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 (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16 #include <sys/cdefs.h> 17 #if defined(LIBM_SCCS) && !defined(lint) 18 __RCSID("$NetBSD: k_tanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $"); 19 #endif 20 21 #include "math.h" 22 #include "math_private.h" 23 static const float 24 one = 1.0000000000e+00, /* 0x3f800000 */ 25 pio4 = 7.8539812565e-01, /* 0x3f490fda */ 26 pio4lo= 3.7748947079e-08, /* 0x33222168 */ 27 T[] = { 28 3.3333334327e-01, /* 0x3eaaaaab */ 29 1.3333334029e-01, /* 0x3e088889 */ 30 5.3968254477e-02, /* 0x3d5d0dd1 */ 31 2.1869488060e-02, /* 0x3cb327a4 */ 32 8.8632395491e-03, /* 0x3c11371f */ 33 3.5920790397e-03, /* 0x3b6b6916 */ 34 1.4562094584e-03, /* 0x3abede48 */ 35 5.8804126456e-04, /* 0x3a1a26c8 */ 36 2.4646313977e-04, /* 0x398137b9 */ 37 7.8179444245e-05, /* 0x38a3f445 */ 38 7.1407252108e-05, /* 0x3895c07a */ 39 -1.8558637748e-05, /* 0xb79bae5f */ 40 2.5907305826e-05, /* 0x37d95384 */ 41 }; 42 43 float 44 __kernel_tanf(float x, float y, int iy) 45 { 46 float z,r,v,w,s; 47 int32_t ix,hx; 48 GET_FLOAT_WORD(hx,x); 49 ix = hx&0x7fffffff; /* high word of |x| */ 50 if(ix<0x31800000) /* x < 2**-28 */ 51 {if((int)x==0) { /* generate inexact */ 52 if((ix|(iy+1))==0) return one/fabsf(x); 53 else return (iy==1)? x: -one/x; 54 } 55 } 56 if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ 57 if(hx<0) {x = -x; y = -y;} 58 z = pio4-x; 59 w = pio4lo-y; 60 x = z+w; y = 0.0; 61 } 62 z = x*x; 63 w = z*z; 64 /* Break x^5*(T[1]+x^2*T[2]+...) into 65 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + 66 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) 67 */ 68 r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); 69 v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); 70 s = z*x; 71 r = y + z*(s*(r+v)+y); 72 r += T[0]*s; 73 w = x+r; 74 if(ix>=0x3f2ca140) { 75 v = (float)iy; 76 return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); 77 } 78 if(iy==1) return w; 79 else { /* if allow error up to 2 ulp, 80 simply return -1.0/(x+r) here */ 81 /* compute -1.0/(x+r) accurately */ 82 float a,t; 83 int32_t i; 84 z = w; 85 GET_FLOAT_WORD(i,z); 86 SET_FLOAT_WORD(z,i&0xfffff000); 87 v = r-(z - x); /* z+v = r+x */ 88 t = a = -(float)1.0/w; /* a = -1.0/w */ 89 GET_FLOAT_WORD(i,t); 90 SET_FLOAT_WORD(t,i&0xfffff000); 91 s = (float)1.0+t*z; 92 return t+a*(s+t*v); 93 } 94 } 95