1 // Copyright 2015 Google Inc. All Rights Reserved.
2 //
3 // Licensed under the Apache License, Version 2.0 (the "License");
4 // you may not use this file except in compliance with the License.
5 // You may obtain a copy of the License at
6 //
7 // http://www.apache.org/licenses/LICENSE-2.0
8 //
9 // Unless required by applicable law or agreed to in writing, software
10 // distributed under the License is distributed on an "AS IS" BASIS,
11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 // See the License for the specific language governing permissions and
13 // limitations under the License.
14
15 // fixedpoint.h: fixed-point arithmetic, with basic operations and
16 // a few math functions such as tanh.
17
18 // This is only used in output.h
19 // for some specific output pipeline stages (tanh); most of gemmlowp
20 // uses only plain integer arithmetic, not fixed-point arithmetic.
21 // At the most basic level, we distinguish between plain integer
22 // arithmetic and fixed-point arithmetic by the type of multiplication
23 // that is used: plain integer arithmetic uses plain (overflowing)
24 // integer multiplication, whereas fixed-point arithmetic uses
25 // "multiply-high" instructions, which means using only the most
26 // significant bits of the product, or equivalently, multiplying
27 // fixed-point numbers in the [-1 .. +1] interval.
28
29 #ifndef GEMMLOWP_INTERNAL_FIXEDPOINT_H_
30 #define GEMMLOWP_INTERNAL_FIXEDPOINT_H_
31
32 #include "common.h"
33
34 #include <limits>
35 #include <cassert>
36
37 namespace gemmlowp {
38
39 template <typename tIntegerType>
BitAnd(tIntegerType a,tIntegerType b)40 tIntegerType BitAnd(tIntegerType a, tIntegerType b) {
41 return a & b;
42 }
43
44 template <typename tIntegerType>
BitOr(tIntegerType a,tIntegerType b)45 tIntegerType BitOr(tIntegerType a, tIntegerType b) {
46 return a | b;
47 }
48
49 template <typename tIntegerType>
BitXor(tIntegerType a,tIntegerType b)50 tIntegerType BitXor(tIntegerType a, tIntegerType b) {
51 return a ^ b;
52 }
53
54 template <typename tIntegerType>
BitNot(tIntegerType a)55 tIntegerType BitNot(tIntegerType a) {
56 return ~a;
57 }
58
59 template <typename tIntegerType>
Add(tIntegerType a,tIntegerType b)60 tIntegerType Add(tIntegerType a, tIntegerType b) {
61 return a + b;
62 }
63
64 template <typename tIntegerType>
Sub(tIntegerType a,tIntegerType b)65 tIntegerType Sub(tIntegerType a, tIntegerType b) {
66 return a - b;
67 }
68
69 template <typename tIntegerType>
Neg(tIntegerType a)70 tIntegerType Neg(tIntegerType a) {
71 return -a;
72 }
73
74 template <typename tIntegerType>
ShiftLeft(tIntegerType a,int offset)75 tIntegerType ShiftLeft(tIntegerType a, int offset) {
76 return a * (1 << offset);
77 }
78
79 template <typename tIntegerType>
ShiftRight(tIntegerType a,int offset)80 tIntegerType ShiftRight(tIntegerType a, int offset) {
81 return a / (1 << offset);
82 }
83
84 template <typename tIntegerType>
SelectUsingMask(tIntegerType if_mask,tIntegerType then_val,tIntegerType else_val)85 tIntegerType SelectUsingMask(tIntegerType if_mask, tIntegerType then_val,
86 tIntegerType else_val) {
87 return BitXor(BitAnd(if_mask, then_val), BitAnd(BitNot(if_mask), else_val));
88 }
89
90 template <typename tIntegerType>
MaskIfNonZero(tIntegerType a)91 tIntegerType MaskIfNonZero(tIntegerType a) {
92 static const tIntegerType zero = 0;
