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https://github.com/ziglang/zig.git
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4c16f9a3c3
This covers the majority of the functions as covered by the C99 specification for a math library. Code is adapted primarily from musl libc, with the pow and standard trigonometric functions adapted from the Go stdlib. Changes: - Remove assert expose in index and import as needed. - Add float log function and merge with existing base 2 integer implementation. See https://github.com/tiehuis/zig-fmath. See #374.
94 lines
2.4 KiB
Zig
94 lines
2.4 KiB
Zig
const math = @import("index.zig");
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const assert = @import("../debug.zig").assert;
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const expo2 = @import("_expo2.zig").expo2;
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pub fn sinh(x: var) -> @typeOf(x) {
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const T = @typeOf(x);
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switch (T) {
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f32 => @inlineCall(sinhf, x),
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f64 => @inlineCall(sinhd, x),
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else => @compileError("sinh not implemented for " ++ @typeName(T)),
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}
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}
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// sinh(x) = (exp(x) - 1 / exp(x)) / 2
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// = (exp(x) - 1 + (exp(x) - 1) / exp(x)) / 2
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// = x + x^3 / 6 + o(x^5)
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fn sinhf(x: f32) -> f32 {
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const u = @bitCast(u32, x);
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const ux = u & 0x7FFFFFFF;
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const ax = @bitCast(f32, ux);
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var h: f32 = 0.5;
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if (u >> 31 != 0) {
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h = -h;
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}
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// |x| < log(FLT_MAX)
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if (ux < 0x42B17217) {
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const t = math.expm1(ax);
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if (ux < 0x3F800000) {
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if (ux < 0x3F800000 - (12 << 23)) {
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return x;
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} else {
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return h * (2 * t - t * t / (t + 1));
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}
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}
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return h * (t + t / (t + 1));
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}
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// |x| > log(FLT_MAX) or nan
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2 * h * expo2(ax)
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}
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fn sinhd(x: f64) -> f64 {
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const u = @bitCast(u64, x);
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const w = u32(u >> 32);
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const ax = @bitCast(f64, u & (@maxValue(u64) >> 1));
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var h: f32 = 0.5;
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if (u >> 63 != 0) {
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h = -h;
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}
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// |x| < log(FLT_MAX)
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if (w < 0x40862E42) {
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const t = math.expm1(ax);
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if (w < 0x3FF00000) {
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if (w < 0x3FF00000 - (26 << 20)) {
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return x;
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} else {
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return h * (2 * t - t * t / (t + 1));
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}
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}
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// NOTE: |x| > log(0x1p26) + eps could be h * exp(x)
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return h * (t + t / (t + 1));
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}
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// |x| > log(DBL_MAX) or nan
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2 * h * expo2(ax)
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}
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test "sinh" {
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assert(sinh(f32(1.5)) == sinhf(1.5));
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assert(sinh(f64(1.5)) == sinhd(1.5));
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}
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test "sinhf" {
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const epsilon = 0.000001;
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assert(math.approxEq(f32, sinhf(0.0), 0.0, epsilon));
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assert(math.approxEq(f32, sinhf(0.2), 0.201336, epsilon));
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assert(math.approxEq(f32, sinhf(0.8923), 1.015512, epsilon));
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assert(math.approxEq(f32, sinhf(1.5), 2.129279, epsilon));
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}
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test "sinhd" {
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const epsilon = 0.000001;
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assert(math.approxEq(f64, sinhd(0.0), 0.0, epsilon));
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assert(math.approxEq(f64, sinhd(0.2), 0.201336, epsilon));
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assert(math.approxEq(f64, sinhd(0.8923), 1.015512, epsilon));
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assert(math.approxEq(f64, sinhd(1.5), 2.129279, epsilon));
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}
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