zig/std/math/sinh.zig
2018-10-26 15:01:51 -04:00

127 lines
3.2 KiB
Zig

// Special Cases:
//
// - sinh(+-0) = +-0
// - sinh(+-inf) = +-inf
// - 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;
const maxInt = std.math.maxInt;
pub fn sinh(x: var) @typeOf(x) {
const T = @typeOf(x);
return switch (T) {
f32 => sinh32(x),
f64 => sinh64(x),
else => @compileError("sinh not implemented for " ++ @typeName(T)),
};
}
// sinh(x) = (exp(x) - 1 / exp(x)) / 2
// = (exp(x) - 1 + (exp(x) - 1) / exp(x)) / 2
// = x + x^3 / 6 + o(x^5)
fn sinh32(x: f32) f32 {
const u = @bitCast(u32, x);
const ux = u & 0x7FFFFFFF;
const ax = @bitCast(f32, ux);
if (x == 0.0 or math.isNan(x)) {
return x;
}
var h: f32 = 0.5;
if (u >> 31 != 0) {
h = -h;
}
// |x| < log(FLT_MAX)
if (ux < 0x42B17217) {
const t = math.expm1(ax);
if (ux < 0x3F800000) {
if (ux < 0x3F800000 - (12 << 23)) {
return x;
} else {
return h * (2 * t - t * t / (t + 1));
}
}
return h * (t + t / (t + 1));
}
// |x| > log(FLT_MAX) or nan
return 2 * h * expo2(ax);
}
fn sinh64(x: f64) f64 {
const u = @bitCast(u64, x);
const w = @intCast(u32, u >> 32);
const ax = @bitCast(f64, u & (maxInt(u64) >> 1));
if (x == 0.0 or math.isNan(x)) {
return x;
}
var h: f32 = 0.5;
if (u >> 63 != 0) {
h = -h;
}
// |x| < log(FLT_MAX)
if (w < 0x40862E42) {
const t = math.expm1(ax);
if (w < 0x3FF00000) {
if (w < 0x3FF00000 - (26 << 20)) {
return x;
} else {
return h * (2 * t - t * t / (t + 1));
}
}
// NOTE: |x| > log(0x1p26) + eps could be h * exp(x)
return h * (t + t / (t + 1));
}
// |x| > log(DBL_MAX) or nan
return 2 * h * expo2(ax);
}
test "math.sinh" {
assert(sinh(f32(1.5)) == sinh32(1.5));
assert(sinh(f64(1.5)) == sinh64(1.5));
}
test "math.sinh32" {
const epsilon = 0.000001;
assert(math.approxEq(f32, sinh32(0.0), 0.0, epsilon));
assert(math.approxEq(f32, sinh32(0.2), 0.201336, epsilon));
assert(math.approxEq(f32, sinh32(0.8923), 1.015512, epsilon));
assert(math.approxEq(f32, sinh32(1.5), 2.129279, epsilon));
}
test "math.sinh64" {
const epsilon = 0.000001;
assert(math.approxEq(f64, sinh64(0.0), 0.0, epsilon));
assert(math.approxEq(f64, sinh64(0.2), 0.201336, epsilon));
assert(math.approxEq(f64, sinh64(0.8923), 1.015512, epsilon));
assert(math.approxEq(f64, sinh64(1.5), 2.129279, epsilon));
}
test "math.sinh32.special" {
assert(sinh32(0.0) == 0.0);
assert(sinh32(-0.0) == -0.0);
assert(math.isPositiveInf(sinh32(math.inf(f32))));
assert(math.isNegativeInf(sinh32(-math.inf(f32))));
assert(math.isNan(sinh32(math.nan(f32))));
}
test "math.sinh64.special" {
assert(sinh64(0.0) == 0.0);
assert(sinh64(-0.0) == -0.0);
assert(math.isPositiveInf(sinh64(math.inf(f64))));
assert(math.isNegativeInf(sinh64(-math.inf(f64))));
assert(math.isNan(sinh64(math.nan(f64))));
}