vx32

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s_erff.c (6784B)


      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 #ifndef lint
     17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_erff.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
     18 #endif
     19 
     20 #include "math.h"
     21 #include "math_private.h"
     22 
     23 static const float
     24 tiny	    = 1e-30,
     25 half=  5.0000000000e-01, /* 0x3F000000 */
     26 one =  1.0000000000e+00, /* 0x3F800000 */
     27 two =  2.0000000000e+00, /* 0x40000000 */
     28 	/* c = (subfloat)0.84506291151 */
     29 erx =  8.4506291151e-01, /* 0x3f58560b */
     30 /*
     31  * Coefficients for approximation to  erf on [0,0.84375]
     32  */
     33 efx =  1.2837916613e-01, /* 0x3e0375d4 */
     34 efx8=  1.0270333290e+00, /* 0x3f8375d4 */
     35 pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
     36 pp1  = -3.2504209876e-01, /* 0xbea66beb */
     37 pp2  = -2.8481749818e-02, /* 0xbce9528f */
     38 pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
     39 pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
     40 qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
     41 qq2  =  6.5022252500e-02, /* 0x3d852a63 */
     42 qq3  =  5.0813062117e-03, /* 0x3ba68116 */
     43 qq4  =  1.3249473704e-04, /* 0x390aee49 */
     44 qq5  = -3.9602282413e-06, /* 0xb684e21a */
     45 /*
     46  * Coefficients for approximation to  erf  in [0.84375,1.25]
     47  */
     48 pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
     49 pa1  =  4.1485610604e-01, /* 0x3ed46805 */
     50 pa2  = -3.7220788002e-01, /* 0xbebe9208 */
     51 pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
     52 pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
     53 pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
     54 pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
     55 qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
     56 qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
     57 qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
     58 qa4  =  1.2617121637e-01, /* 0x3e013307 */
     59 qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
     60 qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
     61 /*
     62  * Coefficients for approximation to  erfc in [1.25,1/0.35]
     63  */
     64 ra0  = -9.8649440333e-03, /* 0xbc21a093 */
     65 ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
     66 ra2  = -1.0558626175e+01, /* 0xc128f022 */
     67 ra3  = -6.2375331879e+01, /* 0xc2798057 */
     68 ra4  = -1.6239666748e+02, /* 0xc322658c */
     69 ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
     70 ra6  = -8.1287437439e+01, /* 0xc2a2932b */
     71 ra7  = -9.8143291473e+00, /* 0xc11d077e */
     72 sa1  =  1.9651271820e+01, /* 0x419d35ce */
     73 sa2  =  1.3765776062e+02, /* 0x4309a863 */
     74 sa3  =  4.3456588745e+02, /* 0x43d9486f */
     75 sa4  =  6.4538726807e+02, /* 0x442158c9 */
     76 sa5  =  4.2900814819e+02, /* 0x43d6810b */
     77 sa6  =  1.0863500214e+02, /* 0x42d9451f */
     78 sa7  =  6.5702495575e+00, /* 0x40d23f7c */
     79 sa8  = -6.0424413532e-02, /* 0xbd777f97 */
     80 /*
     81  * Coefficients for approximation to  erfc in [1/.35,28]
     82  */
     83 rb0  = -9.8649431020e-03, /* 0xbc21a092 */
     84 rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
     85 rb2  = -1.7757955551e+01, /* 0xc18e104b */
     86 rb3  = -1.6063638306e+02, /* 0xc320a2ea */
     87 rb4  = -6.3756646729e+02, /* 0xc41f6441 */
     88 rb5  = -1.0250950928e+03, /* 0xc480230b */
     89 rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
     90 sb1  =  3.0338060379e+01, /* 0x41f2b459 */
     91 sb2  =  3.2579251099e+02, /* 0x43a2e571 */
     92 sb3  =  1.5367296143e+03, /* 0x44c01759 */
     93 sb4  =  3.1998581543e+03, /* 0x4547fdbb */
     94 sb5  =  2.5530502930e+03, /* 0x451f90ce */
     95 sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
     96 sb7  = -2.2440952301e+01; /* 0xc1b38712 */
     97 
     98 float
     99 erff(float x)
    100 {
    101 	int32_t hx,ix,i;
    102 	float R,S,P,Q,s,y,z,r;
    103 	GET_FLOAT_WORD(hx,x);
