diff options
Diffstat (limited to 'vendor/libm/src/math/acos.rs')
| -rw-r--r-- | vendor/libm/src/math/acos.rs | 114 |
1 files changed, 114 insertions, 0 deletions
diff --git a/vendor/libm/src/math/acos.rs b/vendor/libm/src/math/acos.rs new file mode 100644 index 000000000..d5e1f6865 --- /dev/null +++ b/vendor/libm/src/math/acos.rs @@ -0,0 +1,114 @@ +/* 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 + */ + +use super::sqrt; + +const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ +const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ +const PS0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */ +const PS1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */ +const PS2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */ +const PS3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */ +const PS4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */ +const PS5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */ +const QS1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */ +const QS2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */ +const QS3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */ +const QS4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +#[inline] +fn r(z: f64) -> f64 { + let p: f64 = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5))))); + let q: f64 = 1.0 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4))); + p / q +} + +/// Arccosine (f64) +/// +/// Computes the inverse cosine (arc cosine) of the input value. +/// Arguments must be in the range -1 to 1. +/// Returns values in radians, in the range of 0 to pi. +#[inline] +#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] +pub fn acos(x: f64) -> f64 { + let x1p_120f = f64::from_bits(0x3870000000000000); // 0x1p-120 === 2 ^ -120 + let z: f64; + let w: f64; + let s: f64; + let c: f64; + let df: f64; + let hx: u32; + let ix: u32; + + hx = (x.to_bits() >> 32) as u32; + ix = hx & 0x7fffffff; + /* |x| >= 1 or nan */ + if ix >= 0x3ff00000 { + let lx: u32 = x.to_bits() as u32; + + if ((ix - 0x3ff00000) | lx) == 0 { + /* acos(1)=0, acos(-1)=pi */ + if (hx >> 31) != 0 { + return 2. * PIO2_HI + x1p_120f; + } + return 0.; + } + return 0. / (x - x); + } + /* |x| < 0.5 */ + if ix < 0x3fe00000 { + if ix <= 0x3c600000 { + /* |x| < 2**-57 */ + return PIO2_HI + x1p_120f; + } + return PIO2_HI - (x - (PIO2_LO - x * r(x * x))); + } + /* x < -0.5 */ + if (hx >> 31) != 0 { + z = (1.0 + x) * 0.5; + s = sqrt(z); + w = r(z) * s - PIO2_LO; + return 2. * (PIO2_HI - (s + w)); + } + /* x > 0.5 */ + z = (1.0 - x) * 0.5; + s = sqrt(z); + // Set the low 4 bytes to zero + df = f64::from_bits(s.to_bits() & 0xff_ff_ff_ff_00_00_00_00); + + c = (z - df * df) / (s + df); + w = r(z) * s + c; + 2. * (df + w) +} |