s_erff.c revision bd3155dc5ddf09647388ad7f8fdbe6df123fbd6a 
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 */
15
16#include <sys/cdefs.h>
17__FBSDID("$FreeBSD$");
18
19#include "math.h"
20#include "math_private.h"
21
22static const float
23tiny	    = 1e-30,
24half=  5.0000000000e-01, /* 0x3F000000 */
25one =  1.0000000000e+00, /* 0x3F800000 */
26two =  2.0000000000e+00, /* 0x40000000 */
27/*
28 * Coefficients for approximation to  erf on [0,0.84375]
29 */
30efx =  1.2837916613e-01, /* 0x3e0375d4 */
31efx8=  1.0270333290e+00, /* 0x3f8375d4 */
32/*
33 *  Domain [0, 0.84375], range ~[-5.4446e-10,5.5197e-10]:
34 *  |(erf(x) - x)/x - p(x)/q(x)| < 2**-31.
35 */
36pp0  =  1.28379166e-01F, /*  0x1.06eba8p-3 */
37pp1  = -3.36030394e-01F, /* -0x1.58185ap-2 */
38pp2  = -1.86260219e-03F, /* -0x1.e8451ep-10 */
39qq1  =  3.12324286e-01F, /*  0x1.3fd1f0p-2 */
40qq2  =  2.16070302e-02F, /*  0x1.620274p-6 */
41qq3  = -1.98859419e-03F, /* -0x1.04a626p-9 */
42/*
43 * Domain [0.84375, 1.25], range ~[-1.953e-11,1.940e-11]:
44 * |(erf(x) - erx) - p(x)/q(x)| < 2**-36.
45 */
46erx  =  8.42697144e-01F, /*  0x1.af7600p-1.  erf(1) rounded to 16 bits. */
47pa0  =  3.64939137e-06F, /*  0x1.e9d022p-19 */
48pa1  =  4.15109694e-01F, /*  0x1.a91284p-2 */
49pa2  = -1.65179938e-01F, /* -0x1.5249dcp-3 */
50pa3  =  1.10914491e-01F, /*  0x1.c64e46p-4 */
51qa1  =  6.02074385e-01F, /*  0x1.344318p-1 */
52qa2  =  5.35934687e-01F, /*  0x1.126608p-1 */
53qa3  =  1.68576106e-01F, /*  0x1.593e6ep-3 */
54qa4  =  5.62181212e-02F, /*  0x1.cc89f2p-5 */
55/*
56 * Domain [1.25,1/0.35], range ~[-7.043e-10,7.457e-10]:
57 * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-30
58 */
59ra0  = -9.87132732e-03F, /* -0x1.4376b2p-7 */
60ra1  = -5.53605914e-01F, /* -0x1.1b723cp-1 */
61ra2  = -2.17589188e+00F, /* -0x1.1683a0p+1 */
62ra3  = -1.43268085e+00F, /* -0x1.6ec42cp+0 */
63sa1  =  5.45995426e+00F, /*  0x1.5d6fe4p+2 */
64sa2  =  6.69798088e+00F, /*  0x1.acabb8p+2 */
65sa3  =  1.43113089e+00F, /*  0x1.6e5e98p+0 */
66sa4  = -5.77397496e-02F, /* -0x1.d90108p-5 */
67/*
68 * Domain [1/0.35, 11], range ~[-2.264e-13,2.336e-13]:
69 * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-42
70 */
71rb0  = -9.86494310e-03F, /* -0x1.434124p-7 */
72rb1  = -6.25171244e-01F, /* -0x1.401672p-1 */
73rb2  = -6.16498327e+00F, /* -0x1.8a8f16p+2 */
74rb3  = -1.66696873e+01F, /* -0x1.0ab70ap+4 */
75rb4  = -9.53764343e+00F, /* -0x1.313460p+3 */
76sb1  =  1.26884899e+01F, /*  0x1.96081cp+3 */
77sb2  =  4.51839523e+01F, /*  0x1.6978bcp+5 */
78sb3  =  4.72810211e+01F, /*  0x1.7a3f88p+5 */
79sb4  =  8.93033314e+00F; /*  0x1.1dc54ap+3 */
80
81float
82erff(float x)
83{
84	int32_t hx,ix,i;
85	float R,S,P,Q,s,y,z,r;
86	GET_FLOAT_WORD(hx,x);
87	ix = hx&0x7fffffff;
88	if(ix>=0x7f800000) {		/* erf(nan)=nan */
89	    i = ((u_int32_t)hx>>31)<<1;
90	    return (float)(1-i)+one/x;	/* erf(+-inf)=+-1 */
91	}
92
93	if(ix < 0x3f580000) {		/* |x|<0.84375 */
