k_tanf.c revision 152343
1/* k_tanf.c -- float version of k_tan.c 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 */ 4 5/* 6 * ==================================================== 7 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. 8 * 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 */ 14 15#ifndef lint 16static char rcsid[] = "$FreeBSD: head/lib/msun/src/k_tanf.c 152343 2005-11-12 20:06:04Z bde $"; 17#endif 18 19#include "math.h" 20#include "math_private.h" 21 22static const float 23pio4 = 7.8539812565e-01, /* 0x3f490fda */ 24pio4lo= 3.7748947079e-08, /* 0x33222168 */ 25/* |tan(x)/x - t(x)| < 2**-29.2 (~[-1.73e-09, 1.724e-09]). */ 26T[] = { 27 0xaaaaa3.0p-25, /* 0.33333310485 */ 28 0x888b06.0p-26, /* 0.13334283238 */ 29 0xdc84c8.0p-28, /* 0.053837567568 */ 30 0xb9d8f1.0p-29, /* 0.022686453536 */ 31 0xcfe632.0p-31, /* 0.0063445800915 */ 32 0xeaf97e.0p-31, /* 0.0071708550677 */ 33}; 34 35float 36__kernel_tanf(float x, float y, int iy) 37{ 38 float z,r,v,w,s; 39 int32_t ix,hx; 40 41 GET_FLOAT_WORD(hx,x); 42 ix = hx&0x7fffffff; 43 if(ix>=0x3f2ca140) { /* |x|>=0.67434 */ 44 if(hx<0) {x = -x; y = -y;} 45 z = pio4-x; 46 w = pio4lo-y; 47 x = z+w; y = 0.0; 48 } 49 z = x*x; 50 w = z*z; 51 /* Break x^5*(T[1]+x^2*T[2]+...) into 52 * x^5*(T[1]+x^4*T[3]+x^8*T[5]) + 53 * x^5*(x^2*(T[2]+x^4*T[4])) 54 */ 55 r = T[1]+w*(T[3]+w*T[5]); 56 v = z*(T[2]+w*T[4]); 57 s = z*x; 58 r = y + z*(s*(r+v)+y); 59 r += T[0]*s; 60 w = x+r; 61 if(ix>=0x3f2ca140) { 62 v = (float)iy; 63 return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); 64 } 65 if(iy==1) return w; 66 else { /* if allow error up to 2 ulp, 67 simply return -1.0/(x+r) here */ 68 /* compute -1.0/(x+r) accurately */ 69 float a,t; 70 int32_t i; 71 z = w; 72 GET_FLOAT_WORD(i,z); 73 SET_FLOAT_WORD(z,i&0xfffff000); 74 v = r-(z - x); /* z+v = r+x */ 75 t = a = -(float)1.0/w; /* a = -1.0/w */ 76 GET_FLOAT_WORD(i,t); 77 SET_FLOAT_WORD(t,i&0xfffff000); 78 s = (float)1.0+t*z; 79 return t+a*(s+t*v); 80 } 81} 82