    104 	ix = hx&0x7fffffff;
    105 	if(ix>=0x7f800000) {		/* erf(nan)=nan */
    106 	    i = ((u_int32_t)hx>>31)<<1;
    107 	    return (float)(1-i)+one/x;	/* erf(+-inf)=+-1 */
    108 	}
    109 
    110 	if(ix < 0x3f580000) {		/* |x|<0.84375 */
    111 	    if(ix < 0x31800000) { 	/* |x|<2**-28 */
    112 	        if (ix < 0x04000000)
    113 		    /*avoid underflow */
    114 		    return (float)0.125*((float)8.0*x+efx8*x);
    115 		return x + efx*x;
    116 	    }
    117 	    z = x*x;
    118 	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
    119 	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
    120 	    y = r/s;
    121 	    return x + x*y;
    122 	}
    123 	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
    124 	    s = fabsf(x)-one;
    125 	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
    126 	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
    127 	    if(hx>=0) return erx + P/Q; else return -erx - P/Q;
    128 	}
    129 	if (ix >= 0x40c00000) {		/* inf>|x|>=6 */
    130 	    if(hx>=0) return one-tiny; else return tiny-one;
    131 	}
    132 	x = fabsf(x);
    133  	s = one/(x*x);
    134 	if(ix< 0x4036DB6E) {	/* |x| < 1/0.35 */
    135 	    R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
    136 				ra5+s*(ra6+s*ra7))))));
    137 	    S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
    138 				sa5+s*(sa6+s*(sa7+s*sa8)))))));
    139 	} else {	/* |x| >= 1/0.35 */
    140 	    R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
    141 				rb5+s*rb6)))));
    142 	    S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
    143 				sb5+s*(sb6+s*sb7))))));
    144 	}
    145 	GET_FLOAT_WORD(ix,x);
    146 	SET_FLOAT_WORD(z,ix&0xfffff000);
    147 	r  =  __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
    148 	if(hx>=0) return one-r/x; else return  r/x-one;
    149 }
    150 
    151 float
    152 erfcf(float x)
    153 {
    154 	int32_t hx,ix;
    155 	float R,S,P,Q,s,y,z,r;
    156 	GET_FLOAT_WORD(hx,x);
    157 	ix = hx&0x7fffffff;
    158 	if(ix>=0x7f800000) {			/* erfc(nan)=nan */
    159 						/* erfc(+-inf)=0,2 */
    160 	    return (float)(((u_int32_t)hx>>31)<<1)+one/x;
    161 	}
    162 
    163 	if(ix < 0x3f580000) {		/* |x|<0.84375 */
    164 	    if(ix < 0x23800000)  	/* |x|<2**-56 */
    165 		return one-x;
    166 	    z = x*x;
    167 	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
    168 	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
    169 	    y = r/s;
    170 	    if(hx < 0x3e800000) {  	/* x<1/4 */
    171 		return one-(x+x*y);
    172 	    } else {
    173 		r = x*y;
    174 		r += (x-half);
    175 	        return half - r ;
    176 	    }
    177 	}
    178 	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
    179 	    s = fabsf(x)-one;
    180 	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
    181 	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
    182 	    if(hx>=0) {
    183 	        z  = one-erx; return z - P/Q;
    184 	    } else {
    185 		z = erx+P/Q; return one+z;
    186 	    }
    187 	}
    188 	if (ix < 0x41e00000) {		/* |x|<28 */
    189 	    x = fabsf(x);
    190  	    s = one/(x*x);
    191 	    if(ix< 0x4036DB6D) {	/* |x| < 1/.35 ~ 2.857143*/
    192 	        R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
    193 				ra5+s*(ra6+s*ra7))))));
    194 	        S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
    195 				sa5+s*(sa6+s*(sa7+s*sa8)))))));
    196 	    } else {			/* |x| >= 1/.35 ~ 2.857143 */
    197 		if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
    198 	        R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
    199 				rb5+s*rb6)))));
    200 	        S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
    201 				sb5+s*(sb6+s*sb7))))));
    202 	    }
    203 	    GET_FLOAT_WORD(ix,x);
    204 	    SET_FLOAT_WORD(z,ix&0xfffff000);
    205 	    r  =  __ieee754_expf(-z*z-(float)0.5625)*
    206 			__ieee754_expf((z-x)*(z+x)+R/S);
    207 	    if(hx>0) return r/x; else return two-r/x;
    208 	} else {
    209 	    if(hx>0) return tiny*tiny; else return two-tiny;
    210 	}
    211 }