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@@ -1,779 +0,0 @@
-// Copyright 2015 The Gemmlowp Authors. All Rights Reserved.
-//
-// 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
-//
-// http://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.
-
-// fixedpoint.h: fixed-point arithmetic, with basic operations and
-// a few math functions such as tanh.
-
-#ifndef GEMMLOWP_INTERNAL_FIXEDPOINT_H_
-#define GEMMLOWP_INTERNAL_FIXEDPOINT_H_
-
-#include <cassert>
-#include <limits>
-
-#include "../internal/common.h"
-
-namespace gemmlowp {
-
-// Part 1: Low-level integer-arithmetic primitives.
-// The implementations here are generic implementations valid for
-// scalar types (e.g. std::int32_t). Architecture-specific SIMD types
-// (e.g. NEON int32x4_t) may be supported by providing
-// specializations for them in separate files.
-//
-// The purpose of these primitives is two-fold:
-// - They will be used to implement higher-level fixed-point
-// abstractions, namely the FixedPoint class and its arithmetic
-// operators.
-// - They will be directly used to implement some more involved
-// fixed-point computations, e.g. the fixed-point implementation
-// of math functions such as tanh.
-
-// Some compile-time traits around raw types to handle SIMD aspects:
-// number of lanes, underlying scalar type.
-template <typename tIntegerType>
-struct FixedPointRawTypeTraits {};
-
-template <>
-struct FixedPointRawTypeTraits<std::int32_t> {
- typedef std::int32_t ScalarRawType;
- static const int kLanes = 1;
-};
-
-// Returns a SIMD value duplicating a scalar value across all lanes.
-template <typename tRawType>
-tRawType Dup(typename FixedPointRawTypeTraits<tRawType>::ScalarRawType x) {
- return x;
-}
-
-// Plain bit-wise AND
-template <typename tIntegerType>
-tIntegerType BitAnd(tIntegerType a, tIntegerType b) {
- return a & b;
-}
-
-// Plain bit-wise OR
-template <typename tIntegerType>
-tIntegerType BitOr(tIntegerType a, tIntegerType b) {
- return a | b;
-}
-
-// Plain bit-wise XOR
-template <typename tIntegerType>
-tIntegerType BitXor(tIntegerType a, tIntegerType b) {
- return a ^ b;
-}
-
-// Plain bit-wise NOT
-template <typename tIntegerType>
-tIntegerType BitNot(tIntegerType a) {
- return ~a;
-}
-
-// Integer addition. Not saturating. Overflow is undefined behavior.
-template <typename tIntegerType>
-tIntegerType Add(tIntegerType a, tIntegerType b) {
- return a + b;
-}
-
-// Integer subtraction. Not saturating. Overflow is undefined behavior.
-template <typename tIntegerType>
-tIntegerType Mul(tIntegerType a, tIntegerType b) {
- return a * b;
-}
-
-template <typename tIntegerType>
-tIntegerType Sub(tIntegerType a, tIntegerType b) {
- return a - b;
-}
-
-// Integer unary negative. Not saturating. Overflow is undefined behavior.
-template <typename tIntegerType>
-tIntegerType Neg(tIntegerType a) {
- return -a;
-}
-
-// Integer arithmetic left-shift, equivalent to multiplying with a
-// power of two. Not saturating. Overflow is undefined behavior.
-template <typename tIntegerType>
-tIntegerType ShiftLeft(tIntegerType a, int offset) {
- return a << offset;
-}
-
-// Integer arithmetic right-shift. Not rounding.
-// Relying on implementation-defined, but in-practice-consistent,
-// C++ compiler behavior.
-template <typename tIntegerType>
-tIntegerType ShiftRight(tIntegerType a, int offset) {
- return a >> offset;
-}
-
-// Each bit of the result is set to the corresponding bit of either then_val or
-// else_val depending on whether the corresponding bit of if_mask is set.
-// Equivalent to the VBSL instruction in ARM NEON.
-template <typename tIntegerType>
-tIntegerType SelectUsingMask(tIntegerType if_mask, tIntegerType then_val,
- tIntegerType else_val) {
- return BitXor(BitAnd(if_mask, then_val), BitAnd(BitNot(if_mask), else_val));
-}
-
-// For each input scalar, the corresponding bits of the result are set if the
-// input scalar is non-zero.
