Zig 0.17.0-dev (Split by item)

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sin

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 + S1x + ... + S6x where

|sin(x) 2 4 6 8 10 12 | -58 |----- - (1+S1x +S2x +S3x +S4x +S5x +S6x )| <= 2

x
  1. sin(x+y) = sin(x) + sin'(x')y ~ sin(x) + (1-xx/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 + (S1x + (x *(r-y/2)+y))
trig.sin
pub fn sin(x: f64, y: f64, iy: i32) f64

File

lib/compiler_rt/trig.zig:150

Code

pub fn sin(x: f64, y: f64, iy: i32) f64 {
    const S1 = -1.66666666666666324348e-01; // 0xBFC55555, 0x55555549
    const S2 = 8.33333333332248946124e-03; // 0x3F811111, 0x1110F8A6
    const S3 = -1.98412698298579493134e-04; // 0xBF2A01A0, 0x19C161D5
    const S4 = 2.75573137070700676789e-06; // 0x3EC71DE3, 0x57B1FE7D
    const S5 = -2.50507602534068634195e-08; // 0xBE5AE5E6, 0x8A2B9CEB
    const S6 = 1.58969099521155010221e-10; // 0x3DE5D93A, 0x5ACFD57C

    const z = x * x;
    const w = z * z;
    const r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6);
    const v = z * x;
    if (iy == 0) {
        return x + v * (S1 + z * r);
    } else {
        return x - ((z * (0.5 * y - v * r) - y) - v * S1);
    }
}