301 lines
11 KiB
C
301 lines
11 KiB
C
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/*
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* Copyright 2023 Siemens
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*
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* The authors hereby grant permission to use, copy, modify, distribute,
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* and license this software and its documentation for any purpose, provided
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* that existing copyright notices are retained in all copies and that this
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* notice is included verbatim in any distributions. No written agreement,
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* license, or royalty fee is required for any of the authorized uses.
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* Modifications to this software may be copyrighted by their authors
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* and need not follow the licensing terms described here, provided that
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* the new terms are clearly indicated on the first page of each file where
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* they apply.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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*/
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/* Based on newlib/libm/math/erf_lgamma.c in Newlib. */
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#include "amdgcnmach.h"
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static const float two23= 8.3886080000e+06, /* 0x4b000000 */
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half= 5.0000000000e-01, /* 0x3f000000 */
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one = 1.0000000000e+00, /* 0x3f800000 */
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pi = 3.1415927410e+00, /* 0x40490fdb */
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a0 = 7.7215664089e-02, /* 0x3d9e233f */
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a1 = 3.2246702909e-01, /* 0x3ea51a66 */
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a2 = 6.7352302372e-02, /* 0x3d89f001 */
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a3 = 2.0580807701e-02, /* 0x3ca89915 */
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a4 = 7.3855509982e-03, /* 0x3bf2027e */
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a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
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a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
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a7 = 5.1006977446e-04, /* 0x3a05b634 */
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a8 = 2.2086278477e-04, /* 0x39679767 */
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a9 = 1.0801156895e-04, /* 0x38e28445 */
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a10 = 2.5214456400e-05, /* 0x37d383a2 */
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a11 = 4.4864096708e-05, /* 0x383c2c75 */
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tc = 1.4616321325e+00, /* 0x3fbb16c3 */
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tf = -1.2148628384e-01, /* 0xbdf8cdcd */
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/* tt = -(tail of tf) */
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tt = 6.6971006518e-09, /* 0x31e61c52 */
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t0 = 4.8383611441e-01, /* 0x3ef7b95e */
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t1 = -1.4758771658e-01, /* 0xbe17213c */
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t2 = 6.4624942839e-02, /* 0x3d845a15 */
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t3 = -3.2788541168e-02, /* 0xbd064d47 */
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t4 = 1.7970675603e-02, /* 0x3c93373d */
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t5 = -1.0314224288e-02, /* 0xbc28fcfe */
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t6 = 6.1005386524e-03, /* 0x3bc7e707 */
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t7 = -3.6845202558e-03, /* 0xbb7177fe */
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t8 = 2.2596477065e-03, /* 0x3b141699 */
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t9 = -1.4034647029e-03, /* 0xbab7f476 */
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t10 = 8.8108185446e-04, /* 0x3a66f867 */
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t11 = -5.3859531181e-04, /* 0xba0d3085 */
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t12 = 3.1563205994e-04, /* 0x39a57b6b */
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t13 = -3.1275415677e-04, /* 0xb9a3f927 */
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t14 = 3.3552918467e-04, /* 0x39afe9f7 */
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u0 = -7.7215664089e-02, /* 0xbd9e233f */
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u1 = 6.3282704353e-01, /* 0x3f2200f4 */
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u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
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u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
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u4 = 2.2896373272e-01, /* 0x3e6a7578 */
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u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
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v1 = 2.4559779167e+00, /* 0x401d2ebe */
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v2 = 2.1284897327e+00, /* 0x4008392d */
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v3 = 7.6928514242e-01, /* 0x3f44efdf */
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v4 = 1.0422264785e-01, /* 0x3dd572af */
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v5 = 3.2170924824e-03, /* 0x3b52d5db */
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s0 = -7.7215664089e-02, /* 0xbd9e233f */
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s1 = 2.1498242021e-01, /* 0x3e5c245a */
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s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
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s3 = 1.4635047317e-01, /* 0x3e15dce6 */
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s4 = 2.6642270386e-02, /* 0x3cda40e4 */
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s5 = 1.8402845599e-03, /* 0x3af135b4 */
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s6 = 3.1947532989e-05, /* 0x3805ff67 */
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r1 = 1.3920053244e+00, /* 0x3fb22d3b */
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r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
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r3 = 1.7193385959e-01, /* 0x3e300f6e */
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r4 = 1.8645919859e-02, /* 0x3c98bf54 */
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r5 = 7.7794247773e-04, /* 0x3a4beed6 */
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r6 = 7.3266842264e-06, /* 0x36f5d7bd */
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w0 = 4.1893854737e-01, /* 0x3ed67f1d */
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w1 = 8.3333335817e-02, /* 0x3daaaaab */
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w2 = -2.7777778450e-03, /* 0xbb360b61 */
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w3 = 7.9365057172e-04, /* 0x3a500cfd */
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w4 = -5.9518753551e-04, /* 0xba1c065c */
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w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
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w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
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static const float zero= 0.0000000000e+00;
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v64sf v64sf_cosf_aux (v64sf x, v64si __mask);
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v64sf v64sf_logf_aux (v64sf x, v64si __mask);
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v64sf v64sf_sinf_aux (v64sf x, v64si __mask);
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#if defined (__has_builtin) \
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&& __has_builtin (__builtin_gcn_floorvf) \
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&& __has_builtin (__builtin_gcn_fabsvf)
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static v64sf
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v64sf_sin_pif (v64sf x)
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{
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// Explicitly create mask for internal function.
