const std = @import("../std.zig");
const math = std.math;
const expect = std.testing.expect;
const maxInt = std.math.maxInt;
pub fn atanh(x: anytype) @TypeOf(x) {
const T = @TypeOf(x);
return switch (T) {
f32 => atanh_32(x),
f64 => atanh_64(x),
else => @compileError("atanh not implemented for " ++ @typeName(T)),
};
}
fn atanh_32(x: f32) f32 {
const u = @bitCast(u32, x);
const i = u & 0x7FFFFFFF;
const s = u >> 31;
var y = @bitCast(f32, i);
if (y == 1.0) {
return math.copysign(math.inf(f32), x);
}
if (u < 0x3F800000 - (1 << 23)) {
if (u < 0x3F800000 - (32 << 23)) {
if (u < (1 << 23)) {
math.doNotOptimizeAway(y * y);
}
}
else {
y = 0.5 * math.log1p(2 * y + 2 * y * y / (1 - y));
}
} else {
y = 0.5 * math.log1p(2 * (y / (1 - y)));
}
return if (s != 0) -y else y;
}
fn atanh_64(x: f64) f64 {
const u = @bitCast(u64, x);
const e = (u >> 52) & 0x7FF;
const s = u >> 63;
var y = @bitCast(f64, u & (maxInt(u64) >> 1));
if (y == 1.0) {
return math.copysign(math.inf(f64), x);
}
if (e < 0x3FF - 1) {
if (e < 0x3FF - 32) {
if (e == 0) {
math.doNotOptimizeAway(@floatCast(f32, y));
}
}
else {
y = 0.5 * math.log1p(2 * y + 2 * y * y / (1 - y));
}
} else {
y = 0.5 * math.log1p(2 * (y / (1 - y)));
}
return if (s != 0) -y else y;
}
test "math.atanh" {
try expect(atanh(@as(f32, 0.0)) == atanh_32(0.0));
try expect(atanh(@as(f64, 0.0)) == atanh_64(0.0));
}
test "math.atanh_32" {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f32, atanh_32(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f32, atanh_32(0.2), 0.202733, epsilon));
try expect(math.approxEqAbs(f32, atanh_32(0.8923), 1.433099, epsilon));
}
test "math.atanh_64" {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f64, atanh_64(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f64, atanh_64(0.2), 0.202733, epsilon));
try expect(math.approxEqAbs(f64, atanh_64(0.8923), 1.433099, epsilon));
}
test "math.atanh32.special" {
try expect(math.isPositiveInf(atanh_32(1)));
try expect(math.isNegativeInf(atanh_32(-1)));
try expect(math.isSignalNan(atanh_32(1.5)));
try expect(math.isSignalNan(atanh_32(-1.5)));
try expect(math.isNan(atanh_32(math.nan(f32))));
}
test "math.atanh64.special" {
try expect(math.isPositiveInf(atanh_64(1)));
try expect(math.isNegativeInf(atanh_64(-1)));
try expect(math.isSignalNan(atanh_64(1.5)));
try expect(math.isSignalNan(atanh_64(-1.5)));
try expect(math.isNan(atanh_64(math.nan(f64))));
}