-template <typename tIntegerType>
-tIntegerType MaskIfNonZero(tIntegerType a) {
- static const tIntegerType zero = 0;
- return a ? BitNot(zero) : zero;
-}
-
-// For each input scalar, the corresponding bits of the result are set if the
-// input scalar is zero.
-template <typename tIntegerType>
-tIntegerType MaskIfZero(tIntegerType a) {
- return MaskIfNonZero<tIntegerType>(!a);
-}
-
-// For each pair of input scalars, the corresponding bits of the result are
-// set if the input scalars are equal.
-template <typename tIntegerType>
-tIntegerType MaskIfEqual(tIntegerType a, tIntegerType b) {
- return MaskIfNonZero<tIntegerType>(a == b);
-}
-
-// For each pair of input scalars, the corresponding bits of the result are
-// set if the input scalars are not equal.
-template <typename tIntegerType>
-tIntegerType MaskIfNotEqual(tIntegerType a, tIntegerType b) {
- return MaskIfNonZero<tIntegerType>(a != b);
-}
-
-// For each pair of input scalars, the corresponding bits of the result are
-// set if the input scalars a, b satisfy a > b.
-template <typename tIntegerType>
-tIntegerType MaskIfGreaterThan(tIntegerType a, tIntegerType b) {
- return MaskIfNonZero<tIntegerType>(a > b);
-}
-
-// For each pair of input scalars, the corresponding bits of the result are
-// set if the input scalars a, b satisfy a >= b.
-template <typename tIntegerType>
-tIntegerType MaskIfGreaterThanOrEqual(tIntegerType a, tIntegerType b) {
- return MaskIfNonZero<tIntegerType>(a >= b);
-}
-
-// For each pair of input scalars, the corresponding bits of the result are
-// set if the input scalars a, b satisfy a < b.
-template <typename tIntegerType>
-tIntegerType MaskIfLessThan(tIntegerType a, tIntegerType b) {
- return MaskIfNonZero<tIntegerType>(a < b);
-}
-
-// For each pair of input scalars, the corresponding bits of the result are
-// set if the input scalars a, b satisfy a <= b.
-template <typename tIntegerType>
-tIntegerType MaskIfLessThanOrEqual(tIntegerType a, tIntegerType b) {
- return MaskIfNonZero<tIntegerType>(a <= b);
-}
-
-// Returns true if all of the input scalars are nonzero.
-// This function may currently assume that each of the input scalars has either
-// all or none of its bits set. Otherwise, its behavior is currently undefined.
-template <typename tIntegerType>
-bool All(tIntegerType a) {
- return a;
-}
-
-// Returns true if any of the input scalars are nonzero.
-// This function may currently assume that each of the input scalars has either
-// all or none of its bits set. Otherwise, its behavior is currently undefined.
-template <typename tIntegerType>
-bool Any(tIntegerType a) {
- return a;
-}
-
-// Returns (a+b)/2, rounded to the nearest integer.
-// Equivalent to VRHADD in the ARM NEON instruction set.
-template <typename IntegerType>
-IntegerType RoundingHalfSum(IntegerType a, IntegerType b) {
- static_assert(std::is_same<IntegerType, void>::value, "unimplemented");
- return a;
-}
-
-template <>
-inline std::int32_t RoundingHalfSum(std::int32_t a, std::int32_t b) {
- std::int64_t a64 = a;
- std::int64_t b64 = b;
- std::int64_t sum = a64 + b64;
- std::int64_t sign = sum >= 0 ? 1 : -1;
- return static_cast<std::int32_t>((sum + sign) / 2);
-}
-
-// Returns the integer that represents the product of two fixed-point
-// numbers, interpreting all integers as fixed-point values in the
-// interval [-1, 1), rounding to the nearest value, and saturating
-// -1 * -1 to the maximum value (since 1 is not in the half-open
-// interval [-1, 1)).
-//
-// [The explanation below specializes to std::int32_t for example purpose.]
-//
-// The mapping between IntegerType and the interval [-1, 1) is unique and
-// implied by IntegerType, which is assumed to be signed. For example,
-// for IntegerType==std::int32_t, the mapping is
-// real_value = integer_value / 2^31.
-// So in this case, and leaving aside rounding and saturating, this
-// function computes ((a / 2^31) * (b / 2^31)) * 2^31, which simplifies to
-// (a * b) / 2^31.
