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New generic cosf
The same logic used in s_cosf.S version for x86 and powerpc is used to create a generic s_cosf.c, so there is no performance improvement in x86_64 and powerpc64. * sysdeps/ieee754/flt-32/s_cosf.c: New implementation.
This commit is contained in:
Paul Clarke
Tulio Magno Quites Machado Filho
parent
c9cd7b0ce5
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f4b2aea6e1
@ -1,3 +1,7 @@
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2017-12-11 Paul A. Clarke <pc@us.ibm.com>
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* sysdeps/ieee754/flt-32/s_cosf.c: New implementation.
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2017-12-11 Adhemerval Zanella <azanella@linux.vnet.ibm.com>
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Tulio Magno Quites Machado Filho <tuliom@linux.vnet.ibm.com>
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@ -1,21 +1,20 @@
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/* s_cosf.c -- float version of s_cos.c.
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/* Compute cosine of argument.
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Copyright (C) 2017 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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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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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $";
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#endif
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <errno.h>
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#include <math.h>
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@ -28,35 +27,210 @@ static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $";
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# define COSF_FUNC COSF
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#endif
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float COSF_FUNC(float x)
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/* Chebyshev constants for cos, range -PI/4 - PI/4. */
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static const double C0 = -0x1.ffffffffe98aep-2;
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static const double C1 = 0x1.55555545c50c7p-5;
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static const double C2 = -0x1.6c16b348b6874p-10;
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static const double C3 = 0x1.a00eb9ac43ccp-16;
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static const double C4 = -0x1.23c97dd8844d7p-22;
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/* Chebyshev constants for sin, range -PI/4 - PI/4. */
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static const double S0 = -0x1.5555555551cd9p-3;
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static const double S1 = 0x1.1111110c2688bp-7;
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static const double S2 = -0x1.a019f8b4bd1f9p-13;
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static const double S3 = 0x1.71d7264e6b5b4p-19;
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static const double S4 = -0x1.a947e1674b58ap-26;
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/* Chebyshev constants for cos, range 2^-27 - 2^-5. */
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static const double CC0 = -0x1.fffffff5cc6fdp-2;
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static const double CC1 = 0x1.55514b178dac5p-5;
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/* PI/2 with 98 bits of accuracy. */
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static const double PI_2_hi = 0x1.921fb544p+0;
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static const double PI_2_lo = 0x1.0b4611a626332p-34;
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static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
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#define FLOAT_EXPONENT_SHIFT 23
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#define FLOAT_EXPONENT_BIAS 127
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static const double pio2_table[] = {
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0 * M_PI_2,
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1 * M_PI_2,
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2 * M_PI_2,
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3 * M_PI_2,
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4 * M_PI_2,
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5 * M_PI_2
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};
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static const double invpio4_table[] = {
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0x0p+0,
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0x1.45f306cp+0,
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0x1.c9c882ap-28,
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0x1.4fe13a8p-58,
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0x1.f47d4dp-85,
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0x1.bb81b6cp-112,
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0x1.4acc9ep-142,
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0x1.0e4107cp-169
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};
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static const double ones[] = { 1.0, -1.0 };
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/* Compute the cosine value using Chebyshev polynomials where
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THETA is the range reduced absolute value of the input
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and it is less than Pi/4,
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N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
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whether a sine or cosine approximation is more accurate and
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the sign of the result. */
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static inline float
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reduced (double theta, unsigned int n)
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{
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float y[2],z=0.0;
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int32_t n,ix;
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double sign, cx;
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const double theta2 = theta * theta;
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GET_FLOAT_WORD(ix,x);
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/* Determine positive or negative primary interval. */
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n += 2;
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sign = ones[(n >> 2) & 1];
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/* |x| ~< pi/4 */
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ix &= 0x7fffffff;
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if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
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/* Are we in the primary interval of sin or cos? */
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if ((n & 2) == 0)
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{
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/* Here cosf() is calculated using sin Chebyshev polynomial:
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x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
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cx = S3 + theta2 * S4;
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cx = S2 + theta2 * cx;
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cx = S1 + theta2 * cx;
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cx = S0 + theta2 * cx;
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cx = theta + theta * theta2 * cx;
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}
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else
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{
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/* Here cosf() is calculated using cos Chebyshev polynomial:
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1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
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cx = C3 + theta2 * C4;
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cx = C2 + theta2 * cx;
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cx = C1 + theta2 * cx;
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cx = C0 + theta2 * cx;
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cx = 1. + theta2 * cx;
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}
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return sign * cx;
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}
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/* cos(Inf or NaN) is NaN */
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else if (ix>=0x7f800000) {
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if (ix == 0x7f800000)
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__set_errno (EDOM);
