const std = @import("../std.zig");
const math = std.math;
const expect = std.testing.expect;
const expo2 = @import("expo2.zig").expo2;
const maxInt = std.math.maxInt;
pub fn sinh(x: anytype) @TypeOf(x) {
const T = @TypeOf(x);
return switch (T) {
f32 => sinh32(x),
f64 => sinh64(x),
else => @compileError("sinh not implemented for " ++ @typeName(T)),
};
}
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;
}
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));
}
return 2 * h * expo2(ax);
}
fn sinh64(x: f64) f64 {
const u = @bitCast(u64, x);
const w = @intCast(u32, u >> 32) & (maxInt(u32) >> 1);
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;
}
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));
}
}
return h * (t + t / (t + 1));
}
return 2 * h * expo2(ax);
}
test "math.sinh" {
try expect(sinh(@as(f32, 1.5)) == sinh32(1.5));
try expect(sinh(@as(f64, 1.5)) == sinh64(1.5));
}
test "math.sinh32" {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f32, sinh32(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f32, sinh32(0.2), 0.201336, epsilon));
try expect(math.approxEqAbs(f32, sinh32(0.8923), 1.015512, epsilon));
try expect(math.approxEqAbs(f32, sinh32(1.5), 2.129279, epsilon));
try expect(math.approxEqAbs(f32, sinh32(-0.0), -0.0, epsilon));
try expect(math.approxEqAbs(f32, sinh32(-0.2), -0.201336, epsilon));
try expect(math.approxEqAbs(f32, sinh32(-0.8923), -1.015512, epsilon));
try expect(math.approxEqAbs(f32, sinh32(-1.5), -2.129279, epsilon));
}
test "math.sinh64" {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f64, sinh64(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f64, sinh64(0.2), 0.201336, epsilon));
try expect(math.approxEqAbs(f64, sinh64(0.8923), 1.015512, epsilon));
try expect(math.approxEqAbs(f64, sinh64(1.5), 2.129279, epsilon));
try expect(math.approxEqAbs(f64, sinh64(-0.0), -0.0, epsilon));
try expect(math.approxEqAbs(f64, sinh64(-0.2), -0.201336, epsilon));
try expect(math.approxEqAbs(f64, sinh64(-0.8923), -1.015512, epsilon));
try expect(math.approxEqAbs(f64, sinh64(-1.5), -2.129279, epsilon));
}
test "math.sinh32.special" {
try expect(sinh32(0.0) == 0.0);
try expect(sinh32(-0.0) == -0.0);
try expect(math.isPositiveInf(sinh32(math.inf(f32))));
try expect(math.isNegativeInf(sinh32(-math.inf(f32))));
try expect(math.isNan(sinh32(math.nan(f32))));
}
test "math.sinh64.special" {
try expect(sinh64(0.0) == 0.0);
try expect(sinh64(-0.0) == -0.0);
try expect(math.isPositiveInf(sinh64(math.inf(f64))));
try expect(math.isNegativeInf(sinh64(-math.inf(f64))));
try expect(math.isNan(sinh64(math.nan(f64))));
}