k_cos.rs - mozsearch

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// 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.

#[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))