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const std = @import("../../index.zig");
const debug = std.debug;
const math = std.math;
const cmath = math.complex;
const Complex = cmath.Complex;
pub fn atan(z: var) @typeOf(z) {
const T = @typeOf(z.re);
return switch (T) {
f32 => atan32(z),
f64 => atan64(z),
else => @compileError("atan not implemented for " ++ @typeName(z)),
};
}
fn redupif32(x: f32) f32 {
const DP1 = 3.140625;
const DP2 = 9.67502593994140625e-4;
const DP3 = 1.509957990978376432e-7;
var t = x / math.pi;
if (t >= 0.0) {
t += 0.5;
} else {
t -= 0.5;
}
const u = @intToFloat(f32, @floatToInt(i32, t));
return ((x - u * DP1) - u * DP2) - t * DP3;
}
fn atan32(z: Complex(f32)) Complex(f32) {
const maxnum = 1.0e38;
const x = z.re;
const y = z.im;
if ((x == 0.0) and (y > 1.0)) {
// overflow
return Complex(f32).new(maxnum, maxnum);
}
const x2 = x * x;
var a = 1.0 - x2 - (y * y);
if (a == 0.0) {
// overflow
return Complex(f32).new(maxnum, maxnum);
}
var t = 0.5 * math.atan2(f32, 2.0 * x, a);
var w = redupif32(t);
t = y - 1.0;
a = x2 + t * t;
if (a == 0.0) {
// overflow
return Complex(f32).new(maxnum, maxnum);
}
t = y + 1.0;
a = (x2 + (t * t)) / a;
return Complex(f32).new(w, 0.25 * math.ln(a));
}
fn redupif64(x: f64) f64 {
const DP1 = 3.14159265160560607910;
const DP2 = 1.98418714791870343106e-9;
const DP3 = 1.14423774522196636802e-17;
var t = x / math.pi;
if (t >= 0.0) {
t += 0.5;
} else {
t -= 0.5;
}
const u = @intToFloat(f64, @floatToInt(i64, t));
return ((x - u * DP1) - u * DP2) - t * DP3;
}
fn atan64(z: Complex(f64)) Complex(f64) {
const maxnum = 1.0e308;
const x = z.re;
const y = z.im;
if ((x == 0.0) and (y > 1.0)) {
// overflow
return Complex(f64).new(maxnum, maxnum);
}
const x2 = x * x;
var a = 1.0 - x2 - (y * y);
if (a == 0.0) {
// overflow
return Complex(f64).new(maxnum, maxnum);
}
var t = 0.5 * math.atan2(f64, 2.0 * x, a);
var w = redupif64(t);
t = y - 1.0;
a = x2 + t * t;
if (a == 0.0) {
// overflow
return Complex(f64).new(maxnum, maxnum);
}
t = y + 1.0;
a = (x2 + (t * t)) / a;
return Complex(f64).new(w, 0.25 * math.ln(a));
}
const epsilon = 0.0001;
test "complex.catan32" {
const a = Complex(f32).new(5, 3);
const c = atan(a);
debug.assert(math.approxEq(f32, c.re, 1.423679, epsilon));
debug.assert(math.approxEq(f32, c.im, 0.086569, epsilon));
}
test "complex.catan64" {
const a = Complex(f64).new(5, 3);
const c = atan(a);
debug.assert(math.approxEq(f64, c.re, 1.423679, epsilon));
debug.assert(math.approxEq(f64, c.im, 0.086569, epsilon));
}
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