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Side by Side Diff: fusl/src/math/__rem_pio2.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/src/e_rem_pio2.c */ 1 /* origin: FreeBSD /usr/src/lib/msun/src/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 * 5 *
6 * Developed at SunSoft, a Sun Microsystems, Inc. business. 6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this 7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice 8 * software is freely granted, provided that this notice
9 * is preserved. 9 * is preserved.
10 * ==================================================== 10 * ====================================================
11 * 11 *
12 * Optimized by Bruce D. Evans. 12 * Optimized by Bruce D. Evans.
13 */ 13 */
14 /* __rem_pio2(x,y) 14 /* __rem_pio2(x,y)
15 * 15 *
16 * return the remainder of x rem pi/2 in y[0]+y[1] 16 * return the remainder of x rem pi/2 in y[0]+y[1]
17 * use __rem_pio2_large() for large x 17 * use __rem_pio2_large() for large x
18 */ 18 */
19 19
20 #include "libm.h" 20 #include "libm.h"
21 21
22 #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 22 #if FLT_EVAL_METHOD == 0 || FLT_EVAL_METHOD == 1
23 #define EPS DBL_EPSILON 23 #define EPS DBL_EPSILON
24 #elif FLT_EVAL_METHOD==2 24 #elif FLT_EVAL_METHOD == 2
25 #define EPS LDBL_EPSILON 25 #define EPS LDBL_EPSILON
26 #endif 26 #endif
27 27
28 /* 28 /*
29 * invpio2: 53 bits of 2/pi 29 * invpio2: 53 bits of 2/pi
30 * pio2_1: first 33 bit of pi/2 30 * pio2_1: first 33 bit of pi/2
31 * pio2_1t: pi/2 - pio2_1 31 * pio2_1t: pi/2 - pio2_1
32 * pio2_2: second 33 bit of pi/2 32 * pio2_2: second 33 bit of pi/2
33 * pio2_2t: pi/2 - (pio2_1+pio2_2) 33 * pio2_2t: pi/2 - (pio2_1+pio2_2)
34 * pio2_3: third 33 bit of pi/2 34 * pio2_3: third 33 bit of pi/2
35 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 35 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
36 */ 36 */
37 static const double 37 static const double toint = 1.5 / EPS,
38 toint = 1.5/EPS, 38 invpio2 =
39 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 39 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
40 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 40 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
41 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 41 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
42 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 42 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
43 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 43 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
44 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 44 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
45 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 45 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
46 46
47 /* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */ 47 /* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
48 int __rem_pio2(double x, double *y) 48 int __rem_pio2(double x, double* y) {
49 { 49 union {
50 » union {double f; uint64_t i;} u = {x}; 50 double f;
51 » double_t z,w,t,r,fn; 51 uint64_t i;
52 » double tx[3],ty[2]; 52 } u = {x};
53 » uint32_t ix; 53 double_t z, w, t, r, fn;
54 » int sign, n, ex, ey, i; 54 double tx[3], ty[2];
55 uint32_t ix;
56 int sign, n, ex, ey, i;
55 57
