1 /* e_acosf.c -- float version of e_acos.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 pi = 3.1415925026e+00, /* 0x40490fda */ 22 pio2_hi = 1.5707962513e+00; /* 0x3fc90fda */ 23 static volatile float 24 pio2_lo = 7.5497894159e-08; /* 0x33a22168 */ 25 26 /* 27 * The coefficients for the rational approximation were generated over 28 * 0x1p-12f <= x <= 0.5f. The maximum error satisfies log2(e) < -30.084. 29 */ 30 static const float 31 pS0 = 1.66666672e-01f, /* 0x3e2aaaab */ 32 pS1 = -1.19510300e-01f, /* 0xbdf4c1d1 */ 33 pS2 = 5.47002675e-03f, /* 0x3bb33de9 */ 34 qS1 = -1.16706085e+00f, /* 0xbf956240 */ 35 qS2 = 2.90115148e-01f; /* 0x3e9489f9 */ 36 37 float 38 acosf(float x) 39 { 40 float z,p,q,r,w,s,c,df; 41 int32_t hx,ix; 42 GET_FLOAT_WORD(hx,x); 43 ix = hx&0x7fffffff; 44 if(ix>=0x3f800000) { /* |x| >= 1 */ 45 if(ix==0x3f800000) { /* |x| == 1 */ 46 if(hx>0) return 0.0; /* acos(1) = 0 */ 47 else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ 48 } 49 return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 50 } 51 if(ix<0x3f000000) { /* |x| < 0.5 */ 52 if(ix<=0x32800000) return pio2_hi+pio2_lo;/*if|x|<2**-26*/ 53 z = x*x; 54 p = z*(pS0+z*(pS1+z*pS2)); 55 q = one+z*(qS1+z*qS2); 56 r = p/q; 57 return pio2_hi - (x - (pio2_lo-x*r)); 58 } else if (hx<0) { /* x < -0.5 */ 59 z = (one+x)*(float)0.5; 60 p = z*(pS0+z*(pS1+z*pS2)); 61 q = one+z*(qS1+z*qS2); 62 s = sqrtf(z); 63 r = p/q; 64 w = r*s-pio2_lo; 65 return pi - (float)2.0*(s+w); 66 } else { /* x > 0.5 */ 67 int32_t idf; 68 z = (one-x)*(float)0.5; 69 s = sqrtf(z); 70 df = s; 71 GET_FLOAT_WORD(idf,df); 72 SET_FLOAT_WORD(df,idf&0xfffff000); 73 c = (z-df*df)/(s+df); 74 p = z*(pS0+z*(pS1+z*pS2)); 75 q = one+z*(qS1+z*qS2); 76 r = p/q; 77 w = r*s+c; 78 return (float)2.0*(df+w); 79 } 80 } 81