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// Special Cases:
//
// - tan(+-0) = +-0
// - tan(+-inf) = nan
// - tan(nan) = nan
const builtin = @import("builtin");
const std = @import("../index.zig");
const math = std.math;
const assert = std.debug.assert;
pub fn tan(x: var) @typeOf(x) {
const T = @typeOf(x);
return switch (T) {
f32 => tan32(x),
f64 => tan64(x),
else => @compileError("tan not implemented for " ++ @typeName(T)),
};
}
const Tp0 = -1.30936939181383777646E4;
const Tp1 = 1.15351664838587416140E6;
const Tp2 = -1.79565251976484877988E7;
const Tq1 = 1.36812963470692954678E4;
const Tq2 = -1.32089234440210967447E6;
const Tq3 = 2.50083801823357915839E7;
const Tq4 = -5.38695755929454629881E7;
// 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 tan32(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;
}
const z = ((x - y * pi4a) - y * pi4b) - y * pi4c;
const w = z * z;
var r = r: {
if (w > 1e-14) {
break :r z + z * (w * ((Tp0 * w + Tp1) * w + Tp2) / ((((w + Tq1) * w + Tq2) * w + Tq3) * w + Tq4));
} else {
break :r z;
}
};
if (j & 2 == 2) {
r = -1 / r;
}
if (sign) {
r = -r;
}
return r;
}
fn tan64(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;
}
const z = ((x - y * pi4a) - y * pi4b) - y * pi4c;
const w = z * z;
var r = r: {
if (w > 1e-14) {
break :r z + z * (w * ((Tp0 * w + Tp1) * w + Tp2) / ((((w + Tq1) * w + Tq2) * w + Tq3) * w + Tq4));
} else {
break :r z;
}
};
if (j & 2 == 2) {
r = -1 / r;
}
if (sign) {
r = -r;
}
return r;
}
test "math.tan" {
assert(tan(f32(0.0)) == tan32(0.0));
assert(tan(f64(0.0)) == tan64(0.0));
}
test "math.tan32" {
const epsilon = 0.000001;
assert(math.approxEq(f32, tan32(0.0), 0.0, epsilon));
assert(math.approxEq(f32, tan32(0.2), 0.202710, epsilon));
assert(math.approxEq(f32, tan32(0.8923), 1.240422, epsilon));
assert(math.approxEq(f32, tan32(1.5), 14.101420, epsilon));
assert(math.approxEq(f32, tan32(37.45), -0.254397, epsilon));
assert(math.approxEq(f32, tan32(89.123), 2.285852, epsilon));
}
test "math.tan64" {
const epsilon = 0.000001;
assert(math.approxEq(f64, tan64(0.0), 0.0, epsilon));
assert(math.approxEq(f64, tan64(0.2), 0.202710, epsilon));
assert(math.approxEq(f64, tan64(0.8923), 1.240422, epsilon));
assert(math.approxEq(f64, tan64(1.5), 14.101420, epsilon));
assert(math.approxEq(f64, tan64(37.45), -0.254397, epsilon));
assert(math.approxEq(f64, tan64(89.123), 2.2858376, epsilon));
}
test "math.tan32.special" {
assert(tan32(0.0) == 0.0);
assert(tan32(-0.0) == -0.0);
assert(math.isNan(tan32(math.inf(f32))));
assert(math.isNan(tan32(-math.inf(f32))));
assert(math.isNan(tan32(math.nan(f32))));
}
test "math.tan64.special" {
assert(tan64(0.0) == 0.0);
assert(tan64(-0.0) == -0.0);
assert(math.isNan(tan64(math.inf(f64))));
assert(math.isNan(tan64(-math.inf(f64))));
assert(math.isNan(tan64(math.nan(f64))));
}
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