k_tanf.c revision 152343
12116Sjkh/* k_tanf.c -- float version of k_tan.c 22116Sjkh * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 32116Sjkh */ 42116Sjkh 52116Sjkh/* 62116Sjkh * ==================================================== 7129981Sdas * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. 82116Sjkh * 92116Sjkh * Permission to use, copy, modify, and distribute this 108870Srgrimes * software is freely granted, provided that this notice 112116Sjkh * is preserved. 122116Sjkh * ==================================================== 132116Sjkh */ 142116Sjkh 152116Sjkh#ifndef lint 1650476Speterstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/k_tanf.c 152343 2005-11-12 20:06:04Z bde $"; 172116Sjkh#endif 182116Sjkh 192116Sjkh#include "math.h" 202116Sjkh#include "math_private.h" 21152343Sbde 228870Srgrimesstatic const float 232116Sjkhpio4 = 7.8539812565e-01, /* 0x3f490fda */ 242116Sjkhpio4lo= 3.7748947079e-08, /* 0x33222168 */ 25152343Sbde/* |tan(x)/x - t(x)| < 2**-29.2 (~[-1.73e-09, 1.724e-09]). */ 262116SjkhT[] = { 27152343Sbde 0xaaaaa3.0p-25, /* 0.33333310485 */ 28152343Sbde 0x888b06.0p-26, /* 0.13334283238 */ 29152343Sbde 0xdc84c8.0p-28, /* 0.053837567568 */ 30152343Sbde 0xb9d8f1.0p-29, /* 0.022686453536 */ 31152343Sbde 0xcfe632.0p-31, /* 0.0063445800915 */ 32152343Sbde 0xeaf97e.0p-31, /* 0.0071708550677 */ 332116Sjkh}; 342116Sjkh 3597413Salfredfloat 3697413Salfred__kernel_tanf(float x, float y, int iy) 372116Sjkh{ 382116Sjkh float z,r,v,w,s; 392116Sjkh int32_t ix,hx; 40152343Sbde 412116Sjkh GET_FLOAT_WORD(hx,x); 42152343Sbde ix = hx&0x7fffffff; 43152343Sbde if(ix>=0x3f2ca140) { /* |x|>=0.67434 */ 442116Sjkh if(hx<0) {x = -x; y = -y;} 452116Sjkh z = pio4-x; 462116Sjkh w = pio4lo-y; 472116Sjkh x = z+w; y = 0.0; 482116Sjkh } 492116Sjkh z = x*x; 502116Sjkh w = z*z; 512116Sjkh /* Break x^5*(T[1]+x^2*T[2]+...) into 52152284Sbde * x^5*(T[1]+x^4*T[3]+x^8*T[5]) + 53152284Sbde * x^5*(x^2*(T[2]+x^4*T[4])) 542116Sjkh */ 55152284Sbde r = T[1]+w*(T[3]+w*T[5]); 56152284Sbde v = z*(T[2]+w*T[4]); 572116Sjkh s = z*x; 582116Sjkh r = y + z*(s*(r+v)+y); 592116Sjkh r += T[0]*s; 602116Sjkh w = x+r; 612116Sjkh if(ix>=0x3f2ca140) { 622116Sjkh v = (float)iy; 632116Sjkh return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); 642116Sjkh } 652116Sjkh if(iy==1) return w; 668870Srgrimes else { /* if allow error up to 2 ulp, 672116Sjkh simply return -1.0/(x+r) here */ 682116Sjkh /* compute -1.0/(x+r) accurately */ 692116Sjkh float a,t; 702116Sjkh int32_t i; 712116Sjkh z = w; 722116Sjkh GET_FLOAT_WORD(i,z); 732116Sjkh SET_FLOAT_WORD(z,i&0xfffff000); 742116Sjkh v = r-(z - x); /* z+v = r+x */ 752116Sjkh t = a = -(float)1.0/w; /* a = -1.0/w */ 762116Sjkh GET_FLOAT_WORD(i,t); 772116Sjkh SET_FLOAT_WORD(t,i&0xfffff000); 782116Sjkh s = (float)1.0+t*z; 792116Sjkh return t+a*(s+t*v); 802116Sjkh } 812116Sjkh} 82