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gemma.cpp/ops/fast_ops-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 guard for non-SIMD code.
#ifndef THIRD_PARTY_GEMMA_CPP_OPS_FAST_OPS_INL_H_
#define THIRD_PARTY_GEMMA_CPP_OPS_FAST_OPS_INL_H_
#include <stddef.h>
#include "ops/ops.h"
#include "util/threading_context.h"
#include "util/zones.h"
#include "hwy/base.h"
#endif // THIRD_PARTY_GEMMA_CPP_OPS_FAST_OPS_INL_H_
// Include guard for (potentially) SIMD code.
#if defined(THIRD_PARTY_GEMMA_CPP_OPS_FAST_OPS_TOGGLE) == \
defined(HWY_TARGET_TOGGLE)
#ifdef THIRD_PARTY_GEMMA_CPP_OPS_FAST_OPS_TOGGLE
#undef THIRD_PARTY_GEMMA_CPP_OPS_FAST_OPS_TOGGLE
#else
#define THIRD_PARTY_GEMMA_CPP_OPS_FAST_OPS_TOGGLE
#endif
#include "compression/compress-inl.h"
#include "hwy/contrib/math/fast_math-inl.h"
HWY_BEFORE_NAMESPACE();
namespace gcpp {
namespace HWY_NAMESPACE {
namespace hn = hwy::HWY_NAMESPACE;
// We use the tanh approximation for gelu (also used in training).
// gelu(x) = 0.5 * x * (1 + tanh(sqrt(2/π) * (x + 0.044715 * x^3)))
// = 0.5 * x * (1 + tanh(x * (sqrt(2/π) + sqrt(2/π) * 0.044715 * x^2)))
// = 0.5 * x * (1 + tanh(x * (0.79788 + 0.035677 * x^2)))
// = x * (0.5 + 0.5 * tanh(x * (0.79788 + 0.035677 * x^2))))
//
// This uses hn::FastTanh from
// third_party/highway/hwy/contrib/math/fast_math-inl.h
template <class D, HWY_IF_F32_D(D)>
HWY_INLINE hn::Vec<D> FastGelu(D d, hn::Vec<D> v) {
const hn::Vec<D> kMul = hn::Set(d, 0.03567740813636141f);
const hn::Vec<D> kSqrt2OverPi = hn::Set(d, 0.797884560804236f);
const hn::Vec<D> kHalf = hn::Set(d, 0.5f);
const hn::Vec<D> v2 = hn::Mul(v, v);
const hn::Vec<D> arg = hn::Mul(v, hn::MulAdd(kMul, v2, kSqrt2OverPi));
const hn::Vec<D> cdf = hn::MulAdd(kHalf, hn::FastTanh(d, arg), kHalf);
return hn::Mul(v, cdf);
}
// Fast approximation of sigmoid(x) = 1 / (1 + exp(-x))
// Derived from FastTanh by substituting x/2.
template <class D, HWY_IF_F32_D(D)>
HWY_INLINE hn::Vec<D> FastSigmoid(D d, hn::Vec<D> val) {
using T = hn::TFromD<D>;
// Abs(val) and preserve sign for later for symmetric rational approximation
auto y = hn::Abs(val);
constexpr size_t kLanes = HWY_MAX_LANES_D(D);
hn::Vec<D> a, c, d_coef;
if constexpr ((kLanes >= 4 && !HWY_HAVE_SCALABLE) ||
(HWY_HAVE_SCALABLE && sizeof(T) == 4)) {
// Coefficients for P(y/2) ~ index using CF algo
const auto k0 = hn::Set(d, static_cast<T>(-0.1145426548151546));
const auto k1 = hn::Set(d, static_cast<T>(3.4556654973457404));
const auto k2 = hn::Set(d, static_cast<T>(-0.6278480784875462));
const auto k3 = hn::Set(d, static_cast<T>(0.04331384030062471));
// Index calculation: idx = P(y/2)
// Estrin's scheme
// k0 + y * k1 + y^2 * (k2 + y * k3)
const auto y2 = hn::Mul(y, y);
const auto p01 = hn::MulAdd(k1, y, k0);
const auto p23 = hn::MulAdd(k3, y, k2);
auto idx_poly = hn::MulAdd(y2, p23, p01);
// Convert to integer index
using DI = hn::RebindToSigned<D>;
auto idx_i = hn::ConvertTo(DI(), idx_poly);
// Clamp index to 7
idx_i = hn::Min(idx_i, hn::Set(DI(), 7));
HWY_ALIGN static constexpr T arr_a[8] = {
static_cast<T>(-1435.326650329326),
static_cast<T>(-96.9456723845743),
static_cast<T>(-18.628915468855695),
static_cast<T>(-5.90191111348809),
static_cast<T>(-2.356433838423728),
static_cast<T>(-1.0464246812594584),
static_cast<T>(-0.4801959711368016),
static_cast<T>(-0.2132727031175401)};
HWY_ALIGN static constexpr T arr_c[8] = {static_cast<T>(-316.5640994591445),
static_cast<T>(-49.14374182730444),
static_cast<T>(-15.69264419046708),
static_cast<T>(-6.949871926785674),
static_cast<T>(-3.513259738716989),
static_cast<T>(-1.839177585570145),
static_cast<T>(-0.9298342163526662),
static_cast<T>(-0.426230503963466)};
HWY_ALIGN static constexpr T arr_d[8] = {
static_cast<T>(-5676.517069241468), static_cast<T>(-363.0662559912978),
static_cast<T>(-60.61589604370584), static_cast<T>(-14.306713103378062),
static_cast<T>(-2.725237489187118), static_cast<T>(0.7890752292798894),
static_cast<T>(1.8089988725725492), static_cast<T>(1.9956027601801545)};
if constexpr (kLanes >= 8 && !HWY_HAVE_SCALABLE) {
auto idx = hn::IndicesFromVec(d, idx_i);
hn::CappedTag<T, 8> d8;
a = hn::TableLookupLanes(hn::ResizeBitCast(d, hn::Load(d8, arr_a)), idx);
c = hn::TableLookupLanes(hn::ResizeBitCast(d, hn::Load(d8, arr_c)), idx);
d_coef =
hn::TableLookupLanes(hn::ResizeBitCast(d, hn::Load(d8, arr_d)), idx);