-//
-// The 'doubling' part in the name of this function comes from the fact that
-// this operation is very close to a "multiply-high" operation, keeping only
-// the top half bits, except that that would be effectively computing
-// (a * b) / 2^32,
-// so here we are computing 2x that, since
-// 1/2^31 = 2 * 1/2^32.
-// The idea is to use all of the available 32 bits in the destination int32
-// value.
-//
-// [End of the explanation specializing to int32.]
-//
-// This is equivalent to the VQRDMULH instruction in ARM NEON.
-template <typename IntegerType>
-IntegerType SaturatingRoundingDoublingHighMul(IntegerType a, IntegerType b) {
- static_assert(std::is_same<IntegerType, void>::value, "unimplemented");
- return a;
-}
-
-// This function implements the same computation as the ARMv7 NEON VQRDMULH
-// instruction.
-template <>
-inline std::int32_t SaturatingRoundingDoublingHighMul(std::int32_t a,
- std::int32_t b) {
- bool overflow = a == b && a == std::numeric_limits<std::int32_t>::min();
- std::int64_t a_64(a);
- std::int64_t b_64(b);
- std::int64_t ab_64 = a_64 * b_64;
- std::int32_t nudge = ab_64 >= 0 ? (1 << 30) : (1 - (1 << 30));
- std::int32_t ab_x2_high32 =
- static_cast<std::int32_t>((ab_64 + nudge) / (1ll << 31));
- return overflow ? std::numeric_limits<std::int32_t>::max() : ab_x2_high32;
-}
-
-// Correctly-rounded-to-nearest division by a power-of-two.
-// Also known as a rounding arithmetic right shift.
-template <typename IntegerType>
-inline IntegerType RoundingDivideByPOT(IntegerType x, int exponent) {
- using ScalarIntegerType =
- typename FixedPointRawTypeTraits<IntegerType>::ScalarRawType;
- static_assert(std::is_same<ScalarIntegerType, std::int32_t>::value,
- "Currently only supporting int32 scalar and SIMD types");
- assert(exponent >= 0);
- assert(exponent <= 31);
- const IntegerType mask = Dup<IntegerType>((1ll << exponent) - 1);
- const IntegerType zero = Dup<IntegerType>(0);
- const IntegerType one = Dup<IntegerType>(1);
- const IntegerType remainder = BitAnd(x, mask);
- const IntegerType threshold =
- Add(ShiftRight(mask, 1), BitAnd(MaskIfLessThan(x, zero), one));
- return Add(ShiftRight(x, exponent),
- BitAnd(MaskIfGreaterThan(remainder, threshold), one));
-}
-
-// Returns the product of a run-time integer value by a compile-time power
-// of two, with either a positive exponent (equivalent to an arithmetic
-// left shift, saturating) or a negative exponent (equivalent to an arithmetic
-// right shift, rounding to nearest).
-template <int Exponent, typename IntegerType,
- int ExponentSign = (Exponent > 0 ? 1 : Exponent < 0 ? -1 : 0)>
-struct ImplSaturatingRoundingMultiplyByPOT {};
-
-template <int Exponent, typename IntegerType>
-struct ImplSaturatingRoundingMultiplyByPOT<Exponent, IntegerType, 0> {
- static IntegerType eval(IntegerType x) { return x; }
-};
-
-template <int Exponent, typename IntegerType>
-struct ImplSaturatingRoundingMultiplyByPOT<Exponent, IntegerType, 1> {
- static IntegerType eval(IntegerType x) {
- using ScalarIntegerType =
- typename FixedPointRawTypeTraits<IntegerType>::ScalarRawType;
- static_assert(std::is_same<ScalarIntegerType, std::int32_t>::value,
- "Currently only supporting int32 scalar and SIMD types");
- const IntegerType min =
- Dup<IntegerType>(std::numeric_limits<std::int32_t>::min());
- const IntegerType max =
- Dup<IntegerType>(std::numeric_limits<std::int32_t>::max());
-
- const std::int32_t threshold = ((1 << (31 - Exponent)) - 1);
- const IntegerType positive_mask =
- MaskIfGreaterThan(x, Dup<IntegerType>(threshold));
- const IntegerType negative_mask =
- MaskIfLessThan(x, Dup<IntegerType>(-threshold));
-
- IntegerType result = ShiftLeft(x, Exponent);
- result = SelectUsingMask(positive_mask, max, result);
- result = SelectUsingMask(negative_mask, min, result);
- return result;
- }
-};
-
-template <int Exponent, typename IntegerType>
-struct ImplSaturatingRoundingMultiplyByPOT<Exponent, IntegerType, -1> {
- static IntegerType eval(IntegerType x) {
- return RoundingDivideByPOT<IntegerType>(x, -Exponent);
- }
-};
-
-template <int Exponent, typename IntegerType>
-IntegerType SaturatingRoundingMultiplyByPOT(IntegerType x) {
- return ImplSaturatingRoundingMultiplyByPOT<Exponent, IntegerType>::eval(x);
-}
-
-// Part 2: the FixedPoint class.
