utils.h

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// Copyright © 2023-2024 Apple Inc.
 
#pragma once
 
#include <metal_math>
#include "mlx/backend/metal/kernels/bf16.h"
#include "mlx/backend/metal/kernels/complex.h"
#include "mlx/backend/metal/kernels/defines.h"
 
typedef half float16_t;
 
// Type limits utils
 
template <typename U>
struct Limits {
  static const constant U max = metal::numeric_limits<U>::max();
  static const constant U min = metal::numeric_limits<U>::min();
  static const constant U finite_max = metal::numeric_limits<U>::max();
  static const constant U finite_min = metal::numeric_limits<U>::min();
};
 
#define instantiate_default_limit(type)                                      \
  template <>                                                                \
  struct Limits<type> {                                                      \
    static constexpr constant type max = metal::numeric_limits<type>::max(); \
    static constexpr constant type min = metal::numeric_limits<type>::min(); \
    static constexpr constant type finite_max =                              \
        metal::numeric_limits<type>::max();                                  \
    static constexpr constant type finite_min =                              \
        metal::numeric_limits<type>::min();                                  \
  };
 
instantiate_default_limit(uint8_t);
instantiate_default_limit(uint16_t);
instantiate_default_limit(uint32_t);
instantiate_default_limit(uint64_t);
instantiate_default_limit(int8_t);
instantiate_default_limit(int16_t);
instantiate_default_limit(int32_t);
instantiate_default_limit(int64_t);
 
#define instantiate_float_limit(type)             \
  template <>                                     \
  struct Limits<type> {                           \
    static constexpr constant type max =          \
        metal::numeric_limits<type>::infinity();  \
    static constexpr constant type min =          \
        -metal::numeric_limits<type>::infinity(); \
    static constexpr constant type finite_max =   \
        metal::numeric_limits<type>::max();       \
    static constexpr constant type finite_min =   \
        -metal::numeric_limits<type>::max();      \
  };
 
instantiate_float_limit(half);
instantiate_float_limit(float);
instantiate_float_limit(bfloat16_t);
 
template <>
struct Limits<bool> {
  static constexpr constant bool max = true;
  static constexpr constant bool min = false;
};
 
// Indexing utils
 
#define MLX_MTL_PRAGMA_UNROLL _Pragma("clang loop unroll(full)")
 
// Single Array with generic dims
 
template <typename stride_t>
METAL_FUNC stride_t elem_to_loc(
    uint elem,
    device const int* shape,
    device const stride_t* strides,
    int ndim) {
  stride_t loc = 0;
  for (int i = ndim - 1; i >= 0 && elem > 0; --i) {
    loc += (elem % shape[i]) * strides[i];
    elem /= shape[i];
  }
  return loc;
}
 
template <typename stride_t>
METAL_FUNC stride_t elem_to_loc(
    uint elem,
    constant const int* shape,
    constant const stride_t* strides,
    int ndim) {
  stride_t loc = 0;
  for (int i = ndim - 1; i >= 0 && elem > 0; --i) {
    loc += (elem % shape[i]) * strides[i];
    elem /= shape[i];
  }
  return loc;
}
 
// Non templated version to handle arbitrary dims
template <typename stride_t>
METAL_FUNC stride_t elem_to_loc(
    uint3 elem,
    constant const int* shape,
    constant const stride_t* strides,
    int ndim) {
  stride_t loc = elem.x * strides[ndim - 1] + elem.y * strides[ndim - 2];
  for (int d = ndim - 3; d >= 0; --d) {
    loc += (elem.z % shape[d]) * strides[d];
    elem.z /= shape[d];
  }
  return loc;
}
 
// Single Array with fixed N dims
 
template <typename stride_t>
METAL_FUNC stride_t elem_to_loc_1(uint elem, constant const stride_t& stride) {
  return elem * stride;
}
 
template <typename stride_t>
METAL_FUNC stride_t
elem_to_loc_2(uint2 elem, constant const stride_t strides[2]) {
  return elem.x * strides[1] + elem.y * strides[0];
}
 
template <typename stride_t>
METAL_FUNC stride_t
elem_to_loc_3(uint3 elem, constant const stride_t strides[3]) {
  return elem.x * strides[2] + elem.y * strides[1] + elem.z * strides[0];
}
 
template <int NDIM>
METAL_FUNC size_t elem_to_loc_nd(
    uint elem,
    device const int* shape,
    device const size_t* strides) {
  size_t loc = (elem % shape[NDIM - 1]) * strides[NDIM - 1];
 
  MLX_MTL_PRAGMA_UNROLL
  for (int d = NDIM - 2; d >= 0; --d) {
    elem /= shape[d + 1];
    loc += (elem % shape[d]) * strides[d];
  }
 
  return loc;
}
 
template <int NDIM>
METAL_FUNC size_t elem_to_loc_nd(
    uint3 elem,
    constant const int shape[NDIM],
    constant const size_t strides[NDIM]) {
  size_t loc = elem.x * strides[NDIM - 1] + elem.y * strides[NDIM - 2];
  for (int d = NDIM - 3; d >= 0; --d) {
    loc += (elem.z % shape[d]) * strides[d];
    elem.z /= shape[d];
  }
  return loc;
}
 
template <int NDIM>
METAL_FUNC int64_t elem_to_loc_nd(
    uint elem,
    constant const int shape[NDIM],
    constant const int64_t strides[NDIM]) {
  int64_t loc = (elem % shape[NDIM - 1]) * strides[NDIM - 1];
 
