newlib/libm/machine/amdgcn/v64sf_erf.c

   1 /*
   2  * Copyright 2023 Siemens
   3  *
   4  * The authors hereby grant permission to use, copy, modify, distribute,
   5  * and license this software and its documentation for any purpose, provided
   6  * that existing copyright notices are retained in all copies and that this
   7  * notice is included verbatim in any distributions.  No written agreement,
   8  * license, or royalty fee is required for any of the authorized uses.
   9  * Modifications to this software may be copyrighted by their authors
  10  * and need not follow the licensing terms described here, provided that
  11  * the new terms are clearly indicated on the first page of each file where
  12  * they apply.
  13  */
  14
  15 /*
  16  * ====================================================
  17  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  18  *
  19  * Developed at SunPro, a Sun Microsystems, Inc. business.
  20  * Permission to use, copy, modify, and distribute this
  21  * software is freely granted, provided that this notice
  22  * is preserved.
  23  * ====================================================
  24  */
  25
  26 /* Based on newlib/libm/mathfp/sf_erf.c in Newlib.  */
  27
  28 #include "amdgcnmach.h"
  29
  30 v64sf v64sf_expf_aux (v64sf, v64si);
  31
  32 static const float
  33 tiny        = 1e-30,
  34 half=  5.0000000000e-01, /* 0x3F000000 */
  35 one =  1.0000000000e+00, /* 0x3F800000 */
  36 two =  2.0000000000e+00, /* 0x40000000 */
  37         /* c = (subfloat)0.84506291151 */
  38 erx =  8.4506291151e-01, /* 0x3f58560b */
  39 /*
  40  * Coefficients for approximation to  erf on [0,0.84375]
  41  */
  42 efx =  1.2837916613e-01, /* 0x3e0375d4 */
  43 efx8=  1.0270333290e+00, /* 0x3f8375d4 */
  44 pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
  45 pp1  = -3.2504209876e-01, /* 0xbea66beb */
  46 pp2  = -2.8481749818e-02, /* 0xbce9528f */
  47 pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
  48 pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
  49 qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
  50 qq2  =  6.5022252500e-02, /* 0x3d852a63 */
  51 qq3  =  5.0813062117e-03, /* 0x3ba68116 */
  52 qq4  =  1.3249473704e-04, /* 0x390aee49 */
  53 qq5  = -3.9602282413e-06, /* 0xb684e21a */
  54 /*
  55  * Coefficients for approximation to  erf  in [0.84375,1.25]
  56  */
  57 pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
  58 pa1  =  4.1485610604e-01, /* 0x3ed46805 */
  59 pa2  = -3.7220788002e-01, /* 0xbebe9208 */
  60 pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
  61 pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
  62 pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
  63 pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
  64 qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
  65 qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
  66 qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
  67 qa4  =  1.2617121637e-01, /* 0x3e013307 */
  68 qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
  69 qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
  70 /*
  71  * Coefficients for approximation to  erfc in [1.25,1/0.35]
  72  */
  73 ra0  = -9.8649440333e-03, /* 0xbc21a093 */
  74 ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
  75 ra2  = -1.0558626175e+01, /* 0xc128f022 */
  76 ra3  = -6.2375331879e+01, /* 0xc2798057 */
  77 ra4  = -1.6239666748e+02, /* 0xc322658c */
  78 ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
  79 ra6  = -8.1287437439e+01, /* 0xc2a2932b */
  80 ra7  = -9.8143291473e+00, /* 0xc11d077e */
  81 sa1  =  1.9651271820e+01, /* 0x419d35ce */
  82 sa2  =  1.3765776062e+02, /* 0x4309a863 */
  83 sa3  =  4.3456588745e+02, /* 0x43d9486f */
  84 sa4  =  6.4538726807e+02, /* 0x442158c9 */
  85 sa5  =  4.2900814819e+02, /* 0x43d6810b */
  86 sa6  =  1.0863500214e+02, /* 0x42d9451f */
  87 sa7  =  6.5702495575e+00, /* 0x40d23f7c */
  88 sa8  = -6.0424413532e-02, /* 0xbd777f97 */
