utils.h

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// Copyright © 2023-2024 Apple Inc.
 
#pragma once
 
#include <metal_math>
 
// The correct bf16.h is included based on the metal version
// by giving the correct path to -I during compilation
// e.g. mlx/backend/metal/kernels/metal_3_0/ for Metal 3.0
#include "bf16.h"
 
#include "mlx/backend/metal/kernels/bf16_math.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;
};
 
template <>
struct Limits<complex64_t> {
  static constexpr constant complex64_t max = complex64_t(
      metal::numeric_limits<float>::infinity(),
      metal::numeric_limits<float>::infinity());
  static constexpr constant complex64_t min = complex64_t(
      -metal::numeric_limits<float>::infinity(),
      -metal::numeric_limits<float>::infinity());
};
 
// Indexing utils
 
#define MLX_MTL_PRAGMA_UNROLL _Pragma("clang loop unroll(full)")
 
// Single Array with generic dims
 
template <typename StrideT, typename IdxT = StrideT>
METAL_FUNC IdxT elem_to_loc(
    uint elem,
    constant const int* shape,
    constant const StrideT* strides,
    int ndim) {
  IdxT loc = 0;
  for (int i = ndim - 1; i >= 0 && elem > 0; --i) {
    loc += (elem % shape[i]) * IdxT(strides[i]);
    elem /= shape[i];
  }
  return loc;
}
 
template <typename StrideT, typename IdxT = StrideT>
METAL_FUNC IdxT elem_to_loc(
    StrideT elem,
    constant const int* shape,
    constant const StrideT* strides,
    int ndim) {
  IdxT loc = 0;
  for (int i = ndim - 1; i >= 0 && elem > 0; --i) {
    loc += (elem % shape[i]) * IdxT(strides[i]);
    elem /= shape[i];
  }
  return loc;
}
 
// Non templated version to handle arbitrary dims
template <typename StrideT, typename IdxT = StrideT>
METAL_FUNC IdxT elem_to_loc(
    uint3 elem,
    constant const int* shape,
    constant const StrideT* strides,
    int ndim) {
  IdxT loc =
      elem.x * IdxT(strides[ndim - 1]) + elem.y * IdxT(strides[ndim - 2]);
  for (int d = ndim - 3; d >= 0; --d) {
    loc += (elem.z % shape[d]) * IdxT(strides[d]);
    elem.z /= shape[d];
  }
  return loc;
}
 
// Single Array with fixed N dims
 
template <typename StrideT, typename IdxT = StrideT>
METAL_FUNC IdxT elem_to_loc_1(uint elem, constant const StrideT& stride) {
  return elem * IdxT(stride);
}
 
template <typename StrideT, typename IdxT = StrideT>
METAL_FUNC IdxT elem_to_loc_2(uint2 elem, constant const StrideT strides[2]) {
  return elem.x * IdxT(strides[1]) + elem.y * IdxT(strides[0]);
}
 
template <typename StrideT, typename IdxT = StrideT>
METAL_FUNC IdxT elem_to_loc_3(uint3 elem, constant const StrideT strides[3]) {
  return elem.x * IdxT(strides[2]) + elem.y * IdxT(strides[1]) +
      elem.z * IdxT(strides[0]);
}
 
// Multiple Arrays with generic dims
 
template <typename StrideT, typename IdxT = StrideT>
METAL_FUNC vec<IdxT, 2> elem_to_loc_2_nd(
    uint3 elem,
    constant const int* shape,
    constant const StrideT* a_strides,
    constant const StrideT* b_strides,
    int ndim) {
  vec<IdxT, 2> loc = {
      IdxT(
          elem.x * IdxT(a_strides[ndim - 1]) +
          IdxT(elem.y) * IdxT(a_strides[ndim - 2])),
      IdxT(
          elem.x * IdxT(b_strides[ndim - 1]) +
          elem.y * IdxT(b_strides[ndim - 2]))};
  for (int d = ndim - 3; d >= 0; --d) {
    uint l = elem.z % shape[d];
    loc.x += l * IdxT(a_strides[d]);
    loc.y += l * IdxT(b_strides[d]);
    elem.z /= shape[d];
  }
  return loc;
}
 
template <typename IdxT = size_t>
METAL_FUNC vec<IdxT, 3> 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) {
  vec<IdxT, 3> loc = {
      elem.x * IdxT(a_strides[ndim - 1]) + elem.y * IdxT(a_strides[ndim - 2]),
      elem.x * IdxT(b_strides[ndim - 1]) + elem.y * IdxT(b_strides[ndim - 2]),
      elem.x * IdxT(c_strides[ndim - 1]) + elem.y * IdxT(c_strides[ndim - 2])};
  for (int d = ndim - 3; d >= 0; --d) {
    uint l = elem.z % shape[d];
    loc.x += l * IdxT(a_strides[d]);
    loc.y += l * IdxT(b_strides[d]);
    loc.z += l * IdxT(c_strides[d]);
    elem.z /= shape[d];
  }
  return loc;
}
 
// Elem to loc in a loop utils
 
template <int DIM, typename OffsetT = size_t, bool General = true>
struct LoopedElemToLoc {
  int dim;
  LoopedElemToLoc<DIM - 1, OffsetT, General> inner_looper;
  OffsetT offset{0};
  int index{0};
 