-
-// A FixedPoint object represents a fixed-point value stored in the underlying
-// integer type tRawType, if tRawType is a plain scalar integer type.
-// Alternatively, tRawType may be a SIMD type (e.g. NEON int32x4_t) in which
-// case a FixedPoint object represents a corresponding SIMD vector of fixed
-// point values.
-//
-// tIntegerBits describes the range of the fixed-point format: if
-// tIntegerBits == m then the range of representable values is the half-open
-// interval [-2^m; 2^m) where the open boundary on the right side means that
-// 2^m is not representable (how close the maximum representable value is to
-// it, depends on bit-depth of tRawType).
-//
-// In "Q format notation",
-// https://en.wikipedia.org/wiki/Q_(number_format)
-// we are describing the format
-// Qm.n
-// where
-// m = tIntegerBits
-// and
-// n = NumberOfBits(tRawType) - (m + 1)
-// Note that the (m + 1) in the above line is because we adopt the convention
-// that we count the integer bits exclusively of the sign bit; so (m + 1) is
-// the total number of integer bits inclusive of the sign bit.
-//
-// Accordingly, the number of integral representable values in our range
-// [-2^m ; 2^m)
-// is equal to 2^(m+1).
-template <typename tRawType, int tIntegerBits>
-class FixedPoint {
- public:
- typedef tRawType RawType;
-
- typedef FixedPointRawTypeTraits<RawType> RawTypeTraits;
- typedef typename RawTypeTraits::ScalarRawType ScalarRawType;
-
- static const int kTotalBits = 8 * sizeof(ScalarRawType);
- static const int kIntegerBits = tIntegerBits;
- static const int kFractionalBits = kTotalBits - 1 - kIntegerBits;
- static_assert(kIntegerBits >= 0 && kIntegerBits < kTotalBits,
- "bad IntegerBits");
-
- typedef FixedPoint<ScalarRawType, kIntegerBits> ScalarFixedPointType;
-
- static const ScalarRawType ScalarRawMin() {
- return std::numeric_limits<ScalarRawType>::min();
- }
-
- static const ScalarRawType ScalarRawMax() {
- return std::numeric_limits<ScalarRawType>::max();
- }
-
- static const ScalarRawType RawMin() {
- return VectorFromScalar(ScalarRawMin());
- }
-
- static const ScalarRawType RawMax() {
- return VectorFromScalar(ScalarRawMax());
- }
-
- static FixedPoint FromRaw(RawType x) {
- FixedPoint retval;
- retval.raw() = x;
- return retval;
- }
-
- static FixedPoint FromScalarRaw(ScalarRawType x) {
- FixedPoint retval;
- retval.raw() = Dup<RawType>(x);
- return retval;
- }
-
- static FixedPoint FromScalarFixedPoint(ScalarFixedPointType x) {
- return FromScalarRaw(x.raw());
- }
-
- template <int Exponent>
- static FixedPoint ConstantPOT() {
- static const int kOffset = kFractionalBits + Exponent;
- static_assert(
- kOffset < 31,
- "Constant not exactly representable in this fixed-point format");
- return FromScalarRaw(ScalarRawType(1) << kOffset);
- }
-
- static FixedPoint Zero() { return FromScalarRaw(0); }
-
- static FixedPoint One() {
- return FromScalarRaw(kIntegerBits == 0
- ? ScalarRawMax()
- : (ScalarRawType(1) << kFractionalBits));
- }
-
- static FixedPoint FromDouble(double x) {
- const double min_bound = static_cast<double>(ScalarRawMin());
- const double max_bound = static_cast<double>(ScalarRawMax());
- return FromScalarRaw(static_cast<std::int32_t>(std::min(
- std::max(round(x * static_cast<double>(1ll << kFractionalBits)),
- min_bound),
- max_bound)));
- }
-
- RawType raw() const { return i_; }
- RawType& raw() { return i_; }
-
- private:
- RawType i_;
-};
-
-// Part 3: implementation of arithmetic operators for the
-// FixedPoint class, and a few related functions.
