n & ~31);

    const __m256 v4 = _mm256_set1_ps(v);

    __m256 x0, x1, x2, x3;
    __m256 y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        x0 = _mm256_loadu_ps(x + i + 0);
        x1 = _mm256_loadu_ps(x + i + 8);
        x2 = _mm256_loadu_ps(x + i + 16);
        x3 = _mm256_loadu_ps(x + i + 24);

        y0 = _mm256_loadu_ps(y + i + 0);
        y1 = _mm256_loadu_ps(y + i + 8);
        y2 = _mm256_loadu_ps(y + i + 16);
        y3 = _mm256_loadu_ps(y + i + 24);

        y0 = _mm256_add_ps(_mm256_mul_ps(x0, v4), y0);
        y1 = _mm256_add_ps(_mm256_mul_ps(x1, v4), y1);
        y2 = _mm256_add_ps(_mm256_mul_ps(x2, v4), y2);
        y3 = _mm256_add_ps(_mm256_mul_ps(x3, v4), y3);

        _mm256_storeu_ps(y + i + 0, y0);
        _mm256_storeu_ps(y + i + 8, y1);
        _mm256_storeu_ps(y + i + 16, y2);
        _mm256_storeu_ps(y + i + 24, y3);
    }

    // leftovers
    for (int i = n32; i < n; ++i) {
        y[i] += x[i]*v;
    }
#elif defined(__wasm_simd128__)
    // WASM SIMD 128-bit
    const int n16 = (n & ~15);

    const v128_t v4 = wasm_f32x4_splat(v);

    v128_t x0, x1, x2, x3;
    v128_t y0, y1, y2, y3;

    for (int i = 0; i < n16; i += 16) {
        x0 = wasm_v128_load(x + i + 0);
        x1 = wasm_v128_load(x + i + 4);
        x2 = wasm_v128_load(x + i + 8);
        x3 = wasm_v128_load(x + i + 12);

        y0 = wasm_v128_load(y + i + 0);
        y1 = wasm_v128_load(y + i + 4);
        y2 = wasm_v128_load(y + i + 8);
        y3 = wasm_v128_load(y + i + 12);

        y0 = wasm_f32x4_add(y0, wasm_f32x4_mul(x0, v4));
        y1 = wasm_f32x4_add(y1, wasm_f32x4_mul(x1, v4));
        y2 = wasm_f32x4_add(y2, wasm_f32x4_mul(x2, v4));
        y3 = wasm_f32x4_add(y3, wasm_f32x4_mul(x3, v4));

        wasm_v128_store(y + i + 0, y0);
        wasm_v128_store(y + i + 4, y1);
        wasm_v128_store(y + i + 8, y2);
        wasm_v128_store(y + i + 12, y3);
    }

    // leftovers
    for (int i = n16; i < n; ++i) {
        y[i] += x[i]*v;
    }
#else
    // scalar
    for (int i = 0; i < n; ++i) {
        y[i] += x[i]*v;
    }
#endif
}

inline static void ggml_vec_mad_f16(const int n, ggml_fp16_t * restrict y, ggml_fp16_t * restrict x, const float v) {
#ifdef __ARM_NEON
    // NEON 128-bit
    const int n32 = (n & ~31);

#if defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC)
    const float16x8_t v8 = vdupq_n_f16(v);

    float16x8_t x0, x1, x2, x3;
    float16x8_t y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        y0 = vld1q_f16(y + i + 0 );
        y1 = vld1q_f16(y + i + 8 );
        y2 = vld1q_f16(y + i + 16);
        y3 = vld1q_f16(y + i + 24);

        x0 = vld1q_f16(x + i + 0 );
        x1 = vld1q_f16(x + i + 8 );
        x2 = vld1q_f16(x + i + 16);
        x3 = vld1q_f16(x + i + 24);

        y0 = vfmaq_f16(y0, x0, v8);
        y1 = vfmaq_f16(y1, x1, v8);
        y2 = vfmaq_f16(y2, x2, v8);
        y3 = vfmaq_f16(y3, x3, v8);

        vst1q_f16(y + i + 0 , y0);
        vst1q_f16(y + i + 8 , y1);
        vst1q_f16(y + i + 16, y2);
        vst1q_f16(y + i + 24, y3);
    }
#else
    const float32x4_t v40 = vdupq_n_f32(v);
    const float32x4_t v41 = vdupq_n_f32(v);

    float32x4_t x0, x1, x2, x3, x4, x5, x6, x7;
    float32x4_t y0, y1, y2, y3, y4, y5, y6, y7;

    for (int i = 0; i < n32; i += 32) {
        y0 = vcvt_f32_f16(vld1_f16(y + i + 0 ));
        y1 = vcvt_f32_f16(vld1_f16(y + i + 4 ));
        y2 = vcvt_f32_f16(vld1_f16(y + i + 8 ));
        y3 = vcvt_f32_f16(vld1_f16(y + i + 12));
        y4 = vcvt_f32_f16(vld1_f16(y + i + 16));
        y5 = vcvt_f32_f16(vld1_f16(y + i + 20));
        y6 = vcvt_f32_f16(vld1_f16(y + i + 24));
        y7 = vcvt_f32_f16(vld1_f16(y + i + 28));

        x0 = vcvt_f32_f16(vld1_f16(x + i + 0 ));
        x1 = vcvt_f32_f16(vld1_f16(x + i + 4 ));
        x2 = vcvt_f32_f16(vld1_f16(x + i + 8 ));
        x3 = vcvt_f32_f16(vld1_f16(x + i + 12));
        x4 = vcvt_f32_f16(vld1_f16(x + i + 16));
        x5 = vcvt_f32_f16(vld1_f16(x + i + 20));
        x6 = vcvt_f32_f16(vld1_f16(x + i + 24));
        x7 = vcvt_f32_f16(vld1_f16(x + i + 28));

        y0 = vfmaq_f32(y0, x0, v40);
        y1 = vfmaq_f32(y1, x1, v40);
        y2 = vfmaq_f32(y2, x2, v40);
        y3 = vfmaq_f32(y3, x3, v40);
        y4 = vfmaq_f32(y4, x4, v41);
        y5 = vfmaq_f32(y5, x5, v41);
        y6 = vfmaq_f32(y6, x6, v41);
        y7 = vfmaq_f32(y7, x7, v41);

        vst1_f16(y + i + 0 , vcvt_f16_f32(y0));
        vst1_f16(y + i + 4 , vcvt_f16_f32(y1));
        vst1_f16(y + i + 8 , vcvt_f16_f32(y2));
        vst1_f16(y + i + 12, vcvt_f16_f32(y3));
        vst1_f16(y + i + 16, vcvt_f16_f32(y4));
        vst1_f16(y + i + 20, vcvt_f16_f32(y5));
        vst1_f16(y + i + 24, vcvt_f16_f32(y6));
        vst1_f16(y + i + 28, vcvt_f16_f32(y7));
    }
#endif

    // leftovers
    for (int i = n32; i < n; ++i) {
        GGML_ASSERT(false);
        y[i] = GGML_FP32_TO_FP16(GGML_FP16_TO_FP32(y[i]) + GGML_FP16_TO_FP32(x[i])*v);
    }
#elif defined(__AVX2__)
    // AVX 256-bit
    const int n32 = (n & ~31);

    const __m256 v8 = _mm256_set1_ps(v);

    __m256 x0, x1, x2, x3;
    __m256 y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        y0 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 0 )));
        y1 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 8 )));
        y2 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 16)));
        y3 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 24)));

        x0 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 0 )));
        x1 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 8 )));
        x2 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 16)));
        x3 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 24)));

        y0 = _mm256_fmadd_ps(x0, v8, y0);
        y1 = _mm256_fmadd_ps(x1, v8, y1);
        y2 = _mm256_fmadd_ps(x2, v8, y2);
        y3 = _mm256_fmadd_ps(x3, v8, y3);

        _mm_storeu_si128((__m128i*)(y + i + 0 ), _mm256_cvtps_ph(y0, 0));
        _mm_storeu_si128((__m128i*)(y + i + 8 ), _mm256_cvtps_ph(y1, 0));
        _mm_storeu_si128((__m128i*)(y + i + 16), _mm256_cvtps_ph(y2, 0));
        _mm_storeu_si128((__m128i*)(y + i + 24), _mm256_cvtps_ph(y3, 0));
    }

    // leftovers
    for (int i = n32; i < n; ++i) {
        GGML_ASSERT(false);
        y[i] = GGML_FP32_TO_FP16(GGML_FP16_TO_FP32(y[i]) + GGML_FP16_TO_FP32(x[i])*v);
    }
#elif defined(__AVX__)
    // AVX 256-bit
    const int n32 = (n & ~31);

    const __m256 v8 = _mm256_set1_ps(v);

    __m256 x0, x1, x2, x3;
    __m256 y0, y1, y2, y3;

    for (int i = 0; i < n32; i += 32) {
        y0 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 0 )));
        y1 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 8 )));
        y2 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 16)));
        y3 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(y + i + 24)));

        x0 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 0 )));
        x1 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 8 )));
        x2 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 16)));
        x3 = _mm256_cvtph_ps(_mm_loadu_si128((__m128i*)(x + i + 24)));

        y0 = _mm256_add_ps(_mm256_mul_ps(x0, v8), y0);
        y1 = _mm256_add_ps(_mm256_mul_ps(x1, v8), y1);
        y2 = _mm256_add_ps(_mm256_mul_ps(x2, v8), y2);
        y3 = _mm256_add_ps(_mm256_mul_ps(x3, v8), y3);

        _mm_storeu_si128((__m128i*)(y + i + 0 ), _mm256_cvtps_ph(y0, 0));
        _mm_storeu_si128((__m128i*)(y + i + 8 ), _mm256_cvtps_ph(y1, 0));
        _mm_storeu_si128((__m128i*)(y + i + 16), _mm256_cvtps_ph(y2, 0));
        _mm_storeu_si128((__m128i*)(y + i + 24), _mm256_cvtps_ph(y3, 0));
    }

    // leftovers
    for (int i = n32; i < n; ++i) {
        GGML_ASSERT(false);
        y[i] = GGML_FP32_TO_FP16(GGML_FP16_TO_FP32(y[i]) + GGML_FP16_TO_FP32(x[i])*v);
    }
#elif defined(__wasm_simd128__)
    // WASM SIMD 128-bit
    const int n16 = (n & ~15);

    const v128_t v4 = wasm_f32x4_splat(v);

    v128_t x0, x1, x2, x3;
    v128_t y0, y1, y2, y3;

    float tx[16];
    float ty[16];

    for (int i = 0; i < n16; i += 16) {
        for (int k = 0; k < 16; ++k) {
            tx[k] = GGML_FP16_TO_FP32(x[i + k]);
            ty[k] = GGML_FP16_TO_FP32(y[i + k]);
        }

        x0 = wasm_v128_load(tx + 0);
        x1 = wasm_v128_load(tx + 4);
        x2 = wasm_v128_load(tx + 8);
        x3 = wasm_v128_load(tx + 12);

        y0 = wasm_v128_load(ty + 0);
        y1 = wasm_v128_load(ty + 4);
        y2 = wasm_v128_load(ty + 8);
        y3 = wasm_v128_load(ty + 12);

        y0 = wasm_f32x4_add(y0, wasm_f32x4_mul(x0, v4));
        y1 = wasm_f32x4_add(y1, wasm_f32x4_mul(x1, v4));
        y2 = wasm_f32x4_add(y2, wasm_f32x4_mul(x2, v4));
        y3 = wasm_f32x4_add(y3, wasm_f32x4_mul(x3, v4));

        wasm_v128_store(ty + 0, y0);
        wasm_v128_store(ty + 4, y1);
        wasm_v128_store(ty + 8, y2);
        wasm_v128_store(ty + 12, y3);

        for (int k = 0; k < 16; ++k) {
            y[i + k] = GGML_FP32_TO_FP16(ty[k]);
        }
    }

    // leftovers
    for (int i = n16; i < n; ++i) {
        GGML_ASSERT(false);
        y[i] = GGML_FP32_TO_FP16(GGML_FP16_TO_FP32(y[i]) + GGML_FP16_TO_FP32(x[i])*v);
    }
#else
    for (int i = 0; i < n; ++i) {
        y[i] = GGML_FP32_TO_FP16(GGML_FP16_TO_FP32(y[i]) + GGML_FP16_TO_FP32(x[i])*v);
    }
#endif
}

inline static void ggml_vec_scale_f32(const int n, float * y, const float   v) { for (int i = 0; i < n; ++i) y[i] *= v;          }
inline static void ggml_vec_norm_f32 (const int n, float * s, const float * x) { ggml_vec_dot_f32(n, s, x, x); *s = sqrt(*s);   }
inline static void ggml_vec_sqr_f32  (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = x[i]*x[i];   }
inline static void ggml_vec_sqrt_f32 (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = sqrt(x[i]); }
inline static void ggml_vec_abs_f32  (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = fabsf(x[i]); }
inline static void ggml_vec_sgn_f32  (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = (x[i] > 0.f) ? 1.f : ((x[i] < 0.f) ? -1.f : 0.f); }
inline static void ggml_vec_step_f32 (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = (x[i] > 0.f) ? 1.f : 0.f; }
inline static void ggml_vec_relu_f32 (const int n, float * y, const float * x) { for (int i = 0; i < n; ++i) y[i] = (x[i] > 0.f) ? x[i] : 0.f; }

const ggml_float GELU_COEF_A    = 0.044715;
const ggml_float SQRT_2_OVER_PI = 0.79788456080286535587989211986876;

inline static float ggml_gelu_f32(float x) {
    return 0.5*x*(1.0 + tanh(SQRT_2_OVER_PI*x*(1.0 + GELU_COEF_A*x*x)));
}

inline static void ggml_vec_gelu_f16(const int n, ggml_fp16_t * y, const ggml_fp16_t * x) {
    const uint16_t * i16 = (const uint16_t *) x;
    for (int i = 0; i < n; ++i) {
        y[i] = table_gelu_f16[i16[i]];
    }
}

#ifdef GGML_GELU_FP16
inline static void ggml_vec_gelu_f32(const int n, float * y, const float * x) {
    uint16_t t;
    for (int i = 0; i < n; ++i) {
        ggml_fp16_t fp16 = GGML_FP32_TO_FP16(x[i]);
        memcpy(&t, &fp16, sizeof(uint16_t));
        y[i] = GGML_FP16_TO_FP32(table_gelu_f16[t]);
    }
}
#else
inline static void ggml_vec_gelu_f32(const int n, float * y, const float * x) {
    for (int i = 0; i < n; ++i) {
        y[i] = ggml_gelu_f32(x[i]);
    }
}
#endif

inline static void ggml_vec_sum_f32     (const int n, float * s, const float * x) { ggml_float sum = 0.0; for (int i = 0; i < n; ++i) sum += x[i]; *s += sum; }
inline static void ggml_vec_norm_inv_f32(const int n, float * s, const float * x) { ggml_vec_norm_f32(n, s, x); *s = 1./(*s); }

//
// logging
//

#if (GGML_DEBUG >= 1)
#define GGML_PRINT_DEBUG(...) printf(__VA_ARGS__)
#else
#define GGML_PRINT_DEBUG(...)
#endif

#if (GGML_DEBUG >= 5)
#define GGML_PRINT_DEBUG_5(...) printf(__VA_ARGS__)
#else
#define GGML_PRINT_DEBUG_5(...)
#endif

#if (GGML_DEBUG >= 10)
#define GGML_PRINT_DEBUG_10(...) printf(__VA_ARGS__)
#else
#define GGML_PRINT_DEBUG_10(...)
#endif

#define GGML_PRINT(...) printf(__VA_ARGS__)

//
// data types
//

const size_t GGML_TYPE_SIZE[GGML_TYPE_COUNT] = {
    sizeof(int8_t ),
    sizeof(int16_t),
    sizeof(int32_t),
    sizeof(ggml_fp16_t),
    sizeof(float  ),
};

const char * GGML_OP_LABEL[GGML_OP_COUNT] = {
    "NONE",

    "DUP",
    "ADD",
    "SUB",
    "MUL",
    "DIV",
    "SQR",
    "SQRT",
    "SUM",
    "MEAN",
    "REPEAT",
    "ABS",
    "SGN",
    "NEG",
    "STEP",
    "RELU",
    "GELU",
    "NORM",

    "MUL_MAT",

    "SCALE",
    "CPY",
    "RESHAPE",
    "VIEW",
    "PERMUTE",
    "TRANSPOSE",
    "GET_ROWS",
    "DIAG_MASK_INF",
    "SOFT_MAX",
    "ROPE",
    "CONV_1D_1S",
    "CONV_1D_2S",

    "FLASH_ATTN",
    "FLASH_FF",
};

const char * GGML_OP_SYMBOL[GGML_OP_COUNT] = {
    "none",

    "x",
    "x+y",
    "x-y",
    "x*y",
    "x/y",
    "x^2",
    "√x",
    "Σx",
    "Σx/n",
    "repeat(x)",
    "abs(x)",
    "sgn(x)",
    "-x",
    "step(x)",
    "relu(x)",
    "gelu(x)",
    "norm(x)",

    "X*Y",

    "x*v",
    "x-\\>y",
    "reshape(x)",
    "view(x)",
    "permute(x)",
    "transpose(x)",
    "get_rows(x)",
    "diag_mask_inf(x)",
    "soft_max(x)",
    "rope(x)",
    "conv_1d_1s(x)",
    "conv_1d_2s(x)",

    "flash_attn(x)",
    "flash_ff(x)",
};

//
// ggml object
//

struct ggml_object {
    size_t offset;
    size_t size;

    struct ggml_object * next;

    char padding[8];
};

const size_t GGML_OBJECT_SIZE = sizeof(struct ggml_object);

static_assert(sizeof(struct ggml_object)%GGML_MEM_ALIGN == 0, "ggml_object size must be a multiple of GGML_MEM_ALIGN");
static_assert(sizeof(struct ggml_tensor)%GGML_MEM_ALIGN == 0, "ggml_tensor size must be a multiple of GGML_MEM_ALIGN");

//
// ggml context
//

struct ggml_context {
    size_t mem_size;
    void * mem_buffer;
    bool   mem_buffer_owned;

    int n_objects;

    struct ggml_object * objects_begin;
    struct ggml_object * objects_end;
};

struct ggml_context_container {
    bool used;

    struct ggml_context context;
};

//
// compute types
//

enum ggml_task_type {
    GGML_TASK_INIT = 0,
    GGML_TASK_COMPUTE,
    GGML_TASK_FINALIZE,
};

struct ggml_compute_params {
    enum ggml_task_type type;

    int ith, nth;

    // work buffer for all threads
    size_t wsize;
    void * wdata;
};

//
// ggml state
//

struct ggml_state {
    struct ggml_context_container contexts[GGML_MAX_CONTEXTS];
};

// global state
struct ggml_state g_state;
atomic_int g_state_barrier = 0;

////////////////////////////////////////////////////////////////////////////////

void ggml_print_object(const struct ggml_object * obj) {
    GGML_PRINT(" - ggml_object: offset = %zu, size = %zu, next = %p\n",
            obj->offset, obj->size, (const void *) obj->next);
}

void ggml_print_objects(const struct ggml_context * ctx) {
    struct ggml_object * obj = ctx->objects_begin;

    GGML_PRINT("%s: objects in context %p:\n", __func__, (const void *) ctx);

    while (obj != NULL) {
        ggml_print_object(obj);
        obj = obj->next;
    }

    GGML_PRINT("%s: --- end ---\n", __func__);
}

int ggml_nelements(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[0]*tensor->ne[1]*tensor->ne[2]*tensor->ne[3];
}

int ggml_nrows(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[1]*tensor->ne[2]*tensor->ne[3];
}

size_t ggml_nbytes(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return ggml_nelements(tensor)*GGML_TYPE_SIZE[tensor->type];
}

size_t ggml_type_size(enum ggml_type type) {
    return GGML_TYPE_SIZE[type];
}

size_t ggml_element_size(const struct ggml_tensor * tensor) {
    return GGML_TYPE_SIZE[tensor->type];
}

bool ggml_is_scalar(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[0] == 1 && tensor->ne[1] == 1 && tensor->ne[2] == 1 && tensor->ne[3] == 1;
}

bool ggml_is_vector(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[1] == 1 && tensor->ne[2] == 1 && tensor->ne[3] == 1;
}

bool ggml_is_matrix(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return tensor->ne[2] == 1 && tensor->ne[3] == 1;
}

bool ggml_can_mul_mat(const struct ggml_tensor * t0, const struct ggml_tensor * t1) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        (t0->ne[0]  == t1->ne[0])  &&
        (t0->ne[2]  == t1->ne[2])  &&
        (t0->ne[3]  == t1->ne[3]);
}

bool ggml_is_contiguous(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        tensor->nb[0] == GGML_TYPE_SIZE[tensor->type] &&
        tensor->nb[1] == tensor->nb[0]*tensor->ne[0] &&
        tensor->nb[2] == tensor->nb[1]*tensor->ne[1] &&
        tensor->nb[3] == tensor->nb[2]*tensor->ne[2];
}

bool ggml_is_padded_1d(const struct ggml_tensor * tensor) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        tensor->nb[0] == GGML_TYPE_SIZE[tensor->type] &&
        tensor->nb[2] == tensor->nb[1]*tensor->ne[1] &&
        tensor->nb[3] == tensor->nb[2]*tensor->ne[2];;
}

bool ggml_are_same_shape(const struct ggml_tensor * t0, const struct ggml_tensor * t1) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        (t0->ne[0] == t1->ne[0] ) &&
        (t0->ne[1] == t1->ne[1] ) &&
        (t0->ne[2] == t1->ne[2] ) &&
        (t0->ne[3] == t1->ne[3] );
}

// check if t1 can be represented as a repeatition of t0
bool ggml_can_repeat(const struct ggml_tensor * t0, const struct ggml_tensor * t1) {
    static_assert(GGML_MAX_DIMS == 4, "GGML_MAX_DIMS is not 4 - update this function");

    return
        (t1->ne[0]%t0->ne[0] == 0) &&
        (t1->ne[1]%t0->ne[1] == 0) &&
        (t1->ne[2]%t0->ne[2] == 0) &&
        (t1->ne[3]%t0->ne[3] == 0);
}

int ggml_up32(int n) {
    return (n + 31) & ~31;
}

int ggml_up64(int n) {
    return (n + 63) & ~63;
}

// assert that pointer is aligned to GGML_MEM_ALIGN
#define ggml_assert_aligned(ptr) \
    assert(((uintptr_t) (ptr))%GGML_MEM_ALIGN == 0)

