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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;
// TODO when #733 is solved this can be @typeOf(z) instead of Complex(@typeOf(z.re))
pub fn sqrt(z: var) Complex(@typeOf(z.re)) {
const T = @typeOf(z.re);
return switch (T) {
f32 => sqrt32(z),
f64 => sqrt64(z),
else => @compileError("sqrt not implemented for " ++ @typeName(z)),
};
}
fn sqrt32(z: &const Complex(f32)) Complex(f32) {
const x = z.re;
const y = z.im;
if (x == 0 and y == 0) {
return Complex(f32).new(0, y);
}
if (math.isInf(y)) {
return Complex(f32).new(math.inf(f32), y);
}
if (math.isNan(x)) {
// raise invalid if y is not nan
const t = (y - y) / (y - y);
return Complex(f32).new(x, t);
}
if (math.isInf(x)) {
// sqrt(inf + i nan) = inf + nan i
// sqrt(inf + iy) = inf + i0
// sqrt(-inf + i nan) = nan +- inf i
// sqrt(-inf + iy) = 0 + inf i
if (math.signbit(x)) {
return Complex(f32).new(math.fabs(x - y), math.copysign(f32, x, y));
} else {
return Complex(f32).new(x, math.copysign(f32, y - y, y));
}
}
// y = nan special case is handled fine below
// double-precision avoids overflow with correct rounding.
const dx = f64(x);
const dy = f64(y);
if (dx >= 0) {
const t = math.sqrt((dx + math.hypot(f64, dx, dy)) * 0.5);
return Complex(f32).new(f32(t), f32(dy / (2.0 * t)));
} else {
const t = math.sqrt((-dx + math.hypot(f64, dx, dy)) * 0.5);
return Complex(f32).new(f32(math.fabs(y) / (2.0 * t)), f32(math.copysign(f64, t, y)));
}
}
fn sqrt64(z: &const Complex(f64)) Complex(f64) {
// may encounter overflow for im,re >= DBL_MAX / (1 + sqrt(2))
const threshold = 0x1.a827999fcef32p+1022;
var x = z.re;
var y = z.im;
if (x == 0 and y == 0) {
return Complex(f64).new(0, y);
}
if (math.isInf(y)) {
return Complex(f64).new(math.inf(f64), y);
}
if (math.isNan(x)) {
// raise invalid if y is not nan
const t = (y - y) / (y - y);
return Complex(f64).new(x, t);
}
if (math.isInf(x)) {
// sqrt(inf + i nan) = inf + nan i
// sqrt(inf + iy) = inf + i0
// sqrt(-inf + i nan) = nan +- inf i
// sqrt(-inf + iy) = 0 + inf i
if (math.signbit(x)) {
return Complex(f64).new(math.fabs(x - y), math.copysign(f64, x, y));
} else {
return Complex(f64).new(x, math.copysign(f64, y - y, y));
}
}
// y = nan special case is handled fine below
// scale to avoid overflow
var scale = false;
if (math.fabs(x) >= threshold or math.fabs(y) >= threshold) {
x *= 0.25;
y *= 0.25;
scale = true;
}
var result: Complex(f64) = undefined;
if (x >= 0) {
const t = math.sqrt((x + math.hypot(f64, x, y)) * 0.5);
result = Complex(f64).new(t, y / (2.0 * t));
} else {
const t = math.sqrt((-x + math.hypot(f64, x, y)) * 0.5);
result = Complex(f64).new(math.fabs(y) / (2.0 * t), math.copysign(f64, t, y));
}
if (scale) {
result.re *= 2;
result.im *= 2;
}
return result;
}
const epsilon = 0.0001;
test "complex.csqrt32" {
const a = Complex(f32).new(5, 3);
const c = sqrt(a);
debug.assert(math.approxEq(f32, c.re, 2.327117, epsilon));
debug.assert(math.approxEq(f32, c.im, 0.644574, epsilon));
}
test "complex.csqrt64" {
const a = Complex(f64).new(5, 3);
const c = sqrt(a);
debug.assert(math.approxEq(f64, c.re, 2.3271175190399496, epsilon));
debug.assert(math.approxEq(f64, c.im, 0.6445742373246469, epsilon));
}
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