  MLX_MTL_PRAGMA_UNROLL
  for (int d = NDIM - 2; d >= 0; --d) {
    elem /= shape[d + 1];
    loc += (elem % shape[d]) * strides[d];
  }
 
  return loc;
}
 
template <int NDIM>
METAL_FUNC int64_t elem_to_loc_nd(
    uint3 elem,
    constant const int shape[NDIM],
    constant const int64_t strides[NDIM]) {
  int64_t loc = elem.x * strides[NDIM - 1] + elem.y * strides[NDIM - 2];
  for (int d = NDIM - 3; d >= 0; --d) {
    loc += (elem.z % shape[d]) * strides[d];
    elem.z /= shape[d];
  }
  return loc;
}
 
// Multiple Arrays with generic dims
 
METAL_FUNC uint2 elem_to_loc_2_nd(
    uint3 elem,
    constant const int* shape,
    constant const size_t* a_strides,
    constant const size_t* b_strides,
    int ndim) {
  uint2 loc = {
      static_cast<uint>(
          elem.x * a_strides[ndim - 1] + elem.y * a_strides[ndim - 2]),
      static_cast<uint>(
          elem.x * b_strides[ndim - 1] + elem.y * b_strides[ndim - 2])};
  for (int d = ndim - 3; d >= 0; --d) {
    uint l = elem.z % shape[d];
    loc.x += l * a_strides[d];
    loc.y += l * b_strides[d];
    elem.z /= shape[d];
  }
  return loc;
}
 
METAL_FUNC uint3 elem_to_loc_3_nd(
    uint3 elem,
    constant const int* shape,
    constant const size_t* a_strides,
    constant const size_t* b_strides,
    constant const size_t* c_strides,
    int ndim) {
  uint3 loc = {
      static_cast<uint>(
          elem.x * a_strides[ndim - 1] + elem.y * a_strides[ndim - 2]),
      static_cast<uint>(
          elem.x * b_strides[ndim - 1] + elem.y * b_strides[ndim - 2]),
      static_cast<uint>(
          elem.x * c_strides[ndim - 1] + elem.y * c_strides[ndim - 2])};
  for (int d = ndim - 3; d >= 0; --d) {
    uint l = elem.z % shape[d];
    loc.x += l * a_strides[d];
    loc.y += l * b_strides[d];
    loc.z += l * c_strides[d];
    elem.z /= shape[d];
  }
  return loc;
}
 
// Multiple Arrays with fixed N dims
 
template <int NDIM>
METAL_FUNC uint2 elem_to_loc_2_nd(
    uint3 elem,
    constant const int shape[NDIM],
    constant const size_t a_strides[NDIM],
    constant const size_t b_strides[NDIM]) {
  uint2 loc = {
      static_cast<uint>(
          elem.x * a_strides[NDIM - 1] + elem.y * a_strides[NDIM - 2]),
      static_cast<uint>(
          elem.x * b_strides[NDIM - 1] + elem.y * b_strides[NDIM - 2])};
  for (int d = NDIM - 3; d >= 0; --d) {
    uint l = elem.z % shape[d];
    loc.x += l * a_strides[d];
    loc.y += l * b_strides[d];
    elem.z /= shape[d];
  }
  return loc;
}
 
template <int NDIM>
METAL_FUNC uint3 elem_to_loc_3_nd(
    uint3 elem,
    constant const int shape[NDIM],
    constant const size_t a_strides[NDIM],
    constant const size_t b_strides[NDIM],
    constant const size_t c_strides[NDIM]) {
  uint3 loc = {
      static_cast<uint>(
          elem.x * a_strides[NDIM - 1] + elem.y * a_strides[NDIM - 2]),
      static_cast<uint>(
          elem.x * b_strides[NDIM - 1] + elem.y * b_strides[NDIM - 2]),
      static_cast<uint>(
          elem.x * c_strides[NDIM - 1] + elem.y * c_strides[NDIM - 2])};
  for (int d = NDIM - 3; d >= 0; --d) {
    uint l = elem.z % shape[d];
    loc.x += l * a_strides[d];
    loc.y += l * b_strides[d];
    loc.z += l * c_strides[d];
    elem.z /= shape[d];
  }
  return loc;
}
 
// Calculation utils
 
inline size_t ceildiv(size_t N, size_t M) {
  return (N + M - 1) / M;
}
 
// https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html#1202
inline float log1p(float x) {
  float xp1 = 1.0f + x;
  if (xp1 == Limits<float>::max) {
    return Limits<float>::max;
  }
  if (xp1 == 1.0f) {
    return x;
  }
 
  return x * (metal::log(xp1) / (xp1 - 1.0f));
}
 
inline bfloat16_t log1p(bfloat16_t x) {
  float xp1 = 1.0f + static_cast<float>(x);
  if (xp1 == Limits<float>::max) {
    return Limits<bfloat16_t>::max;
  }
  if (xp1 == 1.0f) {
    return x;
  }
 
  return bfloat16_t(x * (metal::log(xp1) / (xp1 - 1.0f)));
}
 
// SIMD shuffle ops
 
inline uint64_t simd_shuffle_down(uint64_t data, uint16_t delta) {
  return as_type<uint64_t>(
      metal::simd_shuffle_down(as_type<uint2>(data), delta));
}
 
inline int64_t simd_shuffle_down(int64_t data, uint16_t delta) {
  return as_type<int64_t>(
      metal::simd_shuffle_down(as_type<uint2>(data), delta));
}
 
inline bool simd_shuffle_down(bool data, uint16_t delta) {
  return simd_shuffle_down(static_cast<uint32_t>(data), delta);
}