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v64si __mask = VECTOR_INIT (-1);
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FUNCTION_INIT (v64sf);
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v64sf y, z;
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v64si n, ix;
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GET_FLOAT_WORD (ix, x, NO_COND);
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ix &= 0x7fffffff;
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VECTOR_IF (ix < 0x3e800000, cond)
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VECTOR_RETURN (v64sf_sinf_aux (pi * x, __mask), cond);
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VECTOR_ENDIF
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y = -x; /* x is assume negative */
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/*
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* argument reduction, make sure inexact flag not raised if input
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* is an integer
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*/
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z = __builtin_gcn_floorvf (y);
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VECTOR_IF (z != y, cond)
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/* inexact anyway */
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VECTOR_COND_MOVE(y, y * 0.5F, cond);
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VECTOR_COND_MOVE(y, 2.0F * (y - __builtin_gcn_floorvf (y)), cond); /* y = |x| mod 2.0 */
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VECTOR_COND_MOVE(n, __builtin_convertvector(y * 4.0F, v64si), cond);
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VECTOR_ELSE (cond)
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VECTOR_IF2 (ix >= 0x4b800000, cond2, cond)
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VECTOR_COND_MOVE(y, VECTOR_INIT(zero), cond2);
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VECTOR_COND_MOVE(n, VECTOR_INIT(0), cond2); /* y must be even */
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VECTOR_ELSE2 (cond2, cond)
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VECTOR_COND_MOVE(z, y + two23 /* exact */, cond2 & (ix < 0x4b000000));
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GET_FLOAT_WORD (n, z, cond2);
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VECTOR_COND_MOVE(n, n & 1, cond2);
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VECTOR_COND_MOVE(y, __builtin_convertvector(n, v64sf), cond2);
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VECTOR_COND_MOVE(n, n << 2, cond2);
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VECTOR_ENDIF
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VECTOR_ENDIF
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VECTOR_IF (n == 0, cond)
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VECTOR_COND_MOVE(y, v64sf_sinf_aux (pi * y, __mask), cond);
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VECTOR_ELSEIF (n == 1 | n == 2, cond)
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VECTOR_COND_MOVE(y, v64sf_cosf_aux (pi * (0.5F - y), __mask), cond);
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VECTOR_ELSEIF (n == 3 | n == 4, cond)
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VECTOR_COND_MOVE(y, v64sf_sinf_aux (pi * (VECTOR_INIT(one) - y), __mask), cond);
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VECTOR_ELSEIF (n == 5 | n == 6, cond)
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VECTOR_COND_MOVE(y, -v64sf_cosf_aux (pi * (y - 1.5F), __mask), cond);
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VECTOR_ELSE (cond)
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VECTOR_COND_MOVE(y, v64sf_sinf_aux (pi * (y - 2.0F), __mask), cond);
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VECTOR_ENDIF
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VECTOR_RETURN(-y, NO_COND);
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FUNCTION_RETURN;
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}
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DEF_VS_MATH_FUNC (v64sf, lgammaf_r, v64sf x, v64si *signgamp)
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{
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FUNCTION_INIT (v64sf);
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v64sf t,y,z,nadj = VECTOR_INIT(0.0F),p,p1,p2,p3,q,r,w;
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v64si i,hx,ix;
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GET_FLOAT_WORD(hx,x,NO_COND);
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/* purge off +-inf, NaN, +-0, and negative arguments */
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*signgamp = VECTOR_INIT(1);
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ix = hx&0x7fffffff;
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VECTOR_IF(ix>=0x7f800000, cond)
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VECTOR_RETURN (x*x, cond);
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VECTOR_ENDIF
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VECTOR_IF(ix==0, cond)
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VECTOR_COND_MOVE(*signgamp, VECTOR_INIT(-1), cond & (hx<0));
