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5a608ccc2d
The flt-32 implementation of tanf produces spurious underflow exceptions for some small arguments, through computing values on the order of x^5. This patch fixes this by adjusting the threshold for returning x (or, as applicable, +/- 1/x) to 2**-13 (the next term in the power series being x^3/3). Tested for x86_64 and x86. [BZ #18221] * sysdeps/ieee754/flt-32/k_tanf.c (__kernel_tanf): Use 2**-13 not 2**-28 as threshold for returning x or +/- 1/x. * math/auto-libm-test-in: Add more tests of tan. * math/auto-libm-test-out: Regenerated.
95 lines
2.7 KiB
C
95 lines
2.7 KiB
C
/* k_tanf.c -- float version of k_tan.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: k_tanf.c,v 1.4 1995/05/10 20:46:39 jtc Exp $";
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#endif
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#include <math.h>
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#include <math_private.h>
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static const float
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one = 1.0000000000e+00, /* 0x3f800000 */
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pio4 = 7.8539812565e-01, /* 0x3f490fda */
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pio4lo= 3.7748947079e-08, /* 0x33222168 */
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T[] = {
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3.3333334327e-01, /* 0x3eaaaaab */
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1.3333334029e-01, /* 0x3e088889 */
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5.3968254477e-02, /* 0x3d5d0dd1 */
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2.1869488060e-02, /* 0x3cb327a4 */
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8.8632395491e-03, /* 0x3c11371f */
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3.5920790397e-03, /* 0x3b6b6916 */
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1.4562094584e-03, /* 0x3abede48 */
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5.8804126456e-04, /* 0x3a1a26c8 */
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2.4646313977e-04, /* 0x398137b9 */
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7.8179444245e-05, /* 0x38a3f445 */
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7.1407252108e-05, /* 0x3895c07a */
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-1.8558637748e-05, /* 0xb79bae5f */
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2.5907305826e-05, /* 0x37d95384 */
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};
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float __kernel_tanf(float x, float y, int iy)
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{
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float z,r,v,w,s;
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int32_t ix,hx;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff; /* high word of |x| */
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if(ix<0x39000000) /* x < 2**-13 */
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{if((int)x==0) { /* generate inexact */
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if((ix|(iy+1))==0) return one/fabsf(x);
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else return (iy==1)? x: -one/x;
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}
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}
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if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
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if(hx<0) {x = -x; y = -y;}
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z = pio4-x;
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w = pio4lo-y;
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x = z+w; y = 0.0;
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if (fabsf (x) < 0x1p-13f)
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return (1 - ((hx >> 30) & 2)) * iy * (1.0f - 2 * iy * x);
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}
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z = x*x;
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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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r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
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v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
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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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if(ix>=0x3f2ca140) {
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v = (float)iy;
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return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
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}
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if(iy==1) return w;
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else { /* 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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float a,t;
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int32_t i;
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z = w;
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GET_FLOAT_WORD(i,z);
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SET_FLOAT_WORD(z,i&0xfffff000);
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v = r-(z - x); /* z+v = r+x */
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t = a = -(float)1.0/w; /* a = -1.0/w */
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GET_FLOAT_WORD(i,t);
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SET_FLOAT_WORD(t,i&0xfffff000);
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s = (float)1.0+t*z;
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return t+a*(s+t*v);
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}
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}
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