94	    if(ix < 0x38800000) { 	/* |x|<2**-14 */
95	        if (ix < 0x04000000)	/* |x|<0x1p-119 */
96		    return (8*x+efx8*x)/8;	/* avoid spurious underflow */
97		return x + efx*x;
98	    }
99	    z = x*x;
100	    r = pp0+z*(pp1+z*pp2);
101	    s = one+z*(qq1+z*(qq2+z*qq3));
102	    y = r/s;
103	    return x + x*y;
104	}
105	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
106	    s = fabsf(x)-one;
107	    P = pa0+s*(pa1+s*(pa2+s*pa3));
108	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4)));
109	    if(hx>=0) return erx + P/Q; else return -erx - P/Q;
110	}
111	if (ix >= 0x40800000) {		/* inf>|x|>=4 */
112	    if(hx>=0) return one-tiny; else return tiny-one;
113	}
114	x = fabsf(x);
115 	s = one/(x*x);
116	if(ix< 0x4036DB6E) {	/* |x| < 1/0.35 */
117	    R=ra0+s*(ra1+s*(ra2+s*ra3));
118	    S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4)));
119	} else {	/* |x| >= 1/0.35 */
120	    R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4)));
121	    S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4)));
122	}
123	SET_FLOAT_WORD(z,hx&0xffffe000);
124	r  = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
125	if(hx>=0) return one-r/x; else return  r/x-one;
126}
127
128float
129erfcf(float x)
130{
131	int32_t hx,ix;
132	float R,S,P,Q,s,y,z,r;
133	GET_FLOAT_WORD(hx,x);
134	ix = hx&0x7fffffff;
135	if(ix>=0x7f800000) {			/* erfc(nan)=nan */
136						/* erfc(+-inf)=0,2 */
137	    return (float)(((u_int32_t)hx>>31)<<1)+one/x;
138	}
139
140	if(ix < 0x3f580000) {		/* |x|<0.84375 */
141	    if(ix < 0x33800000)  	/* |x|<2**-24 */
142		return one-x;
143	    z = x*x;
144	    r = pp0+z*(pp1+z*pp2);
145	    s = one+z*(qq1+z*(qq2+z*qq3));
146	    y = r/s;
147	    if(hx < 0x3e800000) {  	/* x<1/4 */
148		return one-(x+x*y);
149	    } else {
150		r = x*y;
151		r += (x-half);
152	        return half - r ;
153	    }
154	}
155	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
156	    s = fabsf(x)-one;
157	    P = pa0+s*(pa1+s*(pa2+s*pa3));
158	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4)));
159	    if(hx>=0) {
160	        z  = one-erx; return z - P/Q;
161	    } else {
162		z = erx+P/Q; return one+z;
163	    }
164	}
165	if (ix < 0x41300000) {		/* |x|<11 */
166	    x = fabsf(x);
167 	    s = one/(x*x);
168	    if(ix< 0x4036DB6D) {	/* |x| < 1/.35 ~ 2.857143*/
169	        R=ra0+s*(ra1+s*(ra2+s*ra3));
170	        S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4)));
171	    } else {			/* |x| >= 1/.35 ~ 2.857143 */
172		if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */
173	        R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4)));
174		S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4)));
175	    }
176	    SET_FLOAT_WORD(z,hx&0xffffe000);
177	    r  = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
178	    if(hx>0) return r/x; else return two-r/x;
179	} else {
180	    if(hx>0) return tiny*tiny; else return two-tiny;
181	}
182}
183