////////////////////////////////////////////////////////////////////////////////

struct ggml_context * ggml_init(struct ggml_init_params params) {
    // make this function thread safe
    {
        int processing = atomic_fetch_add(&g_state_barrier, 1);
        while (processing > 0) {
            // wait for other threads to finish
            atomic_fetch_sub(&g_state_barrier, 1);
            sched_yield();
            processing = atomic_fetch_add(&g_state_barrier, 1);
        }
    }

    static bool is_first_call = true;
    if (is_first_call) {
        const uint64_t t_start = ggml_time_us(); UNUSED(t_start);

        ggml_fp16_t ii;
        for (int i = 0; i < (1 << 16); ++i) {
            uint16_t ui = i;
            memcpy(&ii, &ui, sizeof(ii));
            const float f = GGML_FP16_TO_FP32(ii);
            table_gelu_f16[i] = GGML_FP32_TO_FP16(ggml_gelu_f32(f));
            table_exp_f16[i]  = GGML_FP32_TO_FP16(exp(f));
        }

        const uint64_t t_end = ggml_time_us(); UNUSED(t_end);

        GGML_PRINT_DEBUG("%s: GELU and EXP tables initialized in %f ms\n", __func__, (t_end - t_start)/1000.0f);

        is_first_call = false;
    }

    // find non-used context in g_state
    struct ggml_context * ctx = NULL;

    static bool first_time = true;
    if (first_time) {
        for (int i = 0; i < GGML_MAX_CONTEXTS; i++) {
            g_state.contexts[i].used = false;
        }
        first_time = false;
    }

    for (int i = 0; i < GGML_MAX_CONTEXTS; i++) {
        if (!g_state.contexts[i].used) {
            g_state.contexts[i].used = true;
            ctx = &g_state.contexts[i].context;

            GGML_PRINT_DEBUG("%s: found unused context %d\n", __func__, i);
            break;
        }
    }

    if (ctx == NULL) {
        GGML_PRINT_DEBUG("%s: no unused context found\n", __func__);

        atomic_fetch_sub(&g_state_barrier, 1);

        return NULL;
    }

    *ctx = (struct ggml_context) {
        .mem_size         = params.mem_size,
        .mem_buffer       = params.mem_buffer ? params.mem_buffer : malloc(params.mem_size),
        .mem_buffer_owned = params.mem_buffer ? false : true,
        .n_objects        = 0,
        .objects_begin    = NULL,
        .objects_end      = NULL,
    };

    ggml_assert_aligned(ctx->mem_buffer);

    GGML_PRINT_DEBUG("%s: context initialized\n", __func__);

    atomic_fetch_sub(&g_state_barrier, 1);

    return ctx;
}

void ggml_free(struct ggml_context * ctx) {
    // make this function thread safe
    {
        int processing = atomic_fetch_add(&g_state_barrier, 1);
        while (processing > 0) {
            // wait for other threads to finish
            atomic_fetch_sub(&g_state_barrier, 1);
            sched_yield();
            processing = atomic_fetch_add(&g_state_barrier, 1);
        }
    }

    for (int i = 0; i < GGML_MAX_CONTEXTS; i++) {
        if (&g_state.contexts[i].context == ctx) {
            g_state.contexts[i].used = false;

            GGML_PRINT_DEBUG("%s: context %d with %d objects has been freed. memory used = %zu\n",
                    __func__, i, ctx->n_objects, ctx->objects_end->offset + ctx->objects_end->size);

            if (ctx->mem_buffer_owned) {
                free(ctx->mem_buffer);
            }

            atomic_fetch_sub(&g_state_barrier, 1);

            return;
        }
    }

    GGML_PRINT_DEBUG("%s: context not found\n", __func__);

    atomic_fetch_sub(&g_state_barrier, 1);
}

size_t ggml_used_mem(const struct ggml_context * ctx) {
    return ctx->objects_end->offset + ctx->objects_end->size;
}

////////////////////////////////////////////////////////////////////////////////

struct ggml_tensor * ggml_new_tensor_impl(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int    n_dims,
        const int* ne,
        void*  data) {
    // always insert objects at the end of the context's memory pool
    struct ggml_object * obj_cur = ctx->objects_end;

    const size_t cur_offset = obj_cur == NULL ? 0 : obj_cur->offset;
    const size_t cur_size   = obj_cur == NULL ? 0 : obj_cur->size;
    const size_t cur_end    = cur_offset + cur_size;

    size_t size_needed = 0;

    if (data == NULL) {
        size_needed += GGML_TYPE_SIZE[type];
        for (int i = 0; i < n_dims; i++) {
            size_needed *= ne[i];
        }
        // align to GGML_MEM_ALIGN
        size_needed = ((size_needed + GGML_MEM_ALIGN - 1)/GGML_MEM_ALIGN)*GGML_MEM_ALIGN;

    }
    size_needed += sizeof(struct ggml_tensor);

    if (cur_end + size_needed + GGML_OBJECT_SIZE > ctx->mem_size) {
        GGML_PRINT("%s: not enough space in the context's memory pool\n", __func__);
        assert(false);
        return NULL;
    }

    char * const mem_buffer = ctx->mem_buffer;

    struct ggml_object * const obj_new = (struct ggml_object *)(mem_buffer + cur_end);

    *obj_new = (struct ggml_object) {
        .offset = cur_end + GGML_OBJECT_SIZE,
        .size   = size_needed,
        .next   = NULL,
    };

    if (obj_cur != NULL) {
        obj_cur->next = obj_new;
    } else {
        // this is the first object in this context
        ctx->objects_begin = obj_new;
    }

    ctx->objects_end = obj_new;

    //GGML_PRINT_DEBUG("%s: inserted new object at %zu\n", __func__, cur_end);

    struct ggml_tensor * const result = (struct ggml_tensor *)(mem_buffer + obj_new->offset);

    ggml_assert_aligned(result);

    *result = (struct ggml_tensor) {
        /*.type         =*/ type,
        /*.n_dims       =*/ n_dims,
        /*.ne           =*/ { 1, 1, 1, 1 },
        /*.nb           =*/ { 0, 0, 0, 0 },
        /*.op           =*/ GGML_OP_NONE,
        /*.is_param     =*/ false,
        /*.grad         =*/ NULL,
        /*.src0         =*/ NULL,
        /*.src1         =*/ NULL,
        /*.opt          =*/ { NULL },
        /*.n_tasks      =*/ 0,
        /*.perf_runs    =*/ 0,
        /*.perf_cycles  =*/ 0,
        /*.perf_time_us =*/ 0,
        /*.data         =*/ data == NULL ? (void *)(result + 1) : data,
        /*.pad          =*/ { 0 },
    };

    ggml_assert_aligned(result->data);

    for (int i = 0; i < n_dims; i++) {
        result->ne[i] = ne[i];
    }

    result->nb[0] = GGML_TYPE_SIZE[type];
    for (int i = 1; i < GGML_MAX_DIMS; i++) {
        result->nb[i] = result->nb[i - 1]*result->ne[i - 1];
    }

    ctx->n_objects++;

    return result;
}

struct ggml_tensor * ggml_new_tensor(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int    n_dims,
        const int* ne) {
    return ggml_new_tensor_impl(ctx, type, n_dims, ne, NULL);
}

struct ggml_tensor * ggml_new_tensor_1d(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int    ne0) {
    return ggml_new_tensor(ctx, type, 1, &ne0);
}

struct ggml_tensor * ggml_new_tensor_2d(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int    ne0,
        int    ne1) {
    const int ne[2] = { ne0, ne1 };
    return ggml_new_tensor(ctx, type, 2, ne);
}

struct ggml_tensor * ggml_new_tensor_3d(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int    ne0,
        int    ne1,
        int    ne2) {
    const int ne[3] = { ne0, ne1, ne2 };
    return ggml_new_tensor(ctx, type, 3, ne);
}

struct ggml_tensor * ggml_new_tensor_4d(
        struct ggml_context * ctx,
        enum   ggml_type type,
        int    ne0,
        int    ne1,
        int    ne2,
        int    ne3) {
    const int ne[4] = { ne0, ne1, ne2, ne3 };
    return ggml_new_tensor(ctx, type, 4, ne);
}

struct ggml_tensor * ggml_new_i32(struct ggml_context * ctx, int32_t value) {
    struct ggml_tensor * result = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 1);

    ggml_set_i32(result, value);

    return result;
}

struct ggml_tensor * ggml_new_f32(struct ggml_context * ctx, float value) {
    struct ggml_tensor * result = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, 1);

    ggml_set_f32(result, value);

    return result;
}

struct ggml_tensor * ggml_dup_tensor(struct ggml_context * ctx, const struct ggml_tensor * src) {
    return ggml_new_tensor_impl(ctx, src->type, src->n_dims, src->ne, NULL);
}

struct ggml_tensor * ggml_set_zero(struct ggml_tensor * tensor) {
    memset(tensor->data, 0, ggml_nbytes(tensor));
    return tensor;
}

struct ggml_tensor * ggml_set_i32 (struct ggml_tensor * tensor, int32_t value) {
    const int n     = ggml_nrows(tensor);
    const int nc    = tensor->ne[0];
    const size_t n1 = tensor->nb[1];

    char * const data = tensor->data;

    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                assert(tensor->nb[0] == sizeof(int8_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i8(nc, (int8_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_I16:
            {
                assert(tensor->nb[0] == sizeof(int16_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i16(nc, (int16_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_I32:
            {
                assert(tensor->nb[0] == sizeof(int32_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i32(nc, (int32_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_F16:
            {
                assert(tensor->nb[0] == sizeof(ggml_fp16_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_f16(nc, (ggml_fp16_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_F32:
            {
                assert(tensor->nb[0] == sizeof(float));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_f32(nc, (float *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }

    return tensor;
}

struct ggml_tensor * ggml_set_f32(struct ggml_tensor * tensor, float value) {
    const int n     = ggml_nrows(tensor);
    const int nc    = tensor->ne[0];
    const size_t n1 = tensor->nb[1];

    char * const data = tensor->data;

    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                assert(tensor->nb[0] == sizeof(int8_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i8(nc, (int8_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_I16:
            {
                assert(tensor->nb[0] == sizeof(int16_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i16(nc, (int16_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_I32:
            {
                assert(tensor->nb[0] == sizeof(int32_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_i32(nc, (int32_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_F16:
            {
                assert(tensor->nb[0] == sizeof(ggml_fp16_t));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_f16(nc, (ggml_fp16_t *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_F32:
            {
                assert(tensor->nb[0] == sizeof(float));
                for (int i = 0; i < n; i++) {
                    ggml_vec_set_f32(nc, (float *)(data + i*n1), value);
                }
            } break;
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }

    return tensor;
}

int32_t ggml_get_i32_1d(const struct ggml_tensor * tensor, int i) {
    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int8_t));
                return ((int8_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_I16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int16_t));
                return ((int16_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_I32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int32_t));
                return ((int32_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_F16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(ggml_fp16_t));
                return GGML_FP16_TO_FP32(((ggml_fp16_t *)(tensor->data))[i]);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(float));
                return ((float *)(tensor->data))[i];
            } break;
        case GGML_TYPE_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }

    return 0.0f;
}

void ggml_set_i32_1d(const struct ggml_tensor * tensor, int i, int32_t value) {
    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int8_t));
                ((int8_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_I16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int16_t));
                ((int16_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_I32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int32_t));
                ((int32_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_F16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(ggml_fp16_t));
                ((ggml_fp16_t *)(tensor->data))[i] = GGML_FP32_TO_FP16(value);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(float));
                ((float *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }
}

float ggml_get_f32_1d(const struct ggml_tensor * tensor, int i) {
    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int8_t));
                return ((int8_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_I16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int16_t));
                return ((int16_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_I32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int32_t));
                return ((int32_t *)(tensor->data))[i];
            } break;
        case GGML_TYPE_F16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(ggml_fp16_t));
                return GGML_FP16_TO_FP32(((ggml_fp16_t *)(tensor->data))[i]);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(float));
                return ((float *)(tensor->data))[i];
            } break;
        case GGML_TYPE_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }

    return 0.0f;
}

void ggml_set_f32_1d(const struct ggml_tensor * tensor, int i, float value) {
    switch (tensor->type) {
        case GGML_TYPE_I8:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int8_t));
                ((int8_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_I16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int16_t));
                ((int16_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_I32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(int32_t));
                ((int32_t *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_F16:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(ggml_fp16_t));
                ((ggml_fp16_t *)(tensor->data))[i] = GGML_FP32_TO_FP16(value);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(tensor->nb[0] == sizeof(float));
                ((float *)(tensor->data))[i] = value;
            } break;
        case GGML_TYPE_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }
}

void * ggml_get_data(const struct ggml_tensor * tensor) {
    return tensor->data;
}

float * ggml_get_data_f32(const struct ggml_tensor * tensor) {
    assert(tensor->type == GGML_TYPE_F32);
    return (float *)(tensor->data);
}

struct ggml_tensor * ggml_view_tensor(
        struct ggml_context * ctx,
        const struct ggml_tensor * src) {
    return ggml_new_tensor_impl(ctx, src->type, src->n_dims, src->ne, src->data);
}

////////////////////////////////////////////////////////////////////////////////

// ggml_dup

struct ggml_tensor * ggml_dup_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_DUP;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_dup(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    return ggml_dup_impl(ctx, a, false);
}

struct ggml_tensor * ggml_dup_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    return ggml_dup_impl(ctx, a, true);
}

// ggml_add

struct ggml_tensor * ggml_add_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        bool inplace) {
    assert(ggml_are_same_shape(a, b));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_ADD;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_add(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_add_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_add_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_add_impl(ctx, a, b, true);
}

// ggml_sub

struct ggml_tensor * ggml_sub_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        bool inplace) {
    assert(ggml_are_same_shape(a, b));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SUB;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_sub(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_sub_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_sub_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_sub_impl(ctx, a, b, true);
}

// ggml_mul

struct ggml_tensor * ggml_mul_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        bool inplace) {
    assert(ggml_are_same_shape(a, b));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    if (inplace) {
        assert(is_node == false);
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_MUL;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_mul(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_mul_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_mul_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_mul_impl(ctx, a, b, true);
}

// ggml_div

struct ggml_tensor * ggml_div_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b,
        bool inplace) {
    assert(ggml_are_same_shape(a, b));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        is_node = true;
    }

    if (inplace) {
        assert(is_node == false);
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_DIV;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_div(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_div_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_div_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    return ggml_div_impl(ctx, a, b, true);
}

// ggml_sqr

struct ggml_tensor * ggml_sqr_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SQR;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_sqr(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sqr_impl(ctx, a, false);
}

struct ggml_tensor * ggml_sqr_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sqr_impl(ctx, a, true);
}

// ggml_sqrt

struct ggml_tensor * ggml_sqrt_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SQRT;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_sqrt(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sqrt_impl(ctx, a, false);
}

struct ggml_tensor * ggml_sqrt_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sqrt_impl(ctx, a, true);
}

// ggml_sum

struct ggml_tensor * ggml_sum(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    struct ggml_tensor * result = ggml_new_tensor_1d(ctx, a->type, 1);

    result->op   = GGML_OP_SUM;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_mean

struct ggml_tensor * ggml_mean(
        struct ggml_context * ctx,
        struct ggml_tensor * a) {
    bool is_node = false;

    if (a->grad) {
        assert(false); // TODO: implement
        is_node = true;
    }

    int ne[GGML_MAX_DIMS] = { 1, a->ne[1], a->ne[2], a->ne[3] };
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, a->n_dims, ne);

    result->op   = GGML_OP_MEAN;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_repeat

struct ggml_tensor * ggml_repeat(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    assert(ggml_can_repeat(a, b));

    bool is_node = false;

    if (a->grad) {
        is_node = true;
    }

    if (ggml_are_same_shape(a, b) && !is_node) {
        return a;
    }

    struct ggml_tensor * result = ggml_new_tensor(ctx, a->type, b->n_dims, b->ne);

    result->op   = GGML_OP_REPEAT;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_abs

struct ggml_tensor * ggml_abs_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_ABS;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_abs(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_abs_impl(ctx, a, false);
}

struct ggml_tensor * ggml_abs_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_abs_impl(ctx, a, true);
}


// ggml_sgn

struct ggml_tensor * ggml_sgn_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_SGN;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_sgn(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sgn_impl(ctx, a, false);
}

struct ggml_tensor * ggml_sgn_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_sgn_impl(ctx, a, true);
}

// ggml_neg

struct ggml_tensor * ggml_neg_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_NEG;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_neg(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_neg_impl(ctx, a, false);
}

struct ggml_tensor * ggml_neg_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_neg_impl(ctx, a, true);
}

// ggml_step

struct ggml_tensor * ggml_step_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_STEP;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_step(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_step_impl(ctx, a, false);
}

struct ggml_tensor * ggml_step_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_step_impl(ctx, a, true);
}

// ggml_relu

struct ggml_tensor * ggml_relu_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_RELU;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_relu(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_relu_impl(ctx, a, false);
}

struct ggml_tensor * ggml_relu_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_relu_impl(ctx, a, true);
}

// ggml_gelu

struct ggml_tensor * ggml_gelu_impl(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_GELU;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_gelu(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_gelu_impl(ctx, a, false);
}

struct ggml_tensor * ggml_gelu_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_gelu_impl(ctx, a, true);
}

// ggml_norm

struct ggml_tensor * ggml_norm_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        bool inplace) {
    bool is_node = false;

    if (!inplace && (a->grad)) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);

    result->op   = GGML_OP_NORM;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL; // TODO: maybe store epsilon here?

    return result;
}

struct ggml_tensor * ggml_norm(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_norm_impl(ctx, a, false);
}

struct ggml_tensor * ggml_norm_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    return ggml_norm_impl(ctx, a, true);
}

// ggml_mul_mat

struct ggml_tensor * ggml_mul_mat(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    assert(ggml_can_mul_mat(a, b));

    bool is_node = false;

    if (a->grad || b->grad) {
        is_node = true;
    }

    const int ne[4] = { a->ne[1], b->ne[1], a->ne[2], b->ne[3] };
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, MIN(a->n_dims, b->n_dims), ne);

    result->op   = GGML_OP_MUL_MAT;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_scale

struct ggml_tensor * ggml_scale_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b,
        bool inplace) {
    assert(ggml_is_scalar(b));
    assert(ggml_is_padded_1d(a));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    // TODO: when implement backward, fix this:
    //struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);
    struct ggml_tensor * result = ggml_view_tensor(ctx, a);

    result->op   = GGML_OP_SCALE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_scale(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_scale_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_scale_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_scale_impl(ctx, a, b, true);
}

// ggml_cpy

struct ggml_tensor * ggml_cpy_impl(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b,
        bool inplace) {
    assert(ggml_nelements(a) == ggml_nelements(b));

    bool is_node = false;

    if (!inplace && (a->grad || b->grad)) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    // make a view of the destination
    struct ggml_tensor * result = ggml_view_tensor(ctx, b);

    result->op   = GGML_OP_CPY;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

struct ggml_tensor * ggml_cpy(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_cpy_impl(ctx, a, b, false);
}

struct ggml_tensor * ggml_cpy_inplace(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    return ggml_cpy_impl(ctx, a, b, true);
}

// ggml_reshape

struct ggml_tensor * ggml_reshape(
        struct ggml_context * ctx,
        struct ggml_tensor * a,
        struct ggml_tensor * b) {
    assert(ggml_is_contiguous(a));
    assert(ggml_is_contiguous(b));
    assert(ggml_nelements(a) == ggml_nelements(b));

    bool is_node = false;

    if (a->grad || b->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, b->n_dims, b->ne, a->data);

    result->op   = GGML_OP_RESHAPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_reshape_2d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   ne0,
        int                   ne1) {
    assert(ggml_is_contiguous(a));
    assert(ggml_nelements(a) == ne0*ne1);

    bool is_node = false;

    if (a->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    const int ne[2] = { ne0, ne1 };
    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 2, ne, a->data);

    result->op   = GGML_OP_RESHAPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

struct ggml_tensor * ggml_reshape_3d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   ne0,
        int                   ne1,
        int                   ne2) {
    assert(ggml_is_contiguous(a));
    assert(ggml_nelements(a) == ne0*ne1*ne2);

    bool is_node = false;

    if (a->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    const int ne[3] = { ne0, ne1, ne2 };
    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 3, ne, a->data);

    result->op   = GGML_OP_RESHAPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_view_1d

struct ggml_tensor * ggml_view_1d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   ne0,
        size_t                offset) {
    if (a->grad) {
        assert(false); // gradient propagation is not supported
    }

    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 1, &ne0, (char *) a->data + offset);

    result->op   = GGML_OP_VIEW;
    result->grad = NULL;
    result->src0 = a;
    result->src1 = NULL; // TODO: maybe store the offset here?

    return result;
}

// ggml_view_2d

struct ggml_tensor * ggml_view_2d(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   ne0,
        int                   ne1,
        size_t                nb1,
        size_t                offset) {
    if (a->grad) {
        assert(false); // gradient propagation is not supported
    }

    const int ne[GGML_MAX_DIMS] = { ne0, ne1, 1, 1 };

    struct ggml_tensor * result = ggml_new_tensor_impl(ctx, a->type, 2, ne, (char *) a->data + offset);

    result->nb[1] = nb1;
    result->nb[2] = result->nb[1]*ne1;
    result->nb[3] = result->nb[2];

    result->op   = GGML_OP_VIEW;
    result->grad = NULL;
    result->src0 = a;
    result->src1 = NULL; // TODO: maybe store the offset here?

    return result;
}

// ggml_permute

struct ggml_tensor * ggml_permute(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   axis0,
        int                   axis1,
        int                   axis2,
        int                   axis3) {
    assert(axis0 >= 0 && axis0 < GGML_MAX_DIMS);
    assert(axis1 >= 0 && axis1 < GGML_MAX_DIMS);
    assert(axis2 >= 0 && axis2 < GGML_MAX_DIMS);
    assert(axis3 >= 0 && axis3 < GGML_MAX_DIMS);

    assert(axis0 != axis1);
    assert(axis0 != axis2);
    assert(axis0 != axis3);
    assert(axis1 != axis2);
    assert(axis1 != axis3);
    assert(axis2 != axis3);

    bool is_node = false;

    if (a->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    struct ggml_tensor * result = ggml_view_tensor(ctx, a);

    int ne[GGML_MAX_DIMS];
    int nb[GGML_MAX_DIMS];

    ne[axis0] = a->ne[0];
    ne[axis1] = a->ne[1];
    ne[axis2] = a->ne[2];
    ne[axis3] = a->ne[3];

    nb[axis0] = a->nb[0];
    nb[axis1] = a->nb[1];
    nb[axis2] = a->nb[2];
    nb[axis3] = a->nb[3];

    result->ne[0] = ne[0];
    result->ne[1] = ne[1];
    result->ne[2] = ne[2];
    result->ne[3] = ne[3];

    result->nb[0] = nb[0];
    result->nb[1] = nb[1];
    result->nb[2] = nb[2];
    result->nb[3] = nb[3];

    result->op   = GGML_OP_PERMUTE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL; // TODO: maybe store the permutation here?

