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    // origin: FreeBSD /usr/src/lib/msun/src/k_sin.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 S1: f64 = -1.66666666666666324348e-01; /* 0xBFC55555, 0x55555549 */
    const S2: f64 = 8.33333333332248946124e-03; /* 0x3F811111, 0x1110F8A6 */
    const S3: f64 = -1.98412698298579493134e-04; /* 0xBF2A01A0, 0x19C161D5 */
    const S4: f64 = 2.75573137070700676789e-06; /* 0x3EC71DE3, 0x57B1FE7D */
    const S5: f64 = -2.50507602534068634195e-08; /* 0xBE5AE5E6, 0x8A2B9CEB */
    const S6: f64 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */

    // kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
    // Input x is assumed to be bounded by ~pi/4 in magnitude.
    // Input y is the tail of x.
    // Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
    //
    // Algorithm
    //      1. Since sin(-x) = -sin(x), we need only to consider positive x.
    //      2. Callers must return sin(-0) = -0 without calling here since our
    //         odd polynomial is not evaluated in a way that preserves -0.
    //         Callers may do the optimization sin(x) ~ x for tiny x.
    //      3. sin(x) is approximated by a polynomial of degree 13 on
    //         [0,pi/4]
    //                               3            13
    //              sin(x) ~ x + S1*x + ... + S6*x
    //         where
    //
    //      |sin(x)         2     4     6     8     10     12  |     -58
    //      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
    //      |  x                                               |
    //
    //      4. sin(x+y) = sin(x) + sin'(x')*y
    //                  ~ sin(x) + (1-x*x/2)*y
    //         For better accuracy, let
    //                   3      2      2      2      2
    //              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
    //         then                   3    2
    //              sin(x) = x + (S1*x + (x *(r-y/2)+y))
    #[inline]
    #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
    pub(crate) fn k_sin(x: f64, y: f64, iy: i32) -> f64 {
        let z = x * x;
        let w = z * z;
        let r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6);
        let v = z * x;
        if iy == 0 {
            x + v * (S1 + z * r)
        } else {
            x - ((z * (0.5 * y - v * r) - y) - v * S1)
        }
    }

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