1//===-- lib/fp_lib.h - Floating-point utilities -------------------*- C -*-===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// This file is a configuration header for soft-float routines in compiler-rt.
10// This file does not provide any part of the compiler-rt interface, but defines
11// many useful constants and utility routines that are used in the
12// implementation of the soft-float routines in compiler-rt.
13//
14// Assumes that float, double and long double correspond to the IEEE-754
15// binary32, binary64 and binary 128 types, respectively, and that integer
16// endianness matches floating point endianness on the target platform.
17//
18//===----------------------------------------------------------------------===//
19
20#ifndef FP_LIB_HEADER
21#define FP_LIB_HEADER
22
23#include "int_lib.h"
24#include "int_math.h"
25#include "int_types.h"
26#include <limits.h>
27#include <stdbool.h>
28#include <stdint.h>
29
30#if defined SINGLE_PRECISION
31
32typedef uint16_t half_rep_t;
33typedef uint32_t rep_t;
34typedef uint64_t twice_rep_t;
35typedef int32_t srep_t;
36typedef float fp_t;
37#define HALF_REP_C UINT16_C
38#define REP_C UINT32_C
39#define significandBits 23
40
41static __inline int rep_clz(rep_t a) { return clzsi(a); }
42
43// 32x32 --> 64 bit multiply
44static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
45 const uint64_t product = (uint64_t)a * b;
46 *hi = (rep_t)(product >> 32);
47 *lo = (rep_t)product;
48}
49COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b);
50
51#elif defined DOUBLE_PRECISION
52
53typedef uint32_t half_rep_t;
54typedef uint64_t rep_t;
55typedef int64_t srep_t;
56typedef double fp_t;
57#define HALF_REP_C UINT32_C
58#define REP_C UINT64_C
59#define significandBits 52
60
61static inline int rep_clz(rep_t a) { return __builtin_clzll(a); }
62
63#define loWord(a) (a & 0xffffffffU)
64#define hiWord(a) (a >> 32)
65
66// 64x64 -> 128 wide multiply for platforms that don't have such an operation;
67// many 64-bit platforms have this operation, but they tend to have hardware
68// floating-point, so we don't bother with a special case for them here.
69static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
70 // Each of the component 32x32 -> 64 products
71 const uint64_t plolo = loWord(a) * loWord(b);
72 const uint64_t plohi = loWord(a) * hiWord(b);
73 const uint64_t philo = hiWord(a) * loWord(b);
74 const uint64_t phihi = hiWord(a) * hiWord(b);
75 // Sum terms that contribute to lo in a way that allows us to get the carry
76 const uint64_t r0 = loWord(plolo);
77 const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
78 *lo = r0 + (r1 << 32);
79 // Sum terms contributing to hi with the carry from lo
80 *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
81}
82#undef loWord
83#undef hiWord
84
85COMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b);
86
87#elif defined QUAD_PRECISION
88#if defined(CRT_HAS_F128) && defined(CRT_HAS_128BIT)
89typedef uint64_t half_rep_t;
90typedef __uint128_t rep_t;
91typedef __int128_t srep_t;
92typedef tf_float fp_t;
93#define HALF_REP_C UINT64_C
94#define REP_C (__uint128_t)
95#if defined(CRT_HAS_IEEE_TF)
96// Note: Since there is no explicit way to tell compiler the constant is a
97// 128-bit integer, we let the constant be casted to 128-bit integer
98#define significandBits 112
99#define TF_MANT_DIG (significandBits + 1)
100
101static __inline int rep_clz(rep_t a) {
102 const union {
103 __uint128_t ll;
104#if _YUGA_BIG_ENDIAN
105 struct {
106 uint64_t high, low;
107 } s;
108#else
109 struct {
110 uint64_t low, high;
111 } s;
112#endif
113 } uu = {.ll = a};
114
115 uint64_t word;
116 uint64_t add;
117
118 if (uu.s.high) {
119 word = uu.s.high;
120 add = 0;
121 } else {
122 word = uu.s.low;
123 add = 64;
124 }
125 return __builtin_clzll(word) + add;
126}
127
128#define Word_LoMask UINT64_C(0x00000000ffffffff)
129#define Word_HiMask UINT64_C(0xffffffff00000000)
130#define Word_FullMask UINT64_C(0xffffffffffffffff)
131#define Word_1(a) (uint64_t)((a >> 96) & Word_LoMask)
132#define Word_2(a) (uint64_t)((a >> 64) & Word_LoMask)
133#define Word_3(a) (uint64_t)((a >> 32) & Word_LoMask)
134#define Word_4(a) (uint64_t)(a & Word_LoMask)
135
136// 128x128 -> 256 wide multiply for platforms that don't have such an operation;
137// many 64-bit platforms have this operation, but they tend to have hardware
138// floating-point, so we don't bother with a special case for them here.
