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gemma.cpp/ops/dot-inl.h

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// Copyright 2024 Google LLC
// SPDX-License-Identifier: Apache-2.0
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include <stddef.h>
#include "hwy/profiler.h"
// Include guard for (potentially) SIMD code.
#if defined(THIRD_PARTY_GEMMA_CPP_DOT_TOGGLE) == defined(HWY_TARGET_TOGGLE)
#ifdef THIRD_PARTY_GEMMA_CPP_DOT_TOGGLE
#undef THIRD_PARTY_GEMMA_CPP_DOT_TOGGLE
#else
#define THIRD_PARTY_GEMMA_CPP_DOT_TOGGLE
#endif
#include "hwy/highway.h"
// After highway.h
#include "compression/compress-inl.h"
#include "ops/fp_arith-inl.h"
#include "hwy/contrib/math/math-inl.h"
HWY_BEFORE_NAMESPACE();
namespace gcpp {
namespace HWY_NAMESPACE {
namespace hn = hwy::HWY_NAMESPACE;
// Our naming convention for dot product arguments is `w` and `v`, in that
// order. This originated in `MatVec`, which computed dot products of a
// compressed "weight" type, and `BF16/float` "vectors". This implementation no
// longer restricts the types of the arguments, but we keep the names for
// consistency, also because there is still a `w_ofs` but not a `v_ofs`.
//------------------------------------------------------------------------------
// Returns 2 * sum(|w.*v|) / |sum(w.*v)|. The log2 of this value
// approximates the number of mantissa bits required for accurate computations.
// See https://en.wikipedia.org/wiki/Condition_number.
template <typename WT, typename VT>
HWY_MAYBE_UNUSED double ConditionNumber(const WT* HWY_RESTRICT w,
const VT* HWY_RESTRICT v, size_t num) {
PROFILER_FUNC;
const hn::ScalableTag<float> df;
using VF = hn::Vec<decltype(df)>;
const size_t N = hn::Lanes(df);
VF sum = hn::Zero(df);
VF sum_err = hn::Zero(df);
VF sum_abs = hn::Zero(df);
VF sum_abs_err = hn::Zero(df);
const auto packed_w = MakeSpan(w, num);
const auto packed_v = MakeSpan(v, num);
size_t i = 0;
if (num >= 2 * N) {
for (; i <= num - 2 * N; i += 2 * N) {
VF w0, w1, v0, v1;
Decompress2(df, packed_w, i, w0, w1);
Decompress2(df, packed_v, i, v0, v1);
const VF mul0 = hn::Mul(w0, v0);
const VF mul1 = hn::Mul(w1, v1);
UpdateCascadedSums(df, mul0, sum, sum_err);
UpdateCascadedSums(df, mul1, sum, sum_err);
UpdateCascadedSums(df, hn::Abs(mul0), sum_abs, sum_abs_err);
UpdateCascadedSums(df, hn::Abs(mul1), sum_abs, sum_abs_err);
}
}
size_t remaining = num - i;
HWY_DASSERT(remaining < 2 * N);
if (HWY_UNLIKELY(remaining != 0)) {
HWY_ALIGN float padded_w[2 * hn::MaxLanes(df)];
HWY_ALIGN float padded_v[2 * hn::MaxLanes(df)];
DecompressAndZeroPad(df, packed_w, i, padded_w, remaining);
DecompressAndZeroPad(df, packed_v, i, padded_v, remaining);
// 1..2 whole vectors, possibly zero-padded.
for (size_t padded_pos = 0; padded_pos < remaining; padded_pos += N) {
const VF w0 = hn::Load(df, padded_w + padded_pos);
const VF v0 = hn::Load(df, padded_v + padded_pos);
const VF mul = hn::Mul(w0, v0);
UpdateCascadedSums(df, mul, sum, sum_err);
UpdateCascadedSums(df, hn::Abs(mul), sum_abs, sum_abs_err);
}
}
const float div = hwy::ScalarAbs(ReduceCascadedSums(df, sum, sum_err));
if (div == 0.0f) return hn::GetLane(hn::Inf(df));
const double cond = 2.0 * ReduceCascadedSums(df, sum_abs, sum_abs_err) /
static_cast<double>(div);
HWY_ASSERT(cond >= 0.0);
return cond;
}
// Same, but for a single vector - just skips the product.
