157 lines
5.0 KiB
C
157 lines
5.0 KiB
C
/*
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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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/* Based on newlib/libm/math/kf_tan.c in Newlib. */
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#include "amdgcnmach.h"
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static const double
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pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
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pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
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T[] = {
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3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
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1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
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5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
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2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
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8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
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3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
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1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
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5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
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2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
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7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
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7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
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-1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
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2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
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};
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#if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsv)
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static v64df
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v64df_kernel_tan (v64df x, v64df y, v64si iy, v64di __mask)
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{
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FUNCTION_INIT (v64df);
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v64si hx;
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GET_HIGH_WORD(hx, x, NO_COND);
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v64si ix = hx & 0x7fffffff; /* high word of |x| */
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VECTOR_IF (ix < 0x3e300000, cond) /* x < 2**-28 */
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VECTOR_IF2(__builtin_convertvector (x, v64si)==0, cond2, cond) /* generate inexact */
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v64si low;
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GET_LOW_WORD (low, x, cond2);
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VECTOR_RETURN (1.0 / __builtin_gcn_fabsv (x), ((ix|low)|(iy+1))==0);
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VECTOR_RETURN (x, cond2 & (iy == 1));
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v64df z, w;
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z = w = x + y;
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SET_LOW_WORD (z, VECTOR_INIT (0.0), cond2);
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v64df v = y - (z - x);
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v64df t, a;
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t = a = -1.0 / w;
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SET_LOW_WORD(t, VECTOR_INIT (0.0), cond2);
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v64df s = 1.0 + t * z;
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VECTOR_RETURN ( t + a * (s + t * v), cond2);
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VECTOR_ENDIF
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VECTOR_ENDIF
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VECTOR_IF(ix>=0x3FE59428, cond) /* |x|>=0.6744 */
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VECTOR_COND_MOVE (x, -x, cond & (hx < 0));
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VECTOR_COND_MOVE (y, -y, cond & (hx < 0));
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v64df z = pio4-x;
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v64df w = pio4lo-y;
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VECTOR_COND_MOVE (x, z+w, cond);
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VECTOR_COND_MOVE (y, VECTOR_INIT (0.0), cond);
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VECTOR_ENDIF
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v64df z = x*x;
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v64df w = z*z;
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/* Break x^5*(T[1]+x^2*T[2]+...) into
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* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
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* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
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*/
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v64df r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
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v64df v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
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v64df s = z*x;
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r = y + z*(s*(r+v)+y);
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r += T[0]*s;
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w = x+r;
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VECTOR_IF(ix>=0x3FE59428, cond)
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v = __builtin_convertvector (iy, v64df);
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VECTOR_RETURN (__builtin_convertvector (1-((hx>>30)&2), v64df)
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* (v-2.0*(x-(w*w/(w+v)-r))), cond);
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VECTOR_ENDIF
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VECTOR_RETURN (w, iy == 1);
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/* if allow error up to 2 ulp,
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simply return -1.0/(x+r) here */
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/* compute -1.0/(x+r) accurately */
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z = w;
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SET_LOW_WORD (z, VECTOR_INIT (0), NO_COND);
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v = r - (z - x); /* z+v = r+x */
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v64df a, t;
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t = a = -1.0/w; /* a = -1.0/w */
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SET_LOW_WORD(t, VECTOR_INIT (0), NO_COND);
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s = 1.0+t*z;
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VECTOR_RETURN (t+a*(s+t*v), NO_COND);
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FUNCTION_RETURN;
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}
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static v64si
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v64df_rem_pio2 (v64df x, v64df *y)
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{
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v64df r = x * __INV_PI_OVER_TWO_2_24;
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v64si n = (__builtin_convertvector (r, v64si) + 0x800000) >> 24;
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x = x - __builtin_convertvector (n, v64df) * __PI_OVER_TWO;
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y[0] = x;
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y[1] = x - y[0];
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return n;
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}
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DEF_VD_MATH_FUNC (v64df, tan, v64df x)
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{
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FUNCTION_INIT (v64df);
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v64si ix;
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GET_HIGH_WORD (ix, x, NO_COND);
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/* |x| ~< pi/4 */
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ix &= 0x7fffffff;
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VECTOR_RETURN (v64df_kernel_tan (x, VECTOR_INIT (0.0), VECTOR_INIT (1), __mask),
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ix <= 0x3fe921fb);
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/* tan(Inf or NaN) is NaN */
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VECTOR_RETURN (x-x, ix >= 0x7ff00000); /* NaN */
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/* argument reduction needed */
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v64df y[2];
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v64si n = v64df_rem_pio2 (x,y);
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VECTOR_RETURN (v64df_kernel_tan (y[0], y[1], 1-((n&1)<<1), __mask), // 1 -- n even
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NO_COND); // -1 -- n odd
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FUNCTION_RETURN;
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}
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DEF_VARIANTS (tan, df, df)
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#endif
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