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 16 static char rcsid[] = "$FreeBSD$"; 17 #endif 18 19 #include "math.h" 20 #include "math_private.h" 21 static const float 22 one = 1.0000000000e+00, /* 0x3f800000 */ 23 pio4 = 7.8539812565e-01, /* 0x3f490fda */ 24 pio4lo= 3.7748947079e-08, /* 0x33222168 */ 25 /* Bounds for tan(x)/x - t(x): ~[-1.73e-09, 1.724e-09]. */ 26 T[] = { 27 0xaaaaa3.0p-25, /* 0.33333310485 */ 28 0x888b06.0p-26, /* 0.13334283238 */ 29 0xdc84c8.0p-28, /* 0.053837567568 */ 30 0xb9d8f1.0p-29, /* 0.022686453536 */ 31 0xcfe632.0p-31, /* 0.0063445800915 */ 32 0xeaf97e.0p-31, /* 0.0071708550677 */ 33 }; 34 35 float 36 __kernel_tanf(float x, float y, int iy) 37 { 38 float z,r,v,w,s; 39 int32_t ix,hx; 40 GET_FLOAT_WORD(hx,x); 41 ix = hx&0x7fffffff; /* high word of |x| */ 42 if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ 43 if(hx<0) {x = -x; y = -y;} 44 z = pio4-x; 45 w = pio4lo-y; 46 x = z+w; y = 0.0; 47 } 48 z = x*x; 49 w = z*z; 50 /* Break x^5*(T[1]+x^2*T[2]+...) into 51 * x^5*(T[1]+x^4*T[3]+x^8*T[5]) + 52 * x^5*(x^2*(T[2]+x^4*T[4])) 53 */ 54 r = T[1]+w*(T[3]+w*T[5]); 55 v = z*(T[2]+w*T[4]); 56 s = z*x; 57 r = y + z*(s*(r+v)+y); 58 r += T[0]*s; 59 w = x+r; 60 if(ix>=0x3f2ca140) { 61 v = (float)iy; 62 return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); 63 } 64 if(iy==1) return w; 65 else { /* if allow error up to 2 ulp, 66 simply return -1.0/(x+r) here */ 67 /* compute -1.0/(x+r) accurately */ 68 float a,t; 69 int32_t i; 70 z = w; 71 GET_FLOAT_WORD(i,z); 72 SET_FLOAT_WORD(z,i&0xfffff000); 73 v = r-(z - x); /* z+v = r+x */ 74 t = a = -(float)1.0/w; /* a = -1.0/w */ 75 GET_FLOAT_WORD(i,t); 76 SET_FLOAT_WORD(t,i&0xfffff000); 77 s = (float)1.0+t*z; 78 return t+a*(s+t*v); 79 } 80 } 81