template <typename VT>
HWY_MAYBE_UNUSED double ConditionNumber(const VT* HWY_RESTRICT v, size_t num) {
PROFILER_FUNC;
const hn::ScalableTag<float> df;
using VF = hn::Vec<decltype(df)>;
const size_t N = hn::Lanes(df);
VF sum = hn::Zero(df);
VF sum_err = hn::Zero(df);
VF sum_abs = hn::Zero(df);
VF sum_abs_err = hn::Zero(df);
const auto packed_v = MakeSpan(v, num);
size_t i = 0;
if (num >= 2 * N) {
for (; i <= num - 2 * N; i += 2 * N) {
VF v0, v1;
Decompress2(df, packed_v, i, v0, v1);
UpdateCascadedSums(df, v0, sum, sum_err);
UpdateCascadedSums(df, v1, sum, sum_err);
UpdateCascadedSums(df, hn::Abs(v0), sum_abs, sum_abs_err);
UpdateCascadedSums(df, hn::Abs(v1), sum_abs, sum_abs_err);
}
}
size_t remaining = num - i;
HWY_DASSERT(remaining < 2 * N);
if (HWY_UNLIKELY(remaining != 0)) {
HWY_ALIGN float padded_v[2 * hn::MaxLanes(df)];
DecompressAndZeroPad(df, packed_v, i, padded_v, remaining);
// 1..2 whole vectors, possibly zero-padded.
for (size_t padded_pos = 0; padded_pos < remaining; padded_pos += N) {
const VF v0 = hn::Load(df, padded_v + padded_pos);
UpdateCascadedSums(df, v0, sum, sum_err);
UpdateCascadedSums(df, hn::Abs(v0), sum_abs, sum_abs_err);
}
}
const float div = hwy::ScalarAbs(ReduceCascadedSums(df, sum, sum_err));
if (div == 0.0f) return hn::GetLane(hn::Inf(df));
const double cond = 2.0 * ReduceCascadedSums(df, sum_abs, sum_abs_err) /
static_cast<double>(div);
HWY_ASSERT(cond >= 0.0);
return cond;
}
// f64 FMA. Inputs are both f32 promoted to f64, or any types that are either
// promoted or even DEMOTED to bf16. Runs at about half the speed of f32 FMA.
struct DotKernelDouble {
// Only `CompressTraits<float>` can `Decompress2` to `double`, so both have
// to be `float` in order to have `Raw = double`. Note that if either type is
// smaller than `float`, we may demote the other type from `float` to `BF16`.
template <typename VT, typename WT>
using Raw = hwy::If<IsF32<VT>() && IsF32<WT>(), double, BF16>;
using State = double;
// Raw = double
template <class DRaw, class VR = hn::Vec<DRaw>, HWY_IF_F64_D(DRaw)>
HWY_INLINE void Update4(DRaw dd, const VR w0, const VR w1, const VR w2,
const VR w3, const VR v0, const VR v1, const VR v2,
const VR v3, VR& sum0, VR& sum1, VR& sum2, VR& sum3,
VR&, VR&, VR&, VR&) const {
sum0 = hn::MulAdd(w0, v0, sum0);
sum1 = hn::MulAdd(w1, v1, sum1);
sum2 = hn::MulAdd(w2, v2, sum2);
sum3 = hn::MulAdd(w3, v3, sum3);
}
// Raw = BF16
template <class DRaw, class VR = hn::Vec<DRaw>, HWY_IF_BF16_D(DRaw),
class DS = hn::Repartition<double, DRaw>, class VS = hn::Vec<DS>>
HWY_INLINE void Update4(DRaw, const VR w0, const VR w1, const VR w2,
const VR w3, const VR v0, const VR v1, const VR v2,
const VR v3, VS& sum0, VS& sum1, VS& sum2, VS& sum3,
VS&, VS&, VS&, VS&) const {
const hn::Repartition<float, DRaw> df;
using VF = hn::Vec<decltype(df)>;
const VF prod0 = hn::WidenMulPairwiseAdd(df, w0, v0);
const VF prod1 = hn::WidenMulPairwiseAdd(df, w1, v1);
// Reduce to two f32 sums so we can promote them to four f64 vectors.
VF sum02, sum13;
if constexpr (HWY_NATIVE_DOT_BF16) {
// Fuse WidenMulPairwiseAdd plus Add into ReorderWidenMulAccumulate.
