35 lines
943 B
Rust
35 lines
943 B
Rust
use super::{logf, log1pf, sqrtf};
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const LN2: f32 = 0.693147180559945309417232121458176568;
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/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
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pub fn asinhf(mut x: f32) -> f32 {
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let u = x.to_bits();
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let i = u & 0x7fffffff;
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let sign = (u >> 31) != 0;
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/* |x| */
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x = f32::from_bits(i);
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if i >= 0x3f800000 + (12<<23) {
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/* |x| >= 0x1p12 or inf or nan */
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x = logf(x) + LN2;
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} else if i >= 0x3f800000 + (1<<23) {
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/* |x| >= 2 */
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x = logf(2.0*x + 1.0/(sqrtf(x*x+1.0)+x));
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} else if i >= 0x3f800000 - (12<<23) {
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/* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */
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x = log1pf(x + x*x/(sqrtf(x*x+1.0)+1.0));
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} else {
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/* |x| < 0x1p-12, raise inexact if x!=0 */
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let x1p120 = f32::from_bits(0x7b800000);
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force_eval!(x + x1p120);
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}
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if sign {
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-x
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} else {
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x
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}
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}
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