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 1.6 1999/07/02 15:37:42 simonb Exp $"); 19 #endif 20 21 #include "math.h" 22 #include "math_private.h" 23 #ifdef __STDC__ 24 static const float 25 #else 26 static float 27 #endif 28 one = 1.0000000000e+00, /* 0x3f800000 */ 29 pio4 = 7.8539812565e-01, /* 0x3f490fda */ 30 pio4lo= 3.7748947079e-08, /* 0x33222168 */ 31 T[] = { 32 3.3333334327e-01, /* 0x3eaaaaab */ 33 1.3333334029e-01, /* 0x3e088889 */ 34 5.3968254477e-02, /* 0x3d5d0dd1 */ 35 2.1869488060e-02, /* 0x3cb327a4 */ 36 8.8632395491e-03, /* 0x3c11371f */ 37 3.5920790397e-03, /* 0x3b6b6916 */ 38 1.4562094584e-03, /* 0x3abede48 */ 39 5.8804126456e-04, /* 0x3a1a26c8 */ 40 2.4646313977e-04, /* 0x398137b9 */ 41 7.8179444245e-05, /* 0x38a3f445 */ 42 7.1407252108e-05, /* 0x3895c07a */ 43 -1.8558637748e-05, /* 0xb79bae5f */ 44 2.5907305826e-05, /* 0x37d95384 */ 45 }; 46 47 #ifdef __STDC__ 48 float __kernel_tanf(float x, float y, int iy) 49 #else 50 float __kernel_tanf(x, y, iy) 51 float x,y; int iy; 52 #endif 53 { 54 float z,r,v,w,s; 55 int32_t ix,hx; 56 GET_FLOAT_WORD(hx,x); 57 ix = hx&0x7fffffff; /* high word of |x| */ 58 if(ix<0x31800000) /* x < 2**-28 */ 59 {if((int)x==0) { /* generate inexact */ 60 if((ix|(iy+1))==0) return one/fabsf(x); 61 else return (iy==1)? x: -one/x; 62 } 63 } 64 if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ 65 if(hx<0) {x = -x; y = -y;} 66 z = pio4-x; 67 w = pio4lo-y; 68 x = z+w; y = 0.0; 69 } 70 z = x*x; 71 w = z*z; 72 /* Break x^5*(T[1]+x^2*T[2]+...) into 73 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + 74 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) 75 */ 76 r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); 77 v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); 78 s = z*x; 79 r = y + z*(s*(r+v)+y); 80 r += T[0]*s; 81 w = x+r; 82 if(ix>=0x3f2ca140) { 83 v = (float)iy; 84 return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); 85 } 86 if(iy==1) return w; 87 else { /* if allow error up to 2 ulp, 88 simply return -1.0/(x+r) here */ 89 /* compute -1.0/(x+r) accurately */ 90 float a,t; 91 int32_t i; 92 z = w; 93 GET_FLOAT_WORD(i,z); 94 SET_FLOAT_WORD(z,i&0xfffff000); 95 v = r-(z - x); /* z+v = r+x */ 96 t = a = -(float)1.0/w; /* a = -1.0/w */ 97 GET_FLOAT_WORD(i,t); 98 SET_FLOAT_WORD(t,i&0xfffff000); 99 s = (float)1.0+t*z; 100 return t+a*(s+t*v); 101 } 102 } 103