| /* 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) |
| } |
