mirror of
https://github.com/ziglang/zig.git
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122 lines
3.2 KiB
Zig
122 lines
3.2 KiB
Zig
// Ported from musl, which is licensed under the MIT license:
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// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
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//
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// https://git.musl-libc.org/cgit/musl/tree/src/math/atanhf.c
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// https://git.musl-libc.org/cgit/musl/tree/src/math/atanh.c
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const std = @import("../std.zig");
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const math = std.math;
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const expect = std.testing.expect;
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const maxInt = std.math.maxInt;
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/// Returns the hyperbolic arc-tangent of x.
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///
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/// Special Cases:
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/// - atanh(+-1) = +-inf with signal
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/// - atanh(x) = nan if |x| > 1 with signal
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/// - atanh(nan) = nan
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pub fn atanh(x: var) @typeOf(x) {
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const T = @typeOf(x);
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return switch (T) {
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f32 => atanh_32(x),
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f64 => atanh_64(x),
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else => @compileError("atanh not implemented for " ++ @typeName(T)),
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};
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}
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// atanh(x) = log((1 + x) / (1 - x)) / 2 = log1p(2x / (1 - x)) / 2 ~= x + x^3 / 3 + o(x^5)
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fn atanh_32(x: f32) f32 {
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const u = @bitCast(u32, x);
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const i = u & 0x7FFFFFFF;
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const s = u >> 31;
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var y = @bitCast(f32, i); // |x|
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if (y == 1.0) {
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return math.copysign(f32, math.inf(f32), x);
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}
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if (u < 0x3F800000 - (1 << 23)) {
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if (u < 0x3F800000 - (32 << 23)) {
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// underflow
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if (u < (1 << 23)) {
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math.forceEval(y * y);
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}
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}
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// |x| < 0.5
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else {
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y = 0.5 * math.log1p(2 * y + 2 * y * y / (1 - y));
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}
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} else {
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y = 0.5 * math.log1p(2 * (y / (1 - y)));
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}
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return if (s != 0) -y else y;
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}
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fn atanh_64(x: f64) f64 {
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const u = @bitCast(u64, x);
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const e = (u >> 52) & 0x7FF;
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const s = u >> 63;
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var y = @bitCast(f64, u & (maxInt(u64) >> 1)); // |x|
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if (y == 1.0) {
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return math.copysign(f64, math.inf(f64), x);
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}
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if (e < 0x3FF - 1) {
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if (e < 0x3FF - 32) {
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// underflow
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if (e == 0) {
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math.forceEval(@floatCast(f32, y));
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}
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}
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// |x| < 0.5
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else {
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y = 0.5 * math.log1p(2 * y + 2 * y * y / (1 - y));
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}
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} else {
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y = 0.5 * math.log1p(2 * (y / (1 - y)));
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}
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return if (s != 0) -y else y;
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}
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test "math.atanh" {
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expect(atanh(f32(0.0)) == atanh_32(0.0));
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expect(atanh(f64(0.0)) == atanh_64(0.0));
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}
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test "math.atanh_32" {
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const epsilon = 0.000001;
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expect(math.approxEq(f32, atanh_32(0.0), 0.0, epsilon));
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expect(math.approxEq(f32, atanh_32(0.2), 0.202733, epsilon));
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expect(math.approxEq(f32, atanh_32(0.8923), 1.433099, epsilon));
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}
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test "math.atanh_64" {
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const epsilon = 0.000001;
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expect(math.approxEq(f64, atanh_64(0.0), 0.0, epsilon));
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expect(math.approxEq(f64, atanh_64(0.2), 0.202733, epsilon));
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expect(math.approxEq(f64, atanh_64(0.8923), 1.433099, epsilon));
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}
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test "math.atanh32.special" {
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expect(math.isPositiveInf(atanh_32(1)));
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expect(math.isNegativeInf(atanh_32(-1)));
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expect(math.isSignalNan(atanh_32(1.5)));
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expect(math.isSignalNan(atanh_32(-1.5)));
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expect(math.isNan(atanh_32(math.nan(f32))));
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}
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test "math.atanh64.special" {
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expect(math.isPositiveInf(atanh_64(1)));
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expect(math.isNegativeInf(atanh_64(-1)));
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expect(math.isSignalNan(atanh_64(1.5)));
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expect(math.isSignalNan(atanh_64(-1.5)));
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expect(math.isNan(atanh_64(math.nan(f64))));
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}
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