139static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
140
141 const uint64_t product11 = Word_1(a) * Word_1(b);
142 const uint64_t product12 = Word_1(a) * Word_2(b);
143 const uint64_t product13 = Word_1(a) * Word_3(b);
144 const uint64_t product14 = Word_1(a) * Word_4(b);
145 const uint64_t product21 = Word_2(a) * Word_1(b);
146 const uint64_t product22 = Word_2(a) * Word_2(b);
147 const uint64_t product23 = Word_2(a) * Word_3(b);
148 const uint64_t product24 = Word_2(a) * Word_4(b);
149 const uint64_t product31 = Word_3(a) * Word_1(b);
150 const uint64_t product32 = Word_3(a) * Word_2(b);
151 const uint64_t product33 = Word_3(a) * Word_3(b);
152 const uint64_t product34 = Word_3(a) * Word_4(b);
153 const uint64_t product41 = Word_4(a) * Word_1(b);
154 const uint64_t product42 = Word_4(a) * Word_2(b);
155 const uint64_t product43 = Word_4(a) * Word_3(b);
156 const uint64_t product44 = Word_4(a) * Word_4(b);
157
158 const __uint128_t sum0 = (__uint128_t)product44;
159 const __uint128_t sum1 = (__uint128_t)product34 + (__uint128_t)product43;
160 const __uint128_t sum2 =
161 (__uint128_t)product24 + (__uint128_t)product33 + (__uint128_t)product42;
162 const __uint128_t sum3 = (__uint128_t)product14 + (__uint128_t)product23 +
163 (__uint128_t)product32 + (__uint128_t)product41;
164 const __uint128_t sum4 =
165 (__uint128_t)product13 + (__uint128_t)product22 + (__uint128_t)product31;
166 const __uint128_t sum5 = (__uint128_t)product12 + (__uint128_t)product21;
167 const __uint128_t sum6 = (__uint128_t)product11;
168
169 const __uint128_t r0 = (sum0 & Word_FullMask) + ((sum1 & Word_LoMask) << 32);
170 const __uint128_t r1 = (sum0 >> 64) + ((sum1 >> 32) & Word_FullMask) +
171 (sum2 & Word_FullMask) + ((sum3 << 32) & Word_HiMask);
172
173 *lo = r0 + (r1 << 64);
174 // The addition above can overflow, in which case `*lo` will be less than
175 // `r0`. Carry any overflow into `hi`.
176 const bool carry = *lo < r0;
177 *hi = (r1 >> 64) + (sum1 >> 96) + (sum2 >> 64) + (sum3 >> 32) + sum4 +
178 (sum5 << 32) + (sum6 << 64) + carry;
179}
180#undef Word_1
181#undef Word_2
182#undef Word_3
183#undef Word_4
184#undef Word_HiMask
185#undef Word_LoMask
186#undef Word_FullMask
187#endif // defined(CRT_HAS_IEEE_TF)
188#else
189typedef long double fp_t;
190#endif // defined(CRT_HAS_F128) && defined(CRT_HAS_128BIT)
191#else
192#error SINGLE_PRECISION, DOUBLE_PRECISION or QUAD_PRECISION must be defined.
