k_cos.rs - source
Description: Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.6/src/math/k_cos.rs`.
Keywords: rust, rustlang, rust-lang

    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62

    // 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))
    }