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Side by Side Diff: fusl/src/math/erff.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/s_erff.c */ 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */
2 /* 2 /*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 */ 4 */
5 /* 5 /*
6 * ==================================================== 6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 * 8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business. 9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this 10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice 11 * software is freely granted, provided that this notice
12 * is preserved. 12 * is preserved.
13 * ==================================================== 13 * ====================================================
14 */ 14 */
15 15
16 #include "libm.h" 16 #include "libm.h"
17 17
18 static const float 18 static const float erx = 8.4506291151e-01, /* 0x3f58560b */
19 erx = 8.4506291151e-01, /* 0x3f58560b */ 19 /*
20 /* 20 * Coefficients for approximation to erf on [0,0.84375]
21 * Coefficients for approximation to erf on [0,0.84375] 21 */
22 */ 22 efx8 = 1.0270333290e+00, /* 0x3f8375d4 */
23 efx8 = 1.0270333290e+00, /* 0x3f8375d4 */ 23 pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
24 pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ 24 pp1 = -3.2504209876e-01, /* 0xbea66beb */
25 pp1 = -3.2504209876e-01, /* 0xbea66beb */ 25 pp2 = -2.8481749818e-02, /* 0xbce9528f */
26 pp2 = -2.8481749818e-02, /* 0xbce9528f */ 26 pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
27 pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ 27 pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
28 pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ 28 qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
29 qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ 29 qq2 = 6.5022252500e-02, /* 0x3d852a63 */
30 qq2 = 6.5022252500e-02, /* 0x3d852a63 */ 30 qq3 = 5.0813062117e-03, /* 0x3ba68116 */
31 qq3 = 5.0813062117e-03, /* 0x3ba68116 */ 31 qq4 = 1.3249473704e-04, /* 0x390aee49 */
32 qq4 = 1.3249473704e-04, /* 0x390aee49 */ 32 qq5 = -3.9602282413e-06, /* 0xb684e21a */
33 qq5 = -3.9602282413e-06, /* 0xb684e21a */ 33 /*
34 /* 34 * Coefficients for approximation to erf in [0.84375,1.25]
35 * Coefficients for approximation to erf in [0.84375,1.25] 35 */
36 */ 36 pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
37 pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ 37 pa1 = 4.1485610604e-01, /* 0x3ed46805 */
38 pa1 = 4.1485610604e-01, /* 0x3ed46805 */ 38 pa2 = -3.7220788002e-01, /* 0xbebe9208 */
39 pa2 = -3.7220788002e-01, /* 0xbebe9208 */ 39 pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
40 pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ 40 pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
41 pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ 41 pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
42 pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ 42 pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
43 pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ 43 qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
44 qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ 44 qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
45 qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ 45 qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
46 qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ 46 qa4 = 1.2617121637e-01, /* 0x3e013307 */
47 qa4 = 1.2617121637e-01, /* 0x3e013307 */ 47 qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
48 qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ 48 qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
49 qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ 49 /*
50 /* 50 * Coefficients for approximation to erfc in [1.25,1/0.35]
51 * Coefficients for approximation to erfc in [1.25,1/0.35] 51 */
52 */ 52 ra0 = -9.8649440333e-03, /* 0xbc21a093 */
53 ra0 = -9.8649440333e-03, /* 0xbc21a093 */ 53 ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
