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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/ctanhf.c
// https://git.musl-libc.org/cgit/musl/tree/src/complex/ctanh.c
const std = @import("../../std.zig");
const testing = std.testing;
const math = std.math;
const cmath = math.complex;
const Complex = cmath.Complex;
/// Returns the hyperbolic tangent of z.
pub fn tanh(z: anytype) Complex(@TypeOf(z.re, z.im)) {
const T = @TypeOf(z.re, z.im);
return switch (T) {
f32 => tanh32(z),
f64 => tanh64(z),
else => @compileError("tan not implemented for " ++ @typeName(z)),
};
}
fn tanh32(z: Complex(f32)) Complex(f32) {
const x = z.re;
const y = z.im;
const hx = @as(u32, @bitCast(x));
const ix = hx & 0x7fffffff;
if (ix >= 0x7f800000) {
if (ix & 0x7fffff != 0) {
const r = if (y == 0) y else x * y;
return Complex(f32).init(x, r);
}
const xx = @as(f32, @bitCast(hx - 0x40000000));
const r = if (math.isInf(y)) y else @sin(y) * @cos(y);
return Complex(f32).init(xx, math.copysign(@as(f32, 0.0), r));
}
if (!math.isFinite(y)) {
const r = if (ix != 0) y - y else x;
return Complex(f32).init(r, y - y);
}
// x >= 11
if (ix >= 0x41300000) {
const exp_mx = @exp(-@abs(x));
return Complex(f32).init(math.copysign(@as(f32, 1.0), x), 4 * @sin(y) * @cos(y) * exp_mx * exp_mx);
}
// Kahan's algorithm
const t = @tan(y);
const beta = 1.0 + t * t;
const s = math.sinh(x);
const rho = @sqrt(1 + s * s);
const den = 1 + beta * s * s;
return Complex(f32).init((beta * rho * s) / den, t / den);
}
fn tanh64(z: Complex(f64)) Complex(f64) {
const x = z.re;
const y = z.im;
const fx: u64 = @bitCast(x);
// TODO: zig should allow this conversion implicitly because it can notice that the value necessarily
// fits in range.
const hx: u32 = @intCast(fx >> 32);
const lx: u32 = @truncate(fx);
const ix = hx & 0x7fffffff;
if (ix >= 0x7ff00000) {
if ((ix & 0x7fffff) | lx != 0) {
const r = if (y == 0) y else x * y;
return Complex(f64).init(x, r);
}
const xx: f64 = @bitCast((@as(u64, hx - 0x40000000) << 32) | lx);
const r = if (math.isInf(y)) y else @sin(y) * @cos(y);
return Complex(f64).init(xx, math.copysign(@as(f64, 0.0), r));
}
if (!math.isFinite(y)) {
const r = if (ix != 0) y - y else x;
return Complex(f64).init(r, y - y);
}
// x >= 22
if (ix >= 0x40360000) {
const exp_mx = @exp(-@abs(x));
return Complex(f64).init(math.copysign(@as(f64, 1.0), x), 4 * @sin(y) * @cos(y) * exp_mx * exp_mx);
}
// Kahan's algorithm
const t = @tan(y);
const beta = 1.0 + t * t;
const s = math.sinh(x);
const rho = @sqrt(1 + s * s);
const den = 1 + beta * s * s;
return Complex(f64).init((beta * rho * s) / den, t / den);
}
const epsilon = 0.0001;
test "complex.ctanh32" {
const a = Complex(f32).init(5, 3);
const c = tanh(a);
try testing.expect(math.approxEqAbs(f32, c.re, 0.999913, epsilon));
try testing.expect(math.approxEqAbs(f32, c.im, -0.000025, epsilon));
}
test "complex.ctanh64" {
const a = Complex(f64).init(5, 3);
const c = tanh(a);
try testing.expect(math.approxEqAbs(f64, c.re, 0.999913, epsilon));
try testing.expect(math.approxEqAbs(f64, c.im, -0.000025, epsilon));
}
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