93 return a ? BitNot(zero) : zero;
94 }
95
96 template <typename tIntegerType>
MaskIfZero(tIntegerType a)97 tIntegerType MaskIfZero(tIntegerType a) {
98 return MaskIfNonZero<tIntegerType>(!a);
99 }
100
101 template <typename tIntegerType>
MaskIfEqual(tIntegerType a,tIntegerType b)102 tIntegerType MaskIfEqual(tIntegerType a, tIntegerType b) {
103 return MaskIfNonZero<tIntegerType>(a == b);
104 }
105
106 template <typename tIntegerType>
MaskIfNotEqual(tIntegerType a,tIntegerType b)107 tIntegerType MaskIfNotEqual(tIntegerType a, tIntegerType b) {
108 return MaskIfNonZero<tIntegerType>(a != b);
109 }
110
111 template <typename tIntegerType>
MaskIfGreaterThan(tIntegerType a,tIntegerType b)112 tIntegerType MaskIfGreaterThan(tIntegerType a, tIntegerType b) {
113 return MaskIfNonZero<tIntegerType>(a > b);
114 }
115
116 template <typename tIntegerType>
MaskIfGreaterThanOrEqual(tIntegerType a,tIntegerType b)117 tIntegerType MaskIfGreaterThanOrEqual(tIntegerType a, tIntegerType b) {
118 return MaskIfNonZero<tIntegerType>(a >= b);
119 }
120
121 template <typename tIntegerType>
MaskIfLessThan(tIntegerType a,tIntegerType b)122 tIntegerType MaskIfLessThan(tIntegerType a, tIntegerType b) {
123 return MaskIfNonZero<tIntegerType>(a < b);
124 }
125
126 template <typename tIntegerType>
MaskIfLessThanOrEqual(tIntegerType a,tIntegerType b)127 tIntegerType MaskIfLessThanOrEqual(tIntegerType a, tIntegerType b) {
128 return MaskIfNonZero<tIntegerType>(a <= b);
129 }
130
131 template <typename tIntegerType>
All(tIntegerType a)132 bool All(tIntegerType a) {
133 return a;
134 }
135
136 template <typename tIntegerType>
Any(tIntegerType a)137 bool Any(tIntegerType a) {
138 return a;
139 }
140
141 template <typename IntegerType>
RoundingHalfSum(IntegerType a,IntegerType b)142 IntegerType RoundingHalfSum(IntegerType a, IntegerType b) {
143 static_assert(std::is_same<IntegerType, void>::value, "unimplemented");
144 return a;
145 }
146
147 template <>
RoundingHalfSum(int32_t a,int32_t b)148 inline int32_t RoundingHalfSum(int32_t a, int32_t b) {
149 int64_t a64 = a;
150 int64_t b64 = b;
151 int64_t sum = a64 + b64;
152 int64_t sign = sum >= 0 ? 1 : -1;
153 return static_cast<int32_t>((sum + sign) / 2);
154 }
155
156 template <typename IntegerType>
SaturatingRoundingDoublingHighMul(IntegerType a,IntegerType b)157 IntegerType SaturatingRoundingDoublingHighMul(IntegerType a, IntegerType b) {
158 static_assert(std::is_same<IntegerType, void>::value, "unimplemented");
159 return a;
160 }
161
162 // This function implements the same computation as the ARMv7 NEON VQRDMULH
163 // instruction.
164 template <>
SaturatingRoundingDoublingHighMul(int32_t a,int32_t b)165 inline int32_t SaturatingRoundingDoublingHighMul(int32_t a, int32_t b) {
166 bool overflow = a == b && a == std::numeric_limits<int32_t>::min();
167 int64_t a_64(a);
168 int64_t b_64(b);
169 int64_t ab_64 = a_64 * b_64;
170 int32_t nudge = ab_64 >= 0 ? (1 << 30) : (1 - (1 << 30));
171 int32_t ab_x2_high32 = static_cast<int32_t>((ab_64 + nudge) / (1ll << 31));
172 return overflow ? std::numeric_limits<int32_t>::max() : ab_x2_high32;
173 }
174
175 template <int Exponent, typename IntegerType,
176 int ExponentSign = (Exponent > 0 ? 1 : Exponent < 0 ? -1 : 0)>
177 struct ImplSaturatingRoundingMultiplyByPOT {};
178
179 template <int Exponent, typename IntegerType>
