fp_lib.h revision 5d71de26cedae3dafc17449fe0182045c0bd20e8 
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
43typedef uint32_t rep_t;
44typedef int32_t srep_t;
45typedef float fp_t;
46#define REP_C UINT32_C
47#define significandBits 23
48
49static inline int rep_clz(rep_t a) {
50    return __builtin_clz(a);
51}
52
53// 32x32 --> 64 bit multiply
54static 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}
59COMPILER_RT_ABI fp_t __addsf3(fp_t a, fp_t b);
60
61#elif defined DOUBLE_PRECISION
62
63typedef uint64_t rep_t;
64typedef int64_t srep_t;
65typedef double fp_t;
66#define REP_C UINT64_C
67#define significandBits 52
68
69static 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.
86static 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
102COMPILER_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
107typedef __uint128_t rep_t;
108typedef __int128_t srep_t;
109typedef 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
115static 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.
151static 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
231static 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
236static 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
241static 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
247static inline void wideLeftShift(rep_t *hi, rep_t *lo, int count) {
248    *hi = *hi << count | *lo >> (typeWidth - count);
249    *lo = *lo << count;
250}
251
252static 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