1 /**
2 University of Illinois/NCSA
3 Open Source License
4
5 Copyright (c) 2009-2014 by the contributors listed in CREDITS.TXT
6
7 All rights reserved.
8
9 Developed by:
10
11 LLVM Team
12
13 University of Illinois at Urbana-Champaign
14
15 http://llvm.org
16
17 Permission is hereby granted, free of charge, to any person obtaining a copy of
18 this software and associated documentation files (the "Software"), to deal with
19 the Software without restriction, including without limitation the rights to
20 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
21 of the Software, and to permit persons to whom the Software is furnished to do
22 so, subject to the following conditions:
23
24 * Redistributions of source code must retain the above copyright notice,
25 this list of conditions and the following disclaimers.
26
27 * Redistributions in binary form must reproduce the above copyright notice,
28 this list of conditions and the following disclaimers in the
29 documentation and/or other materials provided with the distribution.
30
31 * Neither the names of the LLVM Team, University of Illinois at
32 Urbana-Champaign, nor the names of its contributors may be used to
33 endorse or promote products derived from this Software without specific
34 prior written permission.
35
36 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
37 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
38 FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
39 CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
40 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
41 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
42 SOFTWARE.
43 **/
44
45 #ifndef FP_LIB_HEADER
46 #define FP_LIB_HEADER
47
48 #include <stdint.h>
49 #include <stdbool.h>
50 #include <limits.h>
51 #include "int_lib.h"
52
53 #if defined SINGLE_PRECISION
54
55 typedef uint32_t rep_t;
56 typedef int32_t srep_t;
57 typedef float fp_t;
58 #define REP_C UINT32_C
59 #define significandBits 23
60
rep_clz(rep_t a)61 static inline int rep_clz(rep_t a) {
62 return __builtin_clz(a);
63 }
64
65 // 32x32 --> 64 bit multiply
wideMultiply(rep_t a,rep_t b,rep_t * hi,rep_t * lo)66 static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
67 const uint64_t product = (uint64_t)a*b;
68 *hi = product >> 32;
69 *lo = product;
70 }
71 COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b);
72
73 #elif defined DOUBLE_PRECISION
74
75 typedef uint64_t rep_t;
76 typedef int64_t srep_t;
77 typedef double fp_t;
78 #define REP_C UINT64_C
79 #define significandBits 52
80
rep_clz(rep_t a)81 static inline int rep_clz(rep_t a) {
82 #if defined __LP64__
83 return __builtin_clzl(a);
84 #else
85 if (a & REP_C(0xffffffff00000000))
86 return __builtin_clz(a >> 32);
87 else
88 return 32 + __builtin_clz(a & REP_C(0xffffffff));
89 #endif
90 }
91
92 #define loWord(a) (a & 0xffffffffU)
93 #define hiWord(a) (a >> 32)
94
95 // 64x64 -> 128 wide multiply for platforms that don't have such an operation;
96 // many 64-bit platforms have this operation, but they tend to have hardware
97 // 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)98 static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
99 // Each of the component 32x32 -> 64 products
100 const uint64_t plolo = loWord(a) * loWord(b);
101 const uint64_t plohi = loWord(a) * hiWord(b);
102 const uint64_t philo = hiWord(a) * loWord(b);
103 const uint64_t phihi = hiWord(a) * hiWord(b);
104 // Sum terms that contribute to lo in a way that allows us to get the carry
105 const uint64_t r0 = loWord(plolo);
106 const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
107 *lo = r0 + (r1 << 32);
108 // Sum terms contributing to hi with the carry from lo
109 *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
110 }
111 #undef loWord
112 #undef hiWord
113
114 COMPILER_RT_ABI fp_t __adddf3(fp_t a, fp_t b);
115
116 #elif defined QUAD_PRECISION
117 #if __LDBL_MANT_DIG__ == 113
118 #define CRT_LDBL_128BIT
119 typedef __uint128_t rep_t;
120 typedef __int128_t srep_t;
121 typedef long double fp_t;
122 #define REP_C (__uint128_t)
123 // Note: Since there is no explicit way to tell compiler the constant is a
124 // 128-bit integer, we let the constant be casted to 128-bit integer
125 #define significandBits 112
126
rep_clz(rep_t a)127 static inline int rep_clz(rep_t a) {
128 const union
129 {
130 __uint128_t ll;
131 #if _YUGA_BIG_ENDIAN
132 struct { uint64_t high, low; } s;
133 #else
134 struct { uint64_t low, high; } s;
135 #endif
136 } uu = { .ll = a };
137
138 uint64_t word;
139 uint64_t add;
140
141 if (uu.s.high){
142 word = uu.s.high;
143 add = 0;
144 }
145 else{
146 word = uu.s.low;
147 add = 64;
148 }
149 return __builtin_clzll(word) + add;
150 }
151
152 #define Word_LoMask UINT64_C(0x00000000ffffffff)
153 #define Word_HiMask UINT64_C(0xffffffff00000000)
