zig/std/math/cos.zig

// Special Cases:
//
// - cos(+-inf) = nan
// - cos(nan)   = nan

const builtin = @import("builtin");
const std = @import("../index.zig");
const math = std.math;
const assert = std.debug.assert;

pub fn cos(x: var) @typeOf(x) {
    const T = @typeOf(x);
    return switch (T) {
        f32 => cos32(x),
        f64 => cos64(x),
        else => @compileError("cos 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 cos32(x_: f32) f32 {
    const pi4a = 7.85398125648498535156e-1;
    const pi4b = 3.77489470793079817668E-8;
    const pi4c = 2.69515142907905952645E-15;
    const m4pi = 1.273239544735162542821171882678754627704620361328125;

    var x = x_;
    if (math.isNan(x) or math.isInf(x)) {
        return math.nan(f32);
    }

    var sign = false;
    if (x < 0) {
        x = -x;
    }

    var y = math.floor(x * m4pi);
    var j = @floatToInt(i64, y);

    if (j & 1 == 1) {
        j += 1;
        y += 1;
    }

    j &= 7;
    if (j > 3) {
        j -= 4;
        sign = !sign;
    }
    if (j > 1) {
        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 z + z * w * (S5 + w * (S4 + w * (S3 + w * (S2 + w * (S1 + w * S0)))));
        } else {
            break :r 1.0 - 0.5 * w + w * w * (C5 + w * (C4 + w * (C3 + w * (C2 + w * (C1 + w * C0)))));
        }
    };

    if (sign) {
        return -r;
    } else {
        return r;
    }
}

fn cos64(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 (math.isNan(x) or math.isInf(x)) {
        return math.nan(f64);
    }

    var sign = false;
    if (x < 0) {
        x = -x;
    }

    var y = math.floor(x * m4pi);
    var j = @floatToInt(i64, y);

    if (j & 1 == 1) {
        j += 1;
        y += 1;
    }

    j &= 7;
    if (j > 3) {
        j -= 4;
        sign = !sign;
    }
    if (j > 1) {
        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 z + z * w * (S5 + w * (S4 + w * (S3 + w * (S2 + w * (S1 + w * S0)))));
        } else {
            break :r 1.0 - 0.5 * w + w * w * (C5 + w * (C4 + w * (C3 + w * (C2 + w * (C1 + w * C0)))));
        }
    };

    if (sign) {
        return -r;
    } else {
        return r;
    }
}

test "math.cos" {
    assert(cos(f32(0.0)) == cos32(0.0));
    assert(cos(f64(0.0)) == cos64(0.0));
}

test "math.cos32" {
    const epsilon = 0.000001;

    assert(math.approxEq(f32, cos32(0.0), 1.0, epsilon));
    assert(math.approxEq(f32, cos32(0.2), 0.980067, epsilon));
    assert(math.approxEq(f32, cos32(0.8923), 0.627623, epsilon));
    assert(math.approxEq(f32, cos32(1.5), 0.070737, epsilon));
    assert(math.approxEq(f32, cos32(37.45), 0.969132, epsilon));
    assert(math.approxEq(f32, cos32(89.123), 0.400798, epsilon));
}

test "math.cos64" {
    const epsilon = 0.000001;

    assert(math.approxEq(f64, cos64(0.0), 1.0, epsilon));
    assert(math.approxEq(f64, cos64(0.2), 0.980067, epsilon));
    assert(math.approxEq(f64, cos64(0.8923), 0.627623, epsilon));
    assert(math.approxEq(f64, cos64(1.5), 0.070737, epsilon));
    assert(math.approxEq(f64, cos64(37.45), 0.969132, epsilon));
    assert(math.approxEq(f64, cos64(89.123), 0.40080, epsilon));
}

test "math.cos32.special" {
    assert(math.isNan(cos32(math.inf(f32))));
    assert(math.isNan(cos32(-math.inf(f32))));
    assert(math.isNan(cos32(math.nan(f32))));
}

test "math.cos64.special" {
    assert(math.isNan(cos64(math.inf(f64))));
    assert(math.isNan(cos64(-math.inf(f64))));
    assert(math.isNan(cos64(math.nan(f64))));
}