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VECTOR_RETURN(one/(x-x), cond);
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VECTOR_ENDIF
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VECTOR_IF (ix < 0x30800000, cond) /* |x|<2**-30, return -log(|x|) */
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VECTOR_IF2(hx<0, cond2, cond)
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VECTOR_COND_MOVE(*signgamp, VECTOR_INIT(-1), cond);
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VECTOR_RETURN (-v64sf_logf_aux(-x, __mask), cond2);
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VECTOR_ELSE2(cond2, cond)
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VECTOR_RETURN (-v64sf_logf_aux(x, __mask), cond2);
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VECTOR_ENDIF
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VECTOR_ENDIF
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VECTOR_IF (hx < 0, cond)
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VECTOR_IF2(ix>=0x4b000000, cond2, cond) /* |x|>=2**23, must be -integer */
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VECTOR_RETURN(one/(x-x), cond2);
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VECTOR_ENDIF
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VECTOR_COND_MOVE (t, v64sf_sin_pif (x), cond);
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VECTOR_IF2(t==zero, cond2, cond)
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/* tgamma wants NaN instead of INFINITY */
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VECTOR_RETURN(one/(x-x), cond2); /* -integer */
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VECTOR_ENDIF
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VECTOR_COND_MOVE(nadj, v64sf_logf_aux(VECTOR_INIT(pi)/__builtin_gcn_fabsvf(t*x), __mask), cond);
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VECTOR_COND_MOVE(*signgamp, VECTOR_INIT(-1), cond & (t < zero));
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VECTOR_COND_MOVE(x, -x, cond);
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VECTOR_ENDIF
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/* purge off 1 and 2 */
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VECTOR_IF(ix==0x3f800000|ix==0x40000000, cond)
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VECTOR_COND_MOVE(r, VECTOR_INIT(0.0F), cond);
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/* for x < 2.0 */
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VECTOR_ELSEIF(ix<0x40000000, cond)
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VECTOR_IF2(ix<=0x3f666666, cond2, cond)
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/* lgamma(x) = lgamma(x+1)-log(x) */
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r = -v64sf_logf_aux(x, __mask);
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VECTOR_IF2(ix>=0x3f3b4a20, cond3, cond2)
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VECTOR_COND_MOVE(y, one-x, cond3);
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VECTOR_COND_MOVE(i, VECTOR_INIT(0), cond3);
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VECTOR_ELSEIF2(ix>=0x3e6d3308, cond3, cond2)
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VECTOR_COND_MOVE(y, x-(tc-one), cond3);
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VECTOR_COND_MOVE(i, VECTOR_INIT(1), cond3);
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VECTOR_ELSE2(cond3, cond2)
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VECTOR_COND_MOVE(y, x, cond3);
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VECTOR_COND_MOVE(i, VECTOR_INIT(2), cond3);
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VECTOR_ENDIF
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VECTOR_ELSE2(cond2, cond)
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VECTOR_COND_MOVE(r, VECTOR_INIT(zero), cond2);
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VECTOR_IF2(ix>=0x3fdda618, cond3, cond2) /* [1.7316,2] */
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VECTOR_COND_MOVE(y, VECTOR_INIT(2.0F)-x, cond3);
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VECTOR_COND_MOVE(i, VECTOR_INIT(0), cond3);
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VECTOR_ELSEIF2(ix>=0x3F9da620, cond3, cond2) /* [1.23,1.73] */
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VECTOR_COND_MOVE(y, x-tc, cond3);
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VECTOR_COND_MOVE(i, VECTOR_INIT(1), cond3);
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VECTOR_ELSE2(cond3, cond2)
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VECTOR_COND_MOVE(y, x-one, cond3);
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VECTOR_COND_MOVE(i, VECTOR_INIT(2), cond3);
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VECTOR_ENDIF
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VECTOR_ENDIF
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VECTOR_IF2(i==0, cond2, cond)
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VECTOR_COND_MOVE(z, y*y, cond2);
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VECTOR_COND_MOVE(p1, a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))), cond2);