180 struct ImplSaturatingRoundingMultiplyByPOT<Exponent, IntegerType, 0> {
181 static IntegerType eval(IntegerType x) { return x; }
182 };
183
184 template <int Exponent>
185 struct ImplSaturatingRoundingMultiplyByPOT<Exponent, int32_t, 1> {
186 static int32_t eval(int32_t x) {
187 const int64_t min = std::numeric_limits<int32_t>::min();
188 const int64_t max = std::numeric_limits<int32_t>::max();
189 return x >= (1 << (31 - Exponent)) ? max : x <= -(1 << (31 - Exponent))
190 ? min
191 : x * (1 << Exponent);
192 }
193 };
194
195 template <int Exponent>
196 struct ImplSaturatingRoundingMultiplyByPOT<Exponent, int32_t, -1> {
197 static int32_t eval(int32_t x) {
198 int32_t b = (std::abs(x) & (1 << (-Exponent - 1))) >> (-Exponent - 1);
199 int32_t nudge = x >= 0 ? b : -b;
200 return x / (1 << -Exponent) + nudge;
201 }
202 };
203
204 template <int Exponent, typename IntegerType>
205 IntegerType SaturatingRoundingMultiplyByPOT(IntegerType x) {
206 return ImplSaturatingRoundingMultiplyByPOT<Exponent, IntegerType>::eval(x);
207 }
208
209 template <typename tIntegerType>
210 struct FixedPointRawTypeTraits {};
211
212 template <>
213 struct FixedPointRawTypeTraits<int32_t> {
214 typedef int32_t ScalarRawType;
215 static const int kLanes = 1;
216 };
217
218 template <typename tRawType>
219 tRawType Dup(typename FixedPointRawTypeTraits<tRawType>::ScalarRawType x) {
220 return x;
221 }
222
223 template <typename tRawType, int tIntegerBits>
224 class FixedPoint {
225 public:
226 typedef tRawType RawType;
227
228 typedef FixedPointRawTypeTraits<RawType> RawTypeTraits;
229 typedef typename RawTypeTraits::ScalarRawType ScalarRawType;
230
231 static const int kTotalBits = 8 * sizeof(ScalarRawType);
232 static const int kIntegerBits = tIntegerBits;
233 static const int kFractionalBits = kTotalBits - 1 - kIntegerBits;
234 static_assert(kIntegerBits >= 0 && kIntegerBits < kTotalBits,
235 "bad IntegerBits");
236
237 typedef FixedPoint<ScalarRawType, kIntegerBits> ScalarFixedPointType;
238
239 static const ScalarRawType ScalarRawMin() {
240 return std::numeric_limits<ScalarRawType>::min();
241 }
242
243 static const ScalarRawType ScalarRawMax() {
244 return std::numeric_limits<ScalarRawType>::max();
245 }
246
247 static const ScalarRawType RawMin() {
248 return VectorFromScalar(ScalarRawMin());
249 }
250
251 static const ScalarRawType RawMax() {
252 return VectorFromScalar(ScalarRawMax());
253 }
254
255 static FixedPoint FromRaw(RawType x) {
256 FixedPoint retval;
257 retval.raw() = x;
258 return retval;
259 }
260
261 static FixedPoint FromScalarRaw(ScalarRawType x) {
262 FixedPoint retval;
263 retval.raw() = Dup<RawType>(x);
264 return retval;
265 }
266
267 static FixedPoint FromScalarFixedPoint(ScalarFixedPointType x) {
268 return FromScalarRaw(x.raw());
269 }
270
271 template <int Exponent>
272 static FixedPoint ConstantPOT() {
273 static const int kOffset = kFractionalBits + Exponent;
274 static_assert(
275 kOffset < 31,
276 "Constant not exactly representable in this fixed-point format");
277 return FromScalarRaw(ScalarRawType(1) << kOffset);
278 }
279
280 static FixedPoint Zero() { return FromScalarRaw(0); }
281
282 static FixedPoint One() {
283 return FromScalarRaw(kIntegerBits == 0
284 ? ScalarRawMax()
285 : (ScalarRawType(1) << kFractionalBits));
286 }
287
288 RawType raw() const { return i_; }
289 RawType& raw() { return i_; }
290
291 private:
