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/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
* Debugged and optimized by Bruce D. Evans.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* cbrtf(x)
* Return cube root of x
*/
use core::f32;
const B1: u32 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */
const B2: u32 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
/// Cube root (f32)
///
/// Computes the cube root of the argument.
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn cbrtf(x: f32) -> f32 {
let x1p24 = f32::from_bits(0x4b800000); // 0x1p24f === 2 ^ 24
let mut r: f64;
let mut t: f64;
let mut ui: u32 = x.to_bits();
let mut hx: u32 = ui & 0x7fffffff;
if hx >= 0x7f800000 {
/* cbrt(NaN,INF) is itself */
return x + x;
}
/* rough cbrt to 5 bits */
if hx < 0x00800000 {
/* zero or subnormal? */
if hx == 0 {
return x; /* cbrt(+-0) is itself */
}
ui = (x * x1p24).to_bits();
hx = ui & 0x7fffffff;
hx = hx / 3 + B2;
} else {
hx = hx / 3 + B1;
}
ui &= 0x80000000;
ui |= hx;
/*
* First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In
* double precision so that its terms can be arranged for efficiency
* without causing overflow or underflow.
*/
t = f32::from_bits(ui) as f64;
r = t * t * t;
t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
/*
* Second step Newton iteration to 47 bits. In double precision for
* efficiency and accuracy.
*/
r = t * t * t;
t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
/* rounding to 24 bits is perfect in round-to-nearest mode */
t as f32
}
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