| |
| /* @(#)e_acos.c 1.3 95/01/18 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| /* __ieee754_acos(x) |
| * Method : |
| * acos(x) = pi/2 - asin(x) |
| * acos(-x) = pi/2 + asin(x) |
| * For |x|<=0.5 |
| * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) |
| * For x>0.5 |
| * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) |
| * = 2asin(sqrt((1-x)/2)) |
| * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) |
| * = 2f + (2c + 2s*z*R(z)) |
| * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term |
| * for f so that f+c ~ sqrt(z). |
| * For x<-0.5 |
| * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) |
| * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) |
| * |
| * Special cases: |
| * if x is NaN, return x itself; |
| * if |x|>1, return NaN with invalid signal. |
| * |
| * Function needed: sqrt |
| */ |
| |
| #include <float.h> |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| static const double |
| one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ |
| pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ |
| static volatile double |
| pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ |
| static const double |
| pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ |
| pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ |
| pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ |
| pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ |
| pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ |
| pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ |
| qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ |
| qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ |
| qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ |
| qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
| |
| double |
| __ieee754_acos(double x) |
| { |
| double z,p,q,r,w,s,c,df; |
| int32_t hx,ix; |
| GET_HIGH_WORD(hx,x); |
| ix = hx&0x7fffffff; |
| if(ix>=0x3ff00000) { /* |x| >= 1 */ |
| u_int32_t lx; |
| GET_LOW_WORD(lx,x); |
| if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ |
| if(hx>0) return 0.0; /* acos(1) = 0 */ |
| else return pi+2.0*pio2_lo; /* acos(-1)= pi */ |
| } |
| return (x-x)/(x-x); /* acos(|x|>1) is NaN */ |
| } |
| if(ix<0x3fe00000) { /* |x| < 0.5 */ |
| if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ |
| z = x*x; |
| p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
| q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
| r = p/q; |
| return pio2_hi - (x - (pio2_lo-x*r)); |
| } else if (hx<0) { /* x < -0.5 */ |
| z = (one+x)*0.5; |
| p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
| q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
| s = sqrt(z); |
| r = p/q; |
| w = r*s-pio2_lo; |
| return pi - 2.0*(s+w); |
| } else { /* x > 0.5 */ |
| z = (one-x)*0.5; |
| s = sqrt(z); |
| df = s; |
| SET_LOW_WORD(df,0); |
| c = (z-df*df)/(s+df); |
| p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
| q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
| r = p/q; |
| w = r*s+c; |
| return 2.0*(df+w); |
| } |
| } |
| |
| #if LDBL_MANT_DIG == 53 |
| __weak_reference(acos, acosl); |
| #endif |