292 RawType i_;
293 };
294
295 template <typename tRawType, int tIntegerBits_a, int tIntegerBits_b>
296 FixedPoint<tRawType, tIntegerBits_a + tIntegerBits_b> operator*(
297 FixedPoint<tRawType, tIntegerBits_a> a,
298 FixedPoint<tRawType, tIntegerBits_b> b) {
299 FixedPoint<tRawType, tIntegerBits_a + tIntegerBits_b> c;
300 c.raw() = SaturatingRoundingDoublingHighMul(a.raw(), b.raw());
301 return c;
302 }
303
304 template <int tExponent, typename tRawType, int tIntegerBits>
305 FixedPoint<tRawType, tExponent + tIntegerBits> ExactMulByPot(
306 FixedPoint<tRawType, tIntegerBits> a) {
307 FixedPoint<tRawType, tExponent + tIntegerBits> c;
308 c.raw() = a.raw();
309 return c;
310 }
311
312 template <int tExponent, typename tRawType, int tIntegerBits>
313 FixedPoint<tRawType, tIntegerBits> SaturatingRoundingMultiplyByPOT(
314 FixedPoint<tRawType, tIntegerBits> a) {
315 return FixedPoint<tRawType, tIntegerBits>::FromRaw(
316 SaturatingRoundingMultiplyByPOT<tExponent>(a.raw()));
317 }
318
319 #define MAKE_FIXEDPOINT_UNARY_FUNC(FuncName, ImplFuncName) \
320 template <typename tRawType, int tIntegerBits> \
321 FixedPoint<tRawType, tIntegerBits> FuncName( \
322 FixedPoint<tRawType, tIntegerBits> a) { \
323 return FixedPoint<tRawType, tIntegerBits>::FromRaw(ImplFuncName(a.raw())); \
324 }
325
326 #define MAKE_FIXEDPOINT_BINARY_FUNC(FuncName, ImplFuncName) \
327 template <typename tRawType, int tIntegerBits> \
328 FixedPoint<tRawType, tIntegerBits> FuncName( \
329 FixedPoint<tRawType, tIntegerBits> a, \
330 FixedPoint<tRawType, tIntegerBits> b) { \
331 return FixedPoint<tRawType, tIntegerBits>::FromRaw( \
332 ImplFuncName(a.raw(), b.raw())); \
333 }
334
335 MAKE_FIXEDPOINT_UNARY_FUNC(operator-, Neg)
336 MAKE_FIXEDPOINT_UNARY_FUNC(operator~, BitNot)
337 MAKE_FIXEDPOINT_BINARY_FUNC(operator+, Add)
338 MAKE_FIXEDPOINT_BINARY_FUNC(operator-, Sub)
339 MAKE_FIXEDPOINT_BINARY_FUNC(operator&, BitAnd)
340 MAKE_FIXEDPOINT_BINARY_FUNC(operator^, BitXor)
341 MAKE_FIXEDPOINT_BINARY_FUNC(operator|, BitOr)
342 MAKE_FIXEDPOINT_BINARY_FUNC(RoundingHalfSum, RoundingHalfSum)
343
344 #undef MAKE_FIXEDPOINT_UNARY_FUNC
345 #undef MAKE_FIXEDPOINT_BINARY_FUNC
346
347 #define MAKE_FIXEDPOINT_UNARY_FUNC_RETURNING_RAW(FuncName) \
348 template <typename tRawType, int tIntegerBits> \
349 tRawType FuncName(FixedPoint<tRawType, tIntegerBits> a) { \
350 return FuncName(a.raw()); \
351 }
352
353 #define MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(FuncName) \
354 template <typename tRawType, int tIntegerBits> \
355 tRawType FuncName(FixedPoint<tRawType, tIntegerBits> a, \
356 FixedPoint<tRawType, tIntegerBits> b) { \
357 return FuncName(a.raw(), b.raw()); \
358 }
359
360 MAKE_FIXEDPOINT_UNARY_FUNC_RETURNING_RAW(MaskIfZero)
361 MAKE_FIXEDPOINT_UNARY_FUNC_RETURNING_RAW(MaskIfNonZero)
362 MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfEqual)
363 MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfNotEqual)
364 MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfGreaterThan)
365 MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfGreaterThanOrEqual)
366 MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfLessThan)
367 MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW(MaskIfLessThanOrEqual)
368
369 #undef MAKE_FIXEDPOINT_UNARY_FUNC_RETURNING_RAW
370 #undef MAKE_FIXEDPOINT_BINARY_FUNC_RETURNING_RAW
371
