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 <limits.h>
26#include <stdbool.h>
27#include <stdint.h>
28
29#if defined SINGLE_PRECISION
30
31typedef uint16_t half_rep_t;
32typedef uint32_t rep_t;
33typedef uint64_t twice_rep_t;
34typedef int32_t srep_t;
35typedef float fp_t;
36#define HALF_REP_C UINT16_C
37#define REP_C UINT32_C
38#define significandBits 23
39
40static __inline int rep_clz(rep_t a) { return clzsi(a); }
41
42// 32x32 --> 64 bit multiply
43static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
44 const uint64_t product = (uint64_t)a * b;
45 *hi = product >> 32;
46 *lo = product;
47}
48COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b);
49
50#elif defined DOUBLE_PRECISION
51
52typedef uint32_t half_rep_t;
53typedef uint64_t rep_t;
54typedef int64_t srep_t;
55typedef double fp_t;
56#define HALF_REP_C UINT32_C
57#define REP_C UINT64_C
58#define significandBits 52
59
60static __inline int rep_clz(rep_t a) {
61#if defined __LP64__
62 return __builtin_clzl(a);
63#else
64 if (a & REP_C(0xffffffff00000000))
65 return clzsi(a >> 32);
66 else
67 return 32 + clzsi(a & REP_C(0xffffffff));
68#endif
69}
70
71#define loWord(a) (a & 0xffffffffU)
72#define hiWord(a) (a >> 32)
73
74// 64x64 -> 128 wide multiply for platforms that don't have such an operation;
75// many 64-bit platforms have this operation, but they tend to have hardware
76// floating-point, so we don't bother with a special case for them here.
77static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
78 // Each of the component 32x32 -> 64 products
79 const uint64_t plolo = loWord(a) * loWord(b);
80 const uint64_t plohi = loWord(a) * hiWord(b);
81 const uint64_t philo = hiWord(a) * loWord(b);
82 const uint64_t phihi = hiWord(a) * hiWord(b);
83 // Sum terms that contribute to lo in a way that allows us to get the carry
84 const uint64_t r0 = loWord(plolo);
85 const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
86 *lo = r0 + (r1 << 32);
87 // Sum terms contributing to hi with the carry from lo
88 *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
89}
90#undef loWord
91#undef hiWord
92
93COMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b);
94
95#elif defined QUAD_PRECISION
96#if defined(CRT_HAS_TF_MODE)
97typedef uint64_t half_rep_t;
98typedef __uint128_t rep_t;
99typedef __int128_t srep_t;
100typedef tf_float fp_t;
101#define HALF_REP_C UINT64_C
102#define REP_C (__uint128_t)
103// Note: Since there is no explicit way to tell compiler the constant is a
104// 128-bit integer, we let the constant be casted to 128-bit integer
105#define significandBits 112
106#define TF_MANT_DIG (significandBits + 1)
107
108static __inline int rep_clz(rep_t a) {
109 const union {
110 __uint128_t ll;
111#if _YUGA_BIG_ENDIAN
112 struct {
113 uint64_t high, low;
114 } s;
115#else
116 struct {
117 uint64_t low, high;
118 } s;
119#endif
120 } uu = {.ll = a};
121
122 uint64_t word;
123 uint64_t add;
124
125 if (uu.s.high) {
126 word = uu.s.high;
127 add = 0;
128 } else {
129 word = uu.s.low;
130 add = 64;
131 }
132 return __builtin_clzll(word) + add;
133}
134
135#define Word_LoMask UINT64_C(0x00000000ffffffff)
136#define Word_HiMask UINT64_C(0xffffffff00000000)
137#define Word_FullMask UINT64_C(0xffffffffffffffff)
138#define Word_1(a) (uint64_t)((a >> 96) & Word_LoMask)
139#define Word_2(a) (uint64_t)((a >> 64) & Word_LoMask)
140#define Word_3(a) (uint64_t)((a >> 32) & Word_LoMask)
141#define Word_4(a) (uint64_t)(a & Word_LoMask)
142
143// 128x128 -> 256 wide multiply for platforms that don't have such an operation;
144// many 64-bit platforms have this operation, but they tend to have hardware
145// floating-point, so we don't bother with a special case for them here.