193#endif
194
195#if defined(SINGLE_PRECISION) || defined(DOUBLE_PRECISION) || \
196 (defined(QUAD_PRECISION) && defined(CRT_HAS_TF_MODE))
197#define typeWidth (sizeof(rep_t) * CHAR_BIT)
198
199static __inline rep_t toRep(fp_t x) {
200 const union {
201 fp_t f;
202 rep_t i;
203 } rep = {.f = x};
204 return rep.i;
205}
206
207static __inline fp_t fromRep(rep_t x) {
208 const union {
209 fp_t f;
210 rep_t i;
211 } rep = {.i = x};
212 return rep.f;
213}
214
215#if !defined(QUAD_PRECISION) || defined(CRT_HAS_IEEE_TF)
216#define exponentBits (typeWidth - significandBits - 1)
217#define maxExponent ((1 << exponentBits) - 1)
218#define exponentBias (maxExponent >> 1)
219
220#define implicitBit (REP_C(1) << significandBits)
221#define significandMask (implicitBit - 1U)
222#define signBit (REP_C(1) << (significandBits + exponentBits))
223#define absMask (signBit - 1U)
224#define exponentMask (absMask ^ significandMask)
225#define oneRep ((rep_t)exponentBias << significandBits)
226#define infRep exponentMask
227#define quietBit (implicitBit >> 1)
228#define qnanRep (exponentMask | quietBit)
229
230static __inline int normalize(rep_t *significand) {
231 const int shift = rep_clz(a: *significand) - rep_clz(implicitBit);
232 *significand <<= shift;
233 return 1 - shift;
234}
235
236static __inline void wideLeftShift(rep_t *hi, rep_t *lo, unsigned int count) {
237 *hi = *hi << count | *lo >> (typeWidth - count);
238 *lo = *lo << count;
239}
240
241static __inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo,
242 unsigned int count) {
243 if (count < typeWidth) {
244 const bool sticky = (*lo << (typeWidth - count)) != 0;
245 *lo = *hi << (typeWidth - count) | *lo >> count | sticky;
246 *hi = *hi >> count;
247 } else if (count < 2 * typeWidth) {
248 const bool sticky = *hi << (2 * typeWidth - count) | *lo;
249 *lo = *hi >> (count - typeWidth) | sticky;
250 *hi = 0;
251 } else {
252 const bool sticky = *hi | *lo;
253 *lo = sticky;
254 *hi = 0;
255 }
256}
257
258// Implements logb methods (logb, logbf, logbl) for IEEE-754. This avoids
259// pulling in a libm dependency from compiler-rt, but is not meant to replace
260// it (i.e. code calling logb() should get the one from libm, not this), hence
261// the __compiler_rt prefix.
262static __inline fp_t __compiler_rt_logbX(fp_t x) {
263 rep_t rep = toRep(x);
264 int exp = (rep & exponentMask) >> significandBits;
265
266 // Abnormal cases:
267 // 1) +/- inf returns +inf; NaN returns NaN
268 // 2) 0.0 returns -inf
269 if (exp == maxExponent) {
270 if (((rep & signBit) == 0) || (x != x)) {
271 return x; // NaN or +inf: return x
272 } else {
273 return -x; // -inf: return -x
274 }
275 } else if (x == 0.0) {
276 // 0.0: return -inf
277 return fromRep(infRep | signBit);
278 }
279
280 if (exp != 0) {
281 // Normal number
282 return exp - exponentBias; // Unbias exponent
283 } else {
284 // Subnormal number; normalize and repeat
285 rep &= absMask;
286 const int shift = 1 - normalize(significand: &rep);
287 exp = (rep & exponentMask) >> significandBits;
288 return exp - exponentBias - shift; // Unbias exponent
289 }
290}
291
292// Avoid using scalbn from libm. Unlike libc/libm scalbn, this function never
293// sets errno on underflow/overflow.
294static __inline fp_t __compiler_rt_scalbnX(fp_t x, int y) {
295 const rep_t rep = toRep(x);
296 int exp = (rep & exponentMask) >> significandBits;
297
298 if (x == 0.0 || exp == maxExponent)
299 return x; // +/- 0.0, NaN, or inf: return x
300
301 // Normalize subnormal input.
302 rep_t sig = rep & significandMask;
303 if (exp == 0) {
304 exp += normalize(significand: &sig);
305 sig &= ~implicitBit; // clear the implicit bit again
306 }
307
308 if (__builtin_sadd_overflow(exp, y, &exp)) {
309 // Saturate the exponent, which will guarantee an underflow/overflow below.
310 exp = (y >= 0) ? INT_MAX : INT_MIN;
311 }
312
313 // Return this value: [+/-] 1.sig * 2 ** (exp - exponentBias).
314 const rep_t sign = rep & signBit;
315 if (exp >= maxExponent) {
316 // Overflow, which could produce infinity or the largest-magnitude value,
317 // depending on the rounding mode.
