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Side by Side Diff: fusl/src/math/__rem_pio2l.c

Issue 1714623002: [fusl] clang-format fusl (Closed) Base URL: git@github.com:domokit/mojo.git@master
Patch Set: headers too Created 4 years, 10 months ago
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1 /* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */ 1 /* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */
2 /* 2 /*
3 * ==================================================== 3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. 5 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
6 * 6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this 8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice 9 * software is freely granted, provided that this notice
10 * is preserved. 10 * is preserved.
11 * ==================================================== 11 * ====================================================
12 * 12 *
13 * Optimized by Bruce D. Evans. 13 * Optimized by Bruce D. Evans.
14 */ 14 */
15 #include "libm.h" 15 #include "libm.h"
16 #if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 16 #if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
17 /* ld80 and ld128 version of __rem_pio2(x,y) 17 /* ld80 and ld128 version of __rem_pio2(x,y)
18 * 18 *
19 * return the remainder of x rem pi/2 in y[0]+y[1] 19 * return the remainder of x rem pi/2 in y[0]+y[1]
20 * use __rem_pio2_large() for large x 20 * use __rem_pio2_large() for large x
21 */ 21 */
22 22
23 static const long double toint = 1.5/LDBL_EPSILON; 23 static const long double toint = 1.5 / LDBL_EPSILON;
24 24
25 #if LDBL_MANT_DIG == 64 25 #if LDBL_MANT_DIG == 64
26 /* u ~< 0x1p25*pi/2 */ 26 /* u ~< 0x1p25*pi/2 */
27 #define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.m>>48) < ((0x3fff + 25)<<16 | 0x 921f>>1 | 0x8000)) 27 #define SMALL(u) \
28 (((u.i.se & 0x7fffU) << 16 | u.i.m >> 48) < \
29 ((0x3fff + 25) << 16 | 0x921f >> 1 | 0x8000))
28 #define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff) 30 #define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff)
29 #define ROUND1 22 31 #define ROUND1 22
30 #define ROUND2 61 32 #define ROUND2 61
31 #define NX 3 33 #define NX 3
32 #define NY 2 34 #define NY 2
33 /* 35 /*
34 * invpio2: 64 bits of 2/pi 36 * invpio2: 64 bits of 2/pi
35 * pio2_1: first 39 bits of pi/2 37 * pio2_1: first 39 bits of pi/2
36 * pio2_1t: pi/2 - pio2_1 38 * pio2_1t: pi/2 - pio2_1
37 * pio2_2: second 39 bits of pi/2 39 * pio2_2: second 39 bits of pi/2
38 * pio2_2t: pi/2 - (pio2_1+pio2_2) 40 * pio2_2t: pi/2 - (pio2_1+pio2_2)
39 * pio2_3: third 39 bits of pi/2 41 * pio2_3: third 39 bits of pi/2
40 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 42 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
41 */ 43 */
42 static const double 44 static const double pio2_1 =
43 pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */ 45 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
44 pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */ 46 pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
45 pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */ 47 pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
46 static const long double 48 static const long double
47 invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */ 49 invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
48 pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */ 50 pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
49 pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */ 51 pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
50 pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */ 52 pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
51 #elif LDBL_MANT_DIG == 113 53 #elif LDBL_MANT_DIG == 113
52 /* u ~< 0x1p45*pi/2 */ 54 /* u ~< 0x1p45*pi/2 */
53 #define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.top) < ((0x3fff + 45)<<16 | 0x92 1f)) 55 #define SMALL(u) \
56 (((u.i.se & 0x7fffU) << 16 | u.i.top) < ((0x3fff + 45) << 16 | 0x921f))
54 #define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff) 57 #define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff)
55 #define ROUND1 51 58 #define ROUND1 51
56 #define ROUND2 119 59 #define ROUND2 119
57 #define NX 5 60 #define NX 5
58 #define NY 3 61 #define NY 3
59 static const long double 62 static const long double
60 invpio2 = 6.3661977236758134307553505349005747e-01L,» /* 0x145f306dc9c882a53f 84eafa3ea6a.0p-113 */ 63 invpio2 =
61 pio2_1 = 1.5707963267948966192292994253909555e+00L,» /* 0x1921fb54442d184698 00000000000.0p-112 */ 64 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eaf a3ea6a.0p-113
62 pio2_1t = 2.0222662487959507323996846200947577e-21L,» /* 0x13198a2e03707344a4 093822299f3.0p-181 */ 65 */