    return result;
}

// ggml_transpose

struct ggml_tensor * ggml_transpose(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    bool is_node = false;

    if (a->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    struct ggml_tensor * result = ggml_view_tensor(ctx, a);

    result->ne[0] = a->ne[1];
    result->ne[1] = a->ne[0];

    result->nb[0] = a->nb[1];
    result->nb[1] = a->nb[0];

    result->op   = GGML_OP_TRANSPOSE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_get_rows

struct ggml_tensor * ggml_get_rows(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    assert(ggml_is_matrix(a) && ggml_is_vector(b) && b->type == GGML_TYPE_I32);

    bool is_node = false;

    if (a->grad || b->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    // TODO: implement non F32 return
    //struct ggml_tensor * result = ggml_new_tensor_2d(ctx, a->type, a->ne[0], b->ne[0]);
    struct ggml_tensor * result = ggml_new_tensor_2d(ctx, GGML_TYPE_F32, a->ne[0], b->ne[0]);

    result->op   = GGML_OP_GET_ROWS;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_diag_mask_inf

struct ggml_tensor * ggml_diag_mask_inf(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past) {
    bool is_node = false;

    if (a->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    // TODO: when implement backward, fix this:
    //struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);
    struct ggml_tensor * result = ggml_view_tensor(ctx, a);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 1);
    ((int32_t *) b->data)[0] = n_past;

    result->op   = GGML_OP_DIAG_MASK_INF;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_soft_max

struct ggml_tensor * ggml_soft_max(
        struct ggml_context * ctx,
        struct ggml_tensor  * a) {
    bool is_node = false;

    if (a->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    // TODO: when implement backward, fix this:
    //struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);
    struct ggml_tensor * result = ggml_view_tensor(ctx, a);

    result->op   = GGML_OP_SOFT_MAX;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = NULL;

    return result;
}

// ggml_rope

struct ggml_tensor * ggml_rope(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        int                   n_past,
        int                   n_dims,
        int                   mode) {
    assert(n_past >= 0);
    bool is_node = false;

    if (a->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    // TODO: when implement backward, fix this:
    //struct ggml_tensor * result = inplace ? ggml_view_tensor(ctx, a) : ggml_dup_tensor(ctx, a);
    struct ggml_tensor * result = ggml_view_tensor(ctx, a);

    struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 3);
    ((int32_t *) b->data)[0] = n_past;
    ((int32_t *) b->data)[1] = n_dims;
    ((int32_t *) b->data)[2] = mode;

    result->op   = GGML_OP_ROPE;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_conv_1d_1s

struct ggml_tensor * ggml_conv_1d_1s(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    assert(ggml_is_matrix(b));
    assert(a->ne[1] == b->ne[1]);
    assert(a->ne[3] == 1);
    bool is_node = false;

    if (a->grad || b->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    const int ne[4] = { b->ne[0], a->ne[2], 1, 1, };
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, 2, ne);

    result->op   = GGML_OP_CONV_1D_1S;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_conv_1d_2s

struct ggml_tensor * ggml_conv_1d_2s(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b) {
    assert(ggml_is_matrix(b));
    assert(a->ne[1] == b->ne[1]);
    assert(a->ne[3] == 1);
    bool is_node = false;

    if (a->grad || b->grad) {
        assert(false); // TODO: implement backward
        is_node = true;
    }

    const int ne[4] = { b->ne[0]/2, a->ne[2], 1, 1, };
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, 2, ne);

    result->op   = GGML_OP_CONV_1D_2S;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b;

    return result;
}

// ggml_flash_attn

struct ggml_tensor * ggml_flash_attn(
        struct ggml_context * ctx,
        struct ggml_tensor  * q,
        struct ggml_tensor  * k,
        struct ggml_tensor  * v,
        bool                  masked) {
    assert(ggml_can_mul_mat(k, q));
    // TODO: check if vT can be multiplied by (k*qT)

    bool is_node = false;

    if (q->grad || k->grad || v->grad) {
        GGML_ASSERT(false); // TODO: implement backward
        is_node = true;
    }

    //struct ggml_tensor * result = ggml_dup_tensor(ctx, q);
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, q->ne);

    result->op   = GGML_OP_FLASH_ATTN;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = q;
    result->src1 = k;
    result->opt[0] = v;
    result->opt[1] = ggml_new_i32(ctx, masked ? 1 : 0);

    return result;
}

// ggml_flash_ff

struct ggml_tensor * ggml_flash_ff(
        struct ggml_context * ctx,
        struct ggml_tensor  * a,
        struct ggml_tensor  * b0,
        struct ggml_tensor  * b1,
        struct ggml_tensor  * c0,
        struct ggml_tensor  * c1) {
    assert(ggml_can_mul_mat(b0, a));
    // TODO: more checks

    bool is_node = false;

    if (a->grad || b0->grad || b1->grad || c0->grad || c1->grad) {
        GGML_ASSERT(false); // TODO: implement backward
        is_node = true;
    }

    //struct ggml_tensor * result = ggml_dup_tensor(ctx, a);
    struct ggml_tensor * result = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, a->ne);

    result->op   = GGML_OP_FLASH_FF;
    result->grad = is_node ? ggml_dup_tensor(ctx, result) : NULL;
    result->src0 = a;
    result->src1 = b0;
    result->opt[0] = b1;
    result->opt[1] = c0;
    result->opt[2] = c1;

    return result;
}

////////////////////////////////////////////////////////////////////////////////

void ggml_set_param(
        struct ggml_context * ctx,
        struct ggml_tensor * tensor) {
    tensor->is_param = true;

    assert(tensor->grad == NULL);
    tensor->grad = ggml_dup_tensor(ctx, tensor);
}

// ggml_compute_forward_dup

void ggml_compute_forward_dup_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_is_contiguous(dst));
    assert(ggml_nelements(dst) == ggml_nelements(src0));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    //const int ne00 = src0->ne[0];
    //const int ne01 = src0->ne[1];
    //const int ne02 = src0->ne[2];
    //const int ne03 = src0->ne[3];

    //const size_t nb00 = src0->nb[0];
    //const size_t nb01 = src0->nb[1];
    //const size_t nb02 = src0->nb[2];
    //const size_t nb03 = src0->nb[3];

    if (ggml_is_contiguous(src0) && src0->type == dst->type) {
        memcpy(dst->data, src0->data, ggml_nelements(dst) * GGML_TYPE_SIZE[src0->type]);
        return;
    }

    GGML_ASSERT(false); // TODO: implement
}

void ggml_compute_forward_dup_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(params->ith == 0);
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_nelements(dst) == ggml_nelements(src0));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    const int ne03 = src0->ne[3];

    const size_t nb00 = src0->nb[0];
    const size_t nb01 = src0->nb[1];
    const size_t nb02 = src0->nb[2];
    const size_t nb03 = src0->nb[3];

    if (ggml_is_contiguous(src0) && src0->type == dst->type) {
        memcpy(dst->data, src0->data, ggml_nelements(dst) * GGML_TYPE_SIZE[src0->type]);
        return;
    }

    if (src0->nb[0] == sizeof(float)) {
        if (dst->type == GGML_TYPE_F32) {
            int id = 0;
            const size_t rs = ne00*nb00;

            for (int i03 = 0; i03 < ne03; i03++) {
                for (int i02 = 0; i02 < ne02; i02++) {
                    for (int i01 = 0; i01 < ne01; i01++) {
                        const char * src0_ptr = (char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03;
                        char * dst_ptr = (char *) dst->data + id*rs;

                        memcpy(dst_ptr, src0_ptr, rs);

                        id++;
                    }
                }
            }
        } else if (dst->type == GGML_TYPE_F16) {
            int id = 0;
            ggml_fp16_t * dst_ptr = (ggml_fp16_t *) dst->data;

            for (int i03 = 0; i03 < ne03; i03++) {
                for (int i02 = 0; i02 < ne02; i02++) {
                    for (int i01 = 0; i01 < ne01; i01++) {
                        for (int i00 = 0; i00 < ne00; i00++) {
                            const float * src0_ptr = (float *) ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);

                            dst_ptr[id] = GGML_FP32_TO_FP16(*src0_ptr);
                            id++;
                        }
                    }
                }
            }
        } else {
            GGML_ASSERT(false); // TODO: implement
        }
    } else {
        //printf("%s: this is not optimal - fix me\n", __func__);

        if (dst->type == GGML_TYPE_F32) {
            int id = 0;
            float * dst_ptr = (float *) dst->data;

            for (int i03 = 0; i03 < ne03; i03++) {
                for (int i02 = 0; i02 < ne02; i02++) {
                    for (int i01 = 0; i01 < ne01; i01++) {
                        for (int i00 = 0; i00 < ne00; i00++) {
                            const float * src0_ptr = (float *) ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);

                            dst_ptr[id] = *src0_ptr;
                            id++;
                        }
                    }
                }
            }
        } else if (dst->type == GGML_TYPE_F16) {
            int id = 0;
            ggml_fp16_t * dst_ptr = (ggml_fp16_t *) dst->data;

            for (int i03 = 0; i03 < ne03; i03++) {
                for (int i02 = 0; i02 < ne02; i02++) {
                    for (int i01 = 0; i01 < ne01; i01++) {
                        for (int i00 = 0; i00 < ne00; i00++) {
                            const float * src0_ptr = (float *) ((char *) src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);

                            dst_ptr[id] = GGML_FP32_TO_FP16(*src0_ptr);
                            id++;
                        }
                    }
                }
            }
        } else {
            GGML_ASSERT(false); // TODO: implement
        }
    }
}

void ggml_compute_forward_dup(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_dup_f16(params, src0, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_dup_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_add

void ggml_compute_forward_add_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    const size_t nb00 = src0->nb[0];
    const size_t nb01 = src0->nb[1];

    const size_t nb10 = src1->nb[0];
    const size_t nb11 = src1->nb[1];

    const size_t nb0 = dst->nb[0];
    const size_t nb1 = dst->nb[1];

    GGML_ASSERT( nb0 == sizeof(float));
    GGML_ASSERT(nb00 == sizeof(float));

    if (nb10 == sizeof(float)) {
        const int j0 = (n/nth)*ith;
        const int j1 = ith == nth - 1 ? n : (n/nth)*(ith + 1);

        for (int j = j0; j < j1; j++) {
            ggml_vec_add_f32(nc,
                    (float *) ((char *) dst->data  + j*nb1),
                    (float *) ((char *) src0->data + j*nb01),
                    (float *) ((char *) src1->data + j*nb11));
        }
    } else {
        // src1 is not contiguous
        for (int j = ith; j < n; j += nth) {
            float * dst_ptr  = (float *) ((char *) dst->data  + j*nb1);
            float * src0_ptr = (float *) ((char *) src0->data + j*nb01);
            for (int i = 0; i < nc; i++) {
                float * src1_ptr = (float *) ((char *) src1->data + j*nb11 + i*nb10);

                dst_ptr[i] = src0_ptr[i] + *src1_ptr;
            }
        }
    }
}

void ggml_compute_forward_add(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_add_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_sub

void ggml_compute_forward_sub_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));
    assert(src1->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_sub_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])),
                (float *) ((char *) src1->data + i*(src1->nb[1])));
    }
}

void ggml_compute_forward_sub(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sub_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_mul

void ggml_compute_forward_mul_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));
    assert(src1->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_mul_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])),
                (float *) ((char *) src1->data + i*(src1->nb[1])));
    }
}

void ggml_compute_forward_mul(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_mul_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_div

void ggml_compute_forward_div_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, src1) && ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));
    assert(src1->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_div_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])),
                (float *) ((char *) src1->data + i*(src1->nb[1])));
    }
}

void ggml_compute_forward_div(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_div_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_sqr

void ggml_compute_forward_sqr_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n     = ggml_nrows(src0);
    const int nc    = src0->ne[0];

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_sqr_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

void ggml_compute_forward_sqr(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sqr_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_sqrt

void ggml_compute_forward_sqrt_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_sqrt_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

void ggml_compute_forward_sqrt(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sqrt_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_sum

void ggml_compute_forward_sum_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_is_scalar(dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    assert(ggml_is_scalar(dst));
    assert(src0->nb[0] == sizeof(float));

    *(float *) (dst->data) = 0.0f;

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    const int ne03 = src0->ne[3];

    const size_t nb01 = src0->nb[1];
    const size_t nb02 = src0->nb[2];
    const size_t nb03 = src0->nb[3];

    for (int i03 = 0; i03 < ne03; i03++) {
        for (int i02 = 0; i02 < ne02; i02++) {
            for (int i01 = 0; i01 < ne01; i01++) {
                ggml_vec_sum_f32(ne00,
                        (float *) (dst->data),
                        (float *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03));
            }
        }
    }
}

void ggml_compute_forward_sum(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sum_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_mean

void ggml_compute_forward_mean_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    assert(src0->nb[0] == sizeof(float));

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    const int ne03 = src0->ne[3];

    const size_t nb01 = src0->nb[1];
    const size_t nb02 = src0->nb[2];
    const size_t nb03 = src0->nb[3];

    const int ne0 = dst->ne[0];
    const int ne1 = dst->ne[1];
    const int ne2 = dst->ne[2];
    const int ne3 = dst->ne[3];

    assert(ne0 == 1);
    assert(ne1 == ne01);
    assert(ne2 == ne02);
    assert(ne3 == ne03);

    UNUSED(ne0);
    UNUSED(ne1);
    UNUSED(ne2);
    UNUSED(ne3);

    const size_t nb1 = dst->nb[1];
    const size_t nb2 = dst->nb[2];
    const size_t nb3 = dst->nb[3];

    for (int i03 = 0; i03 < ne03; i03++) {
        for (int i02 = 0; i02 < ne02; i02++) {
            for (int i01 = 0; i01 < ne01; i01++) {
                *(float *) ((char *) dst->data + i01*nb1 + i02*nb2 + i03*nb3) = 0.0f;

                ggml_vec_sum_f32(ne00,
                        (float *) ((char *)  dst->data + i01*nb1  + i02*nb2  + i03*nb3),
                        (float *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03));

                *(float *) ((char *) dst->data + i01*nb1 + i02*nb2 + i03*nb3) /= (float) ne00;
            }
        }
    }
}

void ggml_compute_forward_mean(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_mean_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_repeat

void ggml_compute_forward_repeat_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_can_repeat(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // TODO: implement support for rank > 2 tensors
    assert(src0->ne[2] == 1);
    assert(src0->ne[3] == 1);
    assert( dst->ne[2] == 1);
    assert( dst->ne[3] == 1);

    const int nc  = dst->ne[0];
    const int nr  = dst->ne[1];
    const int nc0 = src0->ne[0];
    const int nr0 = src0->ne[1];
    const int ncr = nc/nc0; // guaranteed to be an integer due to the check in ggml_can_repeat
    const int nrr = nr/nr0; // guaranteed to be an integer due to the check in ggml_can_repeat

    // TODO: support for transposed / permuted tensors
    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    // TODO: maybe this is not optimal?
    for (int i = 0; i < nrr; i++) {
        for (int j = 0; j < ncr; j++) {
            for (int k = 0; k < nr0; k++) {
                ggml_vec_cpy_f32(nc0,
                        (float *) ((char *)  dst->data + (i*nr0 + k)*( dst->nb[1]) + j*nc0*( dst->nb[0])),
                        (float *) ((char *) src0->data + (        k)*(src0->nb[1])));
            }
        }
    }
}

void ggml_compute_forward_repeat(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_repeat_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_abs

void ggml_compute_forward_abs_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_abs_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

void ggml_compute_forward_abs(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_abs_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_sgn

void ggml_compute_forward_sgn_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_sgn_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

void ggml_compute_forward_sgn(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_sgn_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_neg

void ggml_compute_forward_neg_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_neg_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

void ggml_compute_forward_neg(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_neg_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_step

void ggml_compute_forward_step_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_step_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

void ggml_compute_forward_step(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_step_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_relu

void ggml_compute_forward_relu_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];

    assert(dst->nb[0]  == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < n; i++) {
        ggml_vec_relu_f32(nc,
                (float *) ((char *) dst->data  + i*( dst->nb[1])),
                (float *) ((char *) src0->data + i*(src0->nb[1])));
    }
}

void ggml_compute_forward_relu(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_relu_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_gelu

void ggml_compute_forward_gelu_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        ggml_vec_gelu_f32(nc,
                (float *) ((char *) dst->data  + i1*( dst->nb[1])),
                (float *) ((char *) src0->data + i1*(src0->nb[1])));

#ifndef NDEBUG
        for (int k = 0; k < nc; k++) {
            const float x = ((float *) ((char *) dst->data + i1*( dst->nb[1])))[k];
            UNUSED(x);
            assert(!isnan(x));
            assert(!isinf(x));
        }
#endif
    }
}

void ggml_compute_forward_gelu(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_gelu_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_norm

void ggml_compute_forward_norm_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    GGML_ASSERT(src0->nb[0] == sizeof(float));

    const int ith = params->ith;
    const int nth = params->nth;

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    const int ne03 = src0->ne[3];

    const size_t nb01 = src0->nb[1];
    const size_t nb02 = src0->nb[2];
    const size_t nb03 = src0->nb[3];

    const size_t nb1 = dst->nb[1];
    const size_t nb2 = dst->nb[2];
    const size_t nb3 = dst->nb[3];

    const ggml_float eps = 1e-5f; // TODO: make this a parameter

    // TODO: optimize
    for (int i03 = 0; i03 < ne03; i03++) {
        for (int i02 = 0; i02 < ne02; i02++) {
            for (int i01 = ith; i01 < ne01; i01 += nth) {
                const float * x = (float *) ((char *) src0->data + i01*nb01 + i02*nb02 + i03*nb03);

                ggml_float mean = 0.0;
                for (int i00 = 0; i00 < ne00; i00++) {
                    mean += x[i00];
                }

                mean /= ne00;

                float * y = (float *) ((char *) dst->data + i01*nb1 + i02*nb2 + i03*nb3);

                ggml_float sum2 = 0.0;
                for (int i00 = 0; i00 < ne00; i00++) {
                    ggml_float v = x[i00] - mean;
                    y[i00] = v;
                    sum2 += v*v;
                }

                const float scale = 1.0/sqrt(sum2/ne00 + eps);

                ggml_vec_scale_f32(ne00, y, scale);
            }
        }
    }
}

void ggml_compute_forward_norm(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_norm_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_mul_mat

// helper function to determine if it is better to use BLAS or not
// for large matrices, BLAS is faster
bool ggml_compute_forward_mul_mat_use_blas(
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    UNUSED(src0);

    const int ne10 = src1->ne[0];

    const int ne0 = dst->ne[0];
    const int ne1 = dst->ne[1];

    // TODO: find the optimal values for these
    if (ggml_is_contiguous(src0) && ggml_is_contiguous(src1) && ne0 >= 32 && ne1 >= 32 && ne10 >= 32) {
        //printf("BLAS: %d %d %d\n", ne0, ne1, ne10);
        return true;
    }

    return false;
}

void ggml_compute_forward_mul_mat_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    const int ne03 = src0->ne[3];

    const int ne10 = src1->ne[0];
    const int ne11 = src1->ne[1];
    const int ne12 = src1->ne[2];
    const int ne13 = src1->ne[3];

    const int ne0  = dst->ne[0];
    const int ne1  = dst->ne[1];
    const int ne2  = dst->ne[2];
    const int ne3  = dst->ne[3];
    const int ne   = ne0*ne1*ne2*ne3;

    const int nb00 = src0->nb[0];
    const int nb01 = src0->nb[1];
    const int nb02 = src0->nb[2];
    const int nb03 = src0->nb[3];

    const int nb10 = src1->nb[0];
    const int nb11 = src1->nb[1];
    const int nb12 = src1->nb[2];
    const int nb13 = src1->nb[3];

    const int nb0  = dst->nb[0];
    const int nb1  = dst->nb[1];
    const int nb2  = dst->nb[2];
    const int nb3  = dst->nb[3];

    const int ith = params->ith;
    const int nth = params->nth;

    assert(ne02 == ne12);
    assert(ne03 == ne13);
    assert(ne2  == ne12);
    assert(ne3  == ne13);

    // TODO: we don't support permuted src0
    assert(nb00 == sizeof(float) || nb01 == sizeof(float));

    // dst cannot be transposed or permuted
    assert(nb0 == sizeof(float));
    assert(nb0 <= nb1);
    assert(nb1 <= nb2);
    assert(nb2 <= nb3);

    assert(ne0 == ne01);
    assert(ne1 == ne11);
    assert(ne2 == ne02);
    assert(ne3 == ne03);

    // nb01 >= nb00 - src0 is not transposed
    //   compute by src0 rows
    //
    // nb00 <  nb01 - src0 is transposed
    //   compute by src0 columns

#if defined(GGML_USE_ACCELERATE) || defined(GGML_USE_OPENBLAS)
    if (ggml_compute_forward_mul_mat_use_blas(src0, src1, dst)) {
        GGML_ASSERT(nb10 == sizeof(float));

        if (params->ith != 0) return;

        if (params->type == GGML_TASK_INIT) {
            return;
        }

        if (params->type == GGML_TASK_FINALIZE) {
            return;
        }

        for (int i03 = 0; i03 < ne03; i03++) {
            for (int i02 = 0; i02 < ne02; i02++) {
                const float * x = (float *) (src0->data);
                const float * y = (float *) ((char *) src1->data + i02*nb12 + i03*nb13);

                float * d = (float *) ((char *) dst->data + i02*nb2 + i03*nb3);

                // zT = y * xT
                {
                    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
                            ne11, ne01, ne10,
                            1.0f,    y, ne10,
                                     x, ne10,
                            0.0f,    d, ne01);
                }
            }
        }

        //printf("CBLAS F32 = %f ms, %d x %d x %d x %d\n", (ggml_perf_time_us() - t0)/1000.0, ne0, ne1, ne2, ne3);

        return;
    }
#endif

    if (params->type == GGML_TASK_INIT) {
        if (nb01 >= nb00) {
            return;
        }

        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        if (nb01 >= nb00) {
            return;
        }