  LoopedElemToLoc(int dim) : dim(dim), inner_looper(dim - 1) {}
 
  void next(const constant int* shape, const constant size_t* strides) {
    if (dim == 0) {
      return;
    }
    index++;
    offset += OffsetT(strides[dim - 1]);
    if (index >= shape[dim - 1]) {
      index = 0;
      inner_looper.next(shape, strides);
      offset = inner_looper.offset;
    }
  }
 
  void next(int n, const constant int* shape, const constant size_t* strides) {
    if (dim == 0) {
      return;
    }
    index += n;
    offset += n * OffsetT(strides[dim - 1]);
 
    if (index >= shape[dim - 1]) {
      int extra = index - shape[dim - 1];
      if (extra >= shape[dim - 1]) {
        inner_looper.next(1 + extra / shape[dim - 1], shape, strides);
        extra = extra % shape[dim - 1];
      } else {
        inner_looper.next(shape, strides);
      }
      index = 0;
      offset = inner_looper.offset;
      if (extra > 0) {
        next(extra, shape, strides);
      }
    }
  }
 
  OffsetT location() {
    return offset;
  }
};
 
template <typename OffsetT>
struct LoopedElemToLoc<1, OffsetT, true> {
  int dim;
  OffsetT offset{0};
  uint index{0};
 
  LoopedElemToLoc(int dim) : dim(dim) {}
 
  void next(const constant int* shape, const constant size_t* strides) {
    index++;
    if (dim > 1) {
      offset = elem_to_loc<size_t, OffsetT>(index, shape, strides, dim);
    } else {
      offset += OffsetT(strides[0]);
    }
  }
 
  void next(int n, const constant int* shape, const constant size_t* strides) {
    index += n;
    if (dim > 1) {
      offset = elem_to_loc<size_t, OffsetT>(index, shape, strides, dim);
    } else {
      offset = index * OffsetT(strides[0]);
    }
  }
 
  OffsetT location() {
    return offset;
  }
};
 
template <typename OffsetT>
struct LoopedElemToLoc<1, OffsetT, false> {
  OffsetT offset{0};
 
  LoopedElemToLoc(int) {}
 
  void next(const constant int*, const constant size_t* strides) {
    offset += OffsetT(strides[0]);
  }
 
  void next(int n, const constant int*, const constant size_t* strides) {
    offset += n * OffsetT(strides[0]);
  }
 
  OffsetT location() {
    return offset;
  }
};
 
// Calculation utils
 
template <typename T, typename U>
inline T ceildiv(T N, U 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);
}
 
inline complex64_t simd_shuffle_down(complex64_t data, uint16_t delta) {
  return complex64_t(
      simd_shuffle_down(data.real, delta), simd_shuffle_down(data.imag, delta));
}
 
inline uint64_t simd_shuffle_up(uint64_t data, uint16_t delta) {
  return as_type<uint64_t>(metal::simd_shuffle_up(as_type<uint2>(data), delta));
}
 
inline int64_t simd_shuffle_up(int64_t data, uint16_t delta) {
  return as_type<int64_t>(metal::simd_shuffle_up(as_type<uint2>(data), delta));
}
 
inline bool simd_shuffle_up(bool data, uint16_t delta) {
  return simd_shuffle_up(static_cast<uint32_t>(data), delta);
}
 
inline complex64_t simd_shuffle_up(complex64_t data, uint16_t delta) {
  return complex64_t(
      simd_shuffle_up(data.real, delta), simd_shuffle_up(data.imag, delta));
}
 
inline uint64_t
simd_shuffle_and_fill_up(uint64_t data, uint64_t filling, uint16_t delta) {
  return as_type<uint64_t>(metal::simd_shuffle_and_fill_up(
      as_type<uint2>(data), as_type<uint2>(filling), delta));
}
 
inline int64_t
simd_shuffle_and_fill_up(int64_t data, int64_t filling, uint16_t delta) {
  return as_type<int64_t>(metal::simd_shuffle_and_fill_up(
      as_type<uint2>(data), as_type<uint2>(filling), delta));
}
 
inline bool simd_shuffle_and_fill_up(bool data, bool filling, uint16_t delta) {
  return simd_shuffle_and_fill_up(
      static_cast<uint32_t>(data), static_cast<uint32_t>(filling), delta);
}
 
inline complex64_t simd_shuffle_and_fill_up(
    complex64_t data,
    complex64_t filling,
    uint16_t delta) {
  return complex64_t(
      simd_shuffle_and_fill_up(data.real, filling.real, delta),
      simd_shuffle_and_fill_up(data.imag, filling.imag, delta));
}
 
inline uint64_t simd_shuffle(uint64_t data, uint16_t lane) {
  return as_type<uint64_t>(metal::simd_shuffle(as_type<uint2>(data), lane));
}
 
inline int64_t simd_shuffle(int64_t data, uint16_t lane) {
  return as_type<int64_t>(metal::simd_shuffle(as_type<uint2>(data), lane));
}
 
inline bool simd_shuffle(bool data, uint16_t lane) {
  return simd_shuffle(static_cast<uint32_t>(data), lane);
}
 
inline complex64_t simd_shuffle(complex64_t data, uint16_t lane) {
  return complex64_t(
      simd_shuffle(data.real, lane), simd_shuffle(data.imag, lane));
}
 
// std::conditional is not included with Metal
template <bool condition, typename T, typename U>
struct ConditionalType {
  using type = U;
};
 
template <typename T, typename U>
struct ConditionalType<true, T, U> {
  using type = T;
};