146static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
147
148 const uint64_t product11 = Word_1(a) * Word_1(b);
149 const uint64_t product12 = Word_1(a) * Word_2(b);
150 const uint64_t product13 = Word_1(a) * Word_3(b);
151 const uint64_t product14 = Word_1(a) * Word_4(b);
152 const uint64_t product21 = Word_2(a) * Word_1(b);
153 const uint64_t product22 = Word_2(a) * Word_2(b);
154 const uint64_t product23 = Word_2(a) * Word_3(b);
155 const uint64_t product24 = Word_2(a) * Word_4(b);
156 const uint64_t product31 = Word_3(a) * Word_1(b);
157 const uint64_t product32 = Word_3(a) * Word_2(b);
158 const uint64_t product33 = Word_3(a) * Word_3(b);
159 const uint64_t product34 = Word_3(a) * Word_4(b);
160 const uint64_t product41 = Word_4(a) * Word_1(b);
161 const uint64_t product42 = Word_4(a) * Word_2(b);
162 const uint64_t product43 = Word_4(a) * Word_3(b);
163 const uint64_t product44 = Word_4(a) * Word_4(b);
164
165 const __uint128_t sum0 = (__uint128_t)product44;
166 const __uint128_t sum1 = (__uint128_t)product34 + (__uint128_t)product43;
167 const __uint128_t sum2 =
168 (__uint128_t)product24 + (__uint128_t)product33 + (__uint128_t)product42;
169 const __uint128_t sum3 = (__uint128_t)product14 + (__uint128_t)product23 +
170 (__uint128_t)product32 + (__uint128_t)product41;
171 const __uint128_t sum4 =
172 (__uint128_t)product13 + (__uint128_t)product22 + (__uint128_t)product31;
173 const __uint128_t sum5 = (__uint128_t)product12 + (__uint128_t)product21;
174 const __uint128_t sum6 = (__uint128_t)product11;
175
176 const __uint128_t r0 = (sum0 & Word_FullMask) + ((sum1 & Word_LoMask) << 32);
177 const __uint128_t r1 = (sum0 >> 64) + ((sum1 >> 32) & Word_FullMask) +
178 (sum2 & Word_FullMask) + ((sum3 << 32) & Word_HiMask);
179
180 *lo = r0 + (r1 << 64);
181 *hi = (r1 >> 64) + (sum1 >> 96) + (sum2 >> 64) + (sum3 >> 32) + sum4 +
182 (sum5 << 32) + (sum6 << 64);
183}
184#undef Word_1
185#undef Word_2
186#undef Word_3
187#undef Word_4
188#undef Word_HiMask
189#undef Word_LoMask
190#undef Word_FullMask
191#endif // defined(CRT_HAS_TF_MODE)
192#else
193#error SINGLE_PRECISION, DOUBLE_PRECISION or QUAD_PRECISION must be defined.
