diff options
author | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-06-07 05:48:48 +0000 |
---|---|---|
committer | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-06-07 05:48:48 +0000 |
commit | ef24de24a82fe681581cc130f342363c47c0969a (patch) | |
tree | 0d494f7e1a38b95c92426f58fe6eaa877303a86c /vendor/libm-0.1.4/src/math/cbrt.rs | |
parent | Releasing progress-linux version 1.74.1+dfsg1-1~progress7.99u1. (diff) | |
download | rustc-ef24de24a82fe681581cc130f342363c47c0969a.tar.xz rustc-ef24de24a82fe681581cc130f342363c47c0969a.zip |
Merging upstream version 1.75.0+dfsg1.
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'vendor/libm-0.1.4/src/math/cbrt.rs')
-rw-r--r-- | vendor/libm-0.1.4/src/math/cbrt.rs | 114 |
1 files changed, 0 insertions, 114 deletions
diff --git a/vendor/libm-0.1.4/src/math/cbrt.rs b/vendor/libm-0.1.4/src/math/cbrt.rs deleted file mode 100644 index 04469b159..000000000 --- a/vendor/libm-0.1.4/src/math/cbrt.rs +++ /dev/null @@ -1,114 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrt.c */ -/* - * ==================================================== - * 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. - * ==================================================== - * - * Optimized by Bruce D. Evans. - */ -/* cbrt(x) - * Return cube root of x - */ - -use core::f64; - -const B1: u32 = 715094163; /* B1 = (1023-1023/3-0.03306235651)*2**20 */ -const B2: u32 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */ - -/* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */ -const P0: f64 = 1.87595182427177009643; /* 0x3ffe03e6, 0x0f61e692 */ -const P1: f64 = -1.88497979543377169875; /* 0xbffe28e0, 0x92f02420 */ -const P2: f64 = 1.621429720105354466140; /* 0x3ff9f160, 0x4a49d6c2 */ -const P3: f64 = -0.758397934778766047437; /* 0xbfe844cb, 0xbee751d9 */ -const P4: f64 = 0.145996192886612446982; /* 0x3fc2b000, 0xd4e4edd7 */ - -// Cube root (f64) -/// -/// Computes the cube root of the argument. -#[inline] -#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] -pub fn cbrt(x: f64) -> f64 { - let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54 - - let mut ui: u64 = x.to_bits(); - let mut r: f64; - let s: f64; - let mut t: f64; - let w: f64; - let mut hx: u32 = (ui >> 32) as u32 & 0x7fffffff; - - if hx >= 0x7ff00000 { - /* cbrt(NaN,INF) is itself */ - return x + x; - } - - /* - * Rough cbrt to 5 bits: - * cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3) - * where e is integral and >= 0, m is real and in [0, 1), and "/" and - * "%" are integer division and modulus with rounding towards minus - * infinity. The RHS is always >= the LHS and has a maximum relative - * error of about 1 in 16. Adding a bias of -0.03306235651 to the - * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE - * floating point representation, for finite positive normal values, - * ordinary integer divison of the value in bits magically gives - * almost exactly the RHS of the above provided we first subtract the - * exponent bias (1023 for doubles) and later add it back. We do the - * subtraction virtually to keep e >= 0 so that ordinary integer - * division rounds towards minus infinity; this is also efficient. - */ - if hx < 0x00100000 { - /* zero or subnormal? */ - ui = (x * x1p54).to_bits(); - hx = (ui >> 32) as u32 & 0x7fffffff; - if hx == 0 { - return x; /* cbrt(0) is itself */ - } - hx = hx / 3 + B2; - } else { - hx = hx / 3 + B1; - } - ui &= 1 << 63; - ui |= (hx as u64) << 32; - t = f64::from_bits(ui); - - /* - * New cbrt to 23 bits: - * cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x) - * where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r) - * to within 2**-23.5 when |r - 1| < 1/10. The rough approximation - * has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this - * gives us bounds for r = t**3/x. - * - * Try to optimize for parallel evaluation as in __tanf.c. - */ - r = (t * t) * (t / x); - t = t * ((P0 + r * (P1 + r * P2)) + ((r * r) * r) * (P3 + r * P4)); - - /* - * Round t away from zero to 23 bits (sloppily except for ensuring that - * the result is larger in magnitude than cbrt(x) but not much more than - * 2 23-bit ulps larger). With rounding towards zero, the error bound - * would be ~5/6 instead of ~4/6. With a maximum error of 2 23-bit ulps - * in the rounded t, the infinite-precision error in the Newton - * approximation barely affects third digit in the final error - * 0.667; the error in the rounded t can be up to about 3 23-bit ulps - * before the final error is larger than 0.667 ulps. - */ - ui = t.to_bits(); - ui = (ui + 0x80000000) & 0xffffffffc0000000; - t = f64::from_bits(ui); - - /* one step Newton iteration to 53 bits with error < 0.667 ulps */ - s = t * t; /* t*t is exact */ - r = x / s; /* error <= 0.5 ulps; |r| < |t| */ - w = t + t; /* t+t is exact */ - r = (r - t) / (w + r); /* r-t is exact; w+r ~= 3*t */ - t = t + t * r; /* error <= 0.5 + 0.5/3 + epsilon */ - t -} |