zig/std/math/sin.zig

189 lines
4.7 KiB
Zig

// Special Cases:
//
// - sin(+-0) = +-0
// - sin(+-inf) = nan
// - sin(nan) = nan
const builtin = @import("builtin");
const std = @import("../index.zig");
const math = std.math;
const assert = std.debug.assert;
pub fn sin(x: var) @typeOf(x) {
const T = @typeOf(x);
return switch (T) {
f32 => sin32(x),
f64 => sin64(x),
else => @compileError("sin not implemented for " ++ @typeName(T)),
};
}
// sin polynomial coefficients
const S0 = 1.58962301576546568060E-10;
const S1 = -2.50507477628578072866E-8;
const S2 = 2.75573136213857245213E-6;
const S3 = -1.98412698295895385996E-4;
const S4 = 8.33333333332211858878E-3;
const S5 = -1.66666666666666307295E-1;
// cos polynomial coeffiecients
const C0 = -1.13585365213876817300E-11;
const C1 = 2.08757008419747316778E-9;
const C2 = -2.75573141792967388112E-7;
const C3 = 2.48015872888517045348E-5;
const C4 = -1.38888888888730564116E-3;
const C5 = 4.16666666666665929218E-2;
// NOTE: This is taken from the go stdlib. The musl implementation is much more complex.
//
// This may have slight differences on some edge cases and may need to replaced if so.
fn sin32(x_: f32) f32 {
@setFloatMode(this, @import("builtin").FloatMode.Strict);
const pi4a = 7.85398125648498535156e-1;
const pi4b = 3.77489470793079817668E-8;
const pi4c = 2.69515142907905952645E-15;
const m4pi = 1.273239544735162542821171882678754627704620361328125;
var x = x_;
if (x == 0 or math.isNan(x)) {
return x;
}
if (math.isInf(x)) {
return math.nan(f32);
}
var sign = false;
if (x < 0) {
x = -x;
sign = true;
}
var y = math.floor(x * m4pi);
var j = i64(y);
if (j & 1 == 1) {
j += 1;
y += 1;
}
j &= 7;
if (j > 3) {
j -= 4;
sign = !sign;
}
const z = ((x - y * pi4a) - y * pi4b) - y * pi4c;
const w = z * z;
const r = r: {
if (j == 1 or j == 2) {
break :r 1.0 - 0.5 * w + w * w * (C5 + w * (C4 + w * (C3 + w * (C2 + w * (C1 + w * C0)))));
} else {
break :r z + z * w * (S5 + w * (S4 + w * (S3 + w * (S2 + w * (S1 + w * S0)))));
}
};
if (sign) {
return -r;
} else {
return r;
}
}
fn sin64(x_: f64) f64 {
const pi4a = 7.85398125648498535156e-1;
const pi4b = 3.77489470793079817668E-8;
const pi4c = 2.69515142907905952645E-15;
const m4pi = 1.273239544735162542821171882678754627704620361328125;
var x = x_;
if (x == 0 or math.isNan(x)) {
return x;
}
if (math.isInf(x)) {
return math.nan(f64);
}
var sign = false;
if (x < 0) {
x = -x;
sign = true;
}
var y = math.floor(x * m4pi);
var j = i64(y);
if (j & 1 == 1) {
j += 1;
y += 1;
}
j &= 7;
if (j > 3) {
j -= 4;
sign = !sign;
}
const z = ((x - y * pi4a) - y * pi4b) - y * pi4c;
const w = z * z;
const r = r: {
if (j == 1 or j == 2) {
break :r 1.0 - 0.5 * w + w * w * (C5 + w * (C4 + w * (C3 + w * (C2 + w * (C1 + w * C0)))));
} else {
break :r z + z * w * (S5 + w * (S4 + w * (S3 + w * (S2 + w * (S1 + w * S0)))));
}
};
if (sign) {
return -r;
} else {
return r;
}
}
test "math.sin" {
assert(sin(f32(0.0)) == sin32(0.0));
assert(sin(f64(0.0)) == sin64(0.0));
assert(comptime (math.sin(f64(2))) == math.sin(f64(2)));
}
test "math.sin32" {
const epsilon = 0.000001;
assert(math.approxEq(f32, sin32(0.0), 0.0, epsilon));
assert(math.approxEq(f32, sin32(0.2), 0.198669, epsilon));
assert(math.approxEq(f32, sin32(0.8923), 0.778517, epsilon));
assert(math.approxEq(f32, sin32(1.5), 0.997495, epsilon));
assert(math.approxEq(f32, sin32(37.45), -0.246544, epsilon));
assert(math.approxEq(f32, sin32(89.123), 0.916166, epsilon));
}
test "math.sin64" {
const epsilon = 0.000001;
assert(math.approxEq(f64, sin64(0.0), 0.0, epsilon));
assert(math.approxEq(f64, sin64(0.2), 0.198669, epsilon));
assert(math.approxEq(f64, sin64(0.8923), 0.778517, epsilon));
assert(math.approxEq(f64, sin64(1.5), 0.997495, epsilon));
assert(math.approxEq(f64, sin64(37.45), -0.246543, epsilon));
assert(math.approxEq(f64, sin64(89.123), 0.916166, epsilon));
}
test "math.sin32.special" {
assert(sin32(0.0) == 0.0);
assert(sin32(-0.0) == -0.0);
assert(math.isNan(sin32(math.inf(f32))));
assert(math.isNan(sin32(-math.inf(f32))));
assert(math.isNan(sin32(math.nan(f32))));
}
test "math.sin64.special" {
assert(sin64(0.0) == 0.0);
assert(sin64(-0.0) == -0.0);
assert(math.isNan(sin64(math.inf(f64))));
assert(math.isNan(sin64(-math.inf(f64))));
assert(math.isNan(sin64(math.nan(f64))));
}