194#endif
195
196#if defined(SINGLE_PRECISION) || defined(DOUBLE_PRECISION) || \
197 (defined(QUAD_PRECISION) && defined(CRT_HAS_TF_MODE))
198#define typeWidth (sizeof(rep_t) * CHAR_BIT)
199#define exponentBits (typeWidth - significandBits - 1)
200#define maxExponent ((1 << exponentBits) - 1)
201#define exponentBias (maxExponent >> 1)
202
203#define implicitBit (REP_C(1) << significandBits)
204#define significandMask (implicitBit - 1U)
205#define signBit (REP_C(1) << (significandBits + exponentBits))
206#define absMask (signBit - 1U)
207#define exponentMask (absMask ^ significandMask)
208#define oneRep ((rep_t)exponentBias << significandBits)
209#define infRep exponentMask
210#define quietBit (implicitBit >> 1)
211#define qnanRep (exponentMask | quietBit)
212
213static __inline rep_t toRep(fp_t x) {
214 const union {
215 fp_t f;
216 rep_t i;
217 } rep = {.f = x};
218 return rep.i;
219}
220
221static __inline fp_t fromRep(rep_t x) {
222 const union {
223 fp_t f;
224 rep_t i;
225 } rep = {.i = x};
226 return rep.f;
227}
228
229static __inline int normalize(rep_t *significand) {
230 const int shift = rep_clz(a: *significand) - rep_clz(implicitBit);
231 *significand <<= shift;
232 return 1 - shift;
233}
234
235static __inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) {
236 *hi = *hi << count | *lo >> (typeWidth - count);
237 *lo = *lo << count;
238}
239
240static __inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo,
241 unsigned int count) {
242 if (count < typeWidth) {
243 const bool sticky = (*lo << (typeWidth - count)) != 0;
244 *lo = *hi << (typeWidth - count) | *lo >> count | sticky;
245 *hi = *hi >> count;
246 } else if (count < 2 * typeWidth) {
247 const bool sticky = *hi << (2 * typeWidth - count) | *lo;
248 *lo = *hi >> (count - typeWidth) | sticky;
249 *hi = 0;
250 } else {
251 const bool sticky = *hi | *lo;
252 *lo = sticky;
253 *hi = 0;
254 }
255}
256
257// Implements logb methods (logb, logbf, logbl) for IEEE-754. This avoids
258// pulling in a libm dependency from compiler-rt, but is not meant to replace
259// it (i.e. code calling logb() should get the one from libm, not this), hence
260// the __compiler_rt prefix.
261static __inline fp_t __compiler_rt_logbX(fp_t x) {
262 rep_t rep = toRep(x);
263 int exp = (rep & exponentMask) >> significandBits;
264
265 // Abnormal cases:
266 // 1) +/- inf returns +inf; NaN returns NaN
267 // 2) 0.0 returns -inf
268 if (exp == maxExponent) {
269 if (((rep & signBit) == 0) || (x != x)) {
270 return x; // NaN or +inf: return x
271 } else {
272 return -x; // -inf: return -x
273 }
274 } else if (x == 0.0) {
275 // 0.0: return -inf
276 return fromRep(infRep | signBit);
277 }
278
279 if (exp != 0) {
280 // Normal number
281 return exp - exponentBias; // Unbias exponent
282 } else {
283 // Subnormal number; normalize and repeat
284 rep &= absMask;
285 const int shift = 1 - normalize(significand: &rep);
286 exp = (rep & exponentMask) >> significandBits;
287 return exp - exponentBias - shift; // Unbias exponent
288 }
289}
290
291// Avoid using scalbn from libm. Unlike libc/libm scalbn, this function never
292// sets errno on underflow/overflow.
293static __inline fp_t __compiler_rt_scalbnX(fp_t x, int y) {
294 const rep_t rep = toRep(x);
295 int exp = (rep & exponentMask) >> significandBits;
296
297 if (x == 0.0 || exp == maxExponent)
298 return x; // +/- 0.0, NaN, or inf: return x
299
300 // Normalize subnormal input.
301 rep_t sig = rep & significandMask;
302 if (exp == 0) {
303 exp += normalize(significand: &sig);
304 sig &= ~implicitBit; // clear the implicit bit again
305 }
306
307 if (__builtin_sadd_overflow(exp, y, &exp)) {
308 // Saturate the exponent, which will guarantee an underflow/overflow below.
309 exp = (y >= 0) ? INT_MAX : INT_MIN;
310 }
311
312 // Return this value: [+/-] 1.sig * 2 ** (exp - exponentBias).
313 const rep_t sign = rep & signBit;
314 if (exp >= maxExponent) {
315 // Overflow, which could produce infinity or the largest-magnitude value,
316 // depending on the rounding mode.
317 return fromRep(x: sign | ((rep_t)(maxExponent - 1) << significandBits)) * 2.0f;
318 } else if (exp <= 0) {
319 // Subnormal or underflow. Use floating-point multiply to handle truncation
320 // correctly.
