newlib/libm/machine/amdgcn/v64df_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/s_erf.c in Newlib.  */
  27
  28 #include "amdgcnmach.h"
  29
  30 v64df v64df_exp_aux (v64df, v64di);
  31
  32 static const double
  33 tiny        = 1e-300,
  34 half=  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  35 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  36 two =  2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
  37 /* c = (float)0.84506291151 */
  38 erx =  8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
  39 /*
  40  * Coefficients for approximation to  erf on [0,0.84375]
  41  */
  42 efx =  1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
  43 efx8=  1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
  44 pp0  =  1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
  45 pp1  = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
  46 pp2  = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
  47 pp3  = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
  48 pp4  = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
  49 qq1  =  3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
  50 qq2  =  6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
  51 qq3  =  5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
  52 qq4  =  1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
  53 qq5  = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
  54 /*
  55  * Coefficients for approximation to  erf  in [0.84375,1.25]
  56  */
  57 pa0  = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
  58 pa1  =  4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
  59 pa2  = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
  60 pa3  =  3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
  61 pa4  = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
  62 pa5  =  3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
  63 pa6  = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
  64 qa1  =  1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
  65 qa2  =  5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
  66 qa3  =  7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
  67 qa4  =  1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
  68 qa5  =  1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
  69 qa6  =  1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
  70 /*
  71  * Coefficients for approximation to  erfc in [1.25,1/0.35]
  72  */
  73 ra0  = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
  74 ra1  = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
  75 ra2  = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
  76 ra3  = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
  77 ra4  = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
  78 ra5  = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
  79 ra6  = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
  80 ra7  = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
  81 sa1  =  1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
  82 sa2  =  1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
  83 sa3  =  4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
  84 sa4  =  6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
  85 sa5  =  4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
  86 sa6  =  1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
  87 sa7  =  6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
  88 sa8  = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
  89 /*
  90  * Coefficients for approximation to  erfc in [1/.35,28]
  91  */
  92 rb0  = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
  93 rb1  = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
  94 rb2  = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
  95 rb3  = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
  96 rb4  = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
  97 rb5  = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
  98 rb6  = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
  99 sb1  =  3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
 100 sb2  =  3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
 101 sb3  =  1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
 102 sb4  =  3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
 103 sb5  =  2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
 104 sb6  =  4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
 105 sb7  = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
 106
 107 #if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsv)
 108
 109 DEF_VD_MATH_FUNC (v64df, erf, v64df x)
 110 {
 111   FUNCTION_INIT (v64df);
 112
 113   v64si hx;
 114   GET_HIGH_WORD (hx, x, NO_COND);
 115   v64si ix = hx & 0x7fffffff;
 116
 117   VECTOR_IF (ix >= 0x7ff00000, cond)            /* erf(nan)=nan */
 118     v64si i = (hx >> 31) << 1;
 119     /* erf(+-inf)=+-1 */
 120     VECTOR_RETURN (__builtin_convertvector (1 - i, v64df) + one / x, cond);
 121   VECTOR_ENDIF
 122
 123   VECTOR_IF (ix < 0x3feb0000, cond)                     /* |x|<0.84375 */
 124     VECTOR_IF2 (ix < 0x3e300000, cond2, cond)           /* |x|<2**-28 */
 125       VECTOR_IF2 (ix < 0x00800000, cond3, cond2)        /* avoid underflow */
 126         VECTOR_RETURN (0.125*(8.0*x + efx8*x), cond3);
 127       VECTOR_ENDIF
 128       VECTOR_RETURN (x + efx*x, cond2);
 129     VECTOR_ENDIF
 130
 131     v64df z = x*x;
 132     v64df r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 133     v64df s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
 134     v64df y = r/s;
 135
 136     VECTOR_RETURN (x + x*y, cond);
 137   VECTOR_ENDIF
 138
 139   VECTOR_IF (ix < 0x3ff40000, cond)     /* 0.84375 <= |x| < 1.25 */
 140     v64df s = __builtin_gcn_fabsv (x) - one;
 141     v64df P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 142     v64df 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 >= 0x40180000, cond)    /* inf>|x|>=6 */
 151     VECTOR_IF2 (hx >= 0, cond2, cond)
 152       VECTOR_RETURN (VECTOR_INIT (1.0 - tiny), cond2);
 153     VECTOR_ELSE2 (cond2, cond)
 154       VECTOR_RETURN (VECTOR_INIT (tiny - 1.0), cond2);
 155     VECTOR_ENDIF
 156   VECTOR_ENDIF
 157
 158   x = __builtin_gcn_fabsv(x);
 159   v64df s = 1.0 / (x*x);
 160   v64df R, S;
 161   VECTOR_IF (ix < 0x4006DB6E, 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   v64df z;
 174   SET_LOW_WORD (z, VECTOR_INIT(0), NO_COND);
 175   v64df r = v64df_exp_aux (-z*z - 0.5625, __mask)
 176             * v64df_exp_aux ((z-x)*(z+x) + R/S, __mask);
 177   VECTOR_RETURN (one - r/x, hx >= 0);
 178   VECTOR_RETURN (r/x - one, hx < 0);
 179
 180   FUNCTION_RETURN;
 181 }
 182
 183 DEF_VARIANTS (erf, df, df)
 184
 185 #endif