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// Ported from musl, which is licensed under the MIT license:
// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
//
// https://git.musl-libc.org/cgit/musl/tree/src/complex/csqrtf.c
// https://git.musl-libc.org/cgit/musl/tree/src/complex/csqrt.c
const std = @import("../../std.zig");
const testing = std.testing;
const math = std.math;
const cmath = math.complex;
const Complex = cmath.Complex;
/// Returns the square root of z. The real and imaginary parts of the result have the same sign
/// as the imaginary part of z.
pub fn sqrt(z: anytype) @TypeOf(z) {
const T = @TypeOf(z.re);
return switch (T) {
f32 => sqrt32(z),
f64 => sqrt64(z),
else => @compileError("sqrt not implemented for " ++ @typeName(T)),
};
}
fn sqrt32(z: Complex(f32)) Complex(f32) {
const x = z.re;
const y = z.im;
if (x == 0 and y == 0) {
return Complex(f32).init(0, y);
}
if (math.isInf(y)) {
return Complex(f32).init(math.inf(f32), y);
}
if (math.isNan(x)) {
// raise invalid if y is not nan
const t = (y - y) / (y - y);
return Complex(f32).init(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).init(@fabs(x - y), math.copysign(x, y));
} else {
return Complex(f32).init(x, math.copysign(y - y, y));
}
}
// y = nan special case is handled fine below
// double-precision avoids overflow with correct rounding.
const dx = @as(f64, x);
const dy = @as(f64, y);
if (dx >= 0) {
const t = @sqrt((dx + math.hypot(f64, dx, dy)) * 0.5);
return Complex(f32).init(
@as(f32, @floatCast(t)),
@as(f32, @floatCast(dy / (2.0 * t))),
);
} else {
const t = @sqrt((-dx + math.hypot(f64, dx, dy)) * 0.5);
return Complex(f32).init(
@as(f32, @floatCast(@fabs(y) / (2.0 * t))),
@as(f32, @floatCast(math.copysign(t, y))),
);
}
}
fn sqrt64(z: 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).init(0, y);
}
if (math.isInf(y)) {
return Complex(f64).init(math.inf(f64), y);
}
if (math.isNan(x)) {
// raise invalid if y is not nan
const t = (y - y) / (y - y);
return Complex(f64).init(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).init(@fabs(x - y), math.copysign(x, y));
} else {
return Complex(f64).init(x, math.copysign(y - y, y));
}
}
// y = nan special case is handled fine below
// scale to avoid overflow
var scale = false;
if (@fabs(x) >= threshold or @fabs(y) >= threshold) {
x *= 0.25;
y *= 0.25;
scale = true;
}
var result: Complex(f64) = undefined;
if (x >= 0) {
const t = @sqrt((x + math.hypot(f64, x, y)) * 0.5);
result = Complex(f64).init(t, y / (2.0 * t));
} else {
const t = @sqrt((-x + math.hypot(f64, x, y)) * 0.5);
result = Complex(f64).init(@fabs(y) / (2.0 * t), math.copysign(t, y));
}
if (scale) {
result.re *= 2;
result.im *= 2;
}
return result;
}
const epsilon = 0.0001;
test "complex.csqrt32" {
const a = Complex(f32).init(5, 3);
const c = sqrt(a);
try testing.expect(math.approxEqAbs(f32, c.re, 2.327117, epsilon));
try testing.expect(math.approxEqAbs(f32, c.im, 0.644574, epsilon));
}
test "complex.csqrt64" {
const a = Complex(f64).init(5, 3);
const c = sqrt(a);
try testing.expect(math.approxEqAbs(f64, c.re, 2.3271175190399496, epsilon));
try testing.expect(math.approxEqAbs(f64, c.im, 0.6445742373246469, epsilon));
}
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