k_tanf.c revision 151969
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 151969 2005-11-02 14:01:45Z bde $"; 17#endif 18 19#include "math.h" 20#include "math_private.h" 21static const float 22one = 1.0000000000e+00, /* 0x3f800000 */ 23pio4 = 7.8539812565e-01, /* 0x3f490fda */ 24pio4lo= 3.7748947079e-08, /* 0x33222168 */ 25T[] = { 26 3.3333334327e-01, /* 0x3eaaaaab */ 27 1.3333334029e-01, /* 0x3e088889 */ 28 5.3968254477e-02, /* 0x3d5d0dd1 */ 29 2.1869488060e-02, /* 0x3cb327a4 */ 30 8.8632395491e-03, /* 0x3c11371f */ 31 3.5920790397e-03, /* 0x3b6b6916 */ 32 1.4562094584e-03, /* 0x3abede48 */ 33 5.8804126456e-04, /* 0x3a1a26c8 */ 34 2.4646313977e-04, /* 0x398137b9 */ 35 7.8179444245e-05, /* 0x38a3f445 */ 36 7.1407252108e-05, /* 0x3895c07a */ 37 -1.8558637748e-05, /* 0xb79bae5f */ 38 2.5907305826e-05, /* 0x37d95384 */ 39}; 40 41float 42__kernel_tanf(float x, float y, int iy) 43{ 44 float z,r,v,w,s; 45 int32_t ix,hx; 46 GET_FLOAT_WORD(hx,x); 47 ix = hx&0x7fffffff; /* high word of |x| */ 48 if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ 49 if(hx<0) {x = -x; y = -y;} 50 z = pio4-x; 51 w = pio4lo-y; 52 x = z+w; y = 0.0; 53 } 54 z = x*x; 55 w = z*z; 56 /* Break x^5*(T[1]+x^2*T[2]+...) into 57 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + 58 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) 59 */ 60 r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); 61 v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); 62 s = z*x; 63 r = y + z*(s*(r+v)+y); 64 r += T[0]*s; 65 w = x+r; 66 if(ix>=0x3f2ca140) { 67 v = (float)iy; 68 return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); 69 } 70 if(iy==1) return w; 71 else { /* if allow error up to 2 ulp, 72 simply return -1.0/(x+r) here */ 73 /* compute -1.0/(x+r) accurately */ 74 float a,t; 75 int32_t i; 76 z = w; 77 GET_FLOAT_WORD(i,z); 78 SET_FLOAT_WORD(z,i&0xfffff000); 79 v = r-(z - x); /* z+v = r+x */ 80 t = a = -(float)1.0/w; /* a = -1.0/w */ 81 GET_FLOAT_WORD(i,t); 82 SET_FLOAT_WORD(t,i&0xfffff000); 83 s = (float)1.0+t*z; 84 return t+a*(s+t*v); 85 } 86} 87