-
-// A FixedPoint multiplication is just a
-// SaturatingRoundingDoublingHighMul operation on the underlying
-// raw integer values. The IntegerBits simply add up, as is obvious
-// from the fact that the range is [-2^IntegerBits, 2^IntegerBits).
-template <typename tRawType, int tIntegerBits_a, int tIntegerBits_b>
-FixedPoint<tRawType, tIntegerBits_a + tIntegerBits_b> operator*(
- FixedPoint<tRawType, tIntegerBits_a> a,
- FixedPoint<tRawType, tIntegerBits_b> b) {
- FixedPoint<tRawType, tIntegerBits_a + tIntegerBits_b> c;
- c.raw() = SaturatingRoundingDoublingHighMul(a.raw(), b.raw());
- return c;
-}
-
-// Tweaking IntegerBits gives exact multiplication by a power of two.
-template <int tExponent, typename tRawType, int tIntegerBits>
-FixedPoint<tRawType, tExponent + tIntegerBits> ExactMulByPot(
- FixedPoint<tRawType, tIntegerBits> a) {
- FixedPoint<tRawType, tExponent + tIntegerBits> c;
- c.raw() = a.raw();
- return c;
-}
-
-// If we want to leave IntegerBits fixed, then multiplication
-// by a power of two has to be saturating/rounding, not exact anymore.
-template <int tExponent, typename tRawType, int tIntegerBits>
-FixedPoint<tRawType, tIntegerBits> SaturatingRoundingMultiplyByPOT(
- FixedPoint<tRawType, tIntegerBits> a) {
- return FixedPoint<tRawType, tIntegerBits>::FromRaw(
- SaturatingRoundingMultiplyByPOT<tExponent>(a.raw()));
-}
-
-// Generic arithmetic operators.
-
-#define MAKE_FIXEDPOINT_UNARY_FUNC(FuncName, ImplFuncName) \
- template <typename tRawType, int tIntegerBits> \
- FixedPoint<tRawType, tIntegerBits> FuncName( \
- FixedPoint<tRawType, tIntegerBits> a) { \
- return FixedPoint<tRawType, tIntegerBits>::FromRaw(ImplFuncName(a.raw())); \
- }
-
-#define MAKE_FIXEDPOINT_BINARY_FUNC(FuncName, ImplFuncName) \
- template <typename tRawType, int tIntegerBits> \
- FixedPoint<tRawType, tIntegerBits> FuncName( \
- FixedPoint<tRawType, tIntegerBits> a, \
- FixedPoint<tRawType, tIntegerBits> b) { \
- return FixedPoint<tRawType, tIntegerBits>::FromRaw( \
- ImplFuncName(a.raw(), b.raw())); \
- }
-
-MAKE_FIXEDPOINT_UNARY_FUNC(operator-, Neg)
-MAKE_FIXEDPOINT_UNARY_FUNC(operator~, BitNot)
-MAKE_FIXEDPOINT_BINARY_FUNC(operator+, Add)
-MAKE_FIXEDPOINT_BINARY_FUNC(operator-, Sub)
-MAKE_FIXEDPOINT_BINARY_FUNC(operator&, BitAnd)
-MAKE_FIXEDPOINT_BINARY_FUNC(operator^, BitXor)
-MAKE_FIXEDPOINT_BINARY_FUNC(operator|, BitOr)
-MAKE_FIXEDPOINT_BINARY_FUNC(RoundingHalfSum, RoundingHalfSum)
-
-#undef MAKE_FIXEDPOINT_UNARY_FUNC
-#undef MAKE_FIXEDPOINT_BINARY_FUNC
-
-#define MAKE_FIXEDPOINT_UNARY_FUNC_RETURNING_RAW(FuncName) \
- template <typename tRawType, int tIntegerBits> \
- tRawType FuncName(FixedPoint<tRawType, tIntegerBits> a) { \
- return FuncName(a.raw()); \
- }
-
-#define MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(FuncName) \
- template <typename tRawType, int tIntegerBits> \
- tRawType FuncName(FixedPoint<tRawType, tIntegerBits> a, \
- FixedPoint<tRawType, tIntegerBits> b) { \
- return FuncName(a.raw(), b.raw()); \
- }
-
-MAKE_FIXEDPOINT_UNARY_FUNC_RETURNING_RAW(MaskIfZero)
-MAKE_FIXEDPOINT_UNARY_FUNC_RETURNING_RAW(MaskIfNonZero)
-MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfEqual)
-MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfNotEqual)
-MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfGreaterThan)
-MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfGreaterThanOrEqual)
-MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfLessThan)
-MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfLessThanOrEqual)
-
-#undef MAKE_FIXEDPOINT_UNARY_FUNC_RETURNING_RAW
-#undef MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW
-
-template <typename tRawType, int tIntegerBits>
-FixedPoint<tRawType, tIntegerBits> SelectUsingMask(
- tRawType if_mask, FixedPoint<tRawType, tIntegerBits> then_val,
- FixedPoint<tRawType, tIntegerBits> else_val) {
- return FixedPoint<tRawType, tIntegerBits>::FromRaw(
- SelectUsingMask(if_mask, then_val.raw(), else_val.raw()));
-}
-
-template <typename tRawType, int tIntegerBits>
-bool operator==(FixedPoint<tRawType, tIntegerBits> a,
- FixedPoint<tRawType, tIntegerBits> b) {
- return All(MaskIfEqual(a.raw(), b.raw()));
-}
-
-template <typename tRawType, int tIntegerBits>
-bool operator!=(FixedPoint<tRawType, tIntegerBits> a,
- FixedPoint<tRawType, tIntegerBits> b) {
- return !(a == b);
-}
-
-// Conversion to floating-point.
-template <typename tRawType, int tIntegerBits>
-double ToDouble(FixedPoint<tRawType, tIntegerBits> x) {
- static_assert(FixedPointRawTypeTraits<tRawType>::kLanes == 1,
- "not applicable to SIMD types");
- typedef FixedPoint<tRawType, tIntegerBits> F;
- return x.raw() / static_cast<double>(1ll << F::kFractionalBits);
-}
-
-// Rescale changes the number of IntegerBits and updates the underlying
-// raw integer value accordingly.
-template <int tIntegerBitsDst, typename tRawType, int tIntegerBitsSrc>
-FixedPoint<tRawType, tIntegerBitsDst> Rescale(
- FixedPoint<tRawType, tIntegerBitsSrc> x) {
- static const int kExponent = tIntegerBitsSrc - tIntegerBitsDst;
- FixedPoint<tRawType, tIntegerBitsDst> result;
- result.raw() = SaturatingRoundingMultiplyByPOT<kExponent>(x.raw());
- return result;
-}
-
-// CheckedFixedPointConstant allows to specify fixed-point constants
-// initialized as real numbers, in a way that does not compile floating-point
-// arithmetic in production code, yet still checks agreement with the
-// floating-point expressions when asserts are enabled.
-#ifdef GEMMLOWP_ENABLE_FIXEDPOINT_CONSTANTS_CHECKS
-template <typename FixedPointType>
-FixedPointType CheckedFixedPointConstant(
- typename FixedPointType::ScalarRawType raw_value, double double_value) {
- typedef typename FixedPointType::RawType RawType;
- const FixedPointType result = FixedPointType::FromScalarRaw(raw_value);
- assert(result == FixedPointType::FromDouble(double_value));
- return result;
-}
-#define GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(FixedPointType, ScalarRawValue, \
- DoubleValue) \
- (CheckedFixedPointConstant<FixedPointType>(ScalarRawValue, DoubleValue))
-
-#else
-#define GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(FixedPointType, ScalarRawValue, \
- DoubleValue) \
- (FixedPointType::FromScalarRaw(ScalarRawValue))
-#endif
-
-// Implementation of exponential function.
-
-// Returns exp(x) for x in [-1/4, 0).
-template <typename tRawType>
-FixedPoint<tRawType, 0> exp_on_interval_between_negative_one_quarter_and_0_excl(
- FixedPoint<tRawType, 0> a) {
- typedef FixedPoint<tRawType, 0> F;
- const F constant_term =
- GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F, 1895147668, std::exp(-1.0 / 8.0));
- const F constant_1_over_3 =
- GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F, 715827883, 1.0 / 3.0);
- // We're evaluating a Taylor expansion around -1/8, so we do the change of
- // variable: x = a + 1/8.
- // In fixed-point with 0 integer bits, 1/8 is represented by 1 << 28.
