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e4e52ff059
Bug 21094 reports 3ulp errors of cosf and tanf for certain arguments near pi/2 arising from the use of an insufficiently accurate range reduction. (To be clear, this is a quality-of-implementation issue relating to the apparent intent of those particular cosf and tanf implementations; 3ulp is within the general glibc accuracy goals, so not inherently a bug.) This patch fixes that error by making a wider range of cases use the existing more accurate range reduction for arguments close to pi/2. The wider range of values is still narrow enough for the "z -= pio2_2;" in the more accurate case to be exact, as the code expects. Tested for x86_64, x86 and mips64; no ulps updates needed (but at least on mips64, the larger ulps were seen if the tests were added without the substantive fix). [BZ #21094] * sysdeps/ieee754/flt-32/e_rem_pio2f.c (__ieee754_rem_pio2f): Use 24+24+24-bit pi for wider range of values around pi/2. * math/auto-libm-test-in: Add more tests of cos and tan. * math/auto-libm-test-out-cos: Regenerated. * math/auto-libm-test-out-tan: Likewise.
180 lines
5.7 KiB
C
180 lines
5.7 KiB
C
/* e_rem_pio2f.c -- float version of e_rem_pio2.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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/*
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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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $";
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#endif
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/* __ieee754_rem_pio2f(x,y)
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*
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* return the remainder of x rem pi/2 in y[0]+y[1]
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* use __kernel_rem_pio2f()
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*/
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#include <math.h>
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#include <math_private.h>
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/*
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* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
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*/
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static const int32_t two_over_pi[] = {
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0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
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0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
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0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
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0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
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0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
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0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
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0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
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0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
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0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
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0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
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0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
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0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
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0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
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0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
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0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
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0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
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0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
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0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
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0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
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0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
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0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
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0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
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};
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/* This array is like the one in e_rem_pio2.c, but the numbers are
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single precision and the last 8 bits are forced to 0. */
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static const int32_t npio2_hw[] = {
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0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
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0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
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0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
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0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
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0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
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0x4242c700, 0x42490f00
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};
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/*
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* invpio2: 24 bits of 2/pi
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* pio2_1: first 17 bit of pi/2
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* pio2_1t: pi/2 - pio2_1
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* pio2_2: second 17 bit of pi/2
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* pio2_2t: pi/2 - (pio2_1+pio2_2)
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* pio2_3: third 17 bit of pi/2
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* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
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*/
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static const float
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zero = 0.0000000000e+00, /* 0x00000000 */
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half = 5.0000000000e-01, /* 0x3f000000 */
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two8 = 2.5600000000e+02, /* 0x43800000 */
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invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
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pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
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pio2_1t = 1.0804334124e-05, /* 0x37354443 */
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pio2_2 = 1.0804273188e-05, /* 0x37354400 */
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pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
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pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
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pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
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int32_t __ieee754_rem_pio2f(float x, float *y)
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{
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float z,w,t,r,fn;
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float tx[3];
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int32_t e0,i,j,nx,n,ix,hx;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff;
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if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
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{y[0] = x; y[1] = 0; return 0;}
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if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
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if(hx>0) {
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z = x - pio2_1;
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if((ix&0xffffffc0)!=0x3fc90fc0) { /* 24+24 bit pi OK */
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y[0] = z - pio2_1t;
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y[1] = (z-y[0])-pio2_1t;
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} else { /* near pi/2, use 24+24+24 bit pi */
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z -= pio2_2;
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y[0] = z - pio2_2t;
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y[1] = (z-y[0])-pio2_2t;
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}
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return 1;
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} else { /* negative x */
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z = x + pio2_1;
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if((ix&0xffffffc0)!=0x3fc90fc0) { /* 24+24 bit pi OK */
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y[0] = z + pio2_1t;
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y[1] = (z-y[0])+pio2_1t;
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} else { /* near pi/2, use 24+24+24 bit pi */
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z += pio2_2;
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y[0] = z + pio2_2t;
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y[1] = (z-y[0])+pio2_2t;
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}
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return -1;
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}
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}
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if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
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t = fabsf(x);
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n = (int32_t) (t*invpio2+half);
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fn = (float)n;
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r = t-fn*pio2_1;
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w = fn*pio2_1t; /* 1st round good to 40 bit */
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if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) {
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y[0] = r-w; /* quick check no cancellation */
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} else {
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u_int32_t high;
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j = ix>>23;
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y[0] = r-w;
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GET_FLOAT_WORD(high,y[0]);
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i = j-((high>>23)&0xff);
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if(i>8) { /* 2nd iteration needed, good to 57 */
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t = r;
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w = fn*pio2_2;
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r = t-w;
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w = fn*pio2_2t-((t-r)-w);
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y[0] = r-w;
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GET_FLOAT_WORD(high,y[0]);
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i = j-((high>>23)&0xff);
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if(i>25) { /* 3rd iteration need, 74 bits acc */
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t = r; /* will cover all possible cases */
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w = fn*pio2_3;
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r = t-w;
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w = fn*pio2_3t-((t-r)-w);
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y[0] = r-w;
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}
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}
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}
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y[1] = (r-y[0])-w;
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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else return n;
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}
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/*
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* all other (large) arguments
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*/
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if(ix>=0x7f800000) { /* x is inf or NaN */
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y[0]=y[1]=x-x; return 0;
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}
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/* set z = scalbn(|x|,ilogb(x)-7) */
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e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */
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SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
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for(i=0;i<2;i++) {
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tx[i] = (float)((int32_t)(z));
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z = (z-tx[i])*two8;
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}
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tx[2] = z;
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nx = 3;
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while(tx[nx-1]==zero) nx--; /* skip zero term */
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n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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return n;
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}
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