        // TODO: fix this memset (wsize is overestimated)
        //assert(params->wsize == (ggml_nbytes(dst) + CACHE_LINE_SIZE)*nth);

        float * const wdata = params->wdata;

        // cols per thread
        const int dc = (ne + nth - 1)/nth;

        // col range for this thread
        const int ic0 = dc*ith;
        const int ic1 = MIN(ic0 + dc, ne);

        ggml_vec_cpy_f32(ic1 - ic0, (float *) dst->data + ic0, wdata + ic0);

        for (int k = 1; k < nth; k++) {
            ggml_vec_acc_f32(ic1 - ic0, (float *) dst->data + ic0, wdata + (ne + CACHE_LINE_SIZE_F32)*k + ic0);
        }

        return;
    }

    if (nb01 >= nb00) {
        // TODO: do not support transposed src1
        assert(nb10 == sizeof(float));

        // parallelize by src0 rows using ggml_vec_dot_f32

        // total rows in src0
        const int nr = ne01*ne02*ne03;

        // rows per thread
        const int dr = (nr + nth - 1)/nth;

        // row range for this thread
        const int ir0 = dr*ith;
        const int ir1 = MIN(ir0 + dr, nr);

        for (int ir = ir0; ir < ir1; ++ir) {
            // src0 indices
            const int i03 = ir/(ne02*ne01);
            const int i02 = (ir - i03*ne02*ne01)/ne01;
            const int i01 = (ir - i03*ne02*ne01 - i02*ne01);

            for (int ic = 0; ic < ne11; ++ic) {
                // src1 indices
                const int i13 = i03;
                const int i12 = i02;
                const int i11 = ic;

                // dst indices
                const int i0 = i01;
                const int i1 = i11;
                const int i2 = i02;
                const int i3 = i03;

                ggml_vec_dot_f32(ne00,
                        (float *) ((char *)  dst->data + (i0*nb0 + i1*nb1 + i2*nb2 + i3*nb3)),
                        (float *) ((char *) src0->data + (i01*nb01 + i02*nb02 + i03*nb03)),
                        (float *) ((char *) src1->data + (i11*nb11 + i12*nb12 + i13*nb13)));
            }
        }
    } else {
        // parallelize by src1 columns using ggml_vec_mad_f32
        // each thread has its own work data
        // during FINALIZE we accumulate all work data into dst

        // total columns in src1
        const int nc = ne10;

        // columns per thread
        const int dc = (nc + nth - 1)/nth;

        // column range for this thread
        const int ic0 = dc*ith;
        const int ic1 = MIN(ic0 + dc, nc);

        // work data for thread
        const int wo = (ne + CACHE_LINE_SIZE_F32)*ith;
        float * const wdata = params->wdata;

        for (int i13 = 0; i13 < ne13; ++i13) {
            for (int i12 = 0; i12 < ne12; ++i12) {
                for (int i11 = 0; i11 < ne11; ++i11) {
                    for (int ic = ic0; ic < ic1; ++ic) {
                        // src1 indices
                        const int i10 = ic;

                        // src0 indices
                        const int i03 = i13;
                        const int i02 = i12;
                        const int i00 = ic;

                        // dst indices
                        const int i1 = i11;
                        const int i2 = i12;
                        const int i3 = i13;

                        assert(sizeof(float)*(wo + i3*ne2*ne1*ne0 + i2*ne1*ne0 + i1*ne0 + ne01) <= params->wsize);

                        ggml_vec_mad_f32(ne01,
                                (float *) (wdata + wo + i3*ne2*ne1*ne0 + i2*ne1*ne0 + i1*ne0),
                                (float *) ((char *) src0->data + (i00*nb00 + i02*nb02 + i03*nb03)),
                               *(float *) ((char *) src1->data + (i10*nb10 + i11*nb11 + i12*nb12 + i13*nb13)));
                    }
                }
            }
        }
    }

    //int64_t t1 = ggml_perf_time_us();
    //static int64_t acc = 0;
    //acc += t1 - t0;
    //if (t1 - t0 > 10) {
    //    printf("\n");
    //    printf("ne00 = %5d, ne01 = %5d, ne02 = %5d, ne03 = %5d\n", ne00, ne01, ne02, ne03);
    //    printf("nb00 = %5d, nb01 = %5d, nb02 = %5d, nb03 = %5d\n", nb00, nb01, nb02, nb03);
    //    printf("ne10 = %5d, ne11 = %5d, ne12 = %5d, ne13 = %5d\n", ne10, ne11, ne12, ne13);
    //    printf("nb10 = %5d, nb11 = %5d, nb12 = %5d, nb13 = %5d\n", nb10, nb11, nb12, nb13);

    //    printf("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX task %d/%d: %d us, acc = %d\n", ith, nth, (int) (t1 - t0), (int) acc);
    //}
}

void ggml_compute_forward_mul_mat_f16_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    const int ne03 = src0->ne[3];

    const int ne10 = src1->ne[0];
    const int ne11 = src1->ne[1];
    const int ne12 = src1->ne[2];
    const int ne13 = src1->ne[3];

    const int ne0  = dst->ne[0];
    const int ne1  = dst->ne[1];
    const int ne2  = dst->ne[2];
    const int ne3  = dst->ne[3];
    const int ne   = ne0*ne1*ne2*ne3;

    const int nb00 = src0->nb[0];
    const int nb01 = src0->nb[1];
    const int nb02 = src0->nb[2];
    const int nb03 = src0->nb[3];

    const int nb10 = src1->nb[0];
    const int nb11 = src1->nb[1];
    const int nb12 = src1->nb[2];
    const int nb13 = src1->nb[3];

    const int nb0  = dst->nb[0];
    const int nb1  = dst->nb[1];
    const int nb2  = dst->nb[2];
    const int nb3  = dst->nb[3];

    const int ith = params->ith;
    const int nth = params->nth;

    GGML_ASSERT(ne02 == ne12);
    GGML_ASSERT(ne03 == ne13);
    GGML_ASSERT(ne2  == ne12);
    GGML_ASSERT(ne3  == ne13);

    // TODO: we don't support permuted src0
    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t) || nb01 == sizeof(ggml_fp16_t));

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    GGML_ASSERT(ne0 == ne01);
    GGML_ASSERT(ne1 == ne11);
    GGML_ASSERT(ne2 == ne02);
    GGML_ASSERT(ne3 == ne03);

    // nb01 >= nb00 - src0 is not transposed
    //   compute by src0 rows
    //
    // nb00 <  nb01 - src0 is transposed
    //   compute by src0 columns

#if defined(GGML_USE_ACCELERATE) || defined(GGML_USE_OPENBLAS)
    if (ggml_compute_forward_mul_mat_use_blas(src0, src1, dst)) {
        GGML_ASSERT(nb10 == sizeof(float));

        if (params->ith != 0) return;

        if (params->type == GGML_TASK_INIT) {
            return;
        }

        if (params->type == GGML_TASK_FINALIZE) {
            return;
        }

        float * const wdata = params->wdata;

        for (int i03 = 0; i03 < ne03; i03++) {
            for (int i02 = 0; i02 < ne02; i02++) {
                {
                    int id = 0;
                    for (int i01 = 0; i01 < ne01; ++i01) {
                        for (int i00 = 0; i00 < ne00; ++i00) {
                            wdata[id++] = GGML_FP16_TO_FP32(*(ggml_fp16_t *) ((char *) src0->data + i03*nb03 + i02*nb02 + i01*nb01 + i00*nb00));
                        }
                    }
                }

                const float * x = wdata;
                const float * y = (float *) ((char *) src1->data + i02*nb12 + i03*nb13);

                //      float * z =                          wdata + ne00*ne01;

                // z = x * yT
                //{
                //    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
                //            ne01, ne11, ne00,
                //            1.0f, x, ne00,
                //                  y, ne00,
                //            0.0f, z, ne11);
                //}

                float * d = (float *) ((char *) dst->data + i02*nb2 + i03*nb3);

                // transpose z
                //for (int j = 0; j < ne11; ++j) {
                //    for (int i = 0; i < ne01; ++i) {
                //        d[j*ne01 + i] = z[i*ne11 + j];
                //    }
                //}

                {
#if 1
                    // zT = y * xT
                    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasTrans,
                            ne11, ne01, ne10,
                            1.0f,    y, ne00,
                                     x, ne00,
                            0.0f,    d, ne01);
#else
                    // zT = (xT * y)T
                    cblas_sgemm(CblasColMajor, CblasTrans, CblasNoTrans,
                            ne01, ne11, ne10,
                            1.0f,    x, ne00,
                                     y, ne00,
                            0.0f,    d, ne01);
#endif
                }
            }
        }

        //printf("CBLAS = %f ms, %d x %d x %d x %d\n", (ggml_perf_time_us() - t0)/1000.0, ne0, ne1, ne2, ne3);

        return;
    }
#endif

    if (params->type == GGML_TASK_INIT) {
        if (nb01 >= nb00) {
            ggml_fp16_t * const wdata = params->wdata;

            int id = 0;
            for (int i13 = 0; i13 < ne13; ++i13) {
                for (int i12 = 0; i12 < ne12; ++i12) {
                    for (int i11 = 0; i11 < ne11; ++i11) {
                        for (int i10 = 0; i10 < ne10; ++i10) {
                            wdata[id++] = GGML_FP32_TO_FP16(*(float *)((char *) src1->data + i13*nb13 + i12*nb12 + i11*nb11 + i10*nb10));
                        }
                    }
                }
            }

            GGML_ASSERT(id*sizeof(ggml_fp16_t) <= params->wsize);

            return;
        }

        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        if (nb01 >= nb00) {
            return;
        }

        // TODO: fix this memset (wsize is overestimated)
        //assert(params->wsize == (ggml_nbytes(dst) + CACHE_LINE_SIZE)*nth);

        ggml_fp16_t * const wdata = params->wdata;

        // cols per thread
        const int dc = (ne + nth - 1)/nth;

        // col range for this thread
        const int ic0 = dc*ith;
        const int ic1 = MIN(ic0 + dc, ne);

        for (int i = ic0; i < ic1; ++i) {
            ((float *) dst->data)[i] = GGML_FP16_TO_FP32(wdata[i]);
        }

        for (int k = 1; k < nth; k++) {
            for (int i = ic0; i < ic1; ++i) {
                ((float *) dst->data)[i] += GGML_FP16_TO_FP32(wdata[(ne + CACHE_LINE_SIZE_F32)*k + i]);
            }
        }

        return;
    }

    if (nb01 >= nb00) {
        // fp16 -> half the size, so divide by 2
        // TODO: do not support transposed src1
        assert(nb10/2 == sizeof(ggml_fp16_t));

        // parallelize by src0 rows using ggml_vec_dot_f32

        // total rows in src0
        const int nr = ne01*ne02*ne03;

        // rows per thread
        const int dr = (nr + nth - 1)/nth;

        // row range for this thread
        const int ir0 = dr*ith;
        const int ir1 = MIN(ir0 + dr, nr);

        ggml_fp16_t * wdata = params->wdata;

        for (int ir = ir0; ir < ir1; ++ir) {
            // src0 indices
            const int i03 = ir/(ne02*ne01);
            const int i02 = (ir - i03*ne02*ne01)/ne01;
            const int i01 = (ir - i03*ne02*ne01 - i02*ne01);

            const int i13 = i03;
            const int i12 = i02;

            const int i0 = i01;
            const int i2 = i02;
            const int i3 = i03;

            ggml_fp16_t * src0_row = (ggml_fp16_t *) ((char *) src0->data + (i01*nb01 + i02*nb02 + i03*nb03));
            ggml_fp16_t * src1_col = wdata + (i13*ne12*ne11 + i12*ne11 + 0)*ne00;

            float * dst_col = (float *) ((char *) dst->data + (i0*nb0 + 0*nb1 + i2*nb2 + i3*nb3));

            for (int ic = 0; ic < ne11; ++ic) {
                assert(ne00 % 32 == 0);

                ggml_vec_dot_f16(ne00, &dst_col[ic*ne0], src0_row, src1_col + ic*ne00);
            }
        }
    } else {
        // parallelize by src1 columns using ggml_vec_mad_f32
        // each thread has its own work data
        // during FINALIZE we accumulate all work data into dst

        // total columns in src1
        const int nc = ne10;

        // columns per thread
        const int dc = (nc + nth - 1)/nth;

        // column range for this thread
        const int ic0 = dc*ith;
        const int ic1 = MIN(ic0 + dc, nc);

        // work data for thread
        const int wo = (ne + CACHE_LINE_SIZE_F32)*ith;
        ggml_fp16_t * const wdata = params->wdata;

        for (int i13 = 0; i13 < ne13; ++i13) {
            for (int i12 = 0; i12 < ne12; ++i12) {
                for (int i11 = 0; i11 < ne11; ++i11) {
                    // dst indices
                    const int i1 = i11;
                    const int i2 = i12;
                    const int i3 = i13;

                    ggml_fp16_t * dst_row = wdata + wo + i3*ne2*ne1*ne0 + i2*ne1*ne0 + i1*ne0;

                    for (int ic = ic0; ic < ic1; ++ic) {
                        // src1 indices
                        const int i10 = ic;

                        // src0 indices
                        const int i03 = i13;
                        const int i02 = i12;
                        const int i00 = ic;

                        assert(sizeof(ggml_fp16_t)*(wo + i3*ne2*ne1*ne0 + i2*ne1*ne0 + i1*ne0 + ne01) <= params->wsize);

                        ggml_fp16_t * src0_col =  (ggml_fp16_t *) ((char *) src0->data + (i00*nb00 + i02*nb02 + i03*nb03));
                        float         src1_val = *      (float *) ((char *) src1->data + (i10*nb10 + i11*nb11 + i12*nb12 + i13*nb13));

                        ggml_vec_mad_f16(ne01, dst_row, src0_col, src1_val);
                    }
                }
            }
        }
    }

    //int64_t t1 = ggml_time_us();
    //static int64_t acc = 0;
    //acc += t1 - t0;
    //if (t1 - t0 > 10) {
    //    printf("\n");
    //    printf("ne00 = %5d, ne01 = %5d, ne02 = %5d, ne03 = %5d\n", ne00, ne01, ne02, ne03);
    //    printf("nb00 = %5d, nb01 = %5d, nb02 = %5d, nb03 = %5d\n", nb00, nb01, nb02, nb03);
    //    printf("ne10 = %5d, ne11 = %5d, ne12 = %5d, ne13 = %5d\n", ne10, ne11, ne12, ne13);

    //    printf("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX task %d/%d: %d us, acc = %d\n", ith, nth, (int) (t1 - t0), (int) acc);
    //}
}

void ggml_compute_forward_mul_mat(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_mul_mat_f16_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_mul_mat_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_scale

void ggml_compute_forward_scale_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));
    GGML_ASSERT(ggml_is_scalar(src1));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // scale factor
    const float v = *(float *) src1->data;

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        ggml_vec_scale_f32(nc, (float *) ((char *) dst->data + i1*(dst->nb[1])), v);
    }
}

void ggml_compute_forward_scale(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_scale_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_cpy

void ggml_compute_forward_cpy(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    ggml_compute_forward_dup(params, src0, dst);
}

// ggml_compute_forward_reshape

void ggml_compute_forward_reshape(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    // NOP
    UNUSED(params);
    UNUSED(src0);
    UNUSED(dst);
}

// ggml_compute_forward_view

void ggml_compute_forward_view(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0) {
    // NOP
    UNUSED(params);
    UNUSED(src0);
}

// ggml_compute_forward_permute

void ggml_compute_forward_permute(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0) {
    // NOP
    UNUSED(params);
    UNUSED(src0);
}

// ggml_compute_forward_transpose

void ggml_compute_forward_transpose(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0) {
    // NOP
    UNUSED(params);
    UNUSED(src0);
}

// ggml_compute_forward_get_rows

void ggml_compute_forward_get_rows_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nc = src0->ne[0];
    const int nr = ggml_nelements(src1);

    assert( dst->ne[0] == nc);
    assert( dst->ne[1] == nr);
    assert(src0->nb[0] == sizeof(ggml_fp16_t));

    for (int i = 0; i < nr; ++i) {
        const int r = ((int32_t *) src1->data)[i];

        for (int j = 0; j < nc; ++j) {
            ggml_fp16_t v = ((ggml_fp16_t *) ((char *) src0->data + r*src0->nb[1]))[j];
            ((float *) ((char *)  dst->data + i*dst->nb[1]))[j] = GGML_FP16_TO_FP32(v);
        }
    }
}

void ggml_compute_forward_get_rows_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    assert(params->ith == 0);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int nc = src0->ne[0];
    const int nr = ggml_nelements(src1);

    assert( dst->ne[0] == nc);
    assert( dst->ne[1] == nr);
    assert(src0->nb[0] == sizeof(float));

    for (int i = 0; i < nr; ++i) {
        const int r = ((int32_t *) src1->data)[i];

        ggml_vec_cpy_f32(nc,
                (float *) ((char *)  dst->data + i*dst->nb[1]),
                (float *) ((char *) src0->data + r*src0->nb[1]));
    }
}

void ggml_compute_forward_get_rows(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_get_rows_f16(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_get_rows_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_diag_mask_inf

void ggml_compute_forward_diag_mask_inf_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(src1->type == GGML_TYPE_I32);
    assert(ggml_nelements(src1) == 1);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n_past = ((int32_t *) src1->data)[0];

    // TODO: handle transposed/permuted matrices

    const int n  = ggml_nrows(src0);
    const int nc = src0->ne[0];
    const int nr = src0->ne[1];
    const int nz = n/nr;

    assert( dst->nb[0] == sizeof(float));
    assert(src0->nb[0] == sizeof(float));

    for (int k = 0; k < nz; k++) {
        for (int j = 0; j < nr; j++) {
            for (int i = n_past; i < nc; i++) {
                if (i > n_past + j) {
                    *(float *)((char *) dst->data + k*dst->nb[2] + j*dst->nb[1] + i*dst->nb[0]) = -INFINITY;
                }
            }
        }
    }
}

void ggml_compute_forward_diag_mask_inf(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_diag_mask_inf_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_soft_max

void ggml_compute_forward_soft_max_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    GGML_ASSERT(ggml_is_contiguous(src0));
    GGML_ASSERT(ggml_is_contiguous(dst));
    GGML_ASSERT(ggml_are_same_shape(src0, dst));

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // TODO: handle transposed/permuted matrices

    const int ith = params->ith;
    const int nth = params->nth;

    const int nc = src0->ne[0];
    const int nr = ggml_nrows(src0);

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float *p = (float *)((char *) dst->data + i1*dst->nb[1]);

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            assert(!isnan(p[i]));
        }
#endif

        float max = -INFINITY;
        for (int i = 0; i < nc; i++) {
            max = MAX(max, p[i]);
        }

        ggml_float sum = 0.0;

        uint16_t ss;
        for (int i = 0; i < nc; i++) {
            if (p[i] == -INFINITY) {
                p[i] = 0.0;
            } else {
                //const float val = (p[i] == -INFINITY) ? 0.0 : exp(p[i] - max);
                ggml_fp16_t s = GGML_FP32_TO_FP16(p[i] - max);
                memcpy(&ss, &s, sizeof(ss));
                const float val = GGML_FP16_TO_FP32(table_exp_f16[ss]);
                sum += val;
                p[i] = val;
            }
        }

        assert(sum > 0.0f);

        sum = 1.0/sum;
        ggml_vec_scale_f32(nc, p, sum);

#ifndef NDEBUG
        for (int i = 0; i < nc; ++i) {
            assert(!isnan(p[i]));
            assert(!isinf(p[i]));
        }
#endif
    }
}

void ggml_compute_forward_soft_max(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_soft_max_f32(params, src0, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_rope

void ggml_compute_forward_rope_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    assert(params->ith == 0);
    assert(src1->type == GGML_TYPE_I32);
    assert(ggml_nelements(src1) == 3);

    if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) {
        return;
    }

    const int n_past = ((int32_t *) src1->data)[0];
    const int n_dims = ((int32_t *) src1->data)[1];
    const int mode   = ((int32_t *) src1->data)[2];

    //const int ne0 = src0->ne[0];
    const int ne1 = src0->ne[1];
    const int ne2 = src0->ne[2];
    const int ne3 = src0->ne[3];

    const int nb0 = src0->nb[0];
    const int nb1 = src0->nb[1];
    const int nb2 = src0->nb[2];
    const int nb3 = src0->nb[3];

    //printf("ne0: %d, ne1: %d, ne2: %d, ne3: %d\n", ne0, ne1, ne2, ne3);
    //printf("n_past = %d, ne2 = %d\n", n_past, ne2);

    assert(nb0 == sizeof(float));

    // TODO: optimize
    for (int i3 = 0; i3 < ne3; i3++) {
        for (int i2 = (mode == 0 ? 0 : n_past); i2 < ne2; i2++) {
            const int p = (mode == 0 ? n_past + i2 : i2);
            for (int i1 = 0; i1 < ne1; i1++) {
                for (int i0 = 0; i0 < n_dims; i0 += 2) {
                    const double theta = pow(10000.0, ((double)-i0)/n_dims);

                    const double cos_theta = cos(p*theta);
                    const double sin_theta = sin(p*theta);

                    const float * const src = (float *)((char *) src0->data + i3*nb3 + i2*nb2 + i1*nb1 + i0*nb0);
                          float * dst_data  = (float *)((char *)  dst->data + i3*nb3 + i2*nb2 + i1*nb1 + i0*nb0);

                    double x0 = src[0];
                    double x1 = src[1];

                    dst_data[0] = x0*cos_theta - x1*sin_theta;
                    dst_data[1] = x0*sin_theta + x1*cos_theta;
                }
            }
        }
    }
}

void ggml_compute_forward_rope(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_rope_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_F16:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_conv_1d_1s

void ggml_compute_forward_conv_1d_1s_f16_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    GGML_ASSERT(src0->type == GGML_TYPE_F16);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT( dst->type == GGML_TYPE_F32);

    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    //const int ne03 = src0->ne[3];

    const int ne10 = src1->ne[0];
    const int ne11 = src1->ne[1];
    //const int ne12 = src1->ne[2];
    //const int ne13 = src1->ne[3];

    //const int ne0  = dst->ne[0];
    //const int ne1  = dst->ne[1];
    //const int ne2  = dst->ne[2];
    //const int ne3  = dst->ne[3];
    //const int ne   = ne0*ne1*ne2*ne3;

    const int nb00 = src0->nb[0];
    const int nb01 = src0->nb[1];
    const int nb02 = src0->nb[2];
    //const int nb03 = src0->nb[3];

    const int nb10 = src1->nb[0];
    const int nb11 = src1->nb[1];
    //const int nb12 = src1->nb[2];
    //const int nb13 = src1->nb[3];

