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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/ccoshf.c
// https://git.musl-libc.org/cgit/musl/tree/src/complex/ccosh.c
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 arc-cosine of z.
pub fn cosh(z: anytype) Complex(@TypeOf(z.re, z.im)) {
const T = @TypeOf(z.re, z.im);
return switch (T) {
f32 => cosh32(z),
f64 => cosh64(z),
else => @compileError("cosh not implemented for " ++ @typeName(z)),
};
}
fn cosh32(z: Complex(f32)) Complex(f32) {
const x = z.re;
const y = z.im;
const hx: u32 = @bitCast(x);
const ix = hx & 0x7fffffff;
const hy: u32 = @bitCast(y);
const iy = hy & 0x7fffffff;
if (ix < 0x7f800000 and iy < 0x7f800000) {
if (iy == 0) {
return Complex(f32).init(math.cosh(x), y);
}
// small x: normal case
if (ix < 0x41100000) {
return Complex(f32).init(math.cosh(x) * @cos(y), math.sinh(x) * @sin(y));
}
// |x|>= 9, so cosh(x) ~= exp(|x|)
if (ix < 0x42b17218) {
// x < 88.7: exp(|x|) won't overflow
const h = @exp(@abs(x)) * 0.5;
return Complex(f32).init(math.copysign(h, x) * @cos(y), h * @sin(y));
}
// x < 192.7: scale to avoid overflow
else if (ix < 0x4340b1e7) {
const v = Complex(f32).init(@abs(x), y);
const r = ldexp_cexp(v, -1);
return Complex(f32).init(r.re, r.im * math.copysign(@as(f32, 1.0), x));
}
// x >= 192.7: result always overflows
else {
const h = 0x1p127 * x;
return Complex(f32).init(h * h * @cos(y), h * @sin(y));
}
}
if (ix == 0 and iy >= 0x7f800000) {
return Complex(f32).init(y - y, math.copysign(@as(f32, 0.0), x * (y - y)));
}
if (iy == 0 and ix >= 0x7f800000) {
if (hx & 0x7fffff == 0) {
return Complex(f32).init(x * x, math.copysign(@as(f32, 0.0), x) * y);
}
return Complex(f32).init(x, math.copysign(@as(f32, 0.0), (x + x) * y));
}
if (ix < 0x7f800000 and iy >= 0x7f800000) {
return Complex(f32).init(y - y, x * (y - y));
}
if (ix >= 0x7f800000 and (hx & 0x7fffff) == 0) {
if (iy >= 0x7f800000) {
return Complex(f32).init(x * x, x * (y - y));
}
return Complex(f32).init((x * x) * @cos(y), x * @sin(y));
}
return Complex(f32).init((x * x) * (y - y), (x + x) * (y - y));
}
fn cosh64(z: Complex(f64)) Complex(f64) {
const x = z.re;
const y = z.im;
const fx: u64 = @bitCast(x);
const hx: u32 = @intCast(fx >> 32);
const lx: u32 = @truncate(fx);
const ix = hx & 0x7fffffff;
const fy: u64 = @bitCast(y);
const hy: u32 = @intCast(fy >> 32);
const ly: u32 = @truncate(fy);
const iy = hy & 0x7fffffff;
// nearly non-exceptional case where x, y are finite
if (ix < 0x7ff00000 and iy < 0x7ff00000) {
if (iy | ly == 0) {
return Complex(f64).init(math.cosh(x), x * y);
}
// small x: normal case
if (ix < 0x40360000) {
return Complex(f64).init(math.cosh(x) * @cos(y), math.sinh(x) * @sin(y));
}
// |x|>= 22, so cosh(x) ~= exp(|x|)
if (ix < 0x40862e42) {
// x < 710: exp(|x|) won't overflow
const h = @exp(@abs(x)) * 0.5;
return Complex(f64).init(h * @cos(y), math.copysign(h, x) * @sin(y));
}
// x < 1455: scale to avoid overflow
else if (ix < 0x4096bbaa) {
const v = Complex(f64).init(@abs(x), y);
const r = ldexp_cexp(v, -1);
return Complex(f64).init(r.re, r.im * math.copysign(@as(f64, 1.0), x));
}
// x >= 1455: result always overflows
else {
const h = 0x1p1023;
return Complex(f64).init(h * h * @cos(y), h * @sin(y));
}
}
if (ix | lx == 0 and iy >= 0x7ff00000) {
return Complex(f64).init(y - y, math.copysign(@as(f64, 0.0), x * (y - y)));
}
if (iy | ly == 0 and ix >= 0x7ff00000) {
if ((hx & 0xfffff) | lx == 0) {
return Complex(f64).init(x * x, math.copysign(@as(f64, 0.0), x) * y);
}
return Complex(f64).init(x * x, math.copysign(@as(f64, 0.0), (x + x) * y));
}
if (ix < 0x7ff00000 and iy >= 0x7ff00000) {
return Complex(f64).init(y - y, x * (y - y));
}
if (ix >= 0x7ff00000 and (hx & 0xfffff) | lx == 0) {
if (iy >= 0x7ff00000) {
return Complex(f64).init(x * x, x * (y - y));
}
return Complex(f64).init(x * x * @cos(y), x * @sin(y));
}
return Complex(f64).init((x * x) * (y - y), (x + x) * (y - y));
}
const epsilon = 0.0001;
test "complex.ccosh32" {
const a = Complex(f32).init(5, 3);
const c = cosh(a);
try testing.expect(math.approxEqAbs(f32, c.re, -73.467300, epsilon));
try testing.expect(math.approxEqAbs(f32, c.im, 10.471557, epsilon));
}
test "complex.ccosh64" {
const a = Complex(f64).init(5, 3);
const c = cosh(a);
try testing.expect(math.approxEqAbs(f64, c.re, -73.467300, epsilon));
try testing.expect(math.approxEqAbs(f64, c.im, 10.471557, epsilon));
}
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