1 //===-- lib/fp_lib.h - Floating-point utilities -------------------*- C -*-===//
2 //
3 // The LLVM Compiler Infrastructure
4 //
5 // This file is dual licensed under the MIT and the University of Illinois Open
6 // Source Licenses. See LICENSE.TXT for details.
7 //
8 //===----------------------------------------------------------------------===//
9 //
10 // This file is a configuration header for soft-float routines in compiler-rt.
11 // This file does not provide any part of the compiler-rt interface, but defines
12 // many useful constants and utility routines that are used in the
13 // implementation of the soft-float routines in compiler-rt.
14 //
15 // Assumes that float, double and long double correspond to the IEEE-754
16 // binary32, binary64 and binary 128 types, respectively, and that integer
17 // endianness matches floating point endianness on the target platform.
18 //
19 //===----------------------------------------------------------------------===//
20
21 #ifndef FP_LIB_HEADER
22 #define FP_LIB_HEADER
23
24 #include <stdint.h>
25 #include <stdbool.h>
26 #include <limits.h>
27 #include "int_lib.h"
28
29 // x86_64 FreeBSD prior v9.3 define fixed-width types incorrectly in
30 // 32-bit mode.
31 #if defined(__FreeBSD__) && defined(__i386__)
32 # include <sys/param.h>
33 # if __FreeBSD_version < 903000 // v9.3
34 # define uint64_t unsigned long long
35 # define int64_t long long
36 # undef UINT64_C
37 # define UINT64_C(c) (c ## ULL)
38 # endif
39 #endif
40
41 #if defined SINGLE_PRECISION
42
43 typedef uint32_t rep_t;
44 typedef int32_t srep_t;
45 typedef float fp_t;
46 #define REP_C UINT32_C
47 #define significandBits 23
48
rep_clz(rep_t a)49 static __inline int rep_clz(rep_t a) {
50 return __builtin_clz(a);
51 }
52
53 // 32x32 --> 64 bit multiply
wideMultiply(rep_t a,rep_t b,rep_t * hi,rep_t * lo)54 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
55 const uint64_t product = (uint64_t)a*b;
56 *hi = product >> 32;
57 *lo = product;
58 }
59 COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b);
60
61 #elif defined DOUBLE_PRECISION
62
63 typedef uint64_t rep_t;
64 typedef int64_t srep_t;
65 typedef double fp_t;
66 #define REP_C UINT64_C
67 #define significandBits 52
68
rep_clz(rep_t a)69 static __inline int rep_clz(rep_t a) {
70 #if defined __LP64__
71 return __builtin_clzl(a);
72 #else
73 if (a & REP_C(0xffffffff00000000))
74 return __builtin_clz(a >> 32);
75 else
76 return 32 + __builtin_clz(a & REP_C(0xffffffff));
77 #endif
78 }
79
80 #define loWord(a) (a & 0xffffffffU)
81 #define hiWord(a) (a >> 32)
82
83 // 64x64 -> 128 wide multiply for platforms that don't have such an operation;
84 // many 64-bit platforms have this operation, but they tend to have hardware
85 // floating-point, so we don't bother with a special case for them here.
wideMultiply(rep_t a,rep_t b,rep_t * hi,rep_t * lo)86 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
87 // Each of the component 32x32 -> 64 products
88 const uint64_t plolo = loWord(a) * loWord(b);
89 const uint64_t plohi = loWord(a) * hiWord(b);
90 const uint64_t philo = hiWord(a) * loWord(b);
91 const uint64_t phihi = hiWord(a) * hiWord(b);
92 // Sum terms that contribute to lo in a way that allows us to get the carry
93 const uint64_t r0 = loWord(plolo);
94 const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
95 *lo = r0 + (r1 << 32);
96 // Sum terms contributing to hi with the carry from lo
97 *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
98 }
99 #undef loWord
100 #undef hiWord
101
102 COMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b);
103
104 #elif defined QUAD_PRECISION
105 #if __LDBL_MANT_DIG__ == 113
106 #define CRT_LDBL_128BIT
107 typedef __uint128_t rep_t;
108 typedef __int128_t srep_t;
109 typedef long double fp_t;
110 #define REP_C (__uint128_t)
111 // Note: Since there is no explicit way to tell compiler the constant is a
112 // 128-bit integer, we let the constant be casted to 128-bit integer
113 #define significandBits 112
114
rep_clz(rep_t a)115 static __inline int rep_clz(rep_t a) {
116 const union
117 {
118 __uint128_t ll;
119 #if _YUGA_BIG_ENDIAN
120 struct { uint64_t high, low; } s;
121 #else
122 struct { uint64_t low, high; } s;
123 #endif
124 } uu = { .ll = a };
125
126 uint64_t word;
127 uint64_t add;
128
129 if (uu.s.high){
130 word = uu.s.high;
131 add = 0;
132 }
133 else{
134 word = uu.s.low;
135 add = 64;
136 }
137 return __builtin_clzll(word) + add;
138 }
139
140 #define Word_LoMask UINT64_C(0x00000000ffffffff)
141 #define Word_HiMask UINT64_C(0xffffffff00000000)
142 #define Word_FullMask UINT64_C(0xffffffffffffffff)
143 #define Word_1(a) (uint64_t)((a >> 96) & Word_LoMask)
144 #define Word_2(a) (uint64_t)((a >> 64) & Word_LoMask)
145 #define Word_3(a) (uint64_t)((a >> 32) & Word_LoMask)
146 #define Word_4(a) (uint64_t)(a & Word_LoMask)
147
148 // 128x128 -> 256 wide multiply for platforms that don't have such an operation;
149 // many 64-bit platforms have this operation, but they tend to have hardware
150 // floating-point, so we don't bother with a special case for them here.
