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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/csinhf.c
// https://git.musl-libc.org/cgit/musl/tree/src/complex/csinh.c
const builtin = @import("builtin");
const std = @import("../../std.zig");
const testing = std.testing;
const math = std.math;
const cmath = math.complex;
const Complex = cmath.Complex;
const ldexp_cexp = @import("ldexp.zig").ldexp_cexp;
/// Returns the hyperbolic sine of z.
pub fn sinh(z: var) @typeOf(z) {
const T = @typeOf(z.re);
return switch (T) {
f32 => sinh32(z),
f64 => sinh64(z),
else => @compileError("tan not implemented for " ++ @typeName(z)),
};
}
fn sinh32(z: Complex(f32)) Complex(f32) {
const x = z.re;
const y = z.im;
const hx = @bitCast(u32, x);
const ix = hx & 0x7fffffff;
const hy = @bitCast(u32, y);
const iy = hy & 0x7fffffff;
if (ix < 0x7f800000 and iy < 0x7f800000) {
if (iy == 0) {
return Complex(f32).new(math.sinh(x), y);
}
// small x: normal case
if (ix < 0x41100000) {
return Complex(f32).new(math.sinh(x) * math.cos(y), math.cosh(x) * math.sin(y));
}
// |x|>= 9, so cosh(x) ~= exp(|x|)
if (ix < 0x42b17218) {
// x < 88.7: exp(|x|) won't overflow
const h = math.exp(math.fabs(x)) * 0.5;
return Complex(f32).new(math.copysign(f32, h, x) * math.cos(y), h * math.sin(y));
}
// x < 192.7: scale to avoid overflow
else if (ix < 0x4340b1e7) {
const v = Complex(f32).new(math.fabs(x), y);
const r = ldexp_cexp(v, -1);
return Complex(f32).new(r.re * math.copysign(f32, 1, x), r.im);
}
// x >= 192.7: result always overflows
else {
const h = 0x1p127 * x;
return Complex(f32).new(h * math.cos(y), h * h * math.sin(y));
}
}
if (ix == 0 and iy >= 0x7f800000) {
return Complex(f32).new(math.copysign(f32, 0, x * (y - y)), y - y);
}
if (iy == 0 and ix >= 0x7f800000) {
if (hx & 0x7fffff == 0) {
return Complex(f32).new(x, y);
}
return Complex(f32).new(x, math.copysign(f32, 0, y));
}
if (ix < 0x7f800000 and iy >= 0x7f800000) {
return Complex(f32).new(y - y, x * (y - y));
}
if (ix >= 0x7f800000 and (hx & 0x7fffff) == 0) {
if (iy >= 0x7f800000) {
return Complex(f32).new(x * x, x * (y - y));
}
return Complex(f32).new(x * math.cos(y), math.inf_f32 * math.sin(y));
}
return Complex(f32).new((x * x) * (y - y), (x + x) * (y - y));
}
fn sinh64(z: Complex(f64)) Complex(f64) {
const x = z.re;
const y = z.im;
const fx = @bitCast(u64, x);
const hx = @intCast(u32, fx >> 32);
const lx = @truncate(u32, fx);
const ix = hx & 0x7fffffff;
const fy = @bitCast(u64, y);
const hy = @intCast(u32, fy >> 32);
const ly = @truncate(u32, fy);
const iy = hy & 0x7fffffff;
if (ix < 0x7ff00000 and iy < 0x7ff00000) {
if (iy | ly == 0) {
return Complex(f64).new(math.sinh(x), y);
}
// small x: normal case
if (ix < 0x40360000) {
return Complex(f64).new(math.sinh(x) * math.cos(y), math.cosh(x) * math.sin(y));
}
// |x|>= 22, so cosh(x) ~= exp(|x|)
if (ix < 0x40862e42) {
// x < 710: exp(|x|) won't overflow
const h = math.exp(math.fabs(x)) * 0.5;
return Complex(f64).new(math.copysign(f64, h, x) * math.cos(y), h * math.sin(y));
}
// x < 1455: scale to avoid overflow
else if (ix < 0x4096bbaa) {
const v = Complex(f64).new(math.fabs(x), y);
const r = ldexp_cexp(v, -1);
return Complex(f64).new(r.re * math.copysign(f64, 1, x), r.im);
}
// x >= 1455: result always overflows
else {
const h = 0x1p1023 * x;
return Complex(f64).new(h * math.cos(y), h * h * math.sin(y));
}
}
if (ix | lx == 0 and iy >= 0x7ff00000) {
return Complex(f64).new(math.copysign(f64, 0, x * (y - y)), y - y);
}
if (iy | ly == 0 and ix >= 0x7ff00000) {
if ((hx & 0xfffff) | lx == 0) {
return Complex(f64).new(x, y);
}
return Complex(f64).new(x, math.copysign(f64, 0, y));
}
if (ix < 0x7ff00000 and iy >= 0x7ff00000) {
return Complex(f64).new(y - y, x * (y - y));
}
if (ix >= 0x7ff00000 and (hx & 0xfffff) | lx == 0) {
if (iy >= 0x7ff00000) {
return Complex(f64).new(x * x, x * (y - y));
}
return Complex(f64).new(x * math.cos(y), math.inf_f64 * math.sin(y));
}
return Complex(f64).new((x * x) * (y - y), (x + x) * (y - y));
}
const epsilon = 0.0001;
test "complex.csinh32" {
const a = Complex(f32).new(5, 3);
const c = sinh(a);
testing.expect(math.approxEq(f32, c.re, -73.460617, epsilon));
testing.expect(math.approxEq(f32, c.im, 10.472508, epsilon));
}
test "complex.csinh64" {
if (builtin.os == .linux and builtin.arch == .arm and builtin.abi == .musleabihf) {
// TODO https://github.com/ziglang/zig/issues/3289
return error.SkipZigTest;
}
const a = Complex(f64).new(5, 3);
const c = sinh(a);
testing.expect(math.approxEq(f64, c.re, -73.460617, epsilon));
testing.expect(math.approxEq(f64, c.im, 10.472508, epsilon));
}
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