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// Special Cases:
//
// - cosh(+-0) = 1
// - cosh(+-inf) = +inf
// - cosh(nan) = nan
const builtin = @import("builtin");
const std = @import("../index.zig");
const math = std.math;
const expo2 = @import("expo2.zig").expo2;
const assert = std.debug.assert;
pub fn cosh(x: var) @typeOf(x) {
const T = @typeOf(x);
return switch (T) {
f32 => cosh32(x),
f64 => cosh64(x),
else => @compileError("cosh not implemented for " ++ @typeName(T)),
};
}
// cosh(x) = (exp(x) + 1 / exp(x)) / 2
// = 1 + 0.5 * (exp(x) - 1) * (exp(x) - 1) / exp(x)
// = 1 + (x * x) / 2 + o(x^4)
fn cosh32(x: f32) f32 {
const u = @bitCast(u32, x);
const ux = u & 0x7FFFFFFF;
const ax = @bitCast(f32, ux);
// |x| < log(2)
if (ux < 0x3F317217) {
if (ux < 0x3F800000 - (12 << 23)) {
math.raiseOverflow();
return 1.0;
}
const t = math.expm1(ax);
return 1 + t * t / (2 * (1 + t));
}
// |x| < log(FLT_MAX)
if (ux < 0x42B17217) {
const t = math.exp(ax);
return 0.5 * (t + 1 / t);
}
// |x| > log(FLT_MAX) or nan
return expo2(ax);
}
fn cosh64(x: f64) f64 {
const u = @bitCast(u64, x);
const w = u32(u >> 32);
const ax = @bitCast(f64, u & (@maxValue(u64) >> 1));
// TODO: Shouldn't need this explicit check.
if (x == 0.0) {
return 1.0;
}
// |x| < log(2)
if (w < 0x3FE62E42) {
if (w < 0x3FF00000 - (26 << 20)) {
if (x != 0) {
math.raiseInexact();
}
return 1.0;
}
const t = math.expm1(ax);
return 1 + t * t / (2 * (1 + t));
}
// |x| < log(DBL_MAX)
if (w < 0x40862E42) {
const t = math.exp(ax);
// NOTE: If x > log(0x1p26) then 1/t is not required.
return 0.5 * (t + 1 / t);
}
// |x| > log(CBL_MAX) or nan
return expo2(ax);
}
test "math.cosh" {
assert(cosh(f32(1.5)) == cosh32(1.5));
assert(cosh(f64(1.5)) == cosh64(1.5));
}
test "math.cosh32" {
const epsilon = 0.000001;
assert(math.approxEq(f32, cosh32(0.0), 1.0, epsilon));
assert(math.approxEq(f32, cosh32(0.2), 1.020067, epsilon));
assert(math.approxEq(f32, cosh32(0.8923), 1.425225, epsilon));
assert(math.approxEq(f32, cosh32(1.5), 2.352410, epsilon));
}
test "math.cosh64" {
const epsilon = 0.000001;
assert(math.approxEq(f64, cosh64(0.0), 1.0, epsilon));
assert(math.approxEq(f64, cosh64(0.2), 1.020067, epsilon));
assert(math.approxEq(f64, cosh64(0.8923), 1.425225, epsilon));
assert(math.approxEq(f64, cosh64(1.5), 2.352410, epsilon));
}
test "math.cosh32.special" {
assert(cosh32(0.0) == 1.0);
assert(cosh32(-0.0) == 1.0);
assert(math.isPositiveInf(cosh32(math.inf(f32))));
assert(math.isPositiveInf(cosh32(-math.inf(f32))));
assert(math.isNan(cosh32(math.nan(f32))));
}
test "math.cosh64.special" {
assert(cosh64(0.0) == 1.0);
assert(cosh64(-0.0) == 1.0);
assert(math.isPositiveInf(cosh64(math.inf(f64))));
assert(math.isPositiveInf(cosh64(-math.inf(f64))));
assert(math.isNan(cosh64(math.nan(f64))));
}
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