- F x = a + F::template ConstantPOT<-3>();
- F x2 = x * x;
- F x3 = x2 * x;
- F x4 = x2 * x2;
- F x4_over_4 = SaturatingRoundingMultiplyByPOT<-2>(x4);
- F x4_over_24_plus_x3_over_6_plus_x2_over_2 =
- SaturatingRoundingMultiplyByPOT<-1>(
- ((x4_over_4 + x3) * constant_1_over_3) + x2);
- return constant_term +
- constant_term * (x + x4_over_24_plus_x3_over_6_plus_x2_over_2);
-}
-
-// Returns exp(x) for x < 0.
-template <typename tRawType, int tIntegerBits>
-FixedPoint<tRawType, 0> exp_on_negative_values(
- FixedPoint<tRawType, tIntegerBits> a) {
- typedef FixedPoint<tRawType, tIntegerBits> InputF;
- typedef FixedPoint<tRawType, 0> ResultF;
- static const int kFractionalBits = InputF::kFractionalBits;
- static const int kIntegerBits = InputF::kIntegerBits;
- static const InputF kOneQuarter = InputF::template ConstantPOT<-2>();
- InputF mask = kOneQuarter - InputF::FromScalarRaw(1);
- InputF a_mod_quarter_minus_one_quarter = (a & mask) - kOneQuarter;
- ResultF result = exp_on_interval_between_negative_one_quarter_and_0_excl(
- Rescale<0>(a_mod_quarter_minus_one_quarter));
- tRawType remainder = (a_mod_quarter_minus_one_quarter - a).raw();
-
-#define GEMMLOWP_EXP_BARREL_SHIFTER(Exponent, FixedPointMultiplier) \
- if (kIntegerBits > Exponent) { \
- const ResultF kMultiplier = GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT( \
- ResultF, FixedPointMultiplier, std::exp(-std::pow(2.0, Exponent))); \
- static constexpr int kShiftAmount = \
- kIntegerBits > Exponent ? kFractionalBits + Exponent : 0; \
- result = SelectUsingMask( \
- MaskIfNonZero(BitAnd(remainder, Dup<tRawType>(1 << kShiftAmount))), \
- result * kMultiplier, result); \
- }
-
- GEMMLOWP_EXP_BARREL_SHIFTER(-2, 1672461947);
- GEMMLOWP_EXP_BARREL_SHIFTER(-1, 1302514674);
- GEMMLOWP_EXP_BARREL_SHIFTER(+0, 790015084);
- GEMMLOWP_EXP_BARREL_SHIFTER(+1, 290630308);
- GEMMLOWP_EXP_BARREL_SHIFTER(+2, 39332535);
- GEMMLOWP_EXP_BARREL_SHIFTER(+3, 720401);
- GEMMLOWP_EXP_BARREL_SHIFTER(+4, 242);
-
-#undef GEMMLOWP_EXP_BARREL_SHIFTER
-
- if (kIntegerBits > 5) {
- static const int b = kIntegerBits > 5 ? kFractionalBits + 5 : 0;
- const InputF clamp =
- GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(InputF, -(1 << b), -32.0);
- result = SelectUsingMask(MaskIfLessThan(a, clamp), ResultF::Zero(), result);
- }
-
- result = SelectUsingMask(MaskIfZero(a), ResultF::One(), result);
- return result;
-}
-
-// Implementation of tanh: (1 - exp(-2x)) / (1 + exp(-2x)).
-
-// Returns (1 - x) / (1 + x) for x in (0, 1).
-template <typename tRawType>
-FixedPoint<tRawType, 0> one_minus_x_over_one_plus_x_for_x_in_0_1(
- FixedPoint<tRawType, 0> a) {
- typedef FixedPoint<tRawType, 0> F0;
- typedef FixedPoint<tRawType, 2> F2;
- F0 half_denominator = RoundingHalfSum(a, F0::One());
- // Newton-Raphson division
- // https://en.wikipedia.org/wiki/Division_algorithm#Newton.E2.80.93Raphson_division
- // Refer to that page for the logic behind the 48/17 and 32/17 constants.
- const F2 constant_48_over_17 =
- GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F2, 1515870810, 48.0 / 17.0);
- const F2 constant_neg_32_over_17 =
- GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F2, -1010580540, -32.0 / 17.0);
- F2 x = constant_48_over_17 + half_denominator * constant_neg_32_over_17;
- for (int i = 0; i < 3; i++) {
- F2 half_denominator_times_x = half_denominator * x;
- F2 one_minus_half_denominator_times_x =
- F2::One() - half_denominator_times_x;
- x = x + Rescale<2>(x * one_minus_half_denominator_times_x);
- }
- return Rescale<0>(x - F2::One());
-}
-
-// Returns -tanh(x) for x < 0.