321 fp_t tmp = fromRep(x: sign | (REP_C(1) << significandBits) | sig);
322 exp += exponentBias - 1;
323 if (exp < 1)
324 exp = 1;
325 tmp *= fromRep(x: (rep_t)exp << significandBits);
326 return tmp;
327 } else
328 return fromRep(x: sign | ((rep_t)exp << significandBits) | sig);
329}
330
331// Avoid using fmax from libm.
332static __inline fp_t __compiler_rt_fmaxX(fp_t x, fp_t y) {
333 // If either argument is NaN, return the other argument. If both are NaN,
334 // arbitrarily return the second one. Otherwise, if both arguments are +/-0,
335 // arbitrarily return the first one.
336 return (crt_isnan(x) || x < y) ? y : x;
337}
338
339#endif
340
341#if defined(SINGLE_PRECISION)
342
343static __inline fp_t __compiler_rt_logbf(fp_t x) {
344 return __compiler_rt_logbX(x);
345}
346static __inline fp_t __compiler_rt_scalbnf(fp_t x, int y) {
347 return __compiler_rt_scalbnX(x, y);
348}
349static __inline fp_t __compiler_rt_fmaxf(fp_t x, fp_t y) {
350#if defined(__aarch64__)
351 // Use __builtin_fmaxf which turns into an fmaxnm instruction on AArch64.
352 return __builtin_fmaxf(x, y);
353#else
354 // __builtin_fmaxf frequently turns into a libm call, so inline the function.
355 return __compiler_rt_fmaxX(x, y);
356#endif
357}
358
359#elif defined(DOUBLE_PRECISION)
360
361static __inline fp_t __compiler_rt_logb(fp_t x) {
362 return __compiler_rt_logbX(x);
363}
364static __inline fp_t __compiler_rt_scalbn(fp_t x, int y) {
365 return __compiler_rt_scalbnX(x, y);
366}
367static __inline fp_t __compiler_rt_fmax(fp_t x, fp_t y) {
368#if defined(__aarch64__)
369 // Use __builtin_fmax which turns into an fmaxnm instruction on AArch64.
370 return __builtin_fmax(x, y);
371#else
372 // __builtin_fmax frequently turns into a libm call, so inline the function.
373 return __compiler_rt_fmaxX(x, y);
374#endif
375}
376
377#elif defined(QUAD_PRECISION) && defined(CRT_HAS_TF_MODE)
378// The generic implementation only works for ieee754 floating point. For other
379// floating point types, continue to rely on the libm implementation for now.
380#if defined(CRT_HAS_IEEE_TF)
381static __inline tf_float __compiler_rt_logbtf(tf_float x) {
382 return __compiler_rt_logbX(x);
383}
384static __inline tf_float __compiler_rt_scalbntf(tf_float x, int y) {
385 return __compiler_rt_scalbnX(x, y);
386}
387static __inline tf_float __compiler_rt_fmaxtf(tf_float x, tf_float y) {
388 return __compiler_rt_fmaxX(x, y);
389}
390#define __compiler_rt_logbl __compiler_rt_logbtf
391#define __compiler_rt_scalbnl __compiler_rt_scalbntf
392#define __compiler_rt_fmaxl __compiler_rt_fmaxtf
393#define crt_fabstf crt_fabsf128
394#define crt_copysigntf crt_copysignf128
395#elif defined(CRT_LDBL_128BIT)
396static __inline tf_float __compiler_rt_logbtf(tf_float x) {
397 return crt_logbl(x);
398}
399static __inline tf_float __compiler_rt_scalbntf(tf_float x, int y) {
400 return crt_scalbnl(x, y);
401}
402static __inline tf_float __compiler_rt_fmaxtf(tf_float x, tf_float y) {
403 return crt_fmaxl(x, y);
404}
405#define __compiler_rt_logbl crt_logbl
406#define __compiler_rt_scalbnl crt_scalbnl
407#define __compiler_rt_fmaxl crt_fmaxl
408#else
409#error Unsupported TF mode type
410#endif
411
412#endif // *_PRECISION
413
414#endif // FP_LIB_HEADER
415

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