56 » sign = u.i>>63; 58 sign = u.i >> 63;
57 » ix = u.i>>32 & 0x7fffffff; 59 ix = u.i >> 32 & 0x7fffffff;
58 » if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 60 if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
59 » » if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 61 if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
60 » » » goto medium; /* cancellation -- use medium case */ 62 goto medium; /* cancellation -- use medium case */
61 » » if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 63 if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
62 » » » if (!sign) { 64 if (!sign) {
63 » » » » z = x - pio2_1; /* one round good to 85 bits */ 65 z = x - pio2_1; /* one round good to 85 bits */
64 » » » » y[0] = z - pio2_1t; 66 y[0] = z - pio2_1t;
65 » » » » y[1] = (z-y[0]) - pio2_1t; 67 y[1] = (z - y[0]) - pio2_1t;
66 » » » » return 1; 68 return 1;
67 » » » } else { 69 } else {
68 » » » » z = x + pio2_1; 70 z = x + pio2_1;
69 » » » » y[0] = z + pio2_1t; 71 y[0] = z + pio2_1t;
70 » » » » y[1] = (z-y[0]) + pio2_1t; 72 y[1] = (z - y[0]) + pio2_1t;
71 » » » » return -1; 73 return -1;
72 » » » } 74 }
73 » » } else { 75 } else {
74 » » » if (!sign) { 76 if (!sign) {
75 » » » » z = x - 2*pio2_1; 77 z = x - 2 * pio2_1;
76 » » » » y[0] = z - 2*pio2_1t; 78 y[0] = z - 2 * pio2_1t;
77 » » » » y[1] = (z-y[0]) - 2*pio2_1t; 79 y[1] = (z - y[0]) - 2 * pio2_1t;
78 » » » » return 2; 80 return 2;
79 » » » } else { 81 } else {
80 » » » » z = x + 2*pio2_1; 82 z = x + 2 * pio2_1;
81 » » » » y[0] = z + 2*pio2_1t; 83 y[0] = z + 2 * pio2_1t;
82 » » » » y[1] = (z-y[0]) + 2*pio2_1t; 84 y[1] = (z - y[0]) + 2 * pio2_1t;
83 » » » » return -2; 85 return -2;
84 » » » } 86 }
85 » » } 87 }
86 » } 88 }
87 » if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 89 if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
88 » » if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 90 if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
89 » » » if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 91 if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
90 » » » » goto medium; 92 goto medium;
91 » » » if (!sign) { 93 if (!sign) {
92 » » » » z = x - 3*pio2_1; 94 z = x - 3 * pio2_1;
93 » » » » y[0] = z - 3*pio2_1t; 95 y[0] = z - 3 * pio2_1t;
94 » » » » y[1] = (z-y[0]) - 3*pio2_1t; 96 y[1] = (z - y[0]) - 3 * pio2_1t;
95 » » » » return 3; 97 return 3;
96 » » » } else { 98 } else {
97 » » » » z = x + 3*pio2_1; 99 z = x + 3 * pio2_1;
98 » » » » y[0] = z + 3*pio2_1t; 100 y[0] = z + 3 * pio2_1t;
99 » » » » y[1] = (z-y[0]) + 3*pio2_1t; 101 y[1] = (z - y[0]) + 3 * pio2_1t;
100 » » » » return -3; 102 return -3;
101 » » » } 103 }
102 » » } else { 104 } else {
103 » » » if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 105 if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
104 » » » » goto medium; 106 goto medium;
105 » » » if (!sign) { 107 if (!sign) {
106 » » » » z = x - 4*pio2_1; 108 z = x - 4 * pio2_1;
107 » » » » y[0] = z - 4*pio2_1t; 109 y[0] = z - 4 * pio2_1t;
108 » » » » y[1] = (z-y[0]) - 4*pio2_1t; 110 y[1] = (z - y[0]) - 4 * pio2_1t;
109 » » » » return 4; 111 return 4;
110 » » » } else { 112 } else {
111 » » » » z = x + 4*pio2_1; 113 z = x + 4 * pio2_1;
112 » » » » y[0] = z + 4*pio2_1t; 114 y[0] = z + 4 * pio2_1t;
113 » » » » y[1] = (z-y[0]) + 4*pio2_1t; 115 y[1] = (z - y[0]) + 4 * pio2_1t;