54 ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ 54 ra2 = -1.0558626175e+01, /* 0xc128f022 */
55 ra2 = -1.0558626175e+01, /* 0xc128f022 */ 55 ra3 = -6.2375331879e+01, /* 0xc2798057 */
56 ra3 = -6.2375331879e+01, /* 0xc2798057 */ 56 ra4 = -1.6239666748e+02, /* 0xc322658c */
57 ra4 = -1.6239666748e+02, /* 0xc322658c */ 57 ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
58 ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ 58 ra6 = -8.1287437439e+01, /* 0xc2a2932b */
59 ra6 = -8.1287437439e+01, /* 0xc2a2932b */ 59 ra7 = -9.8143291473e+00, /* 0xc11d077e */
60 ra7 = -9.8143291473e+00, /* 0xc11d077e */ 60 sa1 = 1.9651271820e+01, /* 0x419d35ce */
61 sa1 = 1.9651271820e+01, /* 0x419d35ce */ 61 sa2 = 1.3765776062e+02, /* 0x4309a863 */
62 sa2 = 1.3765776062e+02, /* 0x4309a863 */ 62 sa3 = 4.3456588745e+02, /* 0x43d9486f */
63 sa3 = 4.3456588745e+02, /* 0x43d9486f */ 63 sa4 = 6.4538726807e+02, /* 0x442158c9 */
64 sa4 = 6.4538726807e+02, /* 0x442158c9 */ 64 sa5 = 4.2900814819e+02, /* 0x43d6810b */
65 sa5 = 4.2900814819e+02, /* 0x43d6810b */ 65 sa6 = 1.0863500214e+02, /* 0x42d9451f */
66 sa6 = 1.0863500214e+02, /* 0x42d9451f */ 66 sa7 = 6.5702495575e+00, /* 0x40d23f7c */
67 sa7 = 6.5702495575e+00, /* 0x40d23f7c */ 67 sa8 = -6.0424413532e-02, /* 0xbd777f97 */
68 sa8 = -6.0424413532e-02, /* 0xbd777f97 */ 68 /*
69 /* 69 * Coefficients for approximation to erfc in [1/.35,28]
70 * Coefficients for approximation to erfc in [1/.35,28] 70 */
71 */ 71 rb0 = -9.8649431020e-03, /* 0xbc21a092 */
72 rb0 = -9.8649431020e-03, /* 0xbc21a092 */ 72 rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
73 rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ 73 rb2 = -1.7757955551e+01, /* 0xc18e104b */
74 rb2 = -1.7757955551e+01, /* 0xc18e104b */ 74 rb3 = -1.6063638306e+02, /* 0xc320a2ea */
75 rb3 = -1.6063638306e+02, /* 0xc320a2ea */ 75 rb4 = -6.3756646729e+02, /* 0xc41f6441 */
76 rb4 = -6.3756646729e+02, /* 0xc41f6441 */ 76 rb5 = -1.0250950928e+03, /* 0xc480230b */
77 rb5 = -1.0250950928e+03, /* 0xc480230b */ 77 rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
78 rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ 78 sb1 = 3.0338060379e+01, /* 0x41f2b459 */
79 sb1 = 3.0338060379e+01, /* 0x41f2b459 */ 79 sb2 = 3.2579251099e+02, /* 0x43a2e571 */
80 sb2 = 3.2579251099e+02, /* 0x43a2e571 */ 80 sb3 = 1.5367296143e+03, /* 0x44c01759 */
81 sb3 = 1.5367296143e+03, /* 0x44c01759 */ 81 sb4 = 3.1998581543e+03, /* 0x4547fdbb */
82 sb4 = 3.1998581543e+03, /* 0x4547fdbb */ 82 sb5 = 2.5530502930e+03, /* 0x451f90ce */
83 sb5 = 2.5530502930e+03, /* 0x451f90ce */ 83 sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
84 sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ 84 sb7 = -2.2440952301e+01; /* 0xc1b38712 */
85 sb7 = -2.2440952301e+01; /* 0xc1b38712 */
86 85
87 static float erfc1(float x) 86 static float erfc1(float x) {
88 { 87 float_t s, P, Q;
89 » float_t s,P,Q;
90 88
91 » s = fabsf(x) - 1; 89 s = fabsf(x) - 1;
92 » P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); 90 P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + s * (pa5 + s * pa6)))));
93 » Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); 91 Q = 1 + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + s * (qa5 + s * qa6)))));
94 » return 1 - erx - P/Q; 92 return 1 - erx - P / Q;
95 } 93 }
96 94
97 static float erfc2(uint32_t ix, float x) 95 static float erfc2(uint32_t ix, float x) {
98 { 96 float_t s, R, S;
99 » float_t s,R,S; 97 float z;
100 » float z;
101 98
102 » if (ix < 0x3fa00000) /* |x| < 1.25 */ 99 if (ix < 0x3fa00000) /* |x| < 1.25 */
103 » » return erfc1(x); 100 return erfc1(x);
104 101
105 » x = fabsf(x); 102 x = fabsf(x);
106 » s = 1/(x*x); 103 s = 1 / (x * x);
107 » if (ix < 0x4036db6d) { /* |x| < 1/0.35 */ 104 if (ix < 0x4036db6d) { /* |x| < 1/0.35 */
108 » » R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( 105 R = ra0 +
109 » » ra5+s*(ra6+s*ra7)))))); 106 s * (ra1 +
110 » » S = 1.0f+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( 107 s * (ra2 +
111 » » sa5+s*(sa6+s*(sa7+s*sa8))))))); 108 s * (ra3 + s * (ra4 + s * (ra5 + s * (ra6 + s * ra7))))));
112 » } else { /* |x| >= 1/0.35 */ 109 S = 1.0f +
