[388] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
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| 2 | /*
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| 3 | * ====================================================
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 5 | *
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| 6 | * Developed at SunSoft, a Sun Microsystems, Inc. business.
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| 7 | * Permission to use, copy, modify, and distribute this
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| 8 | * software is freely granted, provided that this notice
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| 9 | * is preserved.
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| 10 | * ====================================================
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| 11 | */
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| 12 | /* acos(x)
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| 13 | * Method :
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| 14 | * acos(x) = pi/2 - asin(x)
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| 15 | * acos(-x) = pi/2 + asin(x)
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| 16 | * For |x|<=0.5
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| 17 | * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
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| 18 | * For x>0.5
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| 19 | * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
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| 20 | * = 2asin(sqrt((1-x)/2))
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| 21 | * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
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| 22 | * = 2f + (2c + 2s*z*R(z))
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| 23 | * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
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| 24 | * for f so that f+c ~ sqrt(z).
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| 25 | * For x<-0.5
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| 26 | * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
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| 27 | * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
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| 28 | *
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| 29 | * Special cases:
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| 30 | * if x is NaN, return x itself;
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| 31 | * if |x|>1, return NaN with invalid signal.
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| 32 | *
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| 33 | * Function needed: sqrt
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| 34 | */
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| 35 |
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| 36 | #include "libm.h"
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| 37 |
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| 38 | static const double
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| 39 | pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
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| 40 | pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
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| 41 | pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
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| 42 | pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
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| 43 | pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
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| 44 | pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
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| 45 | pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
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| 46 | pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
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| 47 | qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
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| 48 | qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
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| 49 | qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
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| 50 | qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
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| 51 |
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| 52 | static double R(double z)
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| 53 | {
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| 54 | double_t p, q;
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| 55 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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| 56 | q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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| 57 | return p/q;
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| 58 | }
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| 59 |
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| 60 | double acos(double x)
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| 61 | {
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| 62 | double z,w,s,c,df;
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| 63 | uint32_t hx,ix;
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| 64 |
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| 65 | GET_HIGH_WORD(hx, x);
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| 66 | ix = hx & 0x7fffffff;
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| 67 | /* |x| >= 1 or nan */
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| 68 | if (ix >= 0x3ff00000) {
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| 69 | uint32_t lx;
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| 70 |
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| 71 | GET_LOW_WORD(lx,x);
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| 72 | if ((ix-0x3ff00000 | lx) == 0) {
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| 73 | /* acos(1)=0, acos(-1)=pi */
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| 74 | if (hx >> 31)
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| 75 | return 2*pio2_hi + 0x1p-120f;
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| 76 | return 0;
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| 77 | }
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| 78 | return 0/(x-x);
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| 79 | }
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| 80 | /* |x| < 0.5 */
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| 81 | if (ix < 0x3fe00000) {
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| 82 | if (ix <= 0x3c600000) /* |x| < 2**-57 */
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| 83 | return pio2_hi + 0x1p-120f;
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| 84 | return pio2_hi - (x - (pio2_lo-x*R(x*x)));
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| 85 | }
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| 86 | /* x < -0.5 */
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| 87 | if (hx >> 31) {
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| 88 | z = (1.0+x)*0.5;
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| 89 | s = sqrt(z);
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| 90 | w = R(z)*s-pio2_lo;
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| 91 | return 2*(pio2_hi - (s+w));
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| 92 | }
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| 93 | /* x > 0.5 */
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| 94 | z = (1.0-x)*0.5;
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| 95 | s = sqrt(z);
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| 96 | df = s;
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| 97 | SET_LOW_WORD(df,0);
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| 98 | c = (z-df*df)/(s+df);
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| 99 | w = R(z)*s+c;
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| 100 | return 2*(df+w);
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| 101 | }
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