VF unused0 = hn::Zero(df);
VF unused1 = hn::Zero(df);
sum02 = hn::ReorderWidenMulAccumulate(df, w2, v2, prod0, unused0);
sum13 = hn::ReorderWidenMulAccumulate(df, w3, v3, prod1, unused1);
} else {
// ReorderWidenMulAccumulate does not help because we still end up with
// four accumulators.
const VF prod2 = hn::WidenMulPairwiseAdd(df, w2, v2);
const VF prod3 = hn::WidenMulPairwiseAdd(df, w3, v3);
sum02 = hn::Add(prod0, prod2);
sum13 = hn::Add(prod1, prod3);
}
const DS ds;
const VS d0 = hn::PromoteLowerTo(ds, sum02);
const VS d1 = hn::PromoteUpperTo(ds, sum02);
const VS d2 = hn::PromoteLowerTo(ds, sum13);
const VS d3 = hn::PromoteUpperTo(ds, sum13);
sum0 = hn::Add(sum0, d0);
sum1 = hn::Add(sum1, d1);
sum2 = hn::Add(sum2, d2);
sum3 = hn::Add(sum3, d3);
}
// Raw = double
template <class DRaw, class VR = hn::Vec<DRaw>, HWY_IF_F64_D(DRaw)>
HWY_INLINE void Update1(DRaw dd, const VR w0, const VR v0, VR& sum0,
VR&) const {
sum0 = hn::MulAdd(w0, v0, sum0);
}
// Raw = BF16
template <class DRaw, class VR = hn::Vec<DRaw>, HWY_IF_BF16_D(DRaw),
class DS = hn::Repartition<double, DRaw>, class VS = hn::Vec<DS>>
HWY_INLINE void Update1(DRaw, const VR w0, const VR v0, VS& sum0,
VS& extra0) const {
const hn::Repartition<float, DRaw> df;
using VF = hn::Vec<decltype(df)>;
const VF prod0 = hn::WidenMulPairwiseAdd(df, w0, v0);
const DS ds;
const VS d0 = hn::PromoteLowerTo(ds, prod0);
const VS d1 = hn::PromoteUpperTo(ds, prod0);
sum0 = hn::Add(sum0, d0);
extra0 = hn::Add(extra0, d1);
}
template <class DState, class VS = hn::Vec<DState>, HWY_IF_F64_D(DState)>
HWY_INLINE float Reduce(DState dd, VS& sum0, VS& sum1, VS& sum2, VS& sum3,
VS& extra0, VS&, VS&, VS&) const {
// Reduction tree: sum of all accumulators by pairs, then across lanes.
sum0 = hn::Add(sum0, sum1);
sum2 = hn::Add(sum2, sum3);
sum0 = hn::Add(sum0, extra0); // from Update1
sum0 = hn::Add(sum0, sum2);
return static_cast<float>(hn::ReduceSum(dd, sum0));
}
};
template <class D, typename WT, typename VT>
HWY_INLINE float DotDouble(D d, const PackedSpan<const WT>& w, size_t w_ofs,
const VT* HWY_RESTRICT vec, size_t num) {
return DecompressAndCall(d, w, w_ofs, MakeSpan(vec, num), DotKernelDouble());
}
// Algorithm 6.15 from Handbook of Floating-Point Arithmetic. This about as
// accurate as DotKernelDouble but slower, hence we only use this if f64 is
// not supported on this target.
struct DotKernelCompensated {
// The `BF16` overload uses `ReorderWidenMulAccumulate`, which requires both
// `VT` and `WT` to be `BF16`, or smaller types decompressed to `BF16`.
// Otherwise, we decompress both inputs to `float`.
