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Diffstat (limited to '')
| -rw-r--r-- | vendor/compiler_builtins/libm/src/math/cbrt.rs | 113 |
1 files changed, 113 insertions, 0 deletions
diff --git a/vendor/compiler_builtins/libm/src/math/cbrt.rs b/vendor/compiler_builtins/libm/src/math/cbrt.rs new file mode 100644 index 000000000..b4e77eaa2 --- /dev/null +++ b/vendor/compiler_builtins/libm/src/math/cbrt.rs @@ -0,0 +1,113 @@ +/* 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. +#[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 +} |