    //const int nb0  = dst->nb[0];
    const int nb1  = dst->nb[1];
    //const int nb2  = dst->nb[2];
    //const int nb3  = dst->nb[3];

    const int ith = params->ith;
    const int nth = params->nth;

    const int nk = ne00;
    const int nh = nk/2;

    const int ew0 = ggml_up32(ne01);

    GGML_ASSERT(ne00 % 2 == 1); // TODO: support even kernel sizes
    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nb10 == sizeof(float));

    if (params->type == GGML_TASK_INIT) {
        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);

        // prepare kernel data (src0)
        {
            ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + 0;

            for (int i02 = 0; i02 < ne02; i02++) {
                for (int i01 = 0; i01 < ne01; i01++) {
                    const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i02*nb02 + i01*nb01);
                    ggml_fp16_t * dst_data = wdata + i02*ew0*ne00;
                    for (int i00 = 0; i00 < ne00; i00++) {
                        dst_data[i00*ew0 + i01] = src[i00];
                    }
                }
            }
        }

        // prepare source data (src1)
        {
            ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + ne02*ew0*ne00;

            for (int i11 = 0; i11 < ne11; i11++) {
                const float * const src = (float *)((char *) src1->data + i11*nb11);
                ggml_fp16_t * dst_data = wdata;
                for (int i10 = 0; i10 < ne10; i10++) {
                    dst_data[(i10 + nh)*ew0 + i11] = GGML_FP32_TO_FP16(src[i10]);
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // total rows in dst
    const int nr = ne02;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float * dst_data = (float *)((char *) dst->data + i1*nb1);
        for (int i0 = 0; i0 < ne10; ++i0) {
            dst_data[i0] = 0;
            for (int k = -nh; k <= nh; k++) {
                float v = 0.0f;
                ggml_vec_dot_f16(ew0, &v,
                        (ggml_fp16_t *) params->wdata +   i1*ew0*ne00 +      (nh + k)*ew0,
                        (ggml_fp16_t *) params->wdata + ne02*ew0*ne00 + (i0 + nh + k)*ew0);

                dst_data[i0] += v;
            }
        }
    }
}

void ggml_compute_forward_conv_1d_1s_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    GGML_ASSERT(src0->type == GGML_TYPE_F32);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT( dst->type == GGML_TYPE_F32);

    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    //const int ne03 = src0->ne[3];

    const int ne10 = src1->ne[0];
    const int ne11 = src1->ne[1];
    //const int ne12 = src1->ne[2];
    //const int ne13 = src1->ne[3];

    //const int ne0  = dst->ne[0];
    //const int ne1  = dst->ne[1];
    //const int ne2  = dst->ne[2];
    //const int ne3  = dst->ne[3];
    //const int ne   = ne0*ne1*ne2*ne3;

    const int nb00 = src0->nb[0];
    const int nb01 = src0->nb[1];
    const int nb02 = src0->nb[2];
    //const int nb03 = src0->nb[3];

    const int nb10 = src1->nb[0];
    const int nb11 = src1->nb[1];
    //const int nb12 = src1->nb[2];
    //const int nb13 = src1->nb[3];

    //const int nb0  = dst->nb[0];
    const int nb1  = dst->nb[1];
    //const int nb2  = dst->nb[2];
    //const int nb3  = dst->nb[3];

    const int ith = params->ith;
    const int nth = params->nth;

    const int nk = ne00;
    const int nh = nk/2;

    const int ew0 = ggml_up32(ne01);

    GGML_ASSERT(ne00 % 2 == 1); // TODO: support even kernel sizes
    GGML_ASSERT(nb00 == sizeof(float));
    GGML_ASSERT(nb10 == sizeof(float));

    if (params->type == GGML_TASK_INIT) {
        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);

        // prepare kernel data (src0)
        {
            float * const wdata = (float *) params->wdata + 0;

            for (int i02 = 0; i02 < ne02; i02++) {
                for (int i01 = 0; i01 < ne01; i01++) {
                    const float * const src = (float *)((char *) src0->data + i02*nb02 + i01*nb01);
                    float * dst_data = wdata + i02*ew0*ne00;
                    for (int i00 = 0; i00 < ne00; i00++) {
                        dst_data[i00*ew0 + i01] = src[i00];
                    }
                }
            }
        }

        // prepare source data (src1)
        {
            float * const wdata = (float *) params->wdata + ne02*ew0*ne00;

            for (int i11 = 0; i11 < ne11; i11++) {
                const float * const src = (float *)((char *) src1->data + i11*nb11);
                float * dst_data = wdata;
                for (int i10 = 0; i10 < ne10; i10++) {
                    dst_data[(i10 + nh)*ew0 + i11] = src[i10];
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // total rows in dst
    const int nr = ne02;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float * dst_data = (float *)((char *) dst->data + i1*nb1);
        for (int i0 = 0; i0 < ne10; ++i0) {
            dst_data[i0] = 0;
            for (int k = -nh; k <= nh; k++) {
                float v = 0.0f;
                ggml_vec_dot_f32(ew0, &v,
                        (float *) params->wdata +   i1*ew0*ne00 +      (nh + k)*ew0,
                        (float *) params->wdata + ne02*ew0*ne00 + (i0 + nh + k)*ew0);

                dst_data[i0] += v;
            }
        }
    }
}

void ggml_compute_forward_conv_1d_1s(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_conv_1d_1s_f16_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_conv_1d_1s_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_conv_1d_2s

void ggml_compute_forward_conv_1d_2s_f16_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    GGML_ASSERT(src0->type == GGML_TYPE_F16);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT( dst->type == GGML_TYPE_F32);

    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    //const int ne03 = src0->ne[3];

    const int ne10 = src1->ne[0];
    const int ne11 = src1->ne[1];
    //const int ne12 = src1->ne[2];
    //const int ne13 = src1->ne[3];

    //const int ne0  = dst->ne[0];
    //const int ne1  = dst->ne[1];
    //const int ne2  = dst->ne[2];
    //const int ne3  = dst->ne[3];
    //const int ne   = ne0*ne1*ne2*ne3;

    const int nb00 = src0->nb[0];
    const int nb01 = src0->nb[1];
    const int nb02 = src0->nb[2];
    //const int nb03 = src0->nb[3];

    const int nb10 = src1->nb[0];
    const int nb11 = src1->nb[1];
    //const int nb12 = src1->nb[2];
    //const int nb13 = src1->nb[3];

    //const int nb0  = dst->nb[0];
    const int nb1  = dst->nb[1];
    //const int nb2  = dst->nb[2];
    //const int nb3  = dst->nb[3];

    const int ith = params->ith;
    const int nth = params->nth;

    const int nk = ne00;
    const int nh = nk/2;

    const int ew0 = ggml_up32(ne01);

    GGML_ASSERT(ne00 % 2 == 1); // TODO: support even kernel sizes
    GGML_ASSERT(nb00 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nb10 == sizeof(float));

    if (params->type == GGML_TASK_INIT) {
        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);

        // prepare kernel data (src0)
        {
            ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + 0;

            for (int i02 = 0; i02 < ne02; i02++) {
                for (int i01 = 0; i01 < ne01; i01++) {
                    const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i02*nb02 + i01*nb01);
                    ggml_fp16_t * dst_data = wdata + i02*ew0*ne00;
                    for (int i00 = 0; i00 < ne00; i00++) {
                        dst_data[i00*ew0 + i01] = src[i00];
                    }
                }
            }
        }

        // prepare source data (src1)
        {
            ggml_fp16_t * const wdata = (ggml_fp16_t *) params->wdata + ne02*ew0*ne00;

            for (int i11 = 0; i11 < ne11; i11++) {
                const float * const src = (float *)((char *) src1->data + i11*nb11);
                ggml_fp16_t * dst_data = wdata;
                for (int i10 = 0; i10 < ne10; i10++) {
                    dst_data[(i10 + nh)*ew0 + i11] = GGML_FP32_TO_FP16(src[i10]);
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // total rows in dst
    const int nr = ne02;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float * dst_data = (float *)((char *) dst->data + i1*nb1);
        for (int i0 = 0; i0 < ne10; i0 += 2) {
            dst_data[i0/2] = 0;
            for (int k = -nh; k <= nh; k++) {
                float v = 0.0f;
                ggml_vec_dot_f16(ew0, &v,
                        (ggml_fp16_t *) params->wdata +   i1*ew0*ne00 +      (nh + k)*ew0,
                        (ggml_fp16_t *) params->wdata + ne02*ew0*ne00 + (i0 + nh + k)*ew0);

                dst_data[i0/2] += v;
            }
        }
    }
}

void ggml_compute_forward_conv_1d_2s_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
              struct ggml_tensor * dst) {
    GGML_ASSERT(src0->type == GGML_TYPE_F32);
    GGML_ASSERT(src1->type == GGML_TYPE_F32);
    GGML_ASSERT( dst->type == GGML_TYPE_F32);

    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    const int ne00 = src0->ne[0];
    const int ne01 = src0->ne[1];
    const int ne02 = src0->ne[2];
    //const int ne03 = src0->ne[3];

    const int ne10 = src1->ne[0];
    const int ne11 = src1->ne[1];
    //const int ne12 = src1->ne[2];
    //const int ne13 = src1->ne[3];

    //const int ne0  = dst->ne[0];
    //const int ne1  = dst->ne[1];
    //const int ne2  = dst->ne[2];
    //const int ne3  = dst->ne[3];
    //const int ne   = ne0*ne1*ne2*ne3;

    const int nb00 = src0->nb[0];
    const int nb01 = src0->nb[1];
    const int nb02 = src0->nb[2];
    //const int nb03 = src0->nb[3];

    const int nb10 = src1->nb[0];
    const int nb11 = src1->nb[1];
    //const int nb12 = src1->nb[2];
    //const int nb13 = src1->nb[3];

    //const int nb0  = dst->nb[0];
    const int nb1  = dst->nb[1];
    //const int nb2  = dst->nb[2];
    //const int nb3  = dst->nb[3];

    const int ith = params->ith;
    const int nth = params->nth;

    const int nk = ne00;
    const int nh = nk/2;

    const int ew0 = ggml_up32(ne01);

    GGML_ASSERT(ne00 % 2 == 1); // TODO: support even kernel sizes
    GGML_ASSERT(nb00 == sizeof(float));
    GGML_ASSERT(nb10 == sizeof(float));

    if (params->type == GGML_TASK_INIT) {
        // TODO: fix this memset (wsize is overestimated)
        memset(params->wdata, 0, params->wsize);

        // prepare kernel data (src0)
        {
            float * const wdata = (float *) params->wdata + 0;

            for (int i02 = 0; i02 < ne02; i02++) {
                for (int i01 = 0; i01 < ne01; i01++) {
                    const float * const src = (float *)((char *) src0->data + i02*nb02 + i01*nb01);
                    float * dst_data = wdata + i02*ew0*ne00;
                    for (int i00 = 0; i00 < ne00; i00++) {
                        dst_data[i00*ew0 + i01] = src[i00];
                    }
                }
            }
        }

        // prepare source data (src1)
        {
            float * const wdata = (float *) params->wdata + ne02*ew0*ne00;

            for (int i11 = 0; i11 < ne11; i11++) {
                const float * const src = (float *)((char *) src1->data + i11*nb11);
                float * dst_data = wdata;
                for (int i10 = 0; i10 < ne10; i10++) {
                    dst_data[(i10 + nh)*ew0 + i11] = src[i10];
                }
            }
        }

        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // total rows in dst
    const int nr = ne02;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int i1 = ir0; i1 < ir1; i1++) {
        float * dst_data = (float *)((char *) dst->data + i1*nb1);
        for (int i0 = 0; i0 < ne10; i0 += 2) {
            dst_data[i0/2] = 0;
            for (int k = -nh; k <= nh; k++) {
                float v = 0.0f;
                ggml_vec_dot_f32(ew0, &v,
                        (float *) params->wdata +   i1*ew0*ne00 +      (nh + k)*ew0,
                        (float *) params->wdata + ne02*ew0*ne00 + (i0 + nh + k)*ew0);

                dst_data[i0/2] += v;
            }
        }
    }
}

void ggml_compute_forward_conv_1d_2s(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * src0,
        const struct ggml_tensor * src1,
        struct ggml_tensor * dst) {
    switch (src0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_conv_1d_2s_f16_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_conv_1d_2s_f32(params, src0, src1, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    }
}

// ggml_compute_forward_flash_attn

void ggml_compute_forward_flash_attn_f32(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * q,
        const struct ggml_tensor * k,
        const struct ggml_tensor * v,
        const bool masked,
             struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    const int neq0 = q->ne[0];
    const int neq1 = q->ne[1];
    const int neq2 = q->ne[2];
    const int neq3 = q->ne[3];

    const int nek0 = k->ne[0];
    const int nek1 = k->ne[1];
    //const int nek2 = k->ne[2];
    //const int nek3 = k->ne[3];

    //const int nev0 = v->ne[0];
    const int nev1 = v->ne[1];
    //const int nev2 = v->ne[2];
    //const int nev3 = v->ne[3];

    const int ne0  = dst->ne[0];
    const int ne1  = dst->ne[1];
    //const int ne2  = dst->ne[2];
    //const int ne3  = dst->ne[3];

    const int nbk0 = k->nb[0];
    const int nbk1 = k->nb[1];
    const int nbk2 = k->nb[2];
    const int nbk3 = k->nb[3];

    const int nbq0 = q->nb[0];
    const int nbq1 = q->nb[1];
    const int nbq2 = q->nb[2];
    const int nbq3 = q->nb[3];

    const int nbv0 = v->nb[0];
    const int nbv1 = v->nb[1];
    const int nbv2 = v->nb[2];
    const int nbv3 = v->nb[3];

    const int nb0  = dst->nb[0];
    const int nb1  = dst->nb[1];
    const int nb2  = dst->nb[2];
    const int nb3  = dst->nb[3];

    const int ith = params->ith;
    const int nth = params->nth;

    const int D = neq0;
    const int N = neq1;
    const int P = nek1 - N;
    const int M = P + N;

    GGML_ASSERT(ne0 == D);
    GGML_ASSERT(ne1 == N);
    GGML_ASSERT(P >= 0);

    GGML_ASSERT(nbq0 == sizeof(float));
    GGML_ASSERT(nbk0 == sizeof(float));
    GGML_ASSERT(nbv0 == sizeof(float));

    GGML_ASSERT(neq0 == D);
    GGML_ASSERT(nek0 == D);
    GGML_ASSERT(nev1 == D);

    GGML_ASSERT(neq1 == N);
    GGML_ASSERT(nek1 == N + P);
    GGML_ASSERT(nev1 == D);

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    if (params->type == GGML_TASK_INIT) {
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // parallelize by q rows using ggml_vec_dot_f32

    // total rows in q
    const int nr = neq1*neq2*neq3;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    const float scale = 1.0/sqrt((double) D);

    //printf("P=%d N=%d D=%d ir0=%d ir1=%d scale = %f\n", P, N, D, ir0, ir1, scale);

    for (int ir = ir0; ir < ir1; ++ir) {
        // q indices
        const int iq3 = ir/(neq2*neq1);
        const int iq2 = (ir - iq3*neq2*neq1)/neq1;
        const int iq1 = (ir - iq3*neq2*neq1 - iq2*neq1);

        float * S = (float *) params->wdata + ith*(M + CACHE_LINE_SIZE_F32);

        for (int ic = 0; ic < nek1; ++ic) {
            // k indices
            const int ik3 = iq3;
            const int ik2 = iq2;
            const int ik1 = ic;

            // S indices
            const int i1 = ik1;

            ggml_vec_dot_f32(neq0,
                    S + i1,
                    (float *) ((char *) k->data + (ik1*nbk1 + ik2*nbk2 + ik3*nbk3)),
                    (float *) ((char *) q->data + (iq1*nbq1 + iq2*nbq2 + iq3*nbq3)));
        }

        // scale
        ggml_vec_scale_f32(nek1, S, scale);

        if (masked) {
            for (int i = P; i < M; i++) {
                if (i > P + iq1) {
                    S[i] = -INFINITY;
                }
            }
        }

        // softmax
        {
            float max = -INFINITY;
            for (int i = 0; i < M; i++) {
                max = MAX(max, S[i]);
            }

            ggml_float sum = 0.0;

            uint16_t ss;
            for (int i = 0; i < M; i++) {
                if (S[i] == -INFINITY) {
                    S[i] = 0.0;
                } else {
                    //const float val = (S[i] == -INFINITY) ? 0.0 : exp(S[i] - max);
                    ggml_fp16_t s = GGML_FP32_TO_FP16(S[i] - max);
                    memcpy(&ss, &s, sizeof(ss));
                    const float val = GGML_FP16_TO_FP32(table_exp_f16[ss]);
                    sum += val;
                    S[i] = val;
                }
            }

            assert(sum > 0.0f);

            sum = 1.0/sum;
            ggml_vec_scale_f32(M, S, sum);
        }

        for (int ic = 0; ic < nev1; ++ic) {
            // dst indices
            const int i1 = iq1;
            const int i2 = iq2;
            const int i3 = iq3;

            ggml_vec_dot_f32(nek1,
                    (float *) ((char *) dst->data + (ic*nb0 + i1*nb1  + i2*nb2  + i3*nb3)),
                    (float *) ((char *) v->data   + (         ic*nbv1 + i2*nbv2 + i3*nbv3)),
                    S);
        }
    }
}

void ggml_compute_forward_flash_attn_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * q,
        const struct ggml_tensor * k,
        const struct ggml_tensor * v,
        const bool masked,
             struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    const int neq0 = q->ne[0];
    const int neq1 = q->ne[1];
    const int neq2 = q->ne[2];
    const int neq3 = q->ne[3];

    const int nek0 = k->ne[0];
    const int nek1 = k->ne[1];
    //const int nek2 = k->ne[2];
    //const int nek3 = k->ne[3];

    //const int nev0 = v->ne[0];
    const int nev1 = v->ne[1];
    //const int nev2 = v->ne[2];
    //const int nev3 = v->ne[3];

    const int ne0  = dst->ne[0];
    const int ne1  = dst->ne[1];
    //const int ne2  = dst->ne[2];
    //const int ne3  = dst->ne[3];

    const int nbk0 = k->nb[0];
    const int nbk1 = k->nb[1];
    const int nbk2 = k->nb[2];
    const int nbk3 = k->nb[3];

    const int nbq0 = q->nb[0];
    const int nbq1 = q->nb[1];
    const int nbq2 = q->nb[2];
    const int nbq3 = q->nb[3];

    const int nbv0 = v->nb[0];
    const int nbv1 = v->nb[1];
    const int nbv2 = v->nb[2];
    const int nbv3 = v->nb[3];

    const int nb0  = dst->nb[0];
    const int nb1  = dst->nb[1];
    const int nb2  = dst->nb[2];
    const int nb3  = dst->nb[3];

    const int ith = params->ith;
    const int nth = params->nth;

    const int D = neq0;
    const int N = neq1;
    const int P = nek1 - N;
    const int M = P + N;

    GGML_ASSERT(ne0 == D);
    GGML_ASSERT(ne1 == N);
    GGML_ASSERT(P >= 0);

    GGML_ASSERT(nbq0 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbk0 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbv0 == sizeof(ggml_fp16_t));

    GGML_ASSERT(neq0 == D);
    GGML_ASSERT(nek0 == D);
    GGML_ASSERT(nev1 == D);

    GGML_ASSERT(neq1 == N);
    GGML_ASSERT(nek1 == N + P);
    GGML_ASSERT(nev1 == D);

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    if (params->type == GGML_TASK_INIT) {
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // parallelize by q rows using ggml_vec_dot_f32

    // total rows in q
    const int nr = neq1*neq2*neq3;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    const float scale = 1.0/sqrt((double) D);

    //printf("P=%d N=%d D=%d ir0=%d ir1=%d scale = %f\n", P, N, D, ir0, ir1, scale);

    for (int ir = ir0; ir < ir1; ++ir) {
        // q indices
        const int iq3 = ir/(neq2*neq1);
        const int iq2 = (ir - iq3*neq2*neq1)/neq1;
        const int iq1 = (ir - iq3*neq2*neq1 - iq2*neq1);

        float * S = (float *) params->wdata + ith*(2*M + CACHE_LINE_SIZE_F32);

        for (int ic = 0; ic < nek1; ++ic) {
            // k indices
            const int ik3 = iq3;
            const int ik2 = iq2;
            const int ik1 = ic;

            // S indices
            const int i1 = ik1;

            ggml_vec_dot_f16(neq0,
                    S + i1,
                    (ggml_fp16_t *) ((char *) k->data + (ik1*nbk1 + ik2*nbk2 + ik3*nbk3)),
                    (ggml_fp16_t *) ((char *) q->data + (iq1*nbq1 + iq2*nbq2 + iq3*nbq3)));
        }

        // scale
        ggml_vec_scale_f32(nek1, S, scale);

        if (masked) {
            for (int i = P; i < M; i++) {
                if (i > P + iq1) {
                    S[i] = -INFINITY;
                }
            }
        }

        // softmax
        {
            float max = -INFINITY;
            for (int i = 0; i < M; i++) {
                max = MAX(max, S[i]);
            }

            ggml_float sum = 0.0;

            uint16_t ss;
            for (int i = 0; i < M; i++) {
                if (S[i] == -INFINITY) {
                    S[i] = 0.0;
                } else {
                    //const float val = (S[i] == -INFINITY) ? 0.0 : exp(S[i] - max);
                    ggml_fp16_t s = GGML_FP32_TO_FP16(S[i] - max);
                    memcpy(&ss, &s, sizeof(ss));
                    const float val = GGML_FP16_TO_FP32(table_exp_f16[ss]);
                    sum += val;
                    S[i] = val;
                }
            }

            assert(sum > 0.0f);

            sum = 1.0/sum;
            ggml_vec_scale_f32(M, S, sum);
        }

        ggml_fp16_t * S16 = (ggml_fp16_t *) ((float *) params->wdata + ith*(2*M + CACHE_LINE_SIZE_F32) + M);

        for (int i = 0; i < M; i++) {
            S16[i] = GGML_FP32_TO_FP16(S[i]);
        }

        for (int ic = 0; ic < nev1; ++ic) {
            // dst indices
            const int i1 = iq1;
            const int i2 = iq2;
            const int i3 = iq3;

            ggml_vec_dot_f16(nek1,
                    (float *)       ((char *) dst->data + (ic*nb0 + i1*nb1  + i2*nb2  + i3*nb3)),
                    (ggml_fp16_t *) ((char *) v->data   + (         ic*nbv1 + i2*nbv2 + i3*nbv3)),
                    S16);
        }
    }
}

void ggml_compute_forward_flash_attn(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * q,
        const struct ggml_tensor * k,
        const struct ggml_tensor * v,
        const bool masked,
        struct ggml_tensor * dst) {
    switch (q->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_flash_attn_f16(params, q, k, v, masked, dst);
            } break;
        case GGML_TYPE_F32:
            {
                ggml_compute_forward_flash_attn_f32(params, q, k, v, masked, dst);
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

