libm: Sync with FreeBSD (gains 6 long double functions)
[dragonfly.git] / lib / libm / src / s_erff.c
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1/* s_erff.c -- float version of s_erf.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 *
2fedfd5c 15 * $FreeBSD: head/lib/msun/src/s_erff.c 268590 2014-07-13 16:24:16Z kargl $
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16 */
17
967141b1 18
6ff43c94 19#include "math.h"
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20#include "math_private.h"
21
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22/* XXX Prevent compilers from erroneously constant folding: */
23static const volatile float tiny = 1e-30;
24
b34b60bc 25static const float
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26half= 0.5,
27one = 1,
28two = 2,
29erx = 8.42697144e-01, /* 0x3f57bb00 */
b34b60bc 30/*
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31 * In the domain [0, 2**-14], only the first term in the power series
32 * expansion of erf(x) is used. The magnitude of the first neglected
33 * terms is less than 2**-42.
b34b60bc 34 */
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35efx = 1.28379166e-01, /* 0x3e0375d4 */
36efx8= 1.02703333e+00, /* 0x3f8375d4 */
b34b60bc 37/*
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38 * Domain [0, 0.84375], range ~[-5.4419e-10, 5.5179e-10]:
39 * |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-31
967141b1 40 */
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41pp0 = 1.28379166e-01, /* 0x3e0375d4 */
42pp1 = -3.36030394e-01, /* 0xbeac0c2d */
43pp2 = -1.86261395e-03, /* 0xbaf422f4 */
44qq1 = 3.12324315e-01, /* 0x3e9fe8f9 */
45qq2 = 2.16070414e-02, /* 0x3cb10140 */
46qq3 = -1.98859372e-03, /* 0xbb025311 */
967141b1 47/*
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48 * Domain [0.84375, 1.25], range ~[-1.023e-9, 1.023e-9]:
49 * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-31
b34b60bc 50 */
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51pa0 = 3.65041046e-06, /* 0x3674f993 */
52pa1 = 4.15109307e-01, /* 0x3ed48935 */
53pa2 = -2.09395722e-01, /* 0xbe566bd5 */
54pa3 = 8.67677554e-02, /* 0x3db1b34b */
55qa1 = 4.95560974e-01, /* 0x3efdba2b */
56qa2 = 3.71248513e-01, /* 0x3ebe1449 */
57qa3 = 3.92478965e-02, /* 0x3d20c267 */
b34b60bc 58/*
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59 * Domain [1.25,1/0.35], range ~[-4.821e-9, 4.927e-9]:
60 * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-28
b34b60bc 61 */
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62ra0 = -9.88156721e-03, /* 0xbc21e64c */
63ra1 = -5.43658376e-01, /* 0xbf0b2d32 */
64ra2 = -1.66828310e+00, /* 0xbfd58a4d */
65ra3 = -6.91554189e-01, /* 0xbf3109b2 */
66sa1 = 4.48581553e+00, /* 0x408f8bcd */
67sa2 = 4.10799170e+00, /* 0x408374ab */
68sa3 = 5.53855181e-01, /* 0x3f0dc974 */
b34b60bc 69/*
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70 * Domain [2.85715, 11], range ~[-1.484e-9, 1.505e-9]:
71 * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-30
b34b60bc 72 */
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73rb0 = -9.86496918e-03, /* 0xbc21a0ae */
74rb1 = -5.48049808e-01, /* 0xbf0c4cfe */
75rb2 = -1.84115684e+00, /* 0xbfebab07 */
76sb1 = 4.87132740e+00, /* 0x409be1ea */
77sb2 = 3.04982710e+00, /* 0x4043305e */
78sb3 = -7.61900663e-01; /* 0xbf430bec */
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79
80float
81erff(float x)
82{
83 int32_t hx,ix,i;
84 float R,S,P,Q,s,y,z,r;
85 GET_FLOAT_WORD(hx,x);
86 ix = hx&0x7fffffff;
2fedfd5c 87 if(ix>=0x7f800000) { /* erff(nan)=nan */
b34b60bc 88 i = ((u_int32_t)hx>>31)<<1;
2fedfd5c 89 return (float)(1-i)+one/x; /* erff(+-inf)=+-1 */