113 » » R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( 110 s * (sa1 +
114 » » rb5+s*rb6))))); 111 s * (sa2 +
115 » » S = 1.0f+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( 112 s * (sa3 +
116 » » sb5+s*(sb6+s*sb7)))))); 113 s * (sa4 +
117 » } 114 s * (sa5 + s * (sa6 + s * (sa7 + s * sa8)))))));
118 » GET_FLOAT_WORD(ix, x); 115 } else { /* |x| >= 1/0.35 */
119 » SET_FLOAT_WORD(z, ix&0xffffe000); 116 R = rb0 +
120 » return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x; 117 s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 + s * (rb5 + s * rb6)))));
118 S = 1.0f +
119 s * (sb1 +
120 s * (sb2 +
121 s * (sb3 + s * (sb4 + s * (sb5 + s * (sb6 + s * sb7))))));
122 }
123 GET_FLOAT_WORD(ix, x);
124 SET_FLOAT_WORD(z, ix & 0xffffe000);
125 return expf(-z * z - 0.5625f) * expf((z - x) * (z + x) + R / S) / x;
121 } 126 }
122 127
123 float erff(float x) 128 float erff(float x) {
124 { 129 float r, s, z, y;
125 » float r,s,z,y; 130 uint32_t ix;
126 » uint32_t ix; 131 int sign;
127 » int sign;
128 132
129 » GET_FLOAT_WORD(ix, x); 133 GET_FLOAT_WORD(ix, x);
130 » sign = ix>>31; 134 sign = ix >> 31;
131 » ix &= 0x7fffffff; 135 ix &= 0x7fffffff;
132 » if (ix >= 0x7f800000) { 136 if (ix >= 0x7f800000) {
133 » » /* erf(nan)=nan, erf(+-inf)=+-1 */ 137 /* erf(nan)=nan, erf(+-inf)=+-1 */
134 » » return 1-2*sign + 1/x; 138 return 1 - 2 * sign + 1 / x;
135 » } 139 }
136 » if (ix < 0x3f580000) { /* |x| < 0.84375 */ 140 if (ix < 0x3f580000) { /* |x| < 0.84375 */
137 » » if (ix < 0x31800000) { /* |x| < 2**-28 */ 141 if (ix < 0x31800000) { /* |x| < 2**-28 */
138 » » » /*avoid underflow */ 142 /*avoid underflow */
139 » » » return 0.125f*(8*x + efx8*x); 143 return 0.125f * (8 * x + efx8 * x);
140 » » } 144 }
141 » » z = x*x; 145 z = x * x;
142 » » r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 146 r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
143 » » s = 1+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 147 s = 1 + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
144 » » y = r/s; 148 y = r / s;
145 » » return x + x*y; 149 return x + x * y;
146 » } 150 }
147 » if (ix < 0x40c00000) /* |x| < 6 */ 151 if (ix < 0x40c00000) /* |x| < 6 */
148 » » y = 1 - erfc2(ix,x); 152 y = 1 - erfc2(ix, x);
149 » else 153 else
150 » » y = 1 - 0x1p-120f; 154 y = 1 - 0x1p-120f;
151 » return sign ? -y : y; 155 return sign ? -y : y;
152 } 156 }
153 157
154 float erfcf(float x) 158 float erfcf(float x) {
155 { 159 float r, s, z, y;
156 » float r,s,z,y; 160 uint32_t ix;
157 » uint32_t ix; 161 int sign;
158 » int sign;
159 162
160 » GET_FLOAT_WORD(ix, x); 163 GET_FLOAT_WORD(ix, x);
161 » sign = ix>>31; 164 sign = ix >> 31;
162 » ix &= 0x7fffffff; 165 ix &= 0x7fffffff;
163 » if (ix >= 0x7f800000) { 166 if (ix >= 0x7f800000) {
164 » » /* erfc(nan)=nan, erfc(+-inf)=0,2 */ 167 /* erfc(nan)=nan, erfc(+-inf)=0,2 */
165 » » return 2*sign + 1/x; 168 return 2 * sign + 1 / x;
166 » } 169 }
167 170
168 » if (ix < 0x3f580000) { /* |x| < 0.84375 */ 171 if (ix < 0x3f580000) { /* |x| < 0.84375 */
169 » » if (ix < 0x23800000) /* |x| < 2**-56 */ 172 if (ix < 0x23800000) /* |x| < 2**-56 */
170 » » » return 1.0f - x; 173 return 1.0f - x;
171 » » z = x*x; 174 z = x * x;
172 » » r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); 175 r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4)));
173 » » s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); 176 s = 1.0f + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
174 » » y = r/s; 177 y = r / s;
175 » » if (sign || ix < 0x3e800000) /* x < 1/4 */ 178 if (sign || ix < 0x3e800000) /* x < 1/4 */
176 » » » return 1.0f - (x+x*y); 179 return 1.0f - (x + x * y);
177 » » return 0.5f - (x - 0.5f + x*y); 180 return 0.5f - (x - 0.5f + x * y);
178 » } 181 }
179 » if (ix < 0x41e00000) { /* |x| < 28 */ 182 if (ix < 0x41e00000) { /* |x| < 28 */
180 » » return sign ? 2 - erfc2(ix,x) : erfc2(ix,x); 183 return sign ? 2 - erfc2(ix, x) : erfc2(ix, x);
181 » } 184 }
182 » return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f; 185 return sign ? 2 - 0x1p-120f : 0x1p-120f * 0x1p-120f;
183 } 186 }
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