// ggml_compute_forward_flash_ff

void ggml_compute_forward_flash_ff_f16(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,  // F16
        const struct ggml_tensor * b0, // F16 fc_w
        const struct ggml_tensor * b1, // F32 fc_b
        const struct ggml_tensor * c0, // F16 proj_w
        const struct ggml_tensor * c1, // F32 proj_b
        struct ggml_tensor * dst) {
    int64_t t0 = ggml_perf_time_us();
    UNUSED(t0);

    const int nea0 = a->ne[0];
    const int nea1 = a->ne[1];
    const int nea2 = a->ne[2];
    const int nea3 = a->ne[3];

    const int neb00 = b0->ne[0];
    const int neb01 = b0->ne[1];
    //const int neb02 = b0->ne[2];
    //const int neb03 = b0->ne[3];

    const int neb10 = b1->ne[0];
    const int neb11 = b1->ne[1];
    //const int neb12 = b1->ne[2];
    //const int neb13 = b1->ne[3];

    const int nec00 = c0->ne[0];
    const int nec01 = c0->ne[1];
    //const int nec02 = c0->ne[2];
    //const int nec03 = c0->ne[3];

    const int nec10 = c1->ne[0];
    const int nec11 = c1->ne[1];
    //const int nec12 = c1->ne[2];
    //const int nec13 = c1->ne[3];

    const int ne0 = dst->ne[0];
    const int ne1 = dst->ne[1];
    const int ne2 = dst->ne[2];
    //const int ne3 = dst->ne[3];

    const int nba0 = a->nb[0];
    const int nba1 = a->nb[1];
    const int nba2 = a->nb[2];
    const int nba3 = a->nb[3];

    const int nbb00 = b0->nb[0];
    const int nbb01 = b0->nb[1];
    const int nbb02 = b0->nb[2];
    const int nbb03 = b0->nb[3];

    const int nbb10 = b1->nb[0];
    //const int nbb11 = b1->nb[1];
    //const int nbb12 = b1->nb[2];
    //const int nbb13 = b1->nb[3];

    const int nbc00 = c0->nb[0];
    const int nbc01 = c0->nb[1];
    const int nbc02 = c0->nb[2];
    const int nbc03 = c0->nb[3];

    const int nbc10 = c1->nb[0];
    //const int nbc11 = c1->nb[1];
    //const int nbc12 = c1->nb[2];
    //const int nbc13 = c1->nb[3];

    const int nb0 = dst->nb[0];
    const int nb1 = dst->nb[1];
    const int nb2 = dst->nb[2];
    const int nb3 = dst->nb[3];

    const int ith = params->ith;
    const int nth = params->nth;

    const int D = nea0;
    //const int N = nea1;
    const int M = neb01;

    GGML_ASSERT(ne0 == nea0);
    GGML_ASSERT(ne1 == nea1);
    GGML_ASSERT(ne2 == nea2);

    GGML_ASSERT(nba0  == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbb00 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbb10 == sizeof(float));
    GGML_ASSERT(nbc00 == sizeof(ggml_fp16_t));
    GGML_ASSERT(nbc10 == sizeof(float));

    GGML_ASSERT(neb00 == D);
    GGML_ASSERT(neb01 == M);
    GGML_ASSERT(neb10 == M);
    GGML_ASSERT(neb11 == 1);

    GGML_ASSERT(nec00 == M);
    GGML_ASSERT(nec01 == D);
    GGML_ASSERT(nec10 == D);
    GGML_ASSERT(nec11 == 1);

    // dst cannot be transposed or permuted
    GGML_ASSERT(nb0 == sizeof(float));
    GGML_ASSERT(nb0 <= nb1);
    GGML_ASSERT(nb1 <= nb2);
    GGML_ASSERT(nb2 <= nb3);

    if (params->type == GGML_TASK_INIT) {
        return;
    }

    if (params->type == GGML_TASK_FINALIZE) {
        return;
    }

    // parallelize by a rows using ggml_vec_dot_f32

    // total rows in a
    const int nr = nea1*nea2*nea3;

    // rows per thread
    const int dr = (nr + nth - 1)/nth;

    // row range for this thread
    const int ir0 = dr*ith;
    const int ir1 = MIN(ir0 + dr, nr);

    for (int ir = ir0; ir < ir1; ++ir) {
        // a indices
        const int ia3 = ir/(nea2*nea1);
        const int ia2 = (ir - ia3*nea2*nea1)/nea1;
        const int ia1 = (ir - ia3*nea2*nea1 - ia2*nea1);

        float * S = (float *) params->wdata + ith*(2*M + CACHE_LINE_SIZE_F32);

        for (int ic = 0; ic < neb01; ++ic) {
            // b0 indices
            const int ib03 = ia3;
            const int ib02 = ia2;
            const int ib01 = ic;

            // S indices
            const int i1 = ib01;

            ggml_vec_dot_f16(nea0,
                    S + i1,
                    (ggml_fp16_t *) ((char *) b0->data + (ib01*nbb01 + ib02*nbb02 + ib03*nbb03)),
                    (ggml_fp16_t *) ((char *)  a->data + ( ia1*nba1  +  ia2*nba2  +  ia3*nba3)));
        }

        ggml_vec_add_f32(neb01, S, S, (float *) b1->data);
        //ggml_vec_gelu_f32(neb01, S, S);

        ggml_fp16_t * S16 = (ggml_fp16_t *) ((float *) params->wdata + ith*(2*M + CACHE_LINE_SIZE_F32) + M);

        for (int i = 0; i < M; i++) {
            S16[i] = GGML_FP32_TO_FP16(S[i]);
        }

        ggml_vec_gelu_f16(neb01, S16, S16);

        {
            // dst indices
            const int i1 = ia1;
            const int i2 = ia2;
            const int i3 = ia3;

            for (int ic = 0; ic < nec01; ++ic) {

                ggml_vec_dot_f16(neb01,
                        (float *)       ((char *) dst->data + (ic*nb0 + i1*nb1   + i2*nb2   + i3*nb3)),
                        (ggml_fp16_t *) ((char *) c0->data  + (         ic*nbc01 + i2*nbc02 + i3*nbc03)),
                        S16);
            }

            ggml_vec_add_f32(nec01,
                    (float *) ((char *) dst->data + (i1*nb1 + i2*nb2 + i3*nb3)),
                    (float *) ((char *) dst->data + (i1*nb1 + i2*nb2 + i3*nb3)),
                    (float *) c1->data);
        }
    }
}

void ggml_compute_forward_flash_ff(
        const struct ggml_compute_params * params,
        const struct ggml_tensor * a,
        const struct ggml_tensor * b0,
        const struct ggml_tensor * b1,
        const struct ggml_tensor * c0,
        const struct ggml_tensor * c1,
        struct ggml_tensor * dst) {
    switch (b0->type) {
        case GGML_TYPE_F16:
            {
                ggml_compute_forward_flash_ff_f16(params, a, b0, b1, c0, c1, dst);
            } break;
        case GGML_TYPE_F32:
            {
                GGML_ASSERT(false); // TODO
            } break;
        case GGML_TYPE_I8:
        case GGML_TYPE_I16:
        case GGML_TYPE_I32:
        case GGML_TYPE_COUNT:
            {
                assert(false);
            } break;
    }
}

/////////////////////////////////

void ggml_compute_forward(struct ggml_compute_params * params, struct ggml_tensor * tensor) {
    assert(params);

    switch (tensor->op) {
        case GGML_OP_DUP:
            {
                ggml_compute_forward_dup(params, tensor->src0, tensor);
            } break;
        case GGML_OP_ADD:
            {
                ggml_compute_forward_add(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_SUB:
            {
                ggml_compute_forward_sub(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_MUL:
            {
                ggml_compute_forward_mul(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_DIV:
            {
                ggml_compute_forward_div(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_SQR:
            {
                ggml_compute_forward_sqr(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SQRT:
            {
                ggml_compute_forward_sqrt(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SUM:
            {
                ggml_compute_forward_sum(params, tensor->src0, tensor);
            } break;
        case GGML_OP_MEAN:
            {
                ggml_compute_forward_mean(params, tensor->src0, tensor);
            } break;
        case GGML_OP_REPEAT:
            {
                ggml_compute_forward_repeat(params, tensor->src0, tensor);
            } break;
        case GGML_OP_ABS:
            {
                ggml_compute_forward_abs(params, tensor->src0, tensor);
            } break;
        case GGML_OP_SGN:
            {
                ggml_compute_forward_sgn(params, tensor->src0, tensor);
            } break;
        case GGML_OP_NEG:
            {
                ggml_compute_forward_neg(params, tensor->src0, tensor);
            } break;
        case GGML_OP_STEP:
            {
                ggml_compute_forward_step(params, tensor->src0, tensor);
            } break;
        case GGML_OP_RELU:
            {
                ggml_compute_forward_relu(params, tensor->src0, tensor);
            } break;
        case GGML_OP_GELU:
            {
                ggml_compute_forward_gelu(params, tensor->src0, tensor);
            } break;
        case GGML_OP_NORM:
            {
                ggml_compute_forward_norm(params, tensor->src0, tensor);
            } break;
        case GGML_OP_MUL_MAT:
            {
                ggml_compute_forward_mul_mat(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_SCALE:
            {
                ggml_compute_forward_scale(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_CPY:
            {
                ggml_compute_forward_cpy(params, tensor->src0, tensor);
            } break;
        case GGML_OP_RESHAPE:
            {
                ggml_compute_forward_reshape(params, tensor->src0, tensor);
            } break;
        case GGML_OP_VIEW:
            {
                ggml_compute_forward_view(params, tensor->src0);
            } break;
        case GGML_OP_PERMUTE:
            {
                ggml_compute_forward_permute(params, tensor->src0);
            } break;
        case GGML_OP_TRANSPOSE:
            {
                ggml_compute_forward_transpose(params, tensor->src0);
            } break;
        case GGML_OP_GET_ROWS:
            {
                ggml_compute_forward_get_rows(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_DIAG_MASK_INF:
            {
                ggml_compute_forward_diag_mask_inf(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_SOFT_MAX:
            {
                ggml_compute_forward_soft_max(params, tensor->src0, tensor);
            } break;
        case GGML_OP_ROPE:
            {
                ggml_compute_forward_rope(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_CONV_1D_1S:
            {
                ggml_compute_forward_conv_1d_1s(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_CONV_1D_2S:
            {
                ggml_compute_forward_conv_1d_2s(params, tensor->src0, tensor->src1, tensor);
            } break;
        case GGML_OP_FLASH_ATTN:
            {
                int32_t t = ggml_get_i32_1d(tensor->opt[1], 0);
                GGML_ASSERT(t == 0 || t == 1);
                bool masked = t != 0;
                ggml_compute_forward_flash_attn(params, tensor->src0, tensor->src1, tensor->opt[0], masked, tensor);
            } break;
        case GGML_OP_FLASH_FF:
            {
                ggml_compute_forward_flash_ff(params, tensor->src0, tensor->src1, tensor->opt[0], tensor->opt[1], tensor->opt[2], tensor);
            } break;
        case GGML_OP_NONE:
            {
                // nop
            } break;
        case GGML_OP_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    };
}

////////////////////////////////////////////////////////////////////////////////

void ggml_compute_backward(struct ggml_context * ctx, struct ggml_tensor * tensor, bool inplace) {
    struct ggml_tensor * src0 = tensor->src0;
    struct ggml_tensor * src1 = tensor->src1;

    switch (tensor->op) {
        case GGML_OP_DUP:
            {
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
            } break;
        case GGML_OP_ADD:
            {
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
                if (src1->grad) {
                    src1->grad = ggml_add_impl(ctx, src1->grad, tensor->grad, inplace);
                }
            } break;
        case GGML_OP_SUB:
            {
                if (src0->grad) {
                    src0->grad = ggml_add_impl(ctx, src0->grad, tensor->grad, inplace);
                }
                if (src1->grad) {
                    src1->grad = ggml_sub_impl(ctx, src1->grad, tensor->grad, inplace);
                }
            } break;
        case GGML_OP_MUL:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_mul(ctx, src1, tensor->grad),
                                inplace);
                }
                if (src1->grad) {
                    src1->grad =
                        ggml_add_impl(ctx,
                                src1->grad,
                                ggml_mul(ctx, src0, tensor->grad),
                                inplace);
                }
            } break;
        case GGML_OP_DIV:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_div(ctx, tensor->grad, src1),
                                inplace);
                }
                if (src1->grad) {
                    src1->grad =
                        ggml_sub_impl(ctx,
                                src1->grad,
                                ggml_mul(ctx,
                                    tensor->grad,
                                    ggml_div(ctx, tensor, src1)),
                                inplace);
                }
            } break;
        case GGML_OP_SQR:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_mul(ctx,
                                    ggml_mul(ctx, src0, tensor->grad),
                                    ggml_repeat(ctx, ggml_new_f32(ctx, 2.0f), src0)),
                                inplace);
                }
            } break;
        case GGML_OP_SQRT:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_div(ctx,
                                    ggml_repeat(ctx, ggml_new_f32(ctx, 0.5f), tensor),
                                    tensor),
                                inplace);
                }
            } break;
        case GGML_OP_SUM:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_repeat(ctx, tensor->grad, src0->grad),
                                inplace);
                }
            } break;
        case GGML_OP_MEAN:
            {
                assert(false); // TODO: implement
            } break;
        case GGML_OP_REPEAT:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_sum(ctx, tensor->grad),
                                inplace);
                }
            } break;
        case GGML_OP_ABS:
            {
                if (src0->grad) {
                    src0->grad =
                        ggml_add_impl(ctx,
                                src0->grad,
                                ggml_mul(ctx,
                                    ggml_sgn(ctx, src0),
                                    tensor->grad),
                                inplace);
                }
            } break;
        case GGML_OP_SGN:
            {
                if (src0->grad) {
                    // noop
                }
            } break;
        case GGML_OP_NEG:
            {
                if (src0->grad) {
                    src0->grad = ggml_sub_impl(ctx, src0->grad, tensor->grad, inplace);
                }
            } break;
        case GGML_OP_STEP:
            {
                if (src0->grad) {
                    // noop
                }
            } break;
        case GGML_OP_RELU:
            {
                if (src0->grad) {
                    src0->grad = ggml_sub_impl(ctx,
                            src0->grad,
                            ggml_mul(ctx,
                                ggml_step(ctx, src0),
                                tensor->grad),
                            inplace);
                }
            } break;
        case GGML_OP_GELU:
            {
                assert(false); // TODO: not implemented
            } break;
        case GGML_OP_NORM:
            {
                assert(false); // TODO: not implemented
            } break;
        case GGML_OP_MUL_MAT:
            {
                if (src0->grad) {
                    // TODO: this requires outer product - ggml_out_prod(ctx, src1, tensor->grad);
                    assert(false);
                }
                if (src1->grad) {
                    src1->grad =
                        ggml_add_impl(ctx,
                                src1->grad,
                                // TODO: fix transpose, the node will break the graph connections
                                ggml_mul_mat(ctx, ggml_transpose(ctx, src0), tensor->grad),
                                inplace);
                }
            } break;
        case GGML_OP_SCALE:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_CPY:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_RESHAPE:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_VIEW:
            {
                GGML_ASSERT(false); // not supported
            } break;
        case GGML_OP_PERMUTE:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_TRANSPOSE:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_GET_ROWS:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_DIAG_MASK_INF:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_SOFT_MAX:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_ROPE:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_CONV_1D_1S:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_CONV_1D_2S:
            {
                GGML_ASSERT(false); // TODO: not implemented
            } break;
        case GGML_OP_FLASH_ATTN:
            {
                GGML_ASSERT(false); // not supported
            } break;
        case GGML_OP_FLASH_FF:
            {
                GGML_ASSERT(false); // not supported
            } break;
        case GGML_OP_NONE:
            {
                // nop
            } break;
        case GGML_OP_COUNT:
            {
                GGML_ASSERT(false);
            } break;
    };
}

void ggml_visit_parents(struct ggml_cgraph * cgraph, struct ggml_tensor * node) {
    if (node->grad == NULL) {
        // this usually happens when we generate intermediate nodes from constants in the backward pass
        // it can also happen during forward pass, if the user performs computations with constants
        if (node->op != GGML_OP_NONE) {
            //GGML_PRINT_DEBUG("%s: warning: node %p has no grad, but op %d\n", __func__, (void *) node, node->op);
        }
    }

    // check if already visited
    for (int i = 0; i < cgraph->n_nodes; i++) {
        if (cgraph->nodes[i] == node) {
            return;
        }
    }

    for (int i = 0; i < cgraph->n_leafs; i++) {
        if (cgraph->leafs[i] == node) {
            return;
        }
    }

    if (node->src0) {
        ggml_visit_parents(cgraph, node->src0);
    }

    if (node->src1) {
        ggml_visit_parents(cgraph, node->src1);
    }

    for (int i = 0; i < GGML_MAX_OPT; ++i) {
        if (node->opt[i]) {
            ggml_visit_parents(cgraph, node->opt[i]);
        }
    }

    if (node->op == GGML_OP_NONE && node->grad == NULL) {
        // reached a leaf node, not part of the gradient graph (e.g. a constant)
        assert(cgraph->n_leafs < GGML_MAX_NODES);

        cgraph->leafs[cgraph->n_leafs] = node;
        cgraph->n_leafs++;
    } else {
        assert(cgraph->n_nodes < GGML_MAX_NODES);

        cgraph->nodes[cgraph->n_nodes] = node;
        cgraph->grads[cgraph->n_nodes] = node->grad;
        cgraph->n_nodes++;
    }
}

void ggml_build_forward_impl(struct ggml_cgraph * cgraph, struct ggml_tensor * tensor, bool expand) {
    if (!expand) {
        cgraph->n_nodes = 0;
        cgraph->n_leafs = 0;
    }

    const int n0 = cgraph->n_nodes;
    UNUSED(n0);

    ggml_visit_parents(cgraph, tensor);

    const int n_new = cgraph->n_nodes - n0;
    GGML_PRINT_DEBUG("%s: visited %d new nodes\n", __func__, n_new);

    if (n_new > 0) {
        // the last added node should always be starting point
        assert(cgraph->nodes[cgraph->n_nodes - 1] == tensor);
    }
}

void ggml_build_forward_expand(struct ggml_cgraph * cgraph, struct ggml_tensor * tensor) {
    ggml_build_forward_impl(cgraph, tensor, true);
}

struct ggml_cgraph ggml_build_forward(struct ggml_tensor * tensor) {
    struct ggml_cgraph result = {
        /*.n_nodes      =*/ 0,
        /*.n_leafs      =*/ 0,
        /*.n_threads    =*/ 0,
        /*.work_size    =*/ 0,
        /*.work         =*/ NULL,
        /*.nodes        =*/ { NULL },
        /*.grads        =*/ { NULL },
        /*.leafs        =*/ { NULL },
        /*.perf_runs    =*/ 0,
        /*.perf_cycles  =*/ 0,
        /*.perf_time_us =*/ 0,
    };

    ggml_build_forward_impl(&result, tensor, false);

    return result;
}

struct ggml_cgraph ggml_build_backward(struct ggml_context * ctx, struct ggml_cgraph * gf, bool keep) {
    struct ggml_cgraph result = *gf;

    assert(gf->n_nodes > 0);

    // if we are keeping the gradient graph, we have to detach the gradient nodes from the original graph
    if (keep) {
        for (int i = 0; i < gf->n_nodes; i++) {
            struct ggml_tensor * node = gf->nodes[i];

            if (node->grad) {
                node->grad = ggml_dup_tensor(ctx, node);
                gf->grads[i] = node->grad;
            }
        }
    }

    for (int i = gf->n_nodes - 1; i >= 0; i--) {
        struct ggml_tensor * node = gf->nodes[i];

        // because we detached the grad nodes from the original graph, we can afford inplace operations
        if (node->grad) {
            ggml_compute_backward(ctx, node, keep);
        }
    }

    for (int i = gf->n_nodes - 1; i >= 0; i--) {
        struct ggml_tensor * node = gf->nodes[i];

        if (node->is_param) {
            GGML_PRINT_DEBUG("%s: found root node %p\n", __func__, (void *) node);
            ggml_build_forward_impl(&result, node->grad, true);
        }
    }

    return result;
}

//
// thread data
//
// synchronization is done via busy loops
// I tried using spin locks, but not sure how to use them correctly - the things I tried were slower than busy loops
//

#ifdef __APPLE__

//#include <os/lock.h>

//typedef os_unfair_lock ggml_lock_t;
//
//#define ggml_lock_init(x)    UNUSED(x)
//#define ggml_lock_destroy(x) UNUSED(x)
//#define ggml_lock_lock       os_unfair_lock_lock
//#define ggml_lock_unlock     os_unfair_lock_unlock
//
//#define GGML_LOCK_INITIALIZER OS_UNFAIR_LOCK_INIT

typedef int ggml_lock_t;

#define ggml_lock_init(x)    UNUSED(x)
#define ggml_lock_destroy(x) UNUSED(x)
#define ggml_lock_lock(x)    UNUSED(x)
#define ggml_lock_unlock(x)  UNUSED(x)

#define GGML_LOCK_INITIALIZER 0

#else

//typedef pthread_spinlock_t ggml_lock_t;

//#define ggml_lock_init(x) pthread_spin_init(x, PTHREAD_PROCESS_PRIVATE)
//#define ggml_lock_destroy pthread_spin_destroy
//#define ggml_lock_lock    pthread_spin_lock
//#define ggml_lock_unlock  pthread_spin_unlock

typedef int ggml_lock_t;

#define ggml_lock_init(x)    UNUSED(x)
#define ggml_lock_destroy(x) UNUSED(x)
#define ggml_lock_lock(x)    UNUSED(x)
#define ggml_lock_unlock(x)  UNUSED(x)

#define GGML_LOCK_INITIALIZER 0

#endif

struct ggml_compute_state_shared {
    ggml_lock_t spin;

    int n_threads;

