| // 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)) |
| #[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) |
| } |
| } |