} else {
auto idx = hn::IndicesFromVec(d, idx_i);
hn::FixedTag<T, 4> d4;
a = hn::TwoTablesLookupLanes(d, hn::Load(d4, arr_a),
hn::Load(d4, arr_a + 4), idx);
c = hn::TwoTablesLookupLanes(d, hn::Load(d4, arr_c),
hn::Load(d4, arr_c + 4), idx);
d_coef = hn::TwoTablesLookupLanes(d, hn::Load(d4, arr_d),
hn::Load(d4, arr_d + 4), idx);
}
} else {
// --- FALLBACK PATH: Blend Chain ---
// Thresholds for intervals
const auto t0 = hn::Set(d, static_cast<T>(0.3434497447432422));
const auto t1 = hn::Set(d, static_cast<T>(0.6955976007186494));
const auto t2 = hn::Set(d, static_cast<T>(1.1068914127668934));
const auto t3 = hn::Set(d, static_cast<T>(1.608648163822941));
const auto t4 = hn::Set(d, static_cast<T>(2.269039121646492));
const auto t5 = hn::Set(d, static_cast<T>(3.288402547357102));
const auto t6 = hn::Set(d, static_cast<T>(5.271780018997146));
// Start with highest index (7)
a = hn::Set(d, static_cast<T>(-0.2132727031175401));
c = hn::Set(d, static_cast<T>(-0.426230503963466));
d_coef = hn::Set(d, static_cast<T>(1.9956027601801545));
// If y < t6 (idx 6)
auto mask = hn::Lt(y, t6);
a = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-0.4801959711368016)),
a);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-0.9298342163526662)),
c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(1.8089988725725492)), d_coef);
// If y < t5 (idx 5)
mask = hn::Lt(y, t5);
a = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-1.0464246812594584)),
a);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-1.839177585570145)), c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(0.7890752292798894)), d_coef);
// If y < t4 (idx 4)
mask = hn::Lt(y, t4);
a = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-2.356433838423728)), a);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-3.513259738716989)), c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-2.725237489187118)), d_coef);
// If y < t3 (idx 3)
mask = hn::Lt(y, t3);
a = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-5.90191111348809)), a);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-6.949871926785674)), c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-14.306713103378062)), d_coef);
// If y < t2 (idx 2)
mask = hn::Lt(y, t2);
a = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-18.628915468855695)),
a);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-15.69264419046708)), c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-60.61589604370584)), d_coef);
// If y < t1 (idx 1)
mask = hn::Lt(y, t1);
a = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-96.9456723845743)), a);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-49.14374182730444)), c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-363.0662559912978)), d_coef);
// If y < t0 (idx 0)
mask = hn::Lt(y, t0);
a = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-1435.326650329326)), a);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-316.5640994591445)), c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-5676.517069241468)), d_coef);
}
// Math: 0.5 * tanh(y/2) = (ay + 1.0)/(cy + d_coef)
auto num = hn::MulAdd(a, y, hn::Set(d, static_cast<T>(1.0)));
auto den = hn::MulAdd(c, y, d_coef);
auto approx = hn::Div(num, den);
const auto half = hn::Set(d, static_cast<T>(0.5));
// Clamp the approx value to 0.5
approx = hn::Min(approx, half);
// sigmoid(x) = 0.5 + sign(x) * (0.5 * tanh(|x|/2))
return hn::Add(half, hn::CopySign(approx, val));
}
// Activation already has a profiler zone.
template <typename T>
static HWY_NOINLINE HWY_MAYBE_UNUSED void FastGelu(T* HWY_RESTRICT x,
size_t size) {
namespace hn = hwy::HWY_NAMESPACE;
using DF = hn::ScalableTag<float>;
using VF = hn::Vec<DF>;
DecompressAndCompressInplace(
DF(), x, size, [](DF d, VF v) HWY_ATTR -> VF { return FastGelu(d, v); });
}
template <typename T>
static HWY_NOINLINE HWY_MAYBE_UNUSED void FastSigmoid(T* HWY_RESTRICT x,
size_t size) {
namespace hn = hwy::HWY_NAMESPACE;
using DF = hn::ScalableTag<float>;
using VF = hn::Vec<DF>;
DecompressAndCompressInplace(DF(), x, size, [](DF d, VF v) HWY_ATTR -> VF {
return FastSigmoid(d, v);
});
}
// NOLINTNEXTLINE(google-readability-namespace-comments)
} // namespace HWY_NAMESPACE
} // namespace gcpp
HWY_AFTER_NAMESPACE();
#endif // NOLINT
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