mirror of
https://github.com/ziglang/zig.git
synced 2024-12-04 19:09:32 +00:00
100 lines
3.0 KiB
Zig
100 lines
3.0 KiB
Zig
// SPDX-License-Identifier: MIT
|
|
// Copyright (c) 2015-2021 Zig Contributors
|
|
// This file is part of [zig](https://ziglang.org/), which is MIT licensed.
|
|
// The MIT license requires this copyright notice to be included in all copies
|
|
// and substantial portions of the software.
|
|
// 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/math/acoshf.c
|
|
// https://git.musl-libc.org/cgit/musl/tree/src/math/acosh.c
|
|
|
|
const builtin = @import("builtin");
|
|
const std = @import("../std.zig");
|
|
const math = std.math;
|
|
const expect = std.testing.expect;
|
|
|
|
/// Returns the hyperbolic arc-cosine of x.
|
|
///
|
|
/// Special cases:
|
|
/// - acosh(x) = snan if x < 1
|
|
/// - acosh(nan) = nan
|
|
pub fn acosh(x: anytype) @TypeOf(x) {
|
|
const T = @TypeOf(x);
|
|
return switch (T) {
|
|
f32 => acosh32(x),
|
|
f64 => acosh64(x),
|
|
else => @compileError("acosh not implemented for " ++ @typeName(T)),
|
|
};
|
|
}
|
|
|
|
// acosh(x) = log(x + sqrt(x * x - 1))
|
|
fn acosh32(x: f32) f32 {
|
|
const u = @bitCast(u32, x);
|
|
const i = u & 0x7FFFFFFF;
|
|
|
|
// |x| < 2, invalid if x < 1 or nan
|
|
if (i < 0x3F800000 + (1 << 23)) {
|
|
return math.log1p(x - 1 + math.sqrt((x - 1) * (x - 1) + 2 * (x - 1)));
|
|
}
|
|
// |x| < 0x1p12
|
|
else if (i < 0x3F800000 + (12 << 23)) {
|
|
return math.ln(2 * x - 1 / (x + math.sqrt(x * x - 1)));
|
|
}
|
|
// |x| >= 0x1p12
|
|
else {
|
|
return math.ln(x) + 0.693147180559945309417232121458176568;
|
|
}
|
|
}
|
|
|
|
fn acosh64(x: f64) f64 {
|
|
const u = @bitCast(u64, x);
|
|
const e = (u >> 52) & 0x7FF;
|
|
|
|
// |x| < 2, invalid if x < 1 or nan
|
|
if (e < 0x3FF + 1) {
|
|
return math.log1p(x - 1 + math.sqrt((x - 1) * (x - 1) + 2 * (x - 1)));
|
|
}
|
|
// |x| < 0x1p26
|
|
else if (e < 0x3FF + 26) {
|
|
return math.ln(2 * x - 1 / (x + math.sqrt(x * x - 1)));
|
|
}
|
|
// |x| >= 0x1p26 or nan
|
|
else {
|
|
return math.ln(x) + 0.693147180559945309417232121458176568;
|
|
}
|
|
}
|
|
|
|
test "math.acosh" {
|
|
expect(acosh(@as(f32, 1.5)) == acosh32(1.5));
|
|
expect(acosh(@as(f64, 1.5)) == acosh64(1.5));
|
|
}
|
|
|
|
test "math.acosh32" {
|
|
const epsilon = 0.000001;
|
|
|
|
expect(math.approxEqAbs(f32, acosh32(1.5), 0.962424, epsilon));
|
|
expect(math.approxEqAbs(f32, acosh32(37.45), 4.315976, epsilon));
|
|
expect(math.approxEqAbs(f32, acosh32(89.123), 5.183133, epsilon));
|
|
expect(math.approxEqAbs(f32, acosh32(123123.234375), 12.414088, epsilon));
|
|
}
|
|
|
|
test "math.acosh64" {
|
|
const epsilon = 0.000001;
|
|
|
|
expect(math.approxEqAbs(f64, acosh64(1.5), 0.962424, epsilon));
|
|
expect(math.approxEqAbs(f64, acosh64(37.45), 4.315976, epsilon));
|
|
expect(math.approxEqAbs(f64, acosh64(89.123), 5.183133, epsilon));
|
|
expect(math.approxEqAbs(f64, acosh64(123123.234375), 12.414088, epsilon));
|
|
}
|
|
|
|
test "math.acosh32.special" {
|
|
expect(math.isNan(acosh32(math.nan(f32))));
|
|
expect(math.isSignalNan(acosh32(0.5)));
|
|
}
|
|
|
|
test "math.acosh64.special" {
|
|
expect(math.isNan(acosh64(math.nan(f64))));
|
|
expect(math.isSignalNan(acosh64(0.5)));
|
|
}
|