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VECTOR_COND_MOVE(p2, z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))), cond2);
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VECTOR_COND_MOVE(p, y*p1+p2, cond2);
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VECTOR_COND_MOVE(r, r + (p-(float)0.5*y), cond2);
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VECTOR_ELSEIF2(i==1, cond2, cond)
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VECTOR_COND_MOVE(z, y*y, cond2);
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VECTOR_COND_MOVE(w, z*y, cond2);
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VECTOR_COND_MOVE(p1, t0+w*(t3+w*(t6+w*(t9 +w*t12))), cond2); /* parallel comp */
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VECTOR_COND_MOVE(p2, t1+w*(t4+w*(t7+w*(t10+w*t13))), cond2);
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VECTOR_COND_MOVE(p3, t2+w*(t5+w*(t8+w*(t11+w*t14))), cond2);
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VECTOR_COND_MOVE(p, z*p1-(tt-w*(p2+y*p3)), cond2);
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VECTOR_COND_MOVE(r, r + (tf + p), cond2);
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VECTOR_ELSEIF2(i==2, cond2, cond)
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VECTOR_COND_MOVE(p1, y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))), cond2);
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VECTOR_COND_MOVE(p2, one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))), cond2);
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VECTOR_COND_MOVE(r, r + (-(float)0.5*y + p1/p2), cond2);
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VECTOR_ENDIF
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VECTOR_ELSEIF(ix<0x41000000, cond)
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/* x < 8.0 */
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VECTOR_COND_MOVE(i, __builtin_convertvector(x, v64si), cond);
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VECTOR_COND_MOVE(t, VECTOR_INIT(zero), cond);
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VECTOR_COND_MOVE(y, x-__builtin_convertvector(i, v64sf), cond);
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VECTOR_COND_MOVE(p, y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))), cond);
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VECTOR_COND_MOVE(q, one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))), cond);
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VECTOR_COND_MOVE(r, half*y+p/q, cond);
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VECTOR_COND_MOVE(z, VECTOR_INIT(one), cond); /* lgamma(1+s) = log(s) + lgamma(s) */
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VECTOR_IF2(i==7, cond2, cond)
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VECTOR_COND_MOVE(z, z * (y+(float)6.0), cond2);
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VECTOR_ENDIF
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VECTOR_IF2(i==7 | i==6, cond2, cond)
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VECTOR_COND_MOVE(z, z * (y+(float)5.0), cond2);
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VECTOR_ENDIF
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VECTOR_IF2(i<=7 & i>=5, cond2, cond)
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VECTOR_COND_MOVE(z, z * (y+(float)4.0), cond2);
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||
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VECTOR_ENDIF
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||
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VECTOR_IF2(i<=7 & i>=4, cond2, cond)
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||
|
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VECTOR_COND_MOVE(z, z * (y+(float)3.0), cond2);
|
||
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VECTOR_ENDIF
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||
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|
VECTOR_IF2(i<=7 & i>=3, cond2, cond)
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||
|
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VECTOR_COND_MOVE(z, z * (y+(float)2.0), cond2);
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||
|
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VECTOR_COND_MOVE(r, r + v64sf_logf_aux(z, __mask), cond2);
|
||
|
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VECTOR_ENDIF
|
||
|
|
/* 8.0 <= x < 2**58 */
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||
|
|
VECTOR_ELSEIF(ix < 0x5c800000, cond)
|
||
|
|
VECTOR_COND_MOVE(t, v64sf_logf_aux(x, __mask), cond);
|
||
|
|
VECTOR_COND_MOVE(z, one/x, cond);
|
||
|
|
VECTOR_COND_MOVE(y, z*z, cond);
|
||
|
|
VECTOR_COND_MOVE(w, w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))), cond);
|
||
|
|
VECTOR_COND_MOVE(r, (x-half)*(t-one)+w, cond);
|
||
|
|
VECTOR_ELSE(cond)
|
||
|
|
/* 2**58 <= x <= inf */
|
||
|
|
VECTOR_COND_MOVE(r, x*(v64sf_logf_aux(x, __mask)-one), cond);
|
||
|
|
VECTOR_ENDIF
|
||
|
|
VECTOR_IF(hx<0, cond)
|
||
|
|
VECTOR_COND_MOVE(r, nadj - r, cond);
|
||
|
|
VECTOR_ENDIF
|
||
|
|
|
||
|
|
VECTOR_RETURN(r, NO_COND);
|
||
|
|
FUNCTION_RETURN;
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif
|