| /* origin: FreeBSD /usr/src/lib/msun/src/e_asin.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. |
| * ==================================================== |
| */ |
| /* asin(x) |
| * Method : |
| * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... |
| * we approximate asin(x) on [0,0.5] by |
| * asin(x) = x + x*x^2*R(x^2) |
| * where |
| * R(x^2) is a rational approximation of (asin(x)-x)/x^3 |
| * and its remez error is bounded by |
| * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) |
| * |
| * For x in [0.5,1] |
| * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) |
| * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; |
| * then for x>0.98 |
| * asin(x) = pi/2 - 2*(s+s*z*R(z)) |
| * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) |
| * For x<=0.98, let pio4_hi = pio2_hi/2, then |
| * f = hi part of s; |
| * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) |
| * and |
| * asin(x) = pi/2 - 2*(s+s*z*R(z)) |
| * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) |
| * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) |
| * |
| * Special cases: |
| * if x is NaN, return x itself; |
| * if |x|>1, return NaN with invalid signal. |
| * |
| */ |
| |
| use super::{fabs, get_high_word, get_low_word, sqrt, with_set_low_word}; |
| |
| const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ |
| const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ |
| /* coefficients for R(x^2) */ |
| const P_S0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */ |
| const P_S1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */ |
| const P_S2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */ |
| const P_S3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */ |
| const P_S4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */ |
| const P_S5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */ |
| const Q_S1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */ |
| const Q_S2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */ |
| const Q_S3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */ |
| const Q_S4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
| |
| fn comp_r(z: f64) -> f64 { |
| let p = z * (P_S0 + z * (P_S1 + z * (P_S2 + z * (P_S3 + z * (P_S4 + z * P_S5))))); |
| let q = 1.0 + z * (Q_S1 + z * (Q_S2 + z * (Q_S3 + z * Q_S4))); |
| p / q |
| } |
| |
| /// Arcsine (f64) |
| /// |
| /// Computes the inverse sine (arc sine) of the argument `x`. |
| /// Arguments to asin must be in the range -1 to 1. |
| /// Returns values in radians, in the range of -pi/2 to pi/2. |
| #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| pub fn asin(mut x: f64) -> f64 { |
| let z: f64; |
| let r: f64; |
| let s: f64; |
| let hx: u32; |
| let ix: u32; |
| |
| hx = get_high_word(x); |
| ix = hx & 0x7fffffff; |
| /* |x| >= 1 or nan */ |
| if ix >= 0x3ff00000 { |
| let lx: u32; |
| lx = get_low_word(x); |
| if ((ix - 0x3ff00000) | lx) == 0 { |
| /* asin(1) = +-pi/2 with inexact */ |
| return x * PIO2_HI + f64::from_bits(0x3870000000000000); |
| } else { |
| return 0.0 / (x - x); |
| } |
| } |
| /* |x| < 0.5 */ |
| if ix < 0x3fe00000 { |
| /* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */ |
| if ix < 0x3e500000 && ix >= 0x00100000 { |
| return x; |
| } else { |
| return x + x * comp_r(x * x); |
| } |
| } |
| /* 1 > |x| >= 0.5 */ |
| z = (1.0 - fabs(x)) * 0.5; |
| s = sqrt(z); |
| r = comp_r(z); |
| if ix >= 0x3fef3333 { |
| /* if |x| > 0.975 */ |
| x = PIO2_HI - (2. * (s + s * r) - PIO2_LO); |
| } else { |
| let f: f64; |
| let c: f64; |
| /* f+c = sqrt(z) */ |
| f = with_set_low_word(s, 0); |
| c = (z - f * f) / (s + f); |
| x = 0.5 * PIO2_HI - (2.0 * s * r - (PIO2_LO - 2.0 * c) - (0.5 * PIO2_HI - 2.0 * f)); |
| } |
| if hx >> 31 != 0 { |
| -x |
| } else { |
| x |
| } |
| } |
