zig/std/math/atanh.zig

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// Special Cases:
//
// - atanh(+-1) = +-inf with signal
// - atanh(x) = nan if |x| > 1 with signal
// - atanh(nan) = nan
const math = @import("index.zig");
const assert = @import("../debug.zig").assert;
pub fn atanh(x: var) -> @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)),
};
}
// atanh(x) = log((1 + x) / (1 - x)) / 2 = log1p(2x / (1 - x)) / 2 ~= x + x^3 / 3 + o(x^5)
fn atanh_32(x: f32) -> f32 {
const u = @bitCast(u32, x);
const i = u & 0x7FFFFFFF;
const s = u >> 31;
var y = @bitCast(f32, i); // |x|
if (y == 1.0) {
return math.copysign(f32, math.inf(f32), x);
}
if (u < 0x3F800000 - (1 << 23)) {
if (u < 0x3F800000 - (32 << 23)) {
// underflow
if (u < (1 << 23)) {
math.forceEval(y * y);
}
}
// |x| < 0.5
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 & (@maxValue(u64) >> 1)); // |x|
if (y == 1.0) {
return math.copysign(f64, math.inf(f64), x);
}
if (e < 0x3FF - 1) {
if (e < 0x3FF - 32) {
// underflow
if (e == 0) {
math.forceEval(f32(y));
}
}
// |x| < 0.5
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" {
assert(atanh(f32(0.0)) == atanh_32(0.0));
assert(atanh(f64(0.0)) == atanh_64(0.0));
}
test "math.atanh_32" {
const epsilon = 0.000001;
assert(math.approxEq(f32, atanh_32(0.0), 0.0, epsilon));
assert(math.approxEq(f32, atanh_32(0.2), 0.202733, epsilon));
assert(math.approxEq(f32, atanh_32(0.8923), 1.433099, epsilon));
}
test "math.atanh_64" {
const epsilon = 0.000001;
assert(math.approxEq(f64, atanh_64(0.0), 0.0, epsilon));
assert(math.approxEq(f64, atanh_64(0.2), 0.202733, epsilon));
assert(math.approxEq(f64, atanh_64(0.8923), 1.433099, epsilon));
}
test "math.atanh32.special" {
assert(math.isPositiveInf(atanh_32(1)));
assert(math.isNegativeInf(atanh_32(-1)));
assert(math.isSignalNan(atanh_32(1.5)));
assert(math.isSignalNan(atanh_32(-1.5)));
assert(math.isNan(atanh_32(math.nan(f32))));
}
test "math.atanh64.special" {
assert(math.isPositiveInf(atanh_64(1)));
assert(math.isNegativeInf(atanh_64(-1)));
assert(math.isSignalNan(atanh_64(1.5)));
assert(math.isSignalNan(atanh_64(-1.5)));
assert(math.isNan(atanh_64(math.nan(f64))));
}