    // synchronization primitives
    atomic_int  n_ready;
    atomic_bool has_work;
    atomic_bool stop; // stop all threads
};

struct ggml_compute_state {
    pthread_t thrd;

    struct ggml_compute_params params;
    struct ggml_tensor * node;

    struct ggml_compute_state_shared * shared;
};

// function used by each compute thread
void * ggml_graph_compute_one(void * data) {
    struct ggml_compute_state * state = (struct ggml_compute_state *) data;

    ggml_compute_forward(&state->params, state->node);

    return NULL;
}

thread_ret_t ggml_graph_compute_thread(void * data) {
    struct ggml_compute_state * state = (struct ggml_compute_state *) data;

    const int n_threads = state->shared->n_threads;

    while (true) {
        if (atomic_fetch_add(&state->shared->n_ready, 1) == n_threads - 1) {
            atomic_store(&state->shared->has_work, false);
        } else {
            while (atomic_load(&state->shared->has_work)) {
                if (atomic_load(&state->shared->stop)) {
                    return 0;
                }
                ggml_lock_lock  (&state->shared->spin);
                ggml_lock_unlock(&state->shared->spin);
            }
        }

        atomic_fetch_sub(&state->shared->n_ready, 1);

        // wait for work
        while (!atomic_load(&state->shared->has_work)) {
            if (atomic_load(&state->shared->stop)) {
                return 0;
            }
            ggml_lock_lock  (&state->shared->spin);
            ggml_lock_unlock(&state->shared->spin);
        }

        // check if we should stop
        if (atomic_load(&state->shared->stop)) {
            break;
        }

        if (state->node) {
            ggml_compute_forward(&state->params, state->node);
            state->node = NULL;
        } else {
            break;
        }
    }

    return 0;
}

void ggml_graph_compute(struct ggml_context * ctx, struct ggml_cgraph * cgraph) {
    if (cgraph->n_threads <= 0) {
        cgraph->n_threads = 8;
    }

    const int n_threads = cgraph->n_threads;

    struct ggml_compute_state_shared state_shared = {
        /*.spin      =*/ GGML_LOCK_INITIALIZER,
        /*.n_threads =*/ n_threads,
        /*.n_ready   =*/ 0,
        /*.has_work  =*/ false,
        /*.stop      =*/ false,
    };
    struct ggml_compute_state * workers = n_threads > 1 ? alloca(sizeof(struct ggml_compute_state)*(n_threads - 1)) : NULL;

    // create thread pool
    if (n_threads > 1) {
        ggml_lock_init(&state_shared.spin);

        atomic_store(&state_shared.has_work, true);

        for (int j = 0; j < n_threads - 1; j++) {
            workers[j] = (struct ggml_compute_state) {
                .thrd   = 0,
                .params = {
                    .type  = GGML_TASK_COMPUTE,
                    .ith   = j + 1,
                    .nth   = n_threads,
                    .wsize = cgraph->work ? ggml_nbytes(cgraph->work) : 0,
                    .wdata = cgraph->work ? cgraph->work->data : NULL,
                },
                .node   = NULL,
                .shared = &state_shared,
            };
            int rc = pthread_create(&workers[j].thrd, NULL, ggml_graph_compute_thread, &workers[j]);
            assert(rc == 0);
            UNUSED(rc);
        }
    }

    // initialize tasks + work buffer
    {
        size_t work_size = 0;

        // thread scheduling for the different operations
        for (int i = 0; i < cgraph->n_nodes; i++) {
            struct ggml_tensor * node = cgraph->nodes[i];

            switch (node->op) {
                case GGML_OP_DUP:
                    {
                        node->n_tasks = 1;
                    } break;
                case GGML_OP_ADD:
                    {
                        node->n_tasks = n_threads;
                    } break;
                case GGML_OP_SUB:
                case GGML_OP_MUL:
                case GGML_OP_DIV:
                case GGML_OP_SQR:
                case GGML_OP_SQRT:
                case GGML_OP_SUM:
                case GGML_OP_MEAN:
                case GGML_OP_REPEAT:
                case GGML_OP_ABS:
                case GGML_OP_SGN:
                case GGML_OP_NEG:
                case GGML_OP_STEP:
                case GGML_OP_RELU:
                    {
                        node->n_tasks = 1;
                    } break;
                case GGML_OP_GELU:
                    {
                        node->n_tasks = n_threads;
                    } break;
                case GGML_OP_NORM:
                    {
                        node->n_tasks = n_threads;
                    } break;
                case GGML_OP_MUL_MAT:
                    {
                        // TODO: use different scheduling for different matrix sizes
                        node->n_tasks = n_threads;

                        size_t cur = 0;

                        // TODO: better way to determine if the matrix is transposed
                        if (node->src0->nb[1] < node->src0->nb[0]) {
                            cur = ggml_nbytes(node)*node->n_tasks; // TODO: this can become (n_tasks-1)
                        } else {
                            if (node->src0->type == GGML_TYPE_F16 &&
                                node->src1->type == GGML_TYPE_F32) {
#if defined(GGML_USE_ACCELERATE) || defined(GGML_USE_OPENBLAS)
                                if (ggml_compute_forward_mul_mat_use_blas(node->src0, node->src1, node)) {
                                    cur = sizeof(float)*(node->src0->ne[0]*node->src0->ne[1]);
                                } else {
                                    cur = sizeof(ggml_fp16_t)*ggml_nelements(node->src1);
                                }
#else
                                cur = sizeof(ggml_fp16_t)*ggml_nelements(node->src1);
#endif
                            } else if (node->src0->type == GGML_TYPE_F32 &&
                                       node->src1->type == GGML_TYPE_F32) {
                                cur = 0;
                            } else {
                                GGML_ASSERT(false);
                            }
                        }

                        work_size = MAX(work_size, cur);
                    } break;
                case GGML_OP_SCALE:
                    {
                        node->n_tasks = n_threads;
                    } break;
                case GGML_OP_CPY:
                case GGML_OP_RESHAPE:
                case GGML_OP_VIEW:
                case GGML_OP_PERMUTE:
                case GGML_OP_TRANSPOSE:
                case GGML_OP_GET_ROWS:
                case GGML_OP_DIAG_MASK_INF:
                    {
                        node->n_tasks = 1;
                    } break;
                case GGML_OP_SOFT_MAX:
                    {
                        node->n_tasks = n_threads;
                    } break;
                case GGML_OP_ROPE:
                    {
                        node->n_tasks = 1;
                    } break;
                case GGML_OP_CONV_1D_1S:
                case GGML_OP_CONV_1D_2S:
                    {
                        node->n_tasks = n_threads;

                        GGML_ASSERT(node->src0->ne[3] == 1);
                        GGML_ASSERT(node->src1->ne[2] == 1);
                        GGML_ASSERT(node->src1->ne[3] == 1);

                        size_t cur = 0;
                        const int nk = node->src0->ne[0];

                        if (node->src0->type == GGML_TYPE_F16 &&
                            node->src1->type == GGML_TYPE_F32) {
                            cur = sizeof(ggml_fp16_t)*(
                                    nk*ggml_up32(node->src0->ne[1])*node->src0->ne[2] +
                                    ( 2*(nk/2) + node->src1->ne[0])*node->src1->ne[1]
                                    );
                        } else if (node->src0->type == GGML_TYPE_F32 &&
                                   node->src1->type == GGML_TYPE_F32) {
                            cur = sizeof(float)*(
                                    nk*ggml_up32(node->src0->ne[1])*node->src0->ne[2] +
                                    ( 2*(nk/2) + node->src1->ne[0])*node->src1->ne[1]
                                    );
                        } else {
                            GGML_ASSERT(false);
                        }

                        work_size = MAX(work_size, cur);
                    } break;
                case GGML_OP_FLASH_ATTN:
                    {
                        node->n_tasks = n_threads;

                        size_t cur = 0;

                        if (node->src1->type == GGML_TYPE_F32) {
                            cur  = sizeof(float)*node->src1->ne[1]*node->n_tasks; // TODO: this can become (n_tasks-1)
                            cur += sizeof(float)*node->src1->ne[1]*node->n_tasks; // this is overestimated by x2
                        }

                        if (node->src1->type == GGML_TYPE_F16) {
                            cur  = sizeof(float)*node->src1->ne[1]*node->n_tasks; // TODO: this can become (n_tasks-1)
                            cur += sizeof(float)*node->src1->ne[1]*node->n_tasks; // this is overestimated by x2
                        }

                        work_size = MAX(work_size, cur);
                    } break;
                case GGML_OP_FLASH_FF:
                    {
                        node->n_tasks = n_threads;

                        size_t cur = 0;

                        if (node->src1->type == GGML_TYPE_F32) {
                            cur  = sizeof(float)*node->src1->ne[1]*node->n_tasks; // TODO: this can become (n_tasks-1)
                            cur += sizeof(float)*node->src1->ne[1]*node->n_tasks; // this is overestimated by x2
                        }

                        if (node->src1->type == GGML_TYPE_F16) {
                            cur  = sizeof(float)*node->src1->ne[1]*node->n_tasks; // TODO: this can become (n_tasks-1)
                            cur += sizeof(float)*node->src1->ne[1]*node->n_tasks; // this is overestimated by x2
                        }

                        work_size = MAX(work_size, cur);
                    } break;
                case GGML_OP_NONE:
                    {
                        node->n_tasks = 1;
                    } break;
                case GGML_OP_COUNT:
                    {
                        assert(false);
                    } break;
            };
        }

        if (cgraph->work != NULL && work_size > cgraph->work_size) {
            assert(false); // TODO: better handling
        }

        if (work_size > 0 && cgraph->work == NULL) {
            cgraph->work_size = work_size + CACHE_LINE_SIZE*(n_threads - 1);

            GGML_PRINT_DEBUG("%s: allocating work buffer for graph (%zu bytes)\n", __func__, cgraph->work_size);
            cgraph->work = ggml_new_tensor_1d(ctx, GGML_TYPE_I8, cgraph->work_size);
        }
    }

    const int64_t perf_start_cycles  = ggml_perf_cycles();
    const int64_t perf_start_time_us = ggml_perf_time_us();

    for (int i = 0; i < cgraph->n_nodes; i++) {
        GGML_PRINT_DEBUG_5("%s: %d/%d\n", __func__, i, cgraph->n_nodes);

        struct ggml_tensor * node = cgraph->nodes[i];

        // TODO: this could be used to avoid unnecessary computations, but it needs to be improved
        //if (node->grad == NULL && node->perf_runs > 0) {
        //    continue;
        //}

        const int64_t perf_node_start_cycles  = ggml_perf_cycles();
        const int64_t perf_node_start_time_us = ggml_perf_time_us();

        // INIT
        struct ggml_compute_params params = {
            /*.type  =*/ GGML_TASK_INIT,
            /*.ith   =*/ 0,
            /*.nth   =*/ node->n_tasks,
            /*.wsize =*/ cgraph->work ? ggml_nbytes(cgraph->work) : 0,
            /*.wdata =*/ cgraph->work ? cgraph->work->data : NULL,
        };

        ggml_compute_forward(&params, node);

        // COMPUTE
        if (node->n_tasks > 1) {
            if (atomic_fetch_add(&state_shared.n_ready, 1) == n_threads - 1) {
                atomic_store(&state_shared.has_work, false);
            }

            while (atomic_load(&state_shared.has_work)) {
                ggml_lock_lock  (&state_shared.spin);
                ggml_lock_unlock(&state_shared.spin);
            }

            // launch thread pool
            for (int j = 0; j < n_threads - 1; j++) {
                workers[j].params = (struct ggml_compute_params) {
                    .type  = GGML_TASK_COMPUTE,
                    .ith   = j + 1,
                    .nth   = n_threads,
                    .wsize = cgraph->work ? ggml_nbytes(cgraph->work) : 0,
                    .wdata = cgraph->work ? cgraph->work->data : NULL,
                };
                workers[j].node = node;
            }

            atomic_fetch_sub(&state_shared.n_ready, 1);

            while (atomic_load(&state_shared.n_ready) > 0) {
                ggml_lock_lock  (&state_shared.spin);
                ggml_lock_unlock(&state_shared.spin);
            }

            atomic_store(&state_shared.has_work, true);
        }

        params.type = GGML_TASK_COMPUTE;
        ggml_compute_forward(&params, node);

        // wait for thread pool
        if (node->n_tasks > 1) {
            if (atomic_fetch_add(&state_shared.n_ready, 1) == n_threads - 1) {
                atomic_store(&state_shared.has_work, false);
            }

            while (atomic_load(&state_shared.has_work)) {
                ggml_lock_lock  (&state_shared.spin);
                ggml_lock_unlock(&state_shared.spin);
            }

            atomic_fetch_sub(&state_shared.n_ready, 1);

            while (atomic_load(&state_shared.n_ready) != 0) {
                ggml_lock_lock  (&state_shared.spin);
                ggml_lock_unlock(&state_shared.spin);
            }
        }

        // FINALIZE
        if (node->n_tasks > 1) {
            if (atomic_fetch_add(&state_shared.n_ready, 1) == n_threads - 1) {
                atomic_store(&state_shared.has_work, false);
            }

            while (atomic_load(&state_shared.has_work)) {
                ggml_lock_lock  (&state_shared.spin);
                ggml_lock_unlock(&state_shared.spin);
            }

            // launch thread pool
            for (int j = 0; j < n_threads - 1; j++) {
                workers[j].params = (struct ggml_compute_params) {
                    .type  = GGML_TASK_FINALIZE,
                    .ith   = j + 1,
                    .nth   = n_threads,
                    .wsize = cgraph->work ? ggml_nbytes(cgraph->work) : 0,
                    .wdata = cgraph->work ? cgraph->work->data : NULL,
                };
                workers[j].node = node;
            }

            atomic_fetch_sub(&state_shared.n_ready, 1);

            while (atomic_load(&state_shared.n_ready) > 0) {
                ggml_lock_lock  (&state_shared.spin);
                ggml_lock_unlock(&state_shared.spin);
            }

            atomic_store(&state_shared.has_work, true);
        }

        params.type = GGML_TASK_FINALIZE;
        ggml_compute_forward(&params, node);

        // wait for thread pool
        if (node->n_tasks > 1) {
            if (atomic_fetch_add(&state_shared.n_ready, 1) == n_threads - 1) {
                atomic_store(&state_shared.has_work, false);
            }

            while (atomic_load(&state_shared.has_work)) {
                ggml_lock_lock  (&state_shared.spin);
                ggml_lock_unlock(&state_shared.spin);
            }

            atomic_fetch_sub(&state_shared.n_ready, 1);

            while (atomic_load(&state_shared.n_ready) != 0) {
                ggml_lock_lock  (&state_shared.spin);
                ggml_lock_unlock(&state_shared.spin);
            }
        }

        // performance stats (node)
        {
            int64_t perf_cycles_cur  = ggml_perf_cycles()  - perf_node_start_cycles;
            int64_t perf_time_us_cur = ggml_perf_time_us() - perf_node_start_time_us;

            node->perf_runs++;
            node->perf_cycles  += perf_cycles_cur;
            node->perf_time_us += perf_time_us_cur;
        }
    }

    // join thread pool
    if (n_threads > 1) {
        atomic_store(&state_shared.stop, true);
        atomic_store(&state_shared.has_work, true);

        for (int j = 0; j < n_threads - 1; j++) {
            int rc = pthread_join(workers[j].thrd, NULL);
            assert(rc == 0);
            UNUSED(rc);
        }

        ggml_lock_destroy(&state_shared.spin);
    }

    // performance stats (graph)
    {
        int64_t perf_cycles_cur  = ggml_perf_cycles()  - perf_start_cycles;
        int64_t perf_time_us_cur = ggml_perf_time_us() - perf_start_time_us;

        cgraph->perf_runs++;
        cgraph->perf_cycles  += perf_cycles_cur;
        cgraph->perf_time_us += perf_time_us_cur;

        GGML_PRINT_DEBUG("%s: perf (%d) - cpu = %.3f / %.3f ms, wall = %.3f / %.3f ms\n",
                __func__, cgraph->perf_runs,
                (double) perf_cycles_cur      / (double) ggml_cycles_per_ms(),
                (double) cgraph->perf_cycles  / (double) ggml_cycles_per_ms() / (double) cgraph->perf_runs,
                (double) perf_time_us_cur     / 1000.0,
                (double) cgraph->perf_time_us / 1000.0 / cgraph->perf_runs);
    }
}

void ggml_graph_reset(struct ggml_cgraph * cgraph) {
    for (int i = 0; i < cgraph->n_nodes; i++) {
        struct ggml_tensor * grad = cgraph->grads[i];

        if (grad) {
            ggml_set_zero(grad);
        }
    }
}

void ggml_graph_print(const struct ggml_cgraph * cgraph) {
    int64_t perf_total_per_op_us[GGML_OP_COUNT] = {0};

    GGML_PRINT("=== GRAPH ===\n");

    GGML_PRINT_DEBUG("n_threads       = %d\n",       cgraph->n_threads);
    GGML_PRINT_DEBUG("total work size = %zu bytes\n",cgraph->work_size);

    GGML_PRINT("n_nodes = %d\n", cgraph->n_nodes);
    for (int i = 0; i < cgraph->n_nodes; i++) {
        struct ggml_tensor * node = cgraph->nodes[i];

        perf_total_per_op_us[node->op] += node->perf_time_us;

        GGML_PRINT(" - %3d: [ %6d, %6d, %6d] %16s %s (%3d) cpu = %7.3f / %7.3f ms, wall = %7.3f / %7.3f ms\n",
                i,
                node->ne[0], node->ne[1], node->ne[2],
                GGML_OP_LABEL[node->op], node->is_param ? "x" : node->grad ? "g" : " ", node->perf_runs,
                (double) node->perf_cycles  / (double) ggml_cycles_per_ms(),
                (double) node->perf_cycles  / (double) ggml_cycles_per_ms() / (double) node->perf_runs,
                (double) node->perf_time_us / 1000.0,
                (double) node->perf_time_us / 1000.0 / node->perf_runs);
    }

    GGML_PRINT("n_leafs = %d\n", cgraph->n_leafs);
    for (int i = 0; i < cgraph->n_leafs; i++) {
        struct ggml_tensor * node = cgraph->leafs[i];

        GGML_PRINT(" - %3d: [ %6d, %6d] %8s\n",
                i,
                node->ne[0], node->ne[1],
                GGML_OP_LABEL[node->op]);
    }

    for (int i = 0; i < GGML_OP_COUNT; i++) {
        GGML_PRINT("perf_total_per_op_us[%16s] = %7.3f ms\n", GGML_OP_LABEL[i], (double) perf_total_per_op_us[i] / 1000.0);
    }

    GGML_PRINT("========================================\n");
}

// check if node is part of the graph
bool ggml_graph_find(const struct ggml_cgraph * cgraph, const struct ggml_tensor * node) {
    if (cgraph == NULL) {
        return true;
    }

    for (int i = 0; i < cgraph->n_nodes; i++) {
        if (cgraph->nodes[i] == node) {
            return true;
        }
    }

    return false;
}

struct ggml_tensor * ggml_graph_get_parent(const struct ggml_cgraph * cgraph, const struct ggml_tensor * node) {
    for (int i = 0; i < cgraph->n_nodes; i++) {
        struct ggml_tensor * parent = cgraph->nodes[i];

        if (parent->grad == node) {
            return parent;
        }
    }

    return NULL;
}

void ggml_graph_dump_dot(const struct ggml_cgraph * gb, const struct ggml_cgraph * gf, const char * filename) {
    char color[16];

    FILE * fp = fopen(filename, "w");
    assert(fp);

    fprintf(fp, "digraph G {\n");
    fprintf(fp, "  newrank = true;\n");
    fprintf(fp, "  rankdir = LR;\n");

    for (int i = 0; i < gb->n_nodes; i++) {
        struct ggml_tensor * node = gb->nodes[i];

        if (ggml_graph_get_parent(gb, node) != NULL) {
            continue;
        }

        if (node->is_param) {
            snprintf(color, sizeof(color), "yellow");
        } else if (node->grad) {
            if (ggml_graph_find(gf, node)) {
                snprintf(color, sizeof(color), "green");
            } else {
                snprintf(color, sizeof(color), "lightblue");
            }
        } else {
            snprintf(color, sizeof(color), "white");
        }

        fprintf(fp, "  \"%p\" [ \
style = filled; fillcolor = %s; shape = record; \
label=\"%d [%d, %d] | <x>%s",
                (void *) node, color,
                i, node->ne[0], node->ne[1],
                GGML_OP_SYMBOL[node->op]);

        if (node->grad) {
            fprintf(fp, " | <g>%s\"; ]\n", GGML_OP_SYMBOL[node->grad->op]);
        } else {
            fprintf(fp, "\"; ]\n");
        }
    }

    for (int i = 0; i < gb->n_leafs; i++) {
        struct ggml_tensor * node = gb->leafs[i];

        snprintf(color, sizeof(color), "pink");

        if (ggml_nelements(node) == 1) {
            fprintf(fp, "  \"%p\" [ \
style = filled; fillcolor = %s; shape = record; \
label=\"<x>%.1e\"; ]\n",
                    (void *) node, color, ggml_get_f32_1d(node, 0));
        } else {
            fprintf(fp, "  \"%p\" [ \
style = filled; fillcolor = %s; shape = record; \
label=\"<x>CONST %d [%d, %d]\"; ]\n",
                    (void *) node, color,
                    i, node->ne[0], node->ne[1]);
        }
    }

    for (int i = 0; i < gb->n_nodes; i++) {
        struct ggml_tensor * node = gb->nodes[i];

        struct ggml_tensor * parent = ggml_graph_get_parent(gb, node);

        if (node->src0) {
            struct ggml_tensor * parent0 = ggml_graph_get_parent(gb, node->src0);

            fprintf(fp, "  \"%p\":%s -> \"%p\":%s [ arrowhead = %s; style = %s; label = \"x\"; ]\n",
                    parent0 ? (void *) parent0 : (void *) node->src0,
                    parent0 ? "g" : "x",
                    parent ? (void *) parent : (void *) node,
                    parent ? "g" : "x",
                    parent ? "empty" : "vee",
                    parent ? "dashed" : "solid");
        }

        if (node->src1) {
            struct ggml_tensor * parent1 = ggml_graph_get_parent(gb, node->src1);

            fprintf(fp, "  \"%p\":%s -> \"%p\":%s [ arrowhead = %s; style = %s; label = \"y\"; ]\n",
                    parent1 ? (void *) parent1 : (void *) node->src1,
                    parent1 ? "g" : "x",
                    parent ? (void *) parent : (void *) node,
                    parent ? "g" : "x",
                    parent ? "empty" : "vee",
                    parent ? "dashed" : "solid");
        }
    }

    for (int i = 0; i < gb->n_leafs; i++) {
        struct ggml_tensor * node = gb->leafs[i];

        if (node->src0) {
            fprintf(fp, "  \"%p\":%s -> \"%p\":%s [ label = \"x\"; ]\n",
                    (void *) node->src0, "x",
                    (void *) node, "x");
        }

        if (node->src1) {
            fprintf(fp, "  \"%p\":%s -> \"%p\":%s [ label = \"y\"; ]\n",
                    (void *) node->src1, "x",
                    (void *) node, "x");
        }
    }

    fprintf(fp, "}\n");

    fclose(fp);

