93 lines
2.6 KiB
Zig
93 lines
2.6 KiB
Zig
// Special Cases:
|
|
//
|
|
// - acosh(x) = snan if x < 1
|
|
// - acosh(nan) = nan
|
|
|
|
const builtin = @import("builtin");
|
|
const math = @import("index.zig");
|
|
const assert = @import("../debug.zig").assert;
|
|
|
|
pub fn acosh(x: var) -> @typeOf(x) {
|
|
const T = @typeOf(x);
|
|
switch (T) {
|
|
f32 => @inlineCall(acosh32, x),
|
|
f64 => @inlineCall(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)) {
|
|
math.log1p(x - 1 + math.sqrt((x - 1) * (x - 1) + 2 * (x - 1)))
|
|
}
|
|
// |x| < 0x1p12
|
|
else if (i < 0x3F800000 + (12 << 23)) {
|
|
math.ln(2 * x - 1 / (x + math.sqrt(x * x - 1)))
|
|
}
|
|
// |x| >= 0x1p12
|
|
else {
|
|
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) {
|
|
math.log1p(x - 1 + math.sqrt((x - 1) * (x - 1) + 2 * (x - 1)))
|
|
}
|
|
// |x| < 0x1p26
|
|
else if (e < 0x3FF + 26) {
|
|
math.ln(2 * x - 1 / (x + math.sqrt(x * x - 1)))
|
|
}
|
|
// |x| >= 0x1p26 or nan
|
|
else {
|
|
math.ln(x) + 0.693147180559945309417232121458176568
|
|
}
|
|
}
|
|
|
|
test "math.acosh" {
|
|
if (builtin.os == builtin.Os.windows and builtin.arch == builtin.Arch.i386) {
|
|
// TODO get this test passing
|
|
// https://github.com/zig-lang/zig/issues/537
|
|
return;
|
|
}
|
|
assert(acosh(f32(1.5)) == acosh32(1.5));
|
|
assert(acosh(f64(1.5)) == acosh64(1.5));
|
|
}
|
|
|
|
test "math.acosh32" {
|
|
const epsilon = 0.000001;
|
|
|
|
assert(math.approxEq(f32, acosh32(1.5), 0.962424, epsilon));
|
|
assert(math.approxEq(f32, acosh32(37.45), 4.315976, epsilon));
|
|
assert(math.approxEq(f32, acosh32(89.123), 5.183133, epsilon));
|
|
assert(math.approxEq(f32, acosh32(123123.234375), 12.414088, epsilon));
|
|
}
|
|
|
|
test "math.acosh64" {
|
|
const epsilon = 0.000001;
|
|
|
|
assert(math.approxEq(f64, acosh64(1.5), 0.962424, epsilon));
|
|
assert(math.approxEq(f64, acosh64(37.45), 4.315976, epsilon));
|
|
assert(math.approxEq(f64, acosh64(89.123), 5.183133, epsilon));
|
|
assert(math.approxEq(f64, acosh64(123123.234375), 12.414088, epsilon));
|
|
}
|
|
|
|
test "math.acosh32.special" {
|
|
assert(math.isNan(acosh32(math.nan(f32))));
|
|
assert(math.isSignalNan(acosh32(0.5)));
|
|
}
|
|
|
|
test "math.acosh64.special" {
|
|
assert(math.isNan(acosh64(math.nan(f64))));
|
|
assert(math.isSignalNan(acosh64(0.5)));
|
|
}
|