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 "math.h" 17 #include "math_private.h" 18 19 static const float 20 one = 1.0000000000e+00, /* 0x3F800000 */ 21 huge = 1.000e+30; 22 23 /* 24 * The coefficients for the rational approximation were generated over 25 * 0x1p-12f <= x <= 0.5f. The maximum error satisfies log2(e) < -30.084. 26 */ 27 static const float 28 pS0 = 1.66666672e-01f, /* 0x3e2aaaab */ 29 pS1 = -1.19510300e-01f, /* 0xbdf4c1d1 */ 30 pS2 = 5.47002675e-03f, /* 0x3bb33de9 */ 31 qS1 = -1.16706085e+00f, /* 0xbf956240 */ 32 qS2 = 2.90115148e-01f; /* 0x3e9489f9 */ 33 34 static const double 35 pio2 = 1.570796326794896558e+00; 36 37 float 38 asinf(float x) 39 { 40 double s; 41 float t,w,p,q; 42 int32_t hx,ix; 43 GET_FLOAT_WORD(hx,x); 44 ix = hx&0x7fffffff; 45 if(ix>=0x3f800000) { /* |x| >= 1 */ 46 if(ix==0x3f800000) /* |x| == 1 */ 47 return x*pio2; /* asin(+-1) = +-pi/2 with inexact */ 48 return (x-x)/(x-x); /* asin(|x|>1) is NaN */ 49 } else if (ix<0x3f000000) { /* |x|<0.5 */ 50 if(ix<0x39800000) { /* |x| < 2**-12 */ 51 if(huge+x>one) return x;/* return x with inexact if x!=0*/ 52 } 53 t = x*x; 54 p = t*(pS0+t*(pS1+t*pS2)); 55 q = one+t*(qS1+t*qS2); 56 w = p/q; 57 return x+x*w; 58 } 59 /* 1> |x|>= 0.5 */ 60 w = one-fabsf(x); 61 t = w*(float)0.5; 62 p = t*(pS0+t*(pS1+t*pS2)); 63 q = one+t*(qS1+t*qS2); 64 s = sqrt(t); 65 w = p/q; 66 t = pio2-2.0*(s+s*w); 67 if(hx>0) return t; else return -t; 68 } 69