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