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90 }
91
92 if(ix < 0x3f580000) { /* |x|<0.84375 */
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93 if(ix < 0x38800000) { /* |x|<2**-14 */
94 if (ix < 0x04000000) /* |x|<0x1p-119 */
95 return (8*x+efx8*x)/8; /* avoid spurious underflow */
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96 return x + efx*x;
97 }
98 z = x*x;
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99 r = pp0+z*(pp1+z*pp2);
100 s = one+z*(qq1+z*(qq2+z*qq3));
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101 y = r/s;
102 return x + x*y;
103 }
104 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
105 s = fabsf(x)-one;
967141b1 106 P = pa0+s*(pa1+s*(pa2+s*pa3));
2fedfd5c 107 Q = one+s*(qa1+s*(qa2+s*qa3));
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108 if(hx>=0) return erx + P/Q; else return -erx - P/Q;
109 }
967141b1 110 if (ix >= 0x40800000) { /* inf>|x|>=4 */
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111 if(hx>=0) return one-tiny; else return tiny-one;
112 }
113 x = fabsf(x);
114 s = one/(x*x);
2fedfd5c 115 if(ix< 0x4036db8c) { /* |x| < 2.85715 ~ 1/0.35 */
967141b1 116 R=ra0+s*(ra1+s*(ra2+s*ra3));
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117 S=one+s*(sa1+s*(sa2+s*sa3));
118 } else { /* |x| >= 2.85715 ~ 1/0.35 */
119 R=rb0+s*(rb1+s*rb2);
120 S=one+s*(sb1+s*(sb2+s*sb3));
b34b60bc 121 }
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122 SET_FLOAT_WORD(z,hx&0xffffe000);
123 r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
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124 if(hx>=0) return one-r/x; else return r/x-one;
125}
126
127float
128erfcf(float x)
129{
130 int32_t hx,ix;
131 float R,S,P,Q,s,y,z,r;
132 GET_FLOAT_WORD(hx,x);
133 ix = hx&0x7fffffff;
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134 if(ix>=0x7f800000) { /* erfcf(nan)=nan */
135 /* erfcf(+-inf)=0,2 */
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136 return (float)(((u_int32_t)hx>>31)<<1)+one/x;
137 }
138
139 if(ix < 0x3f580000) { /* |x|<0.84375 */
967141b1 140 if(ix < 0x33800000) /* |x|<2**-24 */
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141 return one-x;
142 z = x*x;
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143 r = pp0+z*(pp1+z*pp2);
144 s = one+z*(qq1+z*(qq2+z*qq3));
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145 y = r/s;
146 if(hx < 0x3e800000) { /* x<1/4 */
147 return one-(x+x*y);
148 } else {
149 r = x*y;
150 r += (x-half);
151 return half - r ;
152 }
153 }
154 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
155 s = fabsf(x)-one;
967141b1 156 P = pa0+s*(pa1+s*(pa2+s*pa3));
2fedfd5c 157 Q = one+s*(qa1+s*(qa2+s*qa3));
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158 if(hx>=0) {
159 z = one-erx; return z - P/Q;
160 } else {
161 z = erx+P/Q; return one+z;
162 }
163 }
967141b1 164 if (ix < 0x41300000) { /* |x|<11 */
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165 x = fabsf(x);
166 s = one/(x*x);
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167 if(ix< 0x4036db8c) { /* |x| < 2.85715 ~ 1/.35 */
168 R=ra0+s*(ra1+s*(ra2+s*ra3));
169 S=one+s*(sa1+s*(sa2+s*sa3));
170 } else { /* |x| >= 2.85715 ~ 1/.35 */
967141b1 171 if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */
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172 R=rb0+s*(rb1+s*rb2);
173 S=one+s*(sb1+s*(sb2+s*sb3));
b34b60bc 174 }
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175 SET_FLOAT_WORD(z,hx&0xffffe000);
176 r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
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177 if(hx>0) return r/x; else return two-r/x;
178 } else {
179 if(hx>0) return tiny*tiny; else return two-tiny;
180 }
181}