/* * Copyright 2023 Siemens * * The authors hereby grant permission to use, copy, modify, distribute, * and license this software and its documentation for any purpose, provided * that existing copyright notices are retained in all copies and that this * notice is included verbatim in any distributions. No written agreement, * license, or royalty fee is required for any of the authorized uses. * Modifications to this software may be copyrighted by their authors * and need not follow the licensing terms described here, provided that * the new terms are clearly indicated on the first page of each file where * they apply. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* Based on newlib/libm/mathfp/s_erf.c in Newlib. */ #include "amdgcnmach.h" v64df v64df_exp_aux (v64df, v64di); static const double tiny = 1e-300, half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ /* c = (float)0.84506291151 */ erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ /* * Coefficients for approximation to erf on [0,0.84375] */ efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ /* * Coefficients for approximation to erf in [0.84375,1.25] */ pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ /* * Coefficients for approximation to erfc in [1.25,1/0.35] */ ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ /* * Coefficients for approximation to erfc in [1/.35,28] */ rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ #if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsv) DEF_VD_MATH_FUNC (v64df, erf, v64df x) { FUNCTION_INIT (v64df); v64si hx; GET_HIGH_WORD (hx, x, NO_COND); v64si ix = hx & 0x7fffffff; VECTOR_IF (ix >= 0x7ff00000, cond) /* erf(nan)=nan */ v64si i = (hx >> 31) << 1; /* erf(+-inf)=+-1 */ VECTOR_RETURN (__builtin_convertvector (1 - i, v64df) + one / x, cond); VECTOR_ENDIF VECTOR_IF (ix < 0x3feb0000, cond) /* |x|<0.84375 */ VECTOR_IF2 (ix < 0x3e300000, cond2, cond) /* |x|<2**-28 */ VECTOR_IF2 (ix < 0x00800000, cond3, cond2) /* avoid underflow */ VECTOR_RETURN (0.125*(8.0*x + efx8*x), cond3); VECTOR_ENDIF VECTOR_RETURN (x + efx*x, cond2); VECTOR_ENDIF v64df z = x*x; v64df r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); v64df s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); v64df y = r/s; VECTOR_RETURN (x + x*y, cond); VECTOR_ENDIF VECTOR_IF (ix < 0x3ff40000, cond) /* 0.84375 <= |x| < 1.25 */ v64df s = __builtin_gcn_fabsv (x) - one; v64df P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); v64df Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); VECTOR_IF2 (hx >= 0, cond2, cond) VECTOR_RETURN (erx + P/Q, cond2); VECTOR_ELSE2 (cond2, cond) VECTOR_RETURN (-erx - P/Q, cond2); VECTOR_ENDIF VECTOR_ENDIF VECTOR_IF (ix >= 0x40180000, cond) /* inf>|x|>=6 */ VECTOR_IF2 (hx >= 0, cond2, cond) VECTOR_RETURN (VECTOR_INIT (1.0 - tiny), cond2); VECTOR_ELSE2 (cond2, cond) VECTOR_RETURN (VECTOR_INIT (tiny - 1.0), cond2); VECTOR_ENDIF VECTOR_ENDIF x = __builtin_gcn_fabsv(x); v64df s = 1.0 / (x*x); v64df R, S; VECTOR_IF (ix < 0x4006DB6E, cond) /* |x| < 1/0.35 */ VECTOR_COND_MOVE (R, ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( ra5+s*(ra6+s*ra7)))))), cond); VECTOR_COND_MOVE (S, one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( sa5+s*(sa6+s*(sa7+s*sa8))))))), cond); VECTOR_ELSE (cond) /* |x| >= 1/0.35 */ VECTOR_COND_MOVE (R, rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( rb5+s*rb6))))), cond); VECTOR_COND_MOVE (S, one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( sb5+s*(sb6+s*sb7)))))), cond); VECTOR_ENDIF v64df z; SET_LOW_WORD (z, VECTOR_INIT(0), NO_COND); v64df r = v64df_exp_aux (-z*z - 0.5625, __mask) * v64df_exp_aux ((z-x)*(z+x) + R/S, __mask); VECTOR_RETURN (one - r/x, hx >= 0); VECTOR_RETURN (r/x - one, hx < 0); FUNCTION_RETURN; } DEF_VARIANTS (erf, df, df) #endif