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glibc  2.9
s_erff.c
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00001 /* s_erff.c -- float version of s_erf.c.
00002  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
00003  */
00004 
00005 /*
00006  * ====================================================
00007  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00008  *
00009  * Developed at SunPro, a Sun Microsystems, Inc. business.
00010  * Permission to use, copy, modify, and distribute this
00011  * software is freely granted, provided that this notice 
00012  * is preserved.
00013  * ====================================================
00014  */
00015 
00016 #if defined(LIBM_SCCS) && !defined(lint)
00017 static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $";
00018 #endif
00019 
00020 #include "math.h"
00021 #include "math_private.h"
00022 
00023 #ifdef __STDC__
00024 static const float
00025 #else
00026 static float
00027 #endif
00028 tiny       = 1e-30,
00029 half=  5.0000000000e-01, /* 0x3F000000 */
00030 one =  1.0000000000e+00, /* 0x3F800000 */
00031 two =  2.0000000000e+00, /* 0x40000000 */
00032        /* c = (subfloat)0.84506291151 */
00033 erx =  8.4506291151e-01, /* 0x3f58560b */
00034 /*
00035  * Coefficients for approximation to  erf on [0,0.84375]
00036  */
00037 efx =  1.2837916613e-01, /* 0x3e0375d4 */
00038 efx8=  1.0270333290e+00, /* 0x3f8375d4 */
00039 pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
00040 pp1  = -3.2504209876e-01, /* 0xbea66beb */
00041 pp2  = -2.8481749818e-02, /* 0xbce9528f */
00042 pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
00043 pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
00044 qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
00045 qq2  =  6.5022252500e-02, /* 0x3d852a63 */
00046 qq3  =  5.0813062117e-03, /* 0x3ba68116 */
00047 qq4  =  1.3249473704e-04, /* 0x390aee49 */
00048 qq5  = -3.9602282413e-06, /* 0xb684e21a */
00049 /*
00050  * Coefficients for approximation to  erf  in [0.84375,1.25] 
00051  */
00052 pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
00053 pa1  =  4.1485610604e-01, /* 0x3ed46805 */
00054 pa2  = -3.7220788002e-01, /* 0xbebe9208 */
00055 pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
00056 pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
00057 pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
00058 pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
00059 qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
00060 qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
00061 qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
00062 qa4  =  1.2617121637e-01, /* 0x3e013307 */
00063 qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
00064 qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
00065 /*
00066  * Coefficients for approximation to  erfc in [1.25,1/0.35]
00067  */
00068 ra0  = -9.8649440333e-03, /* 0xbc21a093 */
00069 ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
00070 ra2  = -1.0558626175e+01, /* 0xc128f022 */
00071 ra3  = -6.2375331879e+01, /* 0xc2798057 */
00072 ra4  = -1.6239666748e+02, /* 0xc322658c */
00073 ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
00074 ra6  = -8.1287437439e+01, /* 0xc2a2932b */
00075 ra7  = -9.8143291473e+00, /* 0xc11d077e */
00076 sa1  =  1.9651271820e+01, /* 0x419d35ce */
00077 sa2  =  1.3765776062e+02, /* 0x4309a863 */
00078 sa3  =  4.3456588745e+02, /* 0x43d9486f */
00079 sa4  =  6.4538726807e+02, /* 0x442158c9 */
00080 sa5  =  4.2900814819e+02, /* 0x43d6810b */
00081 sa6  =  1.0863500214e+02, /* 0x42d9451f */
00082 sa7  =  6.5702495575e+00, /* 0x40d23f7c */
00083 sa8  = -6.0424413532e-02, /* 0xbd777f97 */
00084 /*
00085  * Coefficients for approximation to  erfc in [1/.35,28]
00086  */
00087 rb0  = -9.8649431020e-03, /* 0xbc21a092 */
00088 rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
00089 rb2  = -1.7757955551e+01, /* 0xc18e104b */
00090 rb3  = -1.6063638306e+02, /* 0xc320a2ea */
00091 rb4  = -6.3756646729e+02, /* 0xc41f6441 */
00092 rb5  = -1.0250950928e+03, /* 0xc480230b */
00093 rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
00094 sb1  =  3.0338060379e+01, /* 0x41f2b459 */
00095 sb2  =  3.2579251099e+02, /* 0x43a2e571 */
00096 sb3  =  1.5367296143e+03, /* 0x44c01759 */
00097 sb4  =  3.1998581543e+03, /* 0x4547fdbb */
00098 sb5  =  2.5530502930e+03, /* 0x451f90ce */
00099 sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
00100 sb7  = -2.2440952301e+01; /* 0xc1b38712 */
00101 
00102 #ifdef __STDC__
00103        float __erff(float x)
00104 #else
00105        float __erff(x)
00106        float x;
00107 #endif
00108 {
00109        int32_t hx,ix,i;
00110        float R,S,P,Q,s,y,z,r;
00111        GET_FLOAT_WORD(hx,x);
00112        ix = hx&0x7fffffff;
00113        if(ix>=0x7f800000) {        /* erf(nan)=nan */
00114            i = ((u_int32_t)hx>>31)<<1;
00115            return (float)(1-i)+one/x;     /* erf(+-inf)=+-1 */