-template <typename tRawType, int tIntegerBits>
-FixedPoint<tRawType, 0> neg_tanh_on_negative_values(
- FixedPoint<tRawType, tIntegerBits> a) {
- return one_minus_x_over_one_plus_x_for_x_in_0_1(
- exp_on_negative_values(ExactMulByPot<1>(a)));
-}
-
-// Returns tanh(x) for any x.
-template <typename tRawType, int tIntegerBits>
-FixedPoint<tRawType, 0> tanh(FixedPoint<tRawType, tIntegerBits> a) {
- typedef FixedPoint<tRawType, tIntegerBits> InputF;
- typedef FixedPoint<tRawType, 0> ResultF;
- tRawType mask_if_negative = MaskIfLessThan(a, InputF::Zero());
- tRawType mask_if_zero = MaskIfZero(a);
- InputF n = SelectUsingMask(mask_if_negative, a, -a);
- ResultF t = neg_tanh_on_negative_values(n);
- return SelectUsingMask(mask_if_zero, ResultF::Zero(),
- SelectUsingMask(mask_if_negative, -t, t));
-}
-
-// Implementation of logistic function.
-
-// Returns 1 / (1 + x) for x in (0, 1).
-template <typename tRawType>
-FixedPoint<tRawType, 0> one_over_one_plus_x_for_x_in_0_1(
- FixedPoint<tRawType, 0> a) {
- typedef FixedPoint<tRawType, 0> F0;
- typedef FixedPoint<tRawType, 2> F2;
- F0 half_denominator = RoundingHalfSum(a, F0::One());
- // Newton-Raphson division
- // https://en.wikipedia.org/wiki/Division_algorithm#Newton.E2.80.93Raphson_division
- // Refer to that page for the logic behind the 48/17 and 32/17 constants.
- const F2 constant_48_over_17 =
- GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F2, 1515870810, 48.0 / 17.0);
- const F2 constant_neg_32_over_17 =
- GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F2, -1010580540, -32.0 / 17.0);
- F2 x = constant_48_over_17 + half_denominator * constant_neg_32_over_17;
- for (int i = 0; i < 3; i++) {
- F2 half_denominator_times_x = half_denominator * x;
- F2 one_minus_half_denominator_times_x =
- F2::One() - half_denominator_times_x;
- x = x + Rescale<2>(x * one_minus_half_denominator_times_x);
- }
- return Rescale<0>(ExactMulByPot<-1>(x));
-}
-
-// Returns logistic(x) = 1 / (1 + exp(-x)) for x > 0.
-template <typename tRawType, int tIntegerBits>
-FixedPoint<tRawType, 0> logistic_on_positive_values(
- FixedPoint<tRawType, tIntegerBits> a) {
- return one_over_one_plus_x_for_x_in_0_1(exp_on_negative_values(-a));
-}
-
-// Returns logistic(x) = 1 / (1 + exp(-x)) for any x.
-template <typename tRawType, int tIntegerBits>
-FixedPoint<tRawType, 0> logistic(FixedPoint<tRawType, tIntegerBits> a) {
- typedef FixedPoint<tRawType, tIntegerBits> InputF;
- typedef FixedPoint<tRawType, 0> ResultF;
- tRawType mask_if_positive = MaskIfGreaterThan(a, InputF::Zero());
- tRawType mask_if_zero = MaskIfZero(a);
- InputF abs_input = SelectUsingMask(mask_if_positive, a, -a);
- ResultF result_if_positive = logistic_on_positive_values(abs_input);
- ResultF result_if_negative = ResultF::One() - result_if_positive;
- const ResultF one_half =
- GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(ResultF, 1 << 30, 0.5);
- return SelectUsingMask(mask_if_zero, one_half,
- SelectUsingMask(mask_if_positive, result_if_positive,
- result_if_negative));
-}
-
-} // end namespace gemmlowp
-
-#ifdef GEMMLOWP_NEON
-#include "./fixedpoint_neon.h"
-#elif defined(GEMMLOWP_SSE4)
-#include "./fixedpoint_sse.h"
-#endif
-
-#endif // GEMMLOWP_INTERNAL_FIXEDPOINT_H_