63 pio2_2 = 2.0222662487959507323994779168837751e-21L,» /* 0x13198a2e03707344a4 00000000000.0p-181 */ 66 pio2_1 =
64 pio2_2t = 2.0670321098263988236496903051604844e-43L,» /* 0x127044533e63a0105d f531d89cd91.0p-254 */ 67 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000 000000.0p-112
65 pio2_3 = 2.0670321098263988236499468110329591e-43L,» /* 0x127044533e63a0105e 00000000000.0p-254 */ 68 */
66 pio2_3t = -2.5650587247459238361625433492959285e-65L;» /* -0x159c4ec64ddaeb5f78 671cbfb2210.0p-327 */ 69 pio2_1t =
70 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a409382 2299f3.0p-181
71 */
72 pio2_2 =
73 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000 000000.0p-181
74 */
75 pio2_2t =
76 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d 89cd91.0p-254
77 */
78 pio2_3 =
79 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000 000000.0p-254
80 */
81 pio2_3t =
82 -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671c bfb2210.0p-327
83 */
67 #endif 84 #endif
68 85
69 int __rem_pio2l(long double x, long double *y) 86 int __rem_pio2l(long double x, long double* y) {
70 { 87 union ldshape u, uz;
71 » union ldshape u,uz; 88 long double z, w, t, r, fn;
72 » long double z,w,t,r,fn; 89 double tx[NX], ty[NY];
73 » double tx[NX],ty[NY]; 90 int ex, ey, n, i;
74 » int ex,ey,n,i;
75 91
76 » u.f = x; 92 u.f = x;
77 » ex = u.i.se & 0x7fff; 93 ex = u.i.se & 0x7fff;
78 » if (SMALL(u)) { 94 if (SMALL(u)) {
79 » » /* rint(x/(pi/2)), Assume round-to-nearest. */ 95 /* rint(x/(pi/2)), Assume round-to-nearest. */
80 » » fn = x*invpio2 + toint - toint; 96 fn = x * invpio2 + toint - toint;
81 » » n = QUOBITS(fn); 97 n = QUOBITS(fn);
82 » » r = x-fn*pio2_1; 98 r = x - fn * pio2_1;
83 » » w = fn*pio2_1t; /* 1st round good to 102/180 bits (ld80/ld128) */ 99 w = fn * pio2_1t; /* 1st round good to 102/180 bits (ld80/ld128) */
84 » » y[0] = r-w; 100 y[0] = r - w;
85 » » u.f = y[0]; 101 u.f = y[0];
86 » » ey = u.i.se & 0x7fff; 102 ey = u.i.se & 0x7fff;
87 » » if (ex - ey > ROUND1) { /* 2nd iteration needed, good to 141/24 8 (ld80/ld128) */ 103 if (ex - ey >
88 » » » t = r; 104 ROUND1) { /* 2nd iteration needed, good to 141/248 (ld80/ld128) */
89 » » » w = fn*pio2_2; 105 t = r;
90 » » » r = t-w; 106 w = fn * pio2_2;
91 » » » w = fn*pio2_2t-((t-r)-w); 107 r = t - w;
92 » » » y[0] = r-w; 108 w = fn * pio2_2t - ((t - r) - w);
93 » » » u.f = y[0]; 109 y[0] = r - w;
94 » » » ey = u.i.se & 0x7fff; 110 u.f = y[0];
95 » » » if (ex - ey > ROUND2) { /* 3rd iteration, good to 180/3 16 bits */ 111 ey = u.i.se & 0x7fff;
96 » » » » t = r; /* will cover all possible cases (not ver ified for ld128) */ 112 if (ex - ey > ROUND2) { /* 3rd iteration, good to 180/316 bits */
97 » » » » w = fn*pio2_3; 113 t = r; /* will cover all possible cases (not verified for ld128) */
98 » » » » r = t-w; 114 w = fn * pio2_3;
99 » » » » w = fn*pio2_3t-((t-r)-w); 115 r = t - w;
100 » » » » y[0] = r-w; 116 w = fn * pio2_3t - ((t - r) - w);
101 » » » } 117 y[0] = r - w;
102 » » } 118 }
103 » » y[1] = (r - y[0]) - w; 119 }
104 » » return n; 120 y[1] = (r - y[0]) - w;
105 » } 121 return n;
106 » /* 122 }
107 » * all other (large) arguments 123 /*
108 » */ 124 * all other (large) arguments
109 » if (ex == 0x7fff) { /* x is inf or NaN */ 125 */
110 » » y[0] = y[1] = x - x; 126 if (ex == 0x7fff) { /* x is inf or NaN */
111 » » return 0; 127 y[0] = y[1] = x - x;
112 » } 128 return 0;
113 » /* set z = scalbn(|x|,-ilogb(x)+23) */ 129 }
114 » uz.f = x; 130 /* set z = scalbn(|x|,-ilogb(x)+23) */
115 » uz.i.se = 0x3fff + 23; 131 uz.f = x;
116 » z = uz.f; 132 uz.i.se = 0x3fff + 23;
117 » for (i=0; i < NX - 1; i++) { 133 z = uz.f;
118 » » tx[i] = (double)(int32_t)z; 134 for (i = 0; i < NX - 1; i++) {
119 » » z = (z-tx[i])*0x1p24; 135 tx[i] = (double)(int32_t)z;
120 » } 136 z = (z - tx[i]) * 0x1p24;
121 » tx[i] = z; 137 }
122 » while (tx[i] == 0) 138 tx[i] = z;
123 » » i--; 139 while (tx[i] == 0)
124 » n = __rem_pio2_large(tx, ty, ex-0x3fff-23, i+1, NY); 140 i--;
125 » w = ty[1]; 141 n = __rem_pio2_large(tx, ty, ex - 0x3fff - 23, i + 1, NY);
126 » if (NY == 3) 142 w = ty[1];
127 » » w += ty[2]; 143 if (NY == 3)
128 » r = ty[0] + w; 144 w += ty[2];
129 » /* TODO: for ld128 this does not follow the recommendation of the 145 r = ty[0] + w;
130 » comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */ 146 /* TODO: for ld128 this does not follow the recommendation of the
131 » w -= r - ty[0]; 147 comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */
132 » if (u.i.se >> 15) { 148 w -= r - ty[0];
133 » » y[0] = -r; 149 if (u.i.se >> 15) {
134 » » y[1] = -w; 150 y[0] = -r;
135 » » return -n; 151 y[1] = -w;
136 » } 152 return -n;
137 » y[0] = r; 153 }
138 » y[1] = w; 154 y[0] = r;
139 » return n; 155 y[1] = w;
156 return n;
140 } 157 }
141 #endif 158 #endif
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