1 /* e_asinf.c -- float version of e_asin.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 __FBSDID("$FreeBSD$"); 18 19 #include "math.h" 20 #include "math_private.h" 21 22 static const float 23 one = 1.0000000000e+00, /* 0x3F800000 */ 24 huge = 1.000e+30, 25 pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ 26 pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ 27 pio4_hi = 7.8539812565e-01, /* 0x3f490fda */ 28 /* coefficient for R(x^2) */ 29 pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ 30 pS1 = -3.2556581497e-01, /* 0xbea6b090 */ 31 pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ 32 pS3 = -4.0055535734e-02, /* 0xbd241146 */ 33 pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ 34 pS5 = 3.4793309169e-05, /* 0x3811ef08 */ 35 qS1 = -2.4033949375e+00, /* 0xc019d139 */ 36 qS2 = 2.0209457874e+00, /* 0x4001572d */ 37 qS3 = -6.8828397989e-01, /* 0xbf303361 */ 38 qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ 39 40 float 41 __ieee754_asinf(float x) 42 { 43 float t=0.0,w,p,q,c,r,s; 44 int32_t hx,ix; 45 GET_FLOAT_WORD(hx,x); 46 ix = hx&0x7fffffff; 47 if(ix==0x3f800000) { 48 /* asin(1)=+-pi/2 with inexact */ 49 return x*pio2_hi+x*pio2_lo; 50 } else if(ix> 0x3f800000) { /* |x|>= 1 */ 51 return (x-x)/(x-x); /* asin(|x|>1) is NaN */ 52 } else if (ix<0x3f000000) { /* |x|<0.5 */ 53 if(ix<0x32000000) { /* if |x| < 2**-27 */ 54 if(huge+x>one) return x;/* return x with inexact if x!=0*/ 55 } else 56 t = x*x; 57 p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); 58 q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); 59 w = p/q; 60 return x+x*w; 61 } 62 /* 1> |x|>= 0.5 */ 63 w = one-fabsf(x); 64 t = w*(float)0.5; 65 p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); 66 q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); 67 s = __ieee754_sqrtf(t); 68 if(ix>=0x3F79999A) { /* if |x| > 0.975 */ 69 w = p/q; 70 t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo); 71 } else { 72 int32_t iw; 73 w = s; 74 GET_FLOAT_WORD(iw,w); 75 SET_FLOAT_WORD(w,iw&0xfffff000); 76 c = (t-w*w)/(s+w); 77 r = p/q; 78 p = (float)2.0*s*r-(pio2_lo-(float)2.0*c); 79 q = pio4_hi-(float)2.0*w; 80 t = pio4_hi-(p-q); 81 } 82 if(hx>0) return t; else return -t; 83 } 84