318 return fromRep(x: sign | ((rep_t)(maxExponent - 1) << significandBits)) * 2.0f;
319 } else if (exp <= 0) {
320 // Subnormal or underflow. Use floating-point multiply to handle truncation
321 // correctly.
322 fp_t tmp = fromRep(x: sign | (REP_C(1) << significandBits) | sig);
323 exp += exponentBias - 1;
324 if (exp < 1)
325 exp = 1;
326 tmp *= fromRep(x: (rep_t)exp << significandBits);
327 return tmp;
328 } else
329 return fromRep(x: sign | ((rep_t)exp << significandBits) | sig);
330}
331
332#endif // !defined(QUAD_PRECISION) || defined(CRT_HAS_IEEE_TF)
333
334// Avoid using fmax from libm.
335static __inline fp_t __compiler_rt_fmaxX(fp_t x, fp_t y) {
336 // If either argument is NaN, return the other argument. If both are NaN,
337 // arbitrarily return the second one. Otherwise, if both arguments are +/-0,
338 // arbitrarily return the first one.
339 return (crt_isnan(x) || x < y) ? y : x;
340}
341
342#endif
343
344#if defined(SINGLE_PRECISION)
345
346static __inline fp_t __compiler_rt_logbf(fp_t x) {
347 return __compiler_rt_logbX(x);
348}
349static __inline fp_t __compiler_rt_scalbnf(fp_t x, int y) {
350 return __compiler_rt_scalbnX(x, y);
351}
352
353#elif defined(DOUBLE_PRECISION)
354
355static __inline fp_t __compiler_rt_logb(fp_t x) {
356 return __compiler_rt_logbX(x);
357}
358static __inline fp_t __compiler_rt_scalbn(fp_t x, int y) {
359 return __compiler_rt_scalbnX(x, y);
360}
361static __inline fp_t __compiler_rt_fmax(fp_t x, fp_t y) {
362#if defined(__aarch64__) || defined(__arm64ec__)
363 // Use __builtin_fmax which turns into an fmaxnm instruction on AArch64.
364 return __builtin_fmax(x, y);
365#else
366 // __builtin_fmax frequently turns into a libm call, so inline the function.
367 return __compiler_rt_fmaxX(x, y);
368#endif
369}
370
371#elif defined(QUAD_PRECISION) && defined(CRT_HAS_TF_MODE)
372// The generic implementation only works for ieee754 floating point. For other
373// floating point types, continue to rely on the libm implementation for now.
374#if defined(CRT_HAS_IEEE_TF)
375static __inline tf_float __compiler_rt_logbtf(tf_float x) {
376 return __compiler_rt_logbX(x);
377}
378static __inline tf_float __compiler_rt_scalbntf(tf_float x, int y) {
379 return __compiler_rt_scalbnX(x, y);
380}
381static __inline tf_float __compiler_rt_fmaxtf(tf_float x, tf_float y) {
382 return __compiler_rt_fmaxX(x, y);
383}
384#define __compiler_rt_logbl __compiler_rt_logbtf
385#define __compiler_rt_scalbnl __compiler_rt_scalbntf
386#define __compiler_rt_fmaxl __compiler_rt_fmaxtf
387#define crt_fabstf crt_fabsf128
388#define crt_copysigntf crt_copysignf128
389#elif defined(CRT_LDBL_128BIT)
390static __inline tf_float __compiler_rt_logbtf(tf_float x) {
391 return crt_logbl(x);
392}
393static __inline tf_float __compiler_rt_scalbntf(tf_float x, int y) {
394 return crt_scalbnl(x, y);
395}
396static __inline tf_float __compiler_rt_fmaxtf(tf_float x, tf_float y) {
397 return crt_fmaxl(x, y);
398}
399#define __compiler_rt_logbl crt_logbl
400#define __compiler_rt_scalbnl crt_scalbnl
401#define __compiler_rt_fmaxl crt_fmaxl
402#define crt_fabstf crt_fabsl
403#define crt_copysigntf crt_copysignl
404#else
405#error Unsupported TF mode type
406#endif
407
408#endif // *_PRECISION
409
410#endif // FP_LIB_HEADER
411

source code of compiler-rt/lib/builtins/fp_lib.h