52 lines
1.3 KiB
Rust
52 lines
1.3 KiB
Rust
use super::{expm1, expo2};
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// sinh(x) = (exp(x) - 1/exp(x))/2
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// = (exp(x)-1 + (exp(x)-1)/exp(x))/2
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// = x + x^3/6 + o(x^5)
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//
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/// The hyperbolic sine of `x` (f64).
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#[cfg_attr(assert_no_panic, no_panic::no_panic)]
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pub fn sinh(x: f64) -> f64 {
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// union {double f; uint64_t i;} u = {.f = x};
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// uint32_t w;
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// double t, h, absx;
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let mut uf: f64 = x;
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let mut ui: u64 = f64::to_bits(uf);
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let w: u32;
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let t: f64;
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let mut h: f64;
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let absx: f64;
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h = 0.5;
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if ui >> 63 != 0 {
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h = -h;
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}
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/* |x| */
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ui &= !1 / 2;
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uf = f64::from_bits(ui);
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absx = uf;
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w = (ui >> 32) as u32;
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/* |x| < log(DBL_MAX) */
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if w < 0x40862e42 {
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t = expm1(absx);
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if w < 0x3ff00000 {
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if w < 0x3ff00000 - (26 << 20) {
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/* note: inexact and underflow are raised by expm1 */
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/* note: this branch avoids spurious underflow */
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return x;
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}
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return h * (2.0 * t - t * t / (t + 1.0));
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}
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/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
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return h * (t + t / (t + 1.0));
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}
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/* |x| > log(DBL_MAX) or nan */
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/* note: the result is stored to handle overflow */
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t = 2.0 * h * expo2(absx);
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t
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}
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