1// Ported from musl, which is licensed under the MIT license:
  2// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
  3//
  4// https://git.musl-libc.org/cgit/musl/tree/src/math/sinhf.c
  5// https://git.musl-libc.org/cgit/musl/tree/src/math/sinh.c
  6
  7const std = @import("../std.zig");
  8const math = std.math;
  9const expect = std.testing.expect;
 10const expo2 = @import("expo2.zig").expo2;
 11const maxInt = std.math.maxInt;
 12
 13/// Returns the hyperbolic sine of x.
 14///
 15/// Special Cases:
 16///  - sinh(+-0)   = +-0
 17///  - sinh(+-inf) = +-inf
 18///  - sinh(nan)   = nan
 19pub fn sinh(x: anytype) @TypeOf(x) {
 20    const T = @TypeOf(x);
 21    return switch (T) {
 22        f32 => sinh32(x),
 23        f64 => sinh64(x),
 24        else => @compileError("sinh not implemented for " ++ @typeName(T)),
 25    };
 26}
 27
 28// sinh(x) = (exp(x) - 1 / exp(x)) / 2
 29//         = (exp(x) - 1 + (exp(x) - 1) / exp(x)) / 2
 30//         = x + x^3 / 6 + o(x^5)
 31fn sinh32(x: f32) f32 {
 32    const u = @as(u32, @bitCast(x));
 33    const ux = u & 0x7FFFFFFF;
 34    const ax = @as(f32, @bitCast(ux));
 35
 36    if (x == 0.0 or math.isNan(x)) {
 37        return x;
 38    }
 39
 40    var h: f32 = 0.5;
 41    if (u >> 31 != 0) {
 42        h = -h;
 43    }
 44
 45    // |x| < log(FLT_MAX)
 46    if (ux < 0x42B17217) {
 47        const t = math.expm1(ax);
 48        if (ux < 0x3F800000) {
 49            if (ux < 0x3F800000 - (12 << 23)) {
 50                return x;
 51            } else {
 52                return h * (2 * t - t * t / (t + 1));
 53            }
 54        }
 55        return h * (t + t / (t + 1));
 56    }
 57
 58    // |x| > log(FLT_MAX) or nan
 59    return 2 * h * expo2(ax);
 60}
 61
 62fn sinh64(x: f64) f64 {
 63    const u = @as(u64, @bitCast(x));
 64    const w = @as(u32, @intCast(u >> 32)) & (maxInt(u32) >> 1);
 65    const ax = @as(f64, @bitCast(u & (maxInt(u64) >> 1)));
 66
 67    if (x == 0.0 or math.isNan(x)) {
 68        return x;
 69    }
 70
 71    var h: f32 = 0.5;
 72    if (u >> 63 != 0) {
 73        h = -h;
 74    }
 75
 76    // |x| < log(FLT_MAX)
 77    if (w < 0x40862E42) {
 78        const t = math.expm1(ax);
 79        if (w < 0x3FF00000) {
 80            if (w < 0x3FF00000 - (26 << 20)) {
 81                return x;
 82            } else {
 83                return h * (2 * t - t * t / (t + 1));
 84            }
 85        }
 86        // NOTE: |x| > log(0x1p26) + eps could be h * exp(x)
 87        return h * (t + t / (t + 1));
 88    }
 89
 90    // |x| > log(DBL_MAX) or nan
 91    return 2 * h * expo2(ax);
 92}
 93
 94test sinh {
 95    try expect(sinh(@as(f32, 1.5)) == sinh32(1.5));
 96    try expect(sinh(@as(f64, 1.5)) == sinh64(1.5));
 97}
 98
 99test sinh32 {
100    const epsilon = 0.000001;
101
102    try expect(math.approxEqAbs(f32, sinh32(0.0), 0.0, epsilon));
103    try expect(math.approxEqAbs(f32, sinh32(0.2), 0.201336, epsilon));
104    try expect(math.approxEqAbs(f32, sinh32(0.8923), 1.015512, epsilon));
105    try expect(math.approxEqAbs(f32, sinh32(1.5), 2.129279, epsilon));
106    try expect(math.approxEqAbs(f32, sinh32(-0.0), -0.0, epsilon));
107    try expect(math.approxEqAbs(f32, sinh32(-0.2), -0.201336, epsilon));
108    try expect(math.approxEqAbs(f32, sinh32(-0.8923), -1.015512, epsilon));
109    try expect(math.approxEqAbs(f32, sinh32(-1.5), -2.129279, epsilon));
110}
111
112test sinh64 {
113    const epsilon = 0.000001;
114
115    try expect(math.approxEqAbs(f64, sinh64(0.0), 0.0, epsilon));
116    try expect(math.approxEqAbs(f64, sinh64(0.2), 0.201336, epsilon));
117    try expect(math.approxEqAbs(f64, sinh64(0.8923), 1.015512, epsilon));
118    try expect(math.approxEqAbs(f64, sinh64(1.5), 2.129279, epsilon));
119    try expect(math.approxEqAbs(f64, sinh64(-0.0), -0.0, epsilon));
120    try expect(math.approxEqAbs(f64, sinh64(-0.2), -0.201336, epsilon));
121    try expect(math.approxEqAbs(f64, sinh64(-0.8923), -1.015512, epsilon));
122    try expect(math.approxEqAbs(f64, sinh64(-1.5), -2.129279, epsilon));
123}
124
125test "sinh32.special" {
126    try expect(math.isPositiveZero(sinh32(0.0)));
127    try expect(math.isNegativeZero(sinh32(-0.0)));
128    try expect(math.isPositiveInf(sinh32(math.inf(f32))));
129    try expect(math.isNegativeInf(sinh32(-math.inf(f32))));
130    try expect(math.isNan(sinh32(math.nan(f32))));
131}
132
133test "sinh64.special" {
134    try expect(math.isPositiveZero(sinh64(0.0)));
135    try expect(math.isNegativeZero(sinh64(-0.0)));
136    try expect(math.isPositiveInf(sinh64(math.inf(f64))));
137    try expect(math.isNegativeInf(sinh64(-math.inf(f64))));
138    try expect(math.isNan(sinh64(math.nan(f64))));
139}