    GGML_PRINT("%s: dot -Tpng %s -o %s.png && open %s.png\n", __func__, filename, filename, filename);
}

////////////////////////////////////////////////////////////////////////////////

void ggml_opt_set_params(int np, struct ggml_tensor * const ps[], const float * x) {
    int i = 0;
    for (int p = 0; p < np; ++p) {
        const int ne = ggml_nelements(ps[p]) ;
        // TODO: add function to set tensor from array
        for (int j = 0; j < ne; ++j) {
            ggml_set_f32_1d(ps[p], j, x[i++]);
        }
    }
}

void ggml_opt_get_params(int np, struct ggml_tensor * const ps[], float * x) {
    int i = 0;
    for (int p = 0; p < np; ++p) {
        const int ne = ggml_nelements(ps[p]) ;
        // TODO: add function to get all elements at once
        for (int j = 0; j < ne; ++j) {
            x[i++] = ggml_get_f32_1d(ps[p], j);
        }
    }
}

void ggml_opt_get_grad(int np, struct ggml_tensor * const ps[], float * g) {
    int i = 0;
    for (int p = 0; p < np; ++p) {
        const int ne = ggml_nelements(ps[p]) ;
        // TODO: add function to get all elements at once
        for (int j = 0; j < ne; ++j) {
            g[i++] = ggml_get_f32_1d(ps[p]->grad, j);
        }
    }
}

//
// ADAM
//
//   ref: https://arxiv.org/pdf/1412.6980.pdf
//

enum ggml_opt_result ggml_opt_adam(
        struct ggml_context * ctx,
        struct ggml_opt_params params,
        struct ggml_tensor * f,
        struct ggml_cgraph * gf,
        struct ggml_cgraph * gb) {
    assert(ggml_is_scalar(f));

    gf->n_threads = params.n_threads;
    gb->n_threads = params.n_threads;

    // these will store the parameters we want to optimize
    struct ggml_tensor * ps[GGML_MAX_PARAMS];

    int np = 0;
    int nx = 0;
    for (int i = 0; i < gf->n_nodes; ++i) {
        if (gf->nodes[i]->is_param) {
            GGML_PRINT_DEBUG("found param %d: grad->op = %d\n", np, gf->nodes[i]->grad->op);

            assert(np < GGML_MAX_PARAMS);

            ps[np++] = gf->nodes[i];
            nx += ggml_nelements(gf->nodes[i]);
        }
    }

    // constants
    const float alpha = params.adam.alpha;
    const float beta1 = params.adam.beta1;
    const float beta2 = params.adam.beta2;
    const float eps   = params.adam.eps;

    float * x  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // view of the parameters
    float * g1 = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // gradient
    float * g2 = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // gradient squared
    float * m  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // first moment
    float * v  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // second moment
    float * mh = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // first moment hat
    float * vh = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // second moment hat

    float * pf = params.past > 0 ? ggml_new_tensor_1d(ctx, GGML_TYPE_F32, params.past)->data : NULL; // past function values

    // initialize
    ggml_vec_set_f32(nx, m, 0.0f);
    ggml_vec_set_f32(nx, v, 0.0f);

    // update view
    ggml_opt_get_params(np, ps, x);

    // compute the function value
    ggml_graph_reset  (gf);
    ggml_set_f32      (f->grad, 1.0f);
    ggml_graph_compute(ctx, gb);

    float fx_prev = ggml_get_f32_1d(f, 0);
    if (pf) {
        pf[0] = fx_prev;
    }

    int n_no_improvement = 0;
    float fx_best = fx_prev;

    // run the optimizer
    for (int t = 0; t < params.adam.n_iter; ++t) {
        GGML_PRINT_DEBUG  ("=== iter %d ===\n", t);

        GGML_PRINT_DEBUG  ("f      = %10.6f\n", ggml_get_f32_1d(f, 0));
        GGML_PRINT_DEBUG_5("df/dx0 = %10.6f\n", ggml_get_f32_1d(ps[0]->grad, 0));
        GGML_PRINT_DEBUG_5("df/dx1 = %10.6f\n", ggml_get_f32_1d(ps[1]->grad, 0));

        for (int i = 0; i < np; ++i) {
            GGML_PRINT_DEBUG("param %d: %10.6f, g = %10.6f\n", i,
                    ggml_get_f32_1d(ps[i], 0), ggml_get_f32_1d(ps[i]->grad, 0));
        }

        const int64_t t_start_wall = ggml_time_us();
        const int64_t t_start_cpu = ggml_cycles();
        UNUSED(t_start_wall);
        UNUSED(t_start_cpu);

        {
            // update the gradient
            ggml_opt_get_grad(np, ps, g1);

            // m_t = beta1*m_t-1 + (1 - beta1)*g_t
            ggml_vec_scale_f32(nx, m, beta1);
            ggml_vec_mad_f32  (nx, m, g1, 1.0f - beta1);

            // g2 = g1^2
            ggml_vec_sqr_f32  (nx, g2, g1);

            // v_t = beta2*v_t-1 + (1 - beta2)*g_t^2
            ggml_vec_scale_f32(nx, v, beta2);
            ggml_vec_mad_f32  (nx, v, g2, 1.0f - beta2);

            // m^hat = m_t / (1 - beta1^t)
            // v^hat = v_t / (1 - beta2^t)
            // x_t = x_t-1 - alpha*m^hat/(sqrt(v^hat) + eps)
            ggml_vec_cpy_f32  (nx, mh, m);
            ggml_vec_cpy_f32  (nx, vh, v);

            ggml_vec_scale_f32(nx, mh, alpha/(1.0f - powf(beta1, t + 1)));
            ggml_vec_scale_f32(nx, vh,  1.0f/(1.0f - powf(beta2, t + 1)));

            ggml_vec_sqrt_f32 (nx, vh, vh);
            ggml_vec_acc1_f32 (nx, vh, eps);

            ggml_vec_div_f32  (nx, mh, mh, vh);
            ggml_vec_sub_f32  (nx, x,  x,  mh);

            // update the parameters
            ggml_opt_set_params(np, ps, x);
        }

        ggml_graph_reset  (gf);
        ggml_set_f32      (f->grad, 1.0f);
        ggml_graph_compute(ctx, gb);

        const float fx = ggml_get_f32_1d(f, 0);

        // check convergence
        if (fabsf(fx - fx_prev)/fx < params.adam.eps_f) {
            GGML_PRINT_DEBUG("converged\n");

            return GGML_OPT_OK;
        }

        // delta-based convergence test
        if (pf != NULL) {
            // need at least params.past iterations to start checking for convergence
            if (params.past <= t) {
                const float rate = (pf[t%params.past] - fx)/fx;

                if (fabs(rate) < params.delta) {
                    return GGML_OPT_OK;
                }
            }

            pf[t%params.past] = fx;
        }

        // check for improvement
        if (params.max_no_improvement > 0) {
            if (fx_best > fx) {
                fx_best = fx;
                n_no_improvement = 0;
            } else {
                ++n_no_improvement;

                if (n_no_improvement >= params.max_no_improvement) {
                    return GGML_OPT_OK;
                }
            }
        }

        fx_prev = fx;

        {
            const int64_t t_end_cpu = ggml_cycles();
            GGML_PRINT_DEBUG("time iter:      %5.3f s\n", ((float)(t_end_cpu - t_start_cpu))/CLOCKS_PER_SEC);
            UNUSED(t_end_cpu);

            const int64_t t_end_wall = ggml_time_us();
            GGML_PRINT_DEBUG("wall time iter: %5.3f s\n", (t_end_wall - t_start_wall)/1e6);
            UNUSED(t_end_wall);
        }
    }

    return GGML_OPT_DID_NOT_CONVERGE;
}

//
// L-BFGS
//
// the L-BFGS implementation below is based on the following implementation:
//
//   https://github.com/chokkan/liblbfgs
//

struct ggml_lbfgs_iteration_data {
    float alpha;
    float ys;
    float * s;
    float * y;
};

static enum ggml_opt_result linesearch_backtracking(
        struct ggml_context * ctx,
        const struct ggml_opt_params * params,
        int nx,
        float * x,
        float * fx,
        float * g,
        float * d,
        float * step,
        const float * xp,
        struct ggml_tensor * f,
        struct ggml_cgraph * gf,
        struct ggml_cgraph * gb,
        const int np,
        struct ggml_tensor * ps[]) {
    int count = 0;

    float width  = 0.0f;
    float dg     = 0.0f;
    float finit  = 0.0f;
    float dginit = 0.0f;
    float dgtest = 0.0f;

    const float dec = 0.5f;
    const float inc = 2.1f;

    if (*step <= 0.) {
        return GGML_LINESEARCH_INVALID_PARAMETERS;
    }

    // compute the initial gradient in the search direction
    ggml_vec_dot_f32(nx, &dginit, g, d);

    // make sure that d points to a descent direction
    if (0 < dginit) {
        return GGML_LINESEARCH_FAIL;
    }

    // initialize local variables
    finit = *fx;
    dgtest = params->lbfgs.ftol*dginit;

    while (true) {
        ggml_vec_cpy_f32(nx, x, xp);
        ggml_vec_mad_f32(nx, x, d, *step);

        // evaluate the function and gradient values
        {
            ggml_opt_set_params(np, ps, x);

            ggml_graph_reset  (gf);
            ggml_set_f32      (f->grad, 1.0f);
            ggml_graph_compute(ctx, gb);

            ggml_opt_get_grad(np, ps, g);

            *fx = ggml_get_f32_1d(f, 0);
        }

        ++count;

        if (*fx > finit + (*step)*dgtest) {
            width = dec;
        } else {
            // Armijo condition is satisfied
            if (params->lbfgs.linesearch == GGML_LINESEARCH_BACKTRACKING_ARMIJO) {
                return count;
            }

            ggml_vec_dot_f32(nx, &dg, g, d);

            // check the Wolfe condition
            if (dg < params->lbfgs.wolfe * dginit) {
                width = inc;
            } else {
                if(params->lbfgs.linesearch == GGML_LINESEARCH_BACKTRACKING_WOLFE) {
                    // regular Wolfe conditions
                    return count;
                }

                if(dg > -params->lbfgs.wolfe*dginit) {
                    width = dec;
                } else {
                    // strong Wolfe condition (GGML_LINESEARCH_BACKTRACKING_STRONG_WOLFE)
                    return count;
                }
                return count;
            }
        }

        if (*step < params->lbfgs.min_step) {
            return GGML_LINESEARCH_MINIMUM_STEP;
        }
        if (*step > params->lbfgs.max_step) {
            return GGML_LINESEARCH_MAXIMUM_STEP;
        }
        if (params->lbfgs.max_linesearch <= count) {
            return GGML_LINESEARCH_MAXIMUM_ITERATIONS;
        }

        (*step) *= width;
    }

    return GGML_LINESEARCH_FAIL;
}

enum ggml_opt_result ggml_opt_lbfgs(
        struct ggml_context * ctx,
        struct ggml_opt_params params,
        struct ggml_tensor * f,
        struct ggml_cgraph * gf,
        struct ggml_cgraph * gb) {
    if (params.lbfgs.linesearch == GGML_LINESEARCH_BACKTRACKING_WOLFE ||
        params.lbfgs.linesearch == GGML_LINESEARCH_BACKTRACKING_STRONG_WOLFE) {
        if (params.lbfgs.wolfe <= params.lbfgs.ftol || 1. <= params.lbfgs.wolfe) {
            return GGML_OPT_INVALID_WOLFE;
        }
    }

    gf->n_threads = params.n_threads;
    gb->n_threads = params.n_threads;

    const int m = params.lbfgs.m;

    // these will store the parameters we want to optimize
    struct ggml_tensor * ps[GGML_MAX_PARAMS];

    int np = 0;
    int nx = 0;
    for (int i = 0; i < gf->n_nodes; ++i) {
        if (gf->nodes[i]->is_param) {
            GGML_PRINT_DEBUG("found param %d: grad->op = %d\n", np, gf->nodes[i]->grad->op);

            assert(np < GGML_MAX_PARAMS);

            ps[np++] = gf->nodes[i];
            nx += ggml_nelements(gf->nodes[i]);
        }
    }

    float * x  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // current parameters
    float * xp = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // previous parameters
    float * g  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // current gradient
    float * gp = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // previous gradient
    float * d  = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data; // search direction

    float * pf = params.past > 0 ? ggml_new_tensor_1d(ctx, GGML_TYPE_F32, params.past)->data : NULL; // past function values

    float fx    = 0.0f; // cost function value
    float xnorm = 0.0f; // ||x||
    float gnorm = 0.0f; // ||g||
    float step  = 0.0f;

    // initialize x from the graph nodes
    ggml_opt_get_params(np, ps, x);

    // the L-BFGS memory
    struct ggml_lbfgs_iteration_data * lm = alloca(sizeof(struct ggml_lbfgs_iteration_data)*m);

    for (int i = 0; i < m; ++i) {
        lm[i].alpha = 0.0f;
        lm[i].ys    = 0.0f;
        lm[i].s     = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data;
        lm[i].y     = ggml_new_tensor_1d(ctx, GGML_TYPE_F32, nx)->data;
    }

    // evaluate the function value and its gradient
    {
        ggml_opt_set_params(np, ps, x);

        ggml_graph_reset  (gf);
        ggml_set_f32      (f->grad, 1.0f);
        ggml_graph_compute(ctx, gb);

        ggml_opt_get_grad(np, ps, g);

        fx = ggml_get_f32_1d(f, 0);
    }

    if (pf) {
        pf[0] = fx;
    }

    float fx_best = fx;

    // search direction = -gradient
    ggml_vec_neg_f32(nx, d, g);

    // ||x||, ||g||
    ggml_vec_norm_f32(nx, &xnorm, x);
    ggml_vec_norm_f32(nx, &gnorm, g);

    if (xnorm < 1.0f) {
        xnorm = 1.0f;
    }

    // already optimized
    if (gnorm/xnorm <= params.lbfgs.eps) {
        return GGML_OPT_OK;
    }

    // initial step
    ggml_vec_norm_inv_f32(nx, &step, d);

    int j                = 0;
    int k                = 1;
    int ls               = 0;
    int end              = 0;
    int bound            = 0;
    int n_no_improvement = 0;

    float ys   = 0.0f;
    float yy   = 0.0f;
    float beta = 0.0f;

    while (true) {
        // store the current position and gradient vectors
        ggml_vec_cpy_f32(nx, xp, x);
        ggml_vec_cpy_f32(nx, gp, g);

        ls = linesearch_backtracking(ctx, &params, nx, x, &fx, g, d, &step, xp, f, gf, gb, np, ps);

        if (ls < 0) {
            // linesearch failed - go back to the previous point and return
            ggml_vec_cpy_f32(nx, x, xp);
            ggml_vec_cpy_f32(nx, g, gp);

            return ls;
        }

        ggml_vec_norm_f32(nx, &xnorm, x);
        ggml_vec_norm_f32(nx, &gnorm, g);

        GGML_PRINT_DEBUG("f = %10.6f\n", ggml_get_f32_1d(f, 0));

        if (xnorm < 1.0) {
            xnorm = 1.0;
        }
        if (gnorm/xnorm <= params.lbfgs.eps) {
            // converged
            return GGML_OPT_OK;
        }

        // delta-based convergence test
        if (pf != NULL) {
            // need at least params.past iterations to start checking for convergence
            if (params.past <= k) {
                const float rate = (pf[k%params.past] - fx)/fx;

                if (fabs(rate) < params.delta) {
                    return GGML_OPT_OK;
                }
            }

            pf[k%params.past] = fx;
        }

        // check for improvement
        if (params.max_no_improvement > 0) {
            if (fx < fx_best) {
                fx_best = fx;
                n_no_improvement = 0;
            } else {
                n_no_improvement++;

                if (n_no_improvement >= params.max_no_improvement) {
                    return GGML_OPT_OK;
                }
            }
        }

        if (params.lbfgs.n_iter != 0 && params.lbfgs.n_iter < k + 1) {
            // reached the maximum number of iterations
            return GGML_OPT_DID_NOT_CONVERGE;
        }

        // update vectors s and y:
        //   s_{k+1} = x_{k+1} - x_{k} = \step * d_{k}.
        //   y_{k+1} = g_{k+1} - g_{k}.
        //
        ggml_vec_sub_f32(nx, lm[end].s, x, xp);
        ggml_vec_sub_f32(nx, lm[end].y, g, gp);

        // compute scalars ys and yy:
        //     ys = y^t \cdot s    -> 1 / \rho.
        //     yy = y^t \cdot y.
        //
        ggml_vec_dot_f32(nx, &ys, lm[end].y, lm[end].s);
        ggml_vec_dot_f32(nx, &yy, lm[end].y, lm[end].y);

        lm[end].ys = ys;

        // find new search direction
        //   ref: https://en.wikipedia.org/wiki/Limited-memory_BFGS

        bound = (m <= k) ? m : k;
        k++;
        end = (end + 1)%m;

        // initialize search direction with -g
        ggml_vec_neg_f32(nx, d, g);

        j = end;
        for (int i = 0; i < bound; ++i) {
            j = (j + m - 1) % m;
            // \alpha_{j} = \rho_{j} s^{t}_{j} \cdot q_{k+1}
            ggml_vec_dot_f32(nx, &lm[j].alpha, lm[j].s, d);
            lm[j].alpha /= lm[j].ys;
            // q_{i} = q_{i+1} - \alpha_{i} y_{i}
            ggml_vec_mad_f32(nx, d, lm[j].y, -lm[j].alpha);
        }

        ggml_vec_scale_f32(nx, d, ys/yy);

        for (int i = 0; i < bound; ++i) {
            // \beta_{j} = \rho_{j} y^t_{j} \cdot \gamma_{i}
            ggml_vec_dot_f32(nx, &beta, lm[j].y, d);
            beta /= lm[j].ys;
            // \gamma_{i+1} = \gamma_{i} + (\alpha_{j} - \beta_{j}) s_{j}
            ggml_vec_mad_f32(nx, d, lm[j].s, lm[j].alpha - beta);
            j = (j + 1)%m;
        }

        step = 1.0;
    }

    return GGML_OPT_DID_NOT_CONVERGE;
}

struct ggml_opt_params ggml_opt_default_params(enum ggml_opt_type type) {
    struct ggml_opt_params result;

    switch (type) {
        case GGML_OPT_ADAM:
            {
                result = (struct ggml_opt_params) {
                    .type      = GGML_OPT_ADAM,
                    .n_threads = 1,
                    .past      = 0,
                    .delta     = 1e-5f,

                    .max_no_improvement = 100,

                    .print_forward_graph  = true,
                    .print_backward_graph = true,

                    .adam = {
                        .n_iter = 10000,
                        .alpha  = 0.001f,
                        .beta1  = 0.9f,
                        .beta2  = 0.999f,
                        .eps    = 1e-8f,
                        .eps_f  = 1e-5f,
                        .eps_g  = 1e-3f,
                    },
                };
            } break;
        case GGML_OPT_LBFGS:
            {
                result = (struct ggml_opt_params) {
                    .type      = GGML_OPT_LBFGS,
                    .n_threads = 1,
                    .past      = 0,
                    .delta     = 1e-5f,

                    .max_no_improvement = 0,

                    .print_forward_graph  = true,
                    .print_backward_graph = true,

                    .lbfgs = {
                        .m              = 6,
                        .n_iter         = 100,
                        .max_linesearch = 20,

                        .eps      = 1e-5f,
                        .ftol     = 1e-4f,
                        .wolfe    = 0.9f,
                        .min_step = 1e-20f,
                        .max_step = 1e+20f,

                        .linesearch = GGML_LINESEARCH_DEFAULT,
                    },
                };
            } break;
    }

    return result;
}

enum ggml_opt_result ggml_opt(
        struct ggml_context * ctx,
        struct ggml_opt_params params,
        struct ggml_tensor * f) {
    bool free_ctx = false;
    if (ctx == NULL) {
        struct ggml_init_params params_ctx = {
            .mem_size   = 16*1024*1024,
            .mem_buffer = NULL,
        };

        ctx = ggml_init(params_ctx);
        if (ctx == NULL) {
            return GGML_OPT_NO_CONTEXT;
        }

        free_ctx = true;
    }

    enum ggml_opt_result result = GGML_OPT_OK;

    // build forward + backward compute graphs
    struct ggml_cgraph gf = ggml_build_forward (f);
    struct ggml_cgraph gb = ggml_build_backward(ctx, &gf, false);

    switch (params.type) {
        case GGML_OPT_ADAM:
            {
                result = ggml_opt_adam(ctx, params, f, &gf, &gb);
            } break;
        case GGML_OPT_LBFGS:
            {
                result = ggml_opt_lbfgs(ctx, params, f, &gf, &gb);
            } break;
    }

    if (params.print_forward_graph) {
        ggml_graph_print   (&gf);
        ggml_graph_dump_dot(&gf, NULL, "opt-forward.dot");
    }

    if (params.print_backward_graph) {
        ggml_graph_print   (&gb);
        ggml_graph_dump_dot(&gb, &gf, "opt-backward.dot");
    }

    if (free_ctx) {
        ggml_free(ctx);
    }

    return result;
}

////////////////////////////////////////////////////////////////////////////////

int ggml_cpu_has_avx(void) {
#if defined(__AVX__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_avx2(void) {
#if defined(__AVX2__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_avx512(void) {
#if defined(__AVX512F__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_neon(void) {
#if defined(__ARM_NEON)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_f16c(void) {
#if defined(__F16C__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_fp16_va(void) {
#if defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_wasm_simd(void) {
#if defined(__wasm_simd128__)
    return 1;
#else
    return 0;
#endif
}

int ggml_cpu_has_blas(void) {
#if defined(GGML_USE_ACCELERATE) || defined(GGML_USE_OPENBLAS)
    return 1;
#else
    return 0;
#endif
}

////////////////////////////////////////////////////////////////////////////////