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 |
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 | |
32 | typedef uint16_t half_rep_t; |
33 | typedef uint32_t rep_t; |
34 | typedef uint64_t twice_rep_t; |
35 | typedef int32_t srep_t; |
36 | typedef float fp_t; |
37 | #define HALF_REP_C UINT16_C |
38 | #define REP_C UINT32_C |
39 | #define significandBits 23 |
40 | |
41 | static __inline int rep_clz(rep_t a) { return clzsi(a); } |
42 | |
43 | // 32x32 --> 64 bit multiply |
44 | static __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 | } |
49 | COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b); |
50 | |
51 | #elif defined DOUBLE_PRECISION |
52 | |
53 | typedef uint32_t half_rep_t; |
54 | typedef uint64_t rep_t; |
55 | typedef int64_t srep_t; |
56 | typedef double fp_t; |
57 | #define HALF_REP_C UINT32_C |
58 | #define REP_C UINT64_C |
59 | #define significandBits 52 |
60 | |
61 | static 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. |
69 | static __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 | |
85 | COMPILER_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) |
89 | typedef uint64_t half_rep_t; |
90 | typedef __uint128_t rep_t; |
91 | typedef __int128_t srep_t; |
92 | typedef 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 | |
101 | static __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. |
139 | static __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 |
189 | typedef 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 | |
199 | static __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 | |
207 | static __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 | |
230 | static __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 | |
236 | static __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 | |
241 | static __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. |
262 | static __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. |
294 | static __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. |
335 | static __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 | |
346 | static __inline fp_t __compiler_rt_logbf(fp_t x) { |
347 | return __compiler_rt_logbX(x); |
348 | } |
349 | static __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 | |
355 | static __inline fp_t __compiler_rt_logb(fp_t x) { |
356 | return __compiler_rt_logbX(x); |
357 | } |
358 | static __inline fp_t __compiler_rt_scalbn(fp_t x, int y) { |
359 | return __compiler_rt_scalbnX(x, y); |
360 | } |
361 | static __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) |
375 | static __inline tf_float __compiler_rt_logbtf(tf_float x) { |
376 | return __compiler_rt_logbX(x); |
377 | } |
378 | static __inline tf_float __compiler_rt_scalbntf(tf_float x, int y) { |
379 | return __compiler_rt_scalbnX(x, y); |
380 | } |
381 | static __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) |
390 | static __inline tf_float __compiler_rt_logbtf(tf_float x) { |
391 | return crt_logbl(x); |
392 | } |
393 | static __inline tf_float __compiler_rt_scalbntf(tf_float x, int y) { |
394 | return crt_scalbnl(x, y); |
395 | } |
396 | static __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 | |