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Update.
2001-04-16 Stephen L Moshier <moshier@mediaone.net> * sysdeps/ieee754/flt-32/e_asinf.c (pio2_hi, pio2_lo, pio4_hi): Correct the values. (pSx, qSx): Replace by shorter approximation. Use f suffix on float constants. * sysdeps/ieee754/ldbl-128/k_tanl.c: New file. Contributed by Stephen L Moshier <moshier@mediaone.net>.
This commit is contained in:
Ulrich Drepper
parent
c991a86a17
commit
9b7ee67e0c
@ -1,5 +1,14 @@
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2001-04-16 Stephen L Moshier <moshier@mediaone.net>
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* sysdeps/ieee754/flt-32/e_asinf.c (pio2_hi, pio2_lo, pio4_hi):
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Correct the values. (pSx, qSx): Replace by shorter approximation.
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Use f suffix on float constants.
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2001-04-16 Ulrich Drepper <drepper@redhat.com>
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* sysdeps/ieee754/ldbl-128/k_tanl.c: New file.
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Contributed by Stephen L Moshier <moshier@mediaone.net>.
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* string/string.h: Replace const in attribute list with __const__.
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2001-04-16 Roland McGrath <roland@frob.com>
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4
NEWS
4
NEWS
@ -1,4 +1,4 @@
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GNU C Library NEWS -- history of user-visible changes. 2001-4-5
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GNU C Library NEWS -- history of user-visible changes. 2001-4-16
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Copyright (C) 1992-2000, 2001 Free Software Foundation, Inc.
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See the end for copying conditions.
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@ -14,7 +14,7 @@ Version 2.2.3
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in float, double, and long double format.
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* Stephen Moshier implemented j0, j1, jn, y0, y1, yn, lgamma, erf, erfc,
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and asin for the 96-bit long double format and logl for the 128-bit
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and asin for the 96-bit long double format and logl, tanl for the 128-bit
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long double format.
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* The beginning of a last-bit accurate math library by IBM Haifa were added.
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@ -1,3 +1,9 @@
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2001-04-16 Ulrich Drepper <drepper@redhat.com>
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* signals.c (sigwait): NSIG is no signal number. Block all
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signals while in signal handler for signals in SET.
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Patch by Manfred Spraul <manfred@colorfullife.com>.
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2001-04-12 Ulrich Drepper <drepper@redhat.com>
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* tst-cancel.c: Disable most tests. Add new test where all
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@ -188,7 +188,7 @@ int sigwait(const sigset_t * set, int * sig)
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signals in set is unspecified." */
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sigfillset(&mask);
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sigdelset(&mask, __pthread_sig_cancel);
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for (s = 1; s <= NSIG; s++) {
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for (s = 1; s < NSIG; s++) {
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if (sigismember(set, s) &&
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s != __pthread_sig_restart &&
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s != __pthread_sig_cancel &&
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@ -198,7 +198,7 @@ int sigwait(const sigset_t * set, int * sig)
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sighandler[s].old == (arch_sighandler_t) SIG_DFL ||
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sighandler[s].old == (arch_sighandler_t) SIG_IGN) {
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sa.sa_handler = pthread_null_sighandler;
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sigemptyset(&sa.sa_mask);
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sigfillset(&sa.sa_mask);
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sa.sa_flags = 0;
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sigaction(s, &sa, NULL);
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}
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@ -13,6 +13,12 @@
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* ====================================================
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*/
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/*
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Single precision expansion contributed by
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Stephen L. Moshier <moshier@na-net.ornl.gov>
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*/
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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: e_asinf.c,v 1.5 1995/05/12 04:57:25 jtc Exp $";
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#endif
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@ -27,20 +33,19 @@ static float
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#endif
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one = 1.0000000000e+00, /* 0x3F800000 */
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huge = 1.000e+30,
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pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
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pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
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pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */
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/* coefficient for R(x^2) */
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pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
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pS1 = -3.2556581497e-01, /* 0xbea6b090 */
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pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
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pS3 = -4.0055535734e-02, /* 0xbd241146 */
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pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
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pS5 = 3.4793309169e-05, /* 0x3811ef08 */
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qS1 = -2.4033949375e+00, /* 0xc019d139 */
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qS2 = 2.0209457874e+00, /* 0x4001572d */
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qS3 = -6.8828397989e-01, /* 0xbf303361 */
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qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
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pio2_hi = 1.57079637050628662109375f,
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pio2_lo = -4.37113900018624283e-8f,
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pio4_hi = 0.785398185253143310546875f,
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/* asin x = x + x^3 p(x^2)
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-0.5 <= x <= 0.5;
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Peak relative error 4.8e-9 */
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p0 = 1.666675248e-1f,
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p1 = 7.495297643e-2f,
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p2 = 4.547037598e-2f,
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p3 = 2.417951451e-2f,
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p4 = 4.216630880e-2f;
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#ifdef __STDC__
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float __ieee754_asinf(float x)
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@ -63,30 +68,26 @@ qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
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if(huge+x>one) return x;/* return x with inexact if x!=0*/
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} else {
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t = x*x;
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p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
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q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
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w = p/q;
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w = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
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return x+x*w;
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}
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}
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/* 1> |x|>= 0.5 */
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w = one-fabsf(x);
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t = w*(float)0.5;
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p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
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q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
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t = w*0.5f;
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p = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
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s = __ieee754_sqrtf(t);
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if(ix>=0x3F79999A) { /* if |x| > 0.975 */
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w = p/q;
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t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
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t = pio2_hi-(2.0f*(s+s*p)-pio2_lo);
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} else {
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int32_t iw;
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w = s;
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GET_FLOAT_WORD(iw,w);
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SET_FLOAT_WORD(w,iw&0xfffff000);
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c = (t-w*w)/(s+w);
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r = p/q;
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p = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
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q = pio4_hi-(float)2.0*w;
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r = p;
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p = 2.0f*s*r-(pio2_lo-2.0f*c);
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q = pio4_hi-2.0f*w;
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t = pio4_hi-(p-q);
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}
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if(hx>0) return t; else return -t;
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147
sysdeps/ieee754/ldbl-128/k_tanl.c
Normal file
147
sysdeps/ieee754/ldbl-128/k_tanl.c
Normal file
@ -0,0 +1,147 @@
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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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Long double expansions contributed by
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Stephen L. Moshier <moshier@na-net.ornl.gov>
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*/
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/* __kernel_tanl( x, y, k )
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* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
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* Input x is assumed to be bounded by ~pi/4 in magnitude.
