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// Special Cases:
//
// - sinh(+-0) = +-0
// - sinh(+-inf) = +-1
// - sinh(nan) = nan
const builtin = @import("builtin");
const std = @import("../index.zig");
const math = std.math;
const assert = std.debug.assert;
const expo2 = @import("expo2.zig").expo2;
pub fn tanh(x: var) -> @typeOf(x) {
const T = @typeOf(x);
return switch (T) {
f32 => tanh32(x),
f64 => tanh64(x),
else => @compileError("tanh not implemented for " ++ @typeName(T)),
};
}
// tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
// = (exp(2x) - 1) / (exp(2x) - 1 + 2)
// = (1 - exp(-2x)) / (exp(-2x) - 1 + 2)
fn tanh32(x: f32) -> f32 {
const u = @bitCast(u32, x);
const ux = u & 0x7FFFFFFF;
const ax = @bitCast(f32, ux);
var t: f32 = undefined;
if (x == 0.0 or math.isNan(x)) {
return x;
}
// |x| < log(3) / 2 ~= 0.5493 or nan
if (ux > 0x3F0C9F54) {
// |x| > 10
if (ux > 0x41200000) {
t = 1.0;
} else {
t = math.expm1(2 * x);
t = 1 - 2 / (t + 2);
}
}
// |x| > log(5 / 3) / 2 ~= 0.2554
else if (ux > 0x3E82C578) {
t = math.expm1(2 * x);
t = t / (t + 2);
}
// |x| >= 0x1.0p-126
else if (ux >= 0x00800000) {
t = math.expm1(-2 * x);
t = -t / (t + 2);
}
// |x| is subnormal
else {
math.forceEval(x * x);
t = x;
}
if (u >> 31 != 0) {
return -t;
} else {
return t;
}
}
fn tanh64(x: f64) -> f64 {
const u = @bitCast(u64, x);
const w = u32(u >> 32);
const ax = @bitCast(f64, u & (@maxValue(u64) >> 1));
var t: f64 = undefined;
// TODO: Shouldn't need these checks.
if (x == 0.0 or math.isNan(x)) {
return x;
}
// |x| < log(3) / 2 ~= 0.5493 or nan
if (w > 0x3FE193EA) {
// |x| > 20 or nan
if (w > 0x40340000) {
t = 1.0;
} else {
t = math.expm1(2 * x);
t = 1 - 2 / (t + 2);
}
}
// |x| > log(5 / 3) / 2 ~= 0.2554
else if (w > 0x3FD058AE) {
t = math.expm1(2 * x);
t = t / (t + 2);
}
// |x| >= 0x1.0p-1022
else if (w >= 0x00100000) {
t = math.expm1(-2 * x);
t = -t / (t + 2);
}
// |x| is subnormal
else {
math.forceEval(f32(x));
t = x;
}
if (u >> 63 != 0) {
return -t;
} else {
return t;
}
}
test "math.tanh" {
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(tanh(f32(1.5)) == tanh32(1.5));
assert(tanh(f64(1.5)) == tanh64(1.5));
}
test "math.tanh32" {
const epsilon = 0.000001;
assert(math.approxEq(f32, tanh32(0.0), 0.0, epsilon));
assert(math.approxEq(f32, tanh32(0.2), 0.197375, epsilon));
assert(math.approxEq(f32, tanh32(0.8923), 0.712528, epsilon));
assert(math.approxEq(f32, tanh32(1.5), 0.905148, epsilon));
assert(math.approxEq(f32, tanh32(37.45), 1.0, epsilon));
}
test "math.tanh64" {
const epsilon = 0.000001;
assert(math.approxEq(f64, tanh64(0.0), 0.0, epsilon));
assert(math.approxEq(f64, tanh64(0.2), 0.197375, epsilon));
assert(math.approxEq(f64, tanh64(0.8923), 0.712528, epsilon));
assert(math.approxEq(f64, tanh64(1.5), 0.905148, epsilon));
assert(math.approxEq(f64, tanh64(37.45), 1.0, epsilon));
}
test "math.tanh32.special" {
assert(tanh32(0.0) == 0.0);
assert(tanh32(-0.0) == -0.0);
assert(tanh32(math.inf(f32)) == 1.0);
assert(tanh32(-math.inf(f32)) == -1.0);
assert(math.isNan(tanh32(math.nan(f32))));
}
test "math.tanh64.special" {
assert(tanh64(0.0) == 0.0);
assert(tanh64(-0.0) == -0.0);
assert(tanh64(math.inf(f64)) == 1.0);
assert(tanh64(-math.inf(f64)) == -1.0);
assert(math.isNan(tanh64(math.nan(f64))));
}
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