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path: root/src/math/acos.c
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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 ``` ``````/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */ /* * ==================================================== * 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. * ==================================================== */ /* 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 "libm.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 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 */ uint32_t lx; GET_LOW_WORD(lx,x); if ((ix-0x3ff00000 | lx) == 0) { /* |x|==1 */ if (hx > 0) return 0.0; /* acos(1) = 0 */ 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) /* |x| < 2**-57 */ return pio2_hi + pio2_lo; 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); } } ``````