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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> b, c, d_coef;
if constexpr ((kLanes >= 4 && !HWY_HAVE_SCALABLE) ||
(HWY_HAVE_SCALABLE && sizeof(T) == 4 &&
hn::detail::IsFull(d))) {
// 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_b[8] = {
static_cast<T>(-0.0006967055197996615),
static_cast<T>(-0.010315055591476996),
static_cast<T>(-0.05367999021047822),
static_cast<T>(-0.16943664192343108),
static_cast<T>(-0.42437007298661206),
static_cast<T>(-0.9556349519550872),
static_cast<T>(-2.0824831112860647),
static_cast<T>(-4.688832585616333)};
HWY_ALIGN static constexpr T arr_c[8] = {
static_cast<T>(0.220551955463595), static_cast<T>(0.5069204289218385),
static_cast<T>(0.8423809865207907), static_cast<T>(1.1775629610724903),
static_cast<T>(1.4909222917402543), static_cast<T>(1.757582383623199),
static_cast<T>(1.9363640518503402), static_cast<T>(1.9985234759675707)};
HWY_ALIGN static constexpr T arr_d[8] = {
static_cast<T>(3.9548607753775276), static_cast<T>(3.7450486139396544),
static_cast<T>(3.253860706225495), static_cast<T>(2.4240814251983283),
static_cast<T>(1.1565092321921886), static_cast<T>(-0.7540678688218365),
static_cast<T>(-3.767209600467866), static_cast<T>(-9.357047249878605)};
// Since Lookup8 is available for HWY_MIN_BYTES / sizeof(T) >= 4, this
// condition covers all cases we encounter inside the top level if block
// inside FastSigmoid
b = hn::Lookup8(d, arr_b, idx_i);
c = hn::Lookup8(d, arr_c, idx_i);
d_coef = hn::Lookup8(d, arr_d, idx_i);
} 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));
if constexpr (HWY_REGISTERS >= 32) {
// Split into two parallel chains to reduce dependency latency.
// -- Chain 1: Indices 0 to 3 (Evaluated starting from t3 down to t0)
auto b_low = hn::Set(d, static_cast<T>(-0.16943664192343108)); // idx 3
auto c_low = hn::Set(d, static_cast<T>(1.1775629610724903));
auto d_low = hn::Set(d, static_cast<T>(2.4240814251983283));
auto mask = hn::Lt(y, t2);
b_low = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-0.05367999021047822)), b_low);
c_low = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(0.8423809865207907)), c_low);
d_low = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(3.253860706225495)), d_low);
mask = hn::Lt(y, t1);
b_low = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-0.010315055591476996)), b_low);
c_low = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(0.5069204289218385)), c_low);
d_low = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(3.7450486139396544)), d_low);
mask = hn::Lt(y, t0);
b_low = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-0.0006967055197996615)), b_low);
c_low = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(0.220551955463595)), c_low);
d_low = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(3.9548607753775276)), d_low);
// -- Chain 2: Indices 4 to 7 (Evaluated starting from t6 down to t4)
auto b_high = hn::Set(d, static_cast<T>(-4.688832585616333)); // idx 7
auto c_high = hn::Set(d, static_cast<T>(1.9985234759675707));
auto d_high = hn::Set(d, static_cast<T>(-9.357047249878605));
mask = hn::Lt(y, t6);
b_high = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-2.0824831112860647)), b_high);
c_high = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(1.9363640518503402)), c_high);
d_high = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-3.767209600467866)), d_high);
mask = hn::Lt(y, t5);
b_high = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-0.9556349519550872)), b_high);
c_high = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(1.757582383623199)), c_high);
d_high = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-0.7540678688218365)), d_high);
mask = hn::Lt(y, t4);
b_high = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-0.42437007298661206)), b_high);
c_high = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(1.4909222917402543)), c_high);
d_high = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(1.1565092321921886)), d_high);
// -- Merge the two chains
auto merge_mask = hn::Lt(y, t3);
b = hn::IfThenElse(merge_mask, b_low, b_high);
c = hn::IfThenElse(merge_mask, c_low, c_high);
d_coef = hn::IfThenElse(merge_mask, d_low, d_high);
} else {
// Start with highest index (7)
b = hn::Set(d, static_cast<T>(-4.688832585616333));
c = hn::Set(d, static_cast<T>(1.9985234759675707));
d_coef = hn::Set(d, static_cast<T>(-9.357047249878605));
// If y < t6 (idx 6)
auto mask = hn::Lt(y, t6);
b = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-2.0824831112860647)),
b);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(1.9363640518503402)),
c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-3.767209600467866)), d_coef);
// If y < t5 (idx 5)
mask = hn::Lt(y, t5);
b = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-0.9556349519550872)),
b);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(1.757582383623199)),
c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(-0.7540678688218365)), d_coef);
// If y < t4 (idx 4)
mask = hn::Lt(y, t4);
b = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-0.42437007298661206)),
b);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(1.4909222917402543)),
c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(1.1565092321921886)), d_coef);
// If y < t3 (idx 3)
mask = hn::Lt(y, t3);
b = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-0.16943664192343108)),
b);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(1.1775629610724903)),
c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(2.4240814251983283)), d_coef);
// If y < t2 (idx 2)
mask = hn::Lt(y, t2);
b = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(-0.05367999021047822)),
b);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(0.8423809865207907)),
c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(3.253860706225495)), d_coef);
// If y < t1 (idx 1)
mask = hn::Lt(y, t1);
b = hn::IfThenElse(mask,
hn::Set(d, static_cast<T>(-0.010315055591476996)), b);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(0.5069204289218385)),
c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(3.7450486139396544)), d_coef);
// If y < t0 (idx 0)
mask = hn::Lt(y, t0);
b = hn::IfThenElse(mask,
hn::Set(d, static_cast<T>(-0.0006967055197996615)), b);
c = hn::IfThenElse(mask, hn::Set(d, static_cast<T>(0.220551955463595)),
c);
d_coef = hn::IfThenElse(
mask, hn::Set(d, static_cast<T>(3.9548607753775276)), d_coef);
}
}
// Math: 0.5 * tanh(y/2) = (y + b)/(cy + d_coef)
auto num = hn::Add(y, b);
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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