template <typename VT, typename WT>
using Raw = hwy::If<IsF32<VT>() || IsF32<WT>(), float, BF16>;
using State = float;
// Raw = float
template <class DRaw, class VF = hn::Vec<DRaw>, HWY_IF_F32_D(DRaw)>
HWY_INLINE void Update4(DRaw df, const VF w0, const VF w1, const VF w2,
const VF w3, const VF v0, const VF v1, const VF v2,
const VF v3, VF& sum0, VF& sum1, VF& sum2, VF& sum3,
VF& comp0, VF& comp1, VF& comp2, VF& comp3) const {
VF perr0, perr1, perr2, perr3;
const VF prod0 = TwoProducts(df, w0, v0, perr0);
const VF prod1 = TwoProducts(df, w1, v1, perr1);
const VF prod2 = TwoProducts(df, w2, v2, perr2);
const VF prod3 = TwoProducts(df, w3, v3, perr3);
VF serr0, serr1, serr2, serr3;
sum0 = TwoSums(df, prod0, sum0, serr0);
sum1 = TwoSums(df, prod1, sum1, serr1);
sum2 = TwoSums(df, prod2, sum2, serr2);
sum3 = TwoSums(df, prod3, sum3, serr3);
comp0 = hn::Add(comp0, hn::Add(perr0, serr0));
comp1 = hn::Add(comp1, hn::Add(perr1, serr1));
comp2 = hn::Add(comp2, hn::Add(perr2, serr2));
comp3 = hn::Add(comp3, hn::Add(perr3, serr3));
}
// Raw = BF16, State = float
template <class DRaw, class VR = hn::Vec<DRaw>, HWY_IF_BF16_D(DRaw),
class DS = hn::Repartition<float, DRaw>, class VS = hn::Vec<DS>>
HWY_INLINE void Update4(DRaw, const VR w0, const VR w1, const VR w2,
const VR w3, const VR v0, const VR v1, const VR v2,
const VR v3, VS& sum0, VS& sum1, VS& sum2, VS& sum3,
VS& comp0, VS& comp1, VS& comp2, VS& comp3) const {
const DS df;
const VS prod1 = hn::WidenMulPairwiseAdd(df, w1, v1);
const VS prod2 = hn::WidenMulPairwiseAdd(df, w2, v2);
const VS prod3 = hn::WidenMulPairwiseAdd(df, w3, v3);
const VS prod0 = hn::WidenMulPairwiseAdd(df, w0, v0);
VS serr0, serr1, serr2, serr3;
sum0 = TwoSums(df, prod0, sum0, serr0);
sum1 = TwoSums(df, prod1, sum1, serr1);
sum2 = TwoSums(df, prod2, sum2, serr2);
sum3 = TwoSums(df, prod3, sum3, serr3);
comp0 = hn::Add(comp0, serr0);
comp1 = hn::Add(comp1, serr1);
comp2 = hn::Add(comp2, serr2);
comp3 = hn::Add(comp3, serr3);
}
// Raw = float
template <class DF, class VF = hn::Vec<DF>, HWY_IF_F32_D(DF)>
HWY_INLINE void Update1(DF df, const VF w0, const VF v0, VF& sum0,
VF& comp0) const {
VF perr0;
const VF prod0 = TwoProducts(df, w0, v0, perr0);
VF serr0;
sum0 = TwoSums(df, prod0, sum0, serr0);
comp0 = hn::Add(comp0, hn::Add(perr0, serr0));
}
// Raw = BF16, State = float
template <class DRaw, class VR = hn::Vec<DRaw>, HWY_IF_BF16_D(DRaw),
class DS = hn::Repartition<float, DRaw>, class VS = hn::Vec<DS>>
HWY_INLINE void Update1(DRaw, const VR w0, const VR v0, VS& sum0,
VS& comp0) const {
const DS df;
const VS prod0 = WidenMulPairwiseAdd(df, w0, v0);
VS serr0;
sum0 = TwoSums(df, prod0, sum0, serr0);
comp0 = hn::Add(comp0, serr0);
}
template <class DS, class VS = hn::Vec<DS>>
HWY_INLINE float Reduce(DS df, VS& sum0, VS& sum1, VS& sum2, VS& sum3,
VS& comp0, VS& comp1, VS& comp2, VS& comp3) const {
// Reduction tree: sum of all accumulators by pairs, then across lanes.
AssimilateCascadedSums(df, sum1, comp1, sum0, comp0);
AssimilateCascadedSums(df, sum3, comp3, sum2, comp2);
AssimilateCascadedSums(df, sum2, comp2, sum0, comp0);
return ReduceCascadedSums(df, sum0, comp0);
}
};
using DotKernelDefault =
hwy::If<HWY_HAVE_FLOAT64, DotKernelDouble, DotKernelCompensated>;
// `D` only serves to specify the vector size; its lane type is ignored.
template <class D, typename WT, typename VT>
HWY_INLINE float Dot(D d, const PackedSpan<const WT>& w, size_t w_ofs,
const VT* HWY_RESTRICT vec, size_t num) {
return DecompressAndCall(d, w, w_ofs, MakeSpan(vec, num), DotKernelDefault());
}
// Adapter for two pointers, no bounds checking.
template <typename WT, typename VT>
HWY_INLINE float Dot(const WT* HWY_RESTRICT w, const VT* vec, size_t num) {
const hn::ScalableTag<VT> d;
return Dot(d, MakeConstSpan(w, num), /*w_ofs=*/0, vec, num);
}
// NOLINTNEXTLINE(google-readability-namespace-comments)
} // namespace HWY_NAMESPACE
} // namespace gcpp
HWY_AFTER_NAMESPACE();
#endif // NOLINT
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