154 #define Word_FullMask UINT64_C(0xffffffffffffffff)
155 #define Word_1(a) (uint64_t)((a >> 96) & Word_LoMask)
156 #define Word_2(a) (uint64_t)((a >> 64) & Word_LoMask)
157 #define Word_3(a) (uint64_t)((a >> 32) & Word_LoMask)
158 #define Word_4(a) (uint64_t)(a & Word_LoMask)
159
160 // 128x128 -> 256 wide multiply for platforms that don't have such an operation;
161 // many 64-bit platforms have this operation, but they tend to have hardware
162 // 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)163 static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
164
165 const uint64_t product11 = Word_1(a) * Word_1(b);
166 const uint64_t product12 = Word_1(a) * Word_2(b);
167 const uint64_t product13 = Word_1(a) * Word_3(b);
168 const uint64_t product14 = Word_1(a) * Word_4(b);
169 const uint64_t product21 = Word_2(a) * Word_1(b);
170 const uint64_t product22 = Word_2(a) * Word_2(b);
171 const uint64_t product23 = Word_2(a) * Word_3(b);
172 const uint64_t product24 = Word_2(a) * Word_4(b);
173 const uint64_t product31 = Word_3(a) * Word_1(b);
174 const uint64_t product32 = Word_3(a) * Word_2(b);
175 const uint64_t product33 = Word_3(a) * Word_3(b);
176 const uint64_t product34 = Word_3(a) * Word_4(b);
177 const uint64_t product41 = Word_4(a) * Word_1(b);
178 const uint64_t product42 = Word_4(a) * Word_2(b);
179 const uint64_t product43 = Word_4(a) * Word_3(b);
180 const uint64_t product44 = Word_4(a) * Word_4(b);
181
182 const __uint128_t sum0 = (__uint128_t)product44;
183 const __uint128_t sum1 = (__uint128_t)product34 +
184 (__uint128_t)product43;
185 const __uint128_t sum2 = (__uint128_t)product24 +
186 (__uint128_t)product33 +
187 (__uint128_t)product42;
188 const __uint128_t sum3 = (__uint128_t)product14 +
189 (__uint128_t)product23 +
190 (__uint128_t)product32 +
191 (__uint128_t)product41;
192 const __uint128_t sum4 = (__uint128_t)product13 +
193 (__uint128_t)product22 +
194 (__uint128_t)product31;
195 const __uint128_t sum5 = (__uint128_t)product12 +
196 (__uint128_t)product21;
197 const __uint128_t sum6 = (__uint128_t)product11;
198
199 const __uint128_t r0 = (sum0 & Word_FullMask) +
200 ((sum1 & Word_LoMask) << 32);
201 const __uint128_t r1 = (sum0 >> 64) +
202 ((sum1 >> 32) & Word_FullMask) +
203 (sum2 & Word_FullMask) +
204 ((sum3 << 32) & Word_HiMask);
205
206 *lo = r0 + (r1 << 64);
207 *hi = (r1 >> 64) +
208 (sum1 >> 96) +
209 (sum2 >> 64) +
210 (sum3 >> 32) +
211 sum4 +
212 (sum5 << 32) +
213 (sum6 << 64);
214 }
215 #undef Word_1
216 #undef Word_2
217 #undef Word_3
218 #undef Word_4
219 #undef Word_HiMask
220 #undef Word_LoMask
221 #undef Word_FullMask
222 #endif // __LDBL_MANT_DIG__ == 113
223 #else
224 #error SINGLE_PRECISION, DOUBLE_PRECISION or QUAD_PRECISION must be defined.
225 #endif
226
227 #if defined(SINGLE_PRECISION) || defined(DOUBLE_PRECISION) || defined(CRT_LDBL_128BIT)
228 #define typeWidth (sizeof(rep_t)*CHAR_BIT)
229 #define exponentBits (typeWidth - significandBits - 1)
230 #define maxExponent ((1 << exponentBits) - 1)
231 #define exponentBias (maxExponent >> 1)
232
233 #define implicitBit (REP_C(1) << significandBits)
234 #define significandMask (implicitBit - 1U)
235 #define signBit (REP_C(1) << (significandBits + exponentBits))
236 #define absMask (signBit - 1U)
237 #define exponentMask (absMask ^ significandMask)
238 #define oneRep ((rep_t)exponentBias << significandBits)
239 #define infRep exponentMask
240 #define quietBit (implicitBit >> 1)
241 #define qnanRep (exponentMask | quietBit)
242
toRep(fp_t x)243 static inline rep_t toRep(fp_t x) {
244 const union { fp_t f; rep_t i; } rep = {.f = x};
245 return rep.i;
246 }
247
fromRep(rep_t x)248 static inline fp_t fromRep(rep_t x) {
249 const union { fp_t f; rep_t i; } rep = {.i = x};
250 return rep.f;
251 }
252
normalize(rep_t * significand)253 static inline int normalize(rep_t *significand) {
254 const int shift = rep_clz(*significand) - rep_clz(implicitBit);
255 *significand <<= shift;
256 return 1 - shift;
257 }
258
wideLeftShift(rep_t * hi,rep_t * lo,int count)259 static inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) {
260 *hi = *hi << count | *lo >> (typeWidth - count);
261 *lo = *lo << count;
262 }
263
wideRightShiftWithSticky(rep_t * hi,rep_t * lo,unsigned int count)264 static inline void wideRightShiftWithSticky(rep_t *hi, rep_t *lo, unsigned int count) {
265 if (count < typeWidth) {
266 const bool sticky = *lo << (typeWidth - count);
267 *lo = *hi << (typeWidth - count) | *lo >> count | sticky;
268 *hi = *hi >> count;
269 }
270 else if (count < 2*typeWidth) {
271 const bool sticky = *hi << (2*typeWidth - count) | *lo;
272 *lo = *hi >> (count - typeWidth) | sticky;
273 *hi = 0;
274 } else {
275 const bool sticky = *hi | *lo;
276 *lo = sticky;
277 *hi = 0;
278 }
279 }
280 #endif
281
282 #endif // FP_LIB_HEADER
283