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return x-x;
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float
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COSF_FUNC (float x)
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{
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double theta = x;
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double abstheta = fabs (theta);
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if (isless (abstheta, M_PI_4))
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{
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double cx;
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if (abstheta >= 0x1p-5)
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{
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const double theta2 = theta * theta;
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/* Chebyshev polynomial of the form for cos:
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* 1 + x^2 (C0 + x^2 (C1 + x^2 (C2 + x^2 (C3 + x^2 * C4)))). */
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cx = C3 + theta2 * C4;
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cx = C2 + theta2 * cx;
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cx = C1 + theta2 * cx;
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cx = C0 + theta2 * cx;
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cx = 1. + theta2 * cx;
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return cx;
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}
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/* argument reduction needed */
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else {
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n = __ieee754_rem_pio2f(x,y);
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switch(n&3) {
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case 0: return __kernel_cosf(y[0],y[1]);
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case 1: return -__kernel_sinf(y[0],y[1],1);
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case 2: return -__kernel_cosf(y[0],y[1]);
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default:
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return __kernel_sinf(y[0],y[1],1);
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else if (abstheta >= 0x1p-27)
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{
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/* A simpler Chebyshev approximation is close enough for this range:
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* 1 + x^2 (CC0 + x^3 * CC1). */
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const double theta2 = theta * theta;
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cx = CC0 + theta * theta2 * CC1;
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cx = 1.0 + theta2 * cx;
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return cx;
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}
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else
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{
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/* For small enough |theta|, this is close enough. */
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return 1.0 - abstheta;
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}
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}
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else /* |theta| >= Pi/4. */
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{
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if (isless (abstheta, 9 * M_PI_4))
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{
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/* There are cases where FE_UPWARD rounding mode can
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produce a result of abstheta * inv_PI_4 == 9,
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where abstheta < 9pi/4, so the domain for
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pio2_table must go to 5 (9 / 2 + 1). */
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unsigned int n = (abstheta * inv_PI_4) + 1;
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theta = abstheta - pio2_table[n / 2];
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return reduced (theta, n);
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}
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else if (isless (abstheta, INFINITY))
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{
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if (abstheta < 0x1p+23)
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{
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unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
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double x = n / 2;
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theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
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/* Argument reduction needed. */
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return reduced (theta, n);
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}
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else /* |theta| >= 2^23. */
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{
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x = fabsf (x);
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int exponent;
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GET_FLOAT_WORD (exponent, x);
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exponent = (exponent >> FLOAT_EXPONENT_SHIFT)
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- FLOAT_EXPONENT_BIAS;
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exponent += 3;
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exponent /= 28;
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double a = invpio4_table[exponent] * x;
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double b = invpio4_table[exponent + 1] * x;
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double c = invpio4_table[exponent + 2] * x;
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double d = invpio4_table[exponent + 3] * x;
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uint64_t l = a;
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l &= ~0x7;
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a -= l;
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double e = a + b;
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l = e;
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e = a - l;
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if (l & 1)
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{
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e -= 1.0;
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e += b;
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e += c;
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e += d;
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e *= M_PI_4;
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return reduced (e, l + 1);
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}
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else
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{
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e += b;
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e += c;
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e += d;
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if (e <= 1.0)
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{
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e *= M_PI_4;
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return reduced (e, l + 1);
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}
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else
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{
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l++;
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e -= 2.0;
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e *= M_PI_4;
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return reduced (e, l + 1);
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}
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}
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}
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}
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else
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{
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int32_t ix;
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GET_FLOAT_WORD (ix, abstheta);
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/* cos(Inf or NaN) is NaN. */
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if (ix == 0x7f800000) /* Inf. */
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__set_errno (EDOM);
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return x - x;
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}
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}
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}
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#ifndef COSF
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