  89 /*
  90  * Coefficients for approximation to  erfc in [1/.35,28]
  91  */
  92 rb0  = -9.8649431020e-03, /* 0xbc21a092 */
  93 rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
  94 rb2  = -1.7757955551e+01, /* 0xc18e104b */
  95 rb3  = -1.6063638306e+02, /* 0xc320a2ea */
  96 rb4  = -6.3756646729e+02, /* 0xc41f6441 */
  97 rb5  = -1.0250950928e+03, /* 0xc480230b */
  98 rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
  99 sb1  =  3.0338060379e+01, /* 0x41f2b459 */
 100 sb2  =  3.2579251099e+02, /* 0x43a2e571 */
 101 sb3  =  1.5367296143e+03, /* 0x44c01759 */
 102 sb4  =  3.1998581543e+03, /* 0x4547fdbb */
 103 sb5  =  2.5530502930e+03, /* 0x451f90ce */
 104 sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
 105 sb7  = -2.2440952301e+01; /* 0xc1b38712 */
 106
 107 #if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsvf)
 108
 109 DEF_VS_MATH_FUNC (v64sf, erff, v64sf x)
 110 {
 111   FUNCTION_INIT (v64sf);
 112
 113   v64si hx;
 114   GET_FLOAT_WORD (hx, x, NO_COND);
 115   v64si ix = hx & 0x7fffffff;
 116
 117   VECTOR_IF (ix >= 0x7f800000, cond)            /* erf(nan)=nan */
 118     v64si i = (hx >> 31) << 1;
 119     /* erf(+-inf)=+-1 */
 120     VECTOR_RETURN (__builtin_convertvector (1 - i, v64sf) + 1.0f / x, cond);
 121   VECTOR_ENDIF
 122
 123   VECTOR_IF (ix < 0x3f580000, cond)                     /* |x|<0.84375 */
 124     VECTOR_IF2 (ix < 0x31800000, cond2, cond)           /* |x|<2**-28 */
 125       VECTOR_IF2 (ix < 0x04000000, cond3, cond2)        /* avoid underflow */
 126         VECTOR_RETURN (0.125f*(8.0f*x + efx8*x), cond3);
 127       VECTOR_ENDIF
 128       VECTOR_RETURN (x + efx*x, cond2);
 129     VECTOR_ENDIF
 130
 131     v64sf z = x*x;
 132     v64sf r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 133     v64sf s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 134     v64sf y = r/s;
 135
 136     VECTOR_RETURN (x + x*y, cond);
 137   VECTOR_ENDIF
 138
 139   VECTOR_IF (ix < 0x3fa00000, cond)     /* 0.84375 <= |x| < 1.25 */
 140     v64sf s = __builtin_gcn_fabsvf (x) - 1.0f;
 141     v64sf P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 142     v64sf Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
 143     VECTOR_IF2 (hx >= 0, cond2, cond)
 144       VECTOR_RETURN (erx + P/Q, cond2);
 145     VECTOR_ELSE2 (cond2, cond)
 146       VECTOR_RETURN (-erx - P/Q, cond2);
 147     VECTOR_ENDIF
 148   VECTOR_ENDIF
 149
 150   VECTOR_IF (ix >= 0x40c00000, cond)    /* inf>|x|>=6 */
 151     VECTOR_IF2 (hx >= 0, cond2, cond)
 152       VECTOR_RETURN (VECTOR_INIT (1.0f - tiny), cond2);
 153     VECTOR_ELSE2 (cond2, cond)
 154       VECTOR_RETURN (VECTOR_INIT (tiny - 1.0f), cond2);
 155     VECTOR_ENDIF
 156   VECTOR_ENDIF
 157
 158   x = __builtin_gcn_fabsvf(x);
 159   v64sf s = 1.0f / (x*x);
 160   v64sf R, S;
 161   VECTOR_IF (ix < 0x4036DB6E, cond)     /* |x| < 1/0.35 */
 162     VECTOR_COND_MOVE (R, ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 163                          ra5+s*(ra6+s*ra7)))))), cond);
 164     VECTOR_COND_MOVE (S, one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 165                          sa5+s*(sa6+s*(sa7+s*sa8))))))), cond);
 166   VECTOR_ELSE (cond)                    /* |x| >= 1/0.35 */
 167     VECTOR_COND_MOVE (R, rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 168                          rb5+s*rb6))))), cond);
 169     VECTOR_COND_MOVE (S, one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 170                          sb5+s*(sb6+s*sb7)))))), cond);
 171   VECTOR_ENDIF
 172
 173   GET_FLOAT_WORD (ix, x, NO_COND);
 174   v64sf z;
 175   SET_FLOAT_WORD (z, ix & 0xfffff000, NO_COND);
 176   v64sf r = v64sf_expf_aux (-z*z - 0.5625f, __mask)
 177             * v64sf_expf_aux ((z-x)*(z+x) + R/S, __mask);
 178   VECTOR_RETURN (one - r/x, hx >= 0);
 179   VECTOR_RETURN (r/x - one, hx < 0);
 180
 181   FUNCTION_RETURN;
 182 }
 183
 184 DEF_VARIANTS (erff, sf, sf)
 185
 186 #endif