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* Input y is the tail of x.
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* Input k indicates whether tan (if k=1) or
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* -1/tan (if k= -1) is returned.
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*
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* Algorithm
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* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
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* 2. if x < 2^-57, return x with inexact if x!=0.
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* 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
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* on [0,0.67433].
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*
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* Note: tan(x+y) = tan(x) + tan'(x)*y
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* ~ tan(x) + (1+x*x)*y
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* Therefore, for better accuracy in computing tan(x+y), let
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* r = x^3 * R(x^2)
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* then
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* tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
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*
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* 4. For x in [0.67433,pi/4], let y = pi/4 - x, then
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* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
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* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
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*/
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#include "math.h"
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#include "math_private.h"
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#ifdef __STDC__
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static const long double
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#else
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static long double
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#endif
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one = 1.0L,
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pio4hi = 7.8539816339744830961566084581987569936977E-1L,
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pio4lo = 2.1679525325309452561992610065108379921906E-35L,
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/* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
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0 <= x <= 0.6743316650390625
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Peak relative error 8.0e-36 */
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TH = 3.333333333333333333333333333333333333333E-1L,
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T0 = -1.813014711743583437742363284336855889393E7L,
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T1 = 1.320767960008972224312740075083259247618E6L,
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T2 = -2.626775478255838182468651821863299023956E4L,
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T3 = 1.764573356488504935415411383687150199315E2L,
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T4 = -3.333267763822178690794678978979803526092E-1L,
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U0 = -1.359761033807687578306772463253710042010E8L,
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U1 = 6.494370630656893175666729313065113194784E7L,
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U2 = -4.180787672237927475505536849168729386782E6L,
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U3 = 8.031643765106170040139966622980914621521E4L,
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U4 = -5.323131271912475695157127875560667378597E2L;
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/* 1.000000000000000000000000000000000000000E0 */
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#ifdef __STDC__
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long double
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__kernel_tanl (long double x, long double y, int iy)
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#else
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long double
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__kernel_tanl (x, y, iy)
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long double x, y;
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int iy;
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#endif
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{
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long double z, r, v, w, s;
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int32_t ix, sign;
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ieee854_long_double_shape_type u, u1;
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u.value = x;
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ix = u.parts32.w0 & 0x7fffffff;
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if (ix < 0x3fc60000) /* x < 2**-57 */
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{
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if ((int) x == 0)
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{ /* generate inexact */
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if ((ix | u.parts32.w1 | u.parts32.w2 | u.parts32.w3
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| (iy + 1)) == 0)
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return one / fabs (x);
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else
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return (iy == 1) ? x : -one / x;
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}
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}
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if (ix >= 0x3ffe5942) /* |x| >= 0.6743316650390625 */
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{
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if ((u.parts32.w0 & 0x80000000) != 0)
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{
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x = -x;
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y = -y;
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sign = -1;
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}
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else
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sign = 1;
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z = pio4hi - x;
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w = pio4lo - y;
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x = z + w;
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y = 0.0;
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}
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z = x * x;
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r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
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v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
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r = r / v;
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s = z * x;
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r = y + z * (s * r + y);
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r += TH * s;
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w = x + r;
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if (ix >= 0x3ffe5942)
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{
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v = (long double) iy;
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w = (v - 2.0 * (x - (w * w / (w + v) - r)));
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if (sign < 0)
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w = -w;
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return w;
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}
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if (iy == 1)
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return w;
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else
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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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u1.value = w;
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u1.parts32.w2 = 0;
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u1.parts32.w3 = 0;
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v = r - (u1.value - x); /* u1+v = r+x */
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z = -1.0 / w;
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u.value = z;
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u.parts32.w2 = 0;
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u.parts32.w3 = 0;
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s = 1.0 + u.value * u1.value;
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return u.value + z * (s + u.value * v);
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}
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}
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