114 » » » » return -4; 116 return -4;
115 » » » } 117 }
116 » » } 118 }
117 » } 119 }
118 » if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ 120 if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
119 medium: 121 medium:
120 » » /* rint(x/(pi/2)), Assume round-to-nearest. */ 122 /* rint(x/(pi/2)), Assume round-to-nearest. */
121 » » fn = (double_t)x*invpio2 + toint - toint; 123 fn = (double_t)x * invpio2 + toint - toint;
122 » » n = (int32_t)fn; 124 n = (int32_t)fn;
123 » » r = x - fn*pio2_1; 125 r = x - fn * pio2_1;
124 » » w = fn*pio2_1t; /* 1st round, good to 85 bits */ 126 w = fn * pio2_1t; /* 1st round, good to 85 bits */
125 » » y[0] = r - w; 127 y[0] = r - w;
126 » » u.f = y[0]; 128 u.f = y[0];
127 » » ey = u.i>>52 & 0x7ff; 129 ey = u.i >> 52 & 0x7ff;
128 » » ex = ix>>20; 130 ex = ix >> 20;
129 » » if (ex - ey > 16) { /* 2nd round, good to 118 bits */ 131 if (ex - ey > 16) { /* 2nd round, good to 118 bits */
130 » » » t = r; 132 t = r;
131 » » » w = fn*pio2_2; 133 w = fn * pio2_2;
132 » » » r = t - w; 134 r = t - w;
133 » » » w = fn*pio2_2t - ((t-r)-w); 135 w = fn * pio2_2t - ((t - r) - w);
134 » » » y[0] = r - w; 136 y[0] = r - w;
135 » » » u.f = y[0]; 137 u.f = y[0];
136 » » » ey = u.i>>52 & 0x7ff; 138 ey = u.i >> 52 & 0x7ff;
137 » » » if (ex - ey > 49) { /* 3rd round, good to 151 bits, cov ers all cases */ 139 if (ex - ey > 49) { /* 3rd round, good to 151 bits, covers all cases */
138 » » » » t = r; 140 t = r;
139 » » » » w = fn*pio2_3; 141 w = fn * pio2_3;
140 » » » » r = t - w; 142 r = t - w;
141 » » » » w = fn*pio2_3t - ((t-r)-w); 143 w = fn * pio2_3t - ((t - r) - w);
142 » » » » y[0] = r - w; 144 y[0] = r - w;
143 » » » } 145 }
144 » » } 146 }
145 » » y[1] = (r - y[0]) - w; 147 y[1] = (r - y[0]) - w;
146 » » return n; 148 return n;
147 » } 149 }
148 » /* 150 /*
149 » * all other (large) arguments 151 * all other (large) arguments
150 » */ 152 */
151 » if (ix >= 0x7ff00000) { /* x is inf or NaN */ 153 if (ix >= 0x7ff00000) { /* x is inf or NaN */
152 » » y[0] = y[1] = x - x; 154 y[0] = y[1] = x - x;
153 » » return 0; 155 return 0;
154 » } 156 }
155 » /* set z = scalbn(|x|,-ilogb(x)+23) */ 157 /* set z = scalbn(|x|,-ilogb(x)+23) */
156 » u.f = x; 158 u.f = x;
157 » u.i &= (uint64_t)-1>>12; 159 u.i &= (uint64_t)-1 >> 12;
158 » u.i |= (uint64_t)(0x3ff + 23)<<52; 160 u.i |= (uint64_t)(0x3ff + 23) << 52;
159 » z = u.f; 161 z = u.f;
160 » for (i=0; i < 2; i++) { 162 for (i = 0; i < 2; i++) {
161 » » tx[i] = (double)(int32_t)z; 163 tx[i] = (double)(int32_t)z;
162 » » z = (z-tx[i])*0x1p24; 164 z = (z - tx[i]) * 0x1p24;
163 » } 165 }
164 » tx[i] = z; 166 tx[i] = z;
165 » /* skip zero terms, first term is non-zero */ 167 /* skip zero terms, first term is non-zero */
166 » while (tx[i] == 0.0) 168 while (tx[i] == 0.0)
167 » » i--; 169 i--;
168 » n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1); 170 n = __rem_pio2_large(tx, ty, (int)(ix >> 20) - (0x3ff + 23), i + 1, 1);
169 » if (sign) { 171 if (sign) {
170 » » y[0] = -ty[0]; 172 y[0] = -ty[0];
171 » » y[1] = -ty[1]; 173 y[1] = -ty[1];
172 » » return -n; 174 return -n;
173 » } 175 }
174 » y[0] = ty[0]; 176 y[0] = ty[0];
175 » y[1] = ty[1]; 177 y[1] = ty[1];
176 » return n; 178 return n;
177 } 179 }
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