wideMultiply(rep_t a,rep_t b,rep_t * hi,rep_t * lo)151 static __inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
152
153 const uint64_t product11 = Word_1(a) * Word_1(b);
154 const uint64_t product12 = Word_1(a) * Word_2(b);
155 const uint64_t product13 = Word_1(a) * Word_3(b);
156 const uint64_t product14 = Word_1(a) * Word_4(b);
157 const uint64_t product21 = Word_2(a) * Word_1(b);
158 const uint64_t product22 = Word_2(a) * Word_2(b);
159 const uint64_t product23 = Word_2(a) * Word_3(b);
160 const uint64_t product24 = Word_2(a) * Word_4(b);
161 const uint64_t product31 = Word_3(a) * Word_1(b);
162 const uint64_t product32 = Word_3(a) * Word_2(b);
163 const uint64_t product33 = Word_3(a) * Word_3(b);
164 const uint64_t product34 = Word_3(a) * Word_4(b);
165 const uint64_t product41 = Word_4(a) * Word_1(b);
166 const uint64_t product42 = Word_4(a) * Word_2(b);
167 const uint64_t product43 = Word_4(a) * Word_3(b);
168 const uint64_t product44 = Word_4(a) * Word_4(b);
169
170 const __uint128_t sum0 = (__uint128_t)product44;
171 const __uint128_t sum1 = (__uint128_t)product34 +
172 (__uint128_t)product43;
173 const __uint128_t sum2 = (__uint128_t)product24 +
174 (__uint128_t)product33 +
175 (__uint128_t)product42;
176 const __uint128_t sum3 = (__uint128_t)product14 +
177 (__uint128_t)product23 +
178 (__uint128_t)product32 +
179 (__uint128_t)product41;
180 const __uint128_t sum4 = (__uint128_t)product13 +
181 (__uint128_t)product22 +
182 (__uint128_t)product31;
183 const __uint128_t sum5 = (__uint128_t)product12 +
184 (__uint128_t)product21;
185 const __uint128_t sum6 = (__uint128_t)product11;
186
187 const __uint128_t r0 = (sum0 & Word_FullMask) +
188 ((sum1 & Word_LoMask) << 32);
189 const __uint128_t r1 = (sum0 >> 64) +
190 ((sum1 >> 32) & Word_FullMask) +
191 (sum2 & Word_FullMask) +
192 ((sum3 << 32) & Word_HiMask);
193
194 *lo = r0 + (r1 << 64);
195 *hi = (r1 >> 64) +
196 (sum1 >> 96) +
197 (sum2 >> 64) +
198 (sum3 >> 32) +
199 sum4 +
200 (sum5 << 32) +
201 (sum6 << 64);
202 }
203 #undef Word_1
204 #undef Word_2
205 #undef Word_3
206 #undef Word_4
207 #undef Word_HiMask
208 #undef Word_LoMask
209 #undef Word_FullMask
210 #endif // __LDBL_MANT_DIG__ == 113
211 #else
212 #error SINGLE_PRECISION, DOUBLE_PRECISION or QUAD_PRECISION must be defined.
213 #endif
214
215 #if defined(SINGLE_PRECISION) || defined(DOUBLE_PRECISION) || defined(CRT_LDBL_128BIT)
216 #define typeWidth (sizeof(rep_t)*CHAR_BIT)
217 #define exponentBits (typeWidth - significandBits - 1)
218 #define maxExponent ((1 << exponentBits) - 1)
219 #define exponentBias (maxExponent >> 1)
220
221 #define implicitBit (REP_C(1) << significandBits)
222 #define significandMask (implicitBit - 1U)
223 #define signBit (REP_C(1) << (significandBits + exponentBits))
224 #define absMask (signBit - 1U)
225 #define exponentMask (absMask ^ significandMask)
226 #define oneRep ((rep_t)exponentBias << significandBits)
227 #define infRep exponentMask
228 #define quietBit (implicitBit >> 1)
229 #define qnanRep (exponentMask | quietBit)
230
toRep(fp_t x)231 static __inline rep_t toRep(fp_t x) {
232 const union { fp_t f; rep_t i; } rep = {.f = x};
233 return rep.i;
234 }
235
fromRep(rep_t x)236 static __inline fp_t fromRep(rep_t x) {
237 const union { fp_t f; rep_t i; } rep = {.i = x};
238 return rep.f;
239 }
240
normalize(rep_t * significand)241 static __inline int normalize(rep_t *significand) {
242 const int shift = rep_clz(*significand) - rep_clz(implicitBit);
243 *significand <<= shift;
244 return 1 - shift;
245 }
246
wideLeftShift(rep_t * hi,rep_t * lo,int count)247 static __inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) {
248 *hi = *hi << count | *lo >> (typeWidth - count);
249 *lo = *lo << count;
250 }
251
wideRightShiftWithSticky(rep_t * hi,rep_t * lo,unsigned int count)252 static __inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, unsigned int count) {
253 if (count < typeWidth) {
254 const bool sticky = *lo << (typeWidth - count);
255 *lo = *hi << (typeWidth - count) | *lo >> count | sticky;
256 *hi = *hi >> count;
257 }
258 else if (count < 2*typeWidth) {
259 const bool sticky = *hi << (2*typeWidth - count) | *lo;
260 *lo = *hi >> (count - typeWidth) | sticky;
261 *hi = 0;
262 } else {
263 const bool sticky = *hi | *lo;
264 *lo = sticky;
265 *hi = 0;
266 }
267 }
268 #endif
269
270 #endif // FP_LIB_HEADER
271