00116        }
00117 
00118        if(ix < 0x3f580000) {              /* |x|<0.84375 */
00119            if(ix < 0x31800000) {   /* |x|<2**-28 */
00120                if (ix < 0x04000000) 
00121                   /*avoid underflow */
00122                   return (float)0.125*((float)8.0*x+efx8*x);
00123               return x + efx*x;
00124            }
00125            z = x*x;
00126            r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
00127            s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
00128            y = r/s;
00129            return x + x*y;
00130        }
00131        if(ix < 0x3fa00000) {              /* 0.84375 <= |x| < 1.25 */
00132            s = fabsf(x)-one;
00133            P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
00134            Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
00135            if(hx>=0) return erx + P/Q; else return -erx - P/Q;
00136        }
00137        if (ix >= 0x40c00000) {            /* inf>|x|>=6 */
00138            if(hx>=0) return one-tiny; else return tiny-one;
00139        }
00140        x = fabsf(x);
00141        s = one/(x*x);
00142        if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
00143            R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
00144                             ra5+s*(ra6+s*ra7))))));
00145            S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
00146                             sa5+s*(sa6+s*(sa7+s*sa8)))))));
00147        } else {      /* |x| >= 1/0.35 */
00148            R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
00149                             rb5+s*rb6)))));
00150            S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
00151                             sb5+s*(sb6+s*sb7))))));
00152        }
00153        GET_FLOAT_WORD(ix,x);
00154        SET_FLOAT_WORD(z,ix&0xfffff000);
00155        r  =  __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
00156        if(hx>=0) return one-r/x; else return  r/x-one;
00157 }
00158 weak_alias (__erff, erff)
00159 
00160 #ifdef __STDC__
00161        float __erfcf(float x)
00162 #else
00163        float __erfcf(x)
00164        float x;
00165 #endif
00166 {
00167        int32_t hx,ix;
00168        float R,S,P,Q,s,y,z,r;
00169        GET_FLOAT_WORD(hx,x);
00170        ix = hx&0x7fffffff;
00171        if(ix>=0x7f800000) {               /* erfc(nan)=nan */
00172                                           /* erfc(+-inf)=0,2 */
00173            return (float)(((u_int32_t)hx>>31)<<1)+one/x;
00174        }
00175 
00176        if(ix < 0x3f580000) {              /* |x|<0.84375 */
00177            if(ix < 0x23800000)     /* |x|<2**-56 */
00178               return one-x;
00179            z = x*x;
00180            r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
00181            s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
00182            y = r/s;
00183            if(hx < 0x3e800000) {   /* x<1/4 */
00184               return one-(x+x*y);
00185            } else {
00186               r = x*y;
00187               r += (x-half);
00188                return half - r ;
00189            }
00190        }
00191        if(ix < 0x3fa00000) {              /* 0.84375 <= |x| < 1.25 */
00192            s = fabsf(x)-one;
00193            P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
00194            Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
00195            if(hx>=0) {
00196                z  = one-erx; return z - P/Q; 
00197            } else {
00198               z = erx+P/Q; return one+z;
00199            }
00200        }
00201        if (ix < 0x41e00000) {             /* |x|<28 */
00202            x = fabsf(x);
00203            s = one/(x*x);
00204            if(ix< 0x4036DB6D) {    /* |x| < 1/.35 ~ 2.857143*/
00205                R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
00206                             ra5+s*(ra6+s*ra7))))));
00207                S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
00208                             sa5+s*(sa6+s*(sa7+s*sa8)))))));
00209            } else {                /* |x| >= 1/.35 ~ 2.857143 */
00210               if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
00211                R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
00212                             rb5+s*rb6)))));
00213                S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
00214                             sb5+s*(sb6+s*sb7))))));
00215            }
00216            GET_FLOAT_WORD(ix,x);
00217            SET_FLOAT_WORD(z,ix&0xfffff000);
00218            r  =  __ieee754_expf(-z*z-(float)0.5625)*
00219                      __ieee754_expf((z-x)*(z+x)+R/S);
00220            if(hx>0) return r/x; else return two-r/x;
00221        } else {
00222            if(hx>0) return tiny*tiny; else return two-tiny;
00223        }
00224 }
00225 weak_alias (__erfcf, erfcf)