| use super::{Float, log, log1p, sqrt}; |
| |
| const LN2: f64 = 0.693147180559945309417232121458176568; /* 0x3fe62e42, 0xfefa39ef*/ |
| |
| /// Inverse hyperbolic cosine (f64) |
| /// |
| /// Calculates the inverse hyperbolic cosine of `x`. |
| /// Is defined as `log(x + sqrt(x*x-1))`. |
| /// `x` must be a number greater than or equal to 1. |
| #[cfg_attr(assert_no_panic, no_panic::no_panic)] |
| pub fn acosh(x: f64) -> f64 { |
| let ux = x.to_bits(); |
| |
| /* x < 1 domain error is handled in the called functions */ |
| if (ux & !f64::SIGN_MASK) < 2_f64.to_bits() { |
| /* |x| < 2, invalid if x < 1 */ |
| /* up to 2ulp error in [1,1.125] */ |
| let x_1 = x - 1.0; |
| log1p(x_1 + sqrt(x_1 * x_1 + 2.0 * x_1)) |
| } else if ux < ((1 << 26) as f64).to_bits() { |
| /* 2 <= x < 0x1p26 */ |
| log(2.0 * x - 1.0 / (x + sqrt(x * x - 1.0))) |
| } else { |
| /* x >= 0x1p26 or x <= -2 or nan */ |
| log(x) + LN2 |
| } |
| } |