372 template <typename tRawType, int tIntegerBits>
373 FixedPoint<tRawType, tIntegerBits> SelectUsingMask(
374 tRawType if_mask, FixedPoint<tRawType, tIntegerBits> then_val,
375 FixedPoint<tRawType, tIntegerBits> else_val) {
376 return FixedPoint<tRawType, tIntegerBits>::FromRaw(
377 SelectUsingMask(if_mask, then_val.raw(), else_val.raw()));
378 }
379
380 template <typename tRawType, int tIntegerBits>
381 bool operator==(FixedPoint<tRawType, tIntegerBits> a,
382 FixedPoint<tRawType, tIntegerBits> b) {
383 return All(MaskIfEqual(a.raw(), b.raw()));
384 }
385
386 template <typename tRawType, int tIntegerBits>
387 bool operator!=(FixedPoint<tRawType, tIntegerBits> a,
388 FixedPoint<tRawType, tIntegerBits> b) {
389 return !(a == b);
390 }
391
392 template <typename tRawType, int tIntegerBits>
393 double ToDouble(FixedPoint<tRawType, tIntegerBits> x) {
394 static_assert(FixedPointRawTypeTraits<tRawType>::kLanes == 1,
395 "not applicable to SIMD types");
396 typedef FixedPoint<tRawType, tIntegerBits> F;
397 return x.raw() / double(1ll << F::kFractionalBits);
398 }
399
400 template <typename tRawType, int tIntegerBits>
401 FixedPoint<tRawType, tIntegerBits> ToFixedPoint(double x) {
402 typedef FixedPoint<tRawType, tIntegerBits> F;
403 return F::FromScalarRaw(static_cast<int32_t>(
404 std::min(std::max(round(x * double(1ll << F::kFractionalBits)),
405 double(F::ScalarRawMin())),
406 double(F::ScalarRawMax()))));
407 }
408
409 template <int tIntegerBitsDst, typename tRawType, int tIntegerBitsSrc>
410 FixedPoint<tRawType, tIntegerBitsDst> Rescale(
411 FixedPoint<tRawType, tIntegerBitsSrc> x) {
412 static const int kExponent = tIntegerBitsSrc - tIntegerBitsDst;
413 FixedPoint<tRawType, tIntegerBitsDst> result;
414 result.raw() = SaturatingRoundingMultiplyByPOT<kExponent>(x.raw());
415 return result;
416 }
417
418 #ifdef GEMMLOWP_ENABLE_FIXEDPOINT_CONSTANTS_CHECKS
419 template <typename FixedPointType>
420 FixedPointType CheckedFixedPointConstant(
421 typename FixedPointType::ScalarRawType raw_value, double double_value) {
422 typedef typename FixedPointType::RawType RawType;
423 static const int kIntegerBits = FixedPointType::kIntegerBits;
424 FixedPointType ref = FixedPointType::FromScalarRaw(raw_value);
425 FixedPointType check = ToFixedPoint<RawType, kIntegerBits>(double_value);
426 assert(ref == check);
427 return ref;
428 }
429 #define GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(FixedPointType, ScalarRawValue, \
430 DoubleValue) \
431 (CheckedFixedPointConstant<FixedPointType>(ScalarRawValue, DoubleValue))
432
433 #else
434 #define GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(FixedPointType, ScalarRawValue, \
435 DoubleValue) \
436 (FixedPointType::FromScalarRaw(ScalarRawValue))
437 #endif
438
439 template <typename tRawType>
440 FixedPoint<tRawType, 0> exp_on_interval_between_negative_one_quarter_and_0_excl(
441 FixedPoint<tRawType, 0> a) {
442 typedef FixedPoint<tRawType, 0> F;
443 const F constant_term =
444 GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F, 1895147668, std::exp(-1.0 / 8.0));
445 const F constant_1_over_3 =
446 GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F, 715827883, 1.0 / 3.0);
447 // We're evaluating a Taylor expansion around -1/8, so we do the change of
448 // variable: x = a + 1/8.
449 // In fixed-point with 0 integer bits, 1/8 is represented by 1 << 28.
