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Diffstat (limited to 'vendor/libm/src/math/k_cos.rs')
-rw-r--r-- | vendor/libm/src/math/k_cos.rs | 63 |
1 files changed, 63 insertions, 0 deletions
diff --git a/vendor/libm/src/math/k_cos.rs b/vendor/libm/src/math/k_cos.rs new file mode 100644 index 000000000..4687b369a --- /dev/null +++ b/vendor/libm/src/math/k_cos.rs @@ -0,0 +1,63 @@ +// origin: FreeBSD /usr/src/lib/msun/src/k_cos.c +// +// ==================================================== +// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. +// +// Developed at SunSoft, a Sun Microsystems, Inc. business. +// Permission to use, copy, modify, and distribute this +// software is freely granted, provided that this notice +// is preserved. +// ==================================================== + +const C1: f64 = 4.16666666666666019037e-02; /* 0x3FA55555, 0x5555554C */ +const C2: f64 = -1.38888888888741095749e-03; /* 0xBF56C16C, 0x16C15177 */ +const C3: f64 = 2.48015872894767294178e-05; /* 0x3EFA01A0, 0x19CB1590 */ +const C4: f64 = -2.75573143513906633035e-07; /* 0xBE927E4F, 0x809C52AD */ +const C5: f64 = 2.08757232129817482790e-09; /* 0x3E21EE9E, 0xBDB4B1C4 */ +const C6: f64 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ + +// kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 +// Input x is assumed to be bounded by ~pi/4 in magnitude. +// Input y is the tail of x. +// +// Algorithm +// 1. Since cos(-x) = cos(x), we need only to consider positive x. +// 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. +// 3. cos(x) is approximated by a polynomial of degree 14 on +// [0,pi/4] +// 4 14 +// cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x +// where the remez error is +// +// | 2 4 6 8 10 12 14 | -58 +// |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 +// | | +// +// 4 6 8 10 12 14 +// 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then +// cos(x) ~ 1 - x*x/2 + r +// since cos(x+y) ~ cos(x) - sin(x)*y +// ~ cos(x) - x*y, +// a correction term is necessary in cos(x) and hence +// cos(x+y) = 1 - (x*x/2 - (r - x*y)) +// For better accuracy, rearrange to +// cos(x+y) ~ w + (tmp + (r-x*y)) +// where w = 1 - x*x/2 and tmp is a tiny correction term +// (1 - x*x/2 == w + tmp exactly in infinite precision). +// The exactness of w + tmp in infinite precision depends on w +// and tmp having the same precision as x. If they have extra +// precision due to compiler bugs, then the extra precision is +// only good provided it is retained in all terms of the final +// expression for cos(). Retention happens in all cases tested +// under FreeBSD, so don't pessimize things by forcibly clipping +// any extra precision in w. +#[inline] +#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] +pub(crate) fn k_cos(x: f64, y: f64) -> f64 { + let z = x * x; + let w = z * z; + let r = z * (C1 + z * (C2 + z * C3)) + w * w * (C4 + z * (C5 + z * C6)); + let hz = 0.5 * z; + let w = 1.0 - hz; + w + (((1.0 - w) - hz) + (z * r - x * y)) +} |