k_tanf.c revision 152713
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 INLINE_KERNEL_TANF 16#ifndef lint 17static char rcsid[] = "$FreeBSD: head/lib/msun/src/k_tanf.c 152713 2005-11-23 14:27:56Z bde $"; 18#endif 19#endif 20 21#include "math.h" 22#include "math_private.h" 23 24static const double 25pio4 = M_PI_4, 26/* |tan(x)/x - t(x)| < 2**-29.1 (~[-1.72e-09, 1.719e-09]). */ 27T[] = { 28 0x1555545f8b54d0.0p-54, /* 0.333333104424423432022 */ 29 0x111160cdc2c9af.0p-55, /* 0.133342838734802765499 */ 30 0x1b9097e5693cd0.0p-57, /* 0.0538375346701457369036 */ 31 0x173b2333895b6f.0p-58, /* 0.0226865291791357691353 */ 32 0x19fcb197e825ab.0p-60, /* 0.00634450313965243938713 */ 33 0x1d5f3701b44a27.0p-60, /* 0.00717088210082520490646 */ 34}; 35 36#ifdef INLINE_KERNEL_TANF 37extern inline 38#endif 39float 40__kernel_tandf(double x, int iy) 41{ 42 double z,r,v,w,s; 43 int32_t ix,hx; 44 45 GET_FLOAT_WORD(hx,x); 46 ix = hx&0x7fffffff; 47 if(ix>=0x3f2ca140) { /* |x|>=0.67434 */ 48 if(hx<0) {x = -x;} 49 x = pio4-x; 50 } 51 z = x*x; 52 w = z*z; 53 /* Break x^5*(T[1]+x^2*T[2]+...) into 54 * x^5*(T[1]+x^4*T[3]+x^8*T[5]) + 55 * x^5*(x^2*(T[2]+x^4*T[4])) 56 */ 57 r = T[1]+w*(T[3]+w*T[5]); 58 v = z*(T[2]+w*T[4]); 59 s = z*x; 60 r = z*s*(r+v); 61 r += T[0]*s; 62 w = x+r; 63 if(ix>=0x3f2ca140) { 64 v = (double)iy; 65 return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); 66 } 67 if(iy==1) return w; 68 else return -1.0/w; 69} 70