| use super::{log, log1p, sqrt}; |
| |
| const LN2: f64 = 0.693147180559945309417232121458176568; /* 0x3fe62e42, 0xfefa39ef*/ |
| |
| /* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ |
| /// Inverse hyperbolic sine (f64) |
| /// |
| /// Calculates the inverse hyperbolic sine of `x`. |
| /// Is defined as `sgn(x)*log(|x|+sqrt(x*x+1))`. |
| pub fn asinh(mut x: f64) -> f64 { |
| let mut u = x.to_bits(); |
| let e = ((u >> 52) as usize) & 0x7ff; |
| let sign = (u >> 63) != 0; |
| |
| /* |x| */ |
| u &= (!0) >> 1; |
| x = f64::from_bits(u); |
| |
| if e >= 0x3ff + 26 { |
| /* |x| >= 0x1p26 or inf or nan */ |
| x = log(x) + LN2; |
| } else if e >= 0x3ff + 1 { |
| /* |x| >= 2 */ |
| x = log(2.0 * x + 1.0 / (sqrt(x * x + 1.0) + x)); |
| } else if e >= 0x3ff - 26 { |
| /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ |
| x = log1p(x + x * x / (sqrt(x * x + 1.0) + 1.0)); |
| } else { |
| /* |x| < 0x1p-26, raise inexact if x != 0 */ |
| let x1p120 = f64::from_bits(0x4770000000000000); |
| force_eval!(x + x1p120); |
| } |
| |
| if sign { |
| -x |
| } else { |
| x |
| } |
| } |