450 F x = a + F::template ConstantPOT<-3>();
451 F x2 = x * x;
452 F x3 = x2 * x;
453 F x4 = x2 * x2;
454 F x4_over_4 = SaturatingRoundingMultiplyByPOT<-2>(x4);
455 F x4_over_24_plus_x3_over_6_plus_x2_over_2 =
456 SaturatingRoundingMultiplyByPOT<-1>(
457 ((x4_over_4 + x3) * constant_1_over_3) + x2);
458 return constant_term +
459 constant_term * (x + x4_over_24_plus_x3_over_6_plus_x2_over_2);
460 }
461
462 template <typename tRawType, int tIntegerBits>
463 FixedPoint<tRawType, 0> exp_on_negative_values(
464 FixedPoint<tRawType, tIntegerBits> a) {
465 typedef FixedPoint<tRawType, tIntegerBits> InputF;
466 typedef FixedPoint<tRawType, 0> ResultF;
467 static const int kFractionalBits = InputF::kFractionalBits;
468 static const int kIntegerBits = InputF::kIntegerBits;
469 static const InputF kOneQuarter = InputF::template ConstantPOT<-2>();
470 InputF mask = kOneQuarter - InputF::FromScalarRaw(1);
471 InputF a_mod_quarter_minus_one_quarter = (a & mask) - kOneQuarter;
472 ResultF result = exp_on_interval_between_negative_one_quarter_and_0_excl(
473 Rescale<0>(a_mod_quarter_minus_one_quarter));
474 tRawType remainder = (a_mod_quarter_minus_one_quarter - a).raw();
475
476 #define GEMMLOWP_EXP_BARREL_SHIFTER(Exponent, FixedPointMultiplier) \
477 if (kIntegerBits > Exponent) { \
478 const ResultF kMultiplier = GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT( \
479 ResultF, FixedPointMultiplier, std::exp(-std::pow(2.0, Exponent))); \
480 result = SelectUsingMask( \
481 MaskIfNonZero(BitAnd( \
482 remainder, Dup<tRawType>(1 << (kFractionalBits + Exponent)))), \
483 result * kMultiplier, result); \
484 }
485
486 GEMMLOWP_EXP_BARREL_SHIFTER(-2, 1672461947);
487 GEMMLOWP_EXP_BARREL_SHIFTER(-1, 1302514674);
488 GEMMLOWP_EXP_BARREL_SHIFTER(+0, 790015084);
489 GEMMLOWP_EXP_BARREL_SHIFTER(+1, 290630308);
490 GEMMLOWP_EXP_BARREL_SHIFTER(+2, 39332535);
491 GEMMLOWP_EXP_BARREL_SHIFTER(+3, 720401);
492 GEMMLOWP_EXP_BARREL_SHIFTER(+4, 242);
493
494 #undef GEMMLOWP_EXP_BARREL_SHIFTER
495
496 if (kIntegerBits > 5) {
497 static const int b = kIntegerBits > 5 ? kFractionalBits + 5 : 0;
498 const InputF clamp =
499 GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(InputF, -(1 << b), -32.0);
500 result = SelectUsingMask(MaskIfLessThan(a, clamp), ResultF::Zero(), result);
501 }
502
503 result = SelectUsingMask(MaskIfZero(a), ResultF::One(), result);
504 return result;
505 }
506
507 template <typename tRawType>
508 FixedPoint<tRawType, 0> one_minus_x_over_one_plus_x_for_x_in_0_1(
509 FixedPoint<tRawType, 0> a) {
510 typedef FixedPoint<tRawType, 0> F0;
511 typedef FixedPoint<tRawType, 2> F2;
512 F0 half_denominator = RoundingHalfSum(a, F0::One());
513 const F2 constant_48_over_17 =
514 GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F2, 1515870810, 48.0 / 17.0);
515 const F2 constant_neg_32_over_17 =
516 GEMMLOWP_CHECKED_FIXEDPOINT_CONSTANT(F2, -1010580540, -32.0 / 17.0);
517 F2 x = constant_48_over_17 + half_denominator * constant_neg_32_over_17;
518 for (int i = 0; i < 3; i++) {
519 F2 half_denominator_times_x = half_denominator * x;
520 F2 one_minus_half_denominator_times_x =
521 F2::One() - half_denominator_times_x;
522 x = x + Rescale<2>(x * one_minus_half_denominator_times_x);
523 }
524 return Rescale<0>(x - F2::One());
525 }
526
527 template <typename tRawType, int tIntegerBits>
528 FixedPoint<tRawType, 0> neg_tanh_on_negative_values(
529 FixedPoint<tRawType, tIntegerBits> a) {
530 return one_minus_x_over_one_plus_x_for_x_in_0_1(
531 exp_on_negative_values(ExactMulByPot<1>(a)));
532 }
533
534 template <typename tRawType, int tIntegerBits>
535 FixedPoint<tRawType, 0> tanh(FixedPoint<tRawType, tIntegerBits> a) {
536 typedef FixedPoint<tRawType, tIntegerBits> InputF;
537 typedef FixedPoint<tRawType, 0> ResultF;
538 tRawType mask_if_negative = MaskIfLessThan(a, InputF::Zero());
539 tRawType mask_if_zero = MaskIfZero(a);
540 InputF n = SelectUsingMask(mask_if_negative, a, -a);
541 ResultF t = neg_tanh_on_negative_values(n);
542 return SelectUsingMask(mask_if_zero, ResultF::Zero(),
543 SelectUsingMask(mask_if_negative, -t, t));
544 }
545
546 } // end namespace gemmlowp
547
548 #ifdef GEMMLOWP_NEON
549 #include "fixedpoint_neon.h"
550 #endif
551
552 #endif // GEMMLOWP_INTERNAL_FIXEDPOINT_H_
553