mirror of
https://github.com/ziglang/zig.git
synced 2026-01-03 12:03:19 +00:00
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.
96 lines
2.9 KiB
Zig
96 lines
2.9 KiB
Zig
const math = @import("index.zig");
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const assert = @import("../debug.zig").assert;
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pub fn asinh(x: var) -> @typeOf(x) {
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const T = @typeOf(x);
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switch (T) {
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f32 => @inlineCall(asinhf, x),
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f64 => @inlineCall(asinhd, x),
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else => @compileError("asinh not implemented for " ++ @typeName(T)),
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}
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}
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// asinh(x) = sign(x) * log(|x| + sqrt(x * x + 1)) ~= x - x^3/6 + o(x^5)
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fn asinhf(x: f32) -> f32 {
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const u = @bitCast(u32, x);
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const i = u & 0x7FFFFFFF;
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const s = i >> 31;
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var rx = @bitCast(f32, i); // |x|
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// |x| >= 0x1p12 or inf or nan
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if (i >= 0x3F800000 + (12 << 23)) {
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rx = math.ln(rx) + 0.69314718055994530941723212145817656;
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}
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// |x| >= 2
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else if (i >= 0x3F800000 + (1 << 23)) {
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rx = math.ln(2 * x + 1 / (math.sqrt(x * x + 1) + x));
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}
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// |x| >= 0x1p-12, up to 1.6ulp error
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else if (i >= 0x3F800000 - (12 << 23)) {
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rx = math.log1p(x + x * x / (math.sqrt(x * x + 1) + 1));
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}
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// |x| < 0x1p-12, inexact if x != 0
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else {
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math.forceEval(x + 0x1.0p120);
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}
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if (s != 0) -rx else rx
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}
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fn asinhd(x: f64) -> f64 {
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const u = @bitCast(u64, x);
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const e = (u >> 52) & 0x7FF;
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const s = u >> 63;
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var rx = @bitCast(f64, u & (@maxValue(u64) >> 1)); // |x|
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// |x| >= 0x1p26 or inf or nan
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if (e >= 0x3FF + 26) {
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rx = math.ln(rx) + 0.693147180559945309417232121458176568;
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}
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// |x| >= 2
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else if (e >= 0x3FF + 1) {
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rx = math.ln(2 * x + 1 / (math.sqrt(x * x + 1) + x));
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}
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// |x| >= 0x1p-12, up to 1.6ulp error
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else if (e >= 0x3FF - 26) {
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rx = math.log1p(x + x * x / (math.sqrt(x * x + 1) + 1));
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}
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// |x| < 0x1p-12, inexact if x != 0
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else {
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math.forceEval(x + 0x1.0p120);
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}
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if (s != 0) -rx else rx
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}
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test "asinh" {
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assert(asinh(f32(0.0)) == asinhf(0.0));
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assert(asinh(f64(0.0)) == asinhd(0.0));
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}
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test "asinhf" {
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const epsilon = 0.000001;
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assert(math.approxEq(f32, asinhf(0.0), 0.0, epsilon));
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assert(math.approxEq(f32, asinhf(0.2), 0.198690, epsilon));
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assert(math.approxEq(f32, asinhf(0.8923), 0.803133, epsilon));
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assert(math.approxEq(f32, asinhf(1.5), 1.194763, epsilon));
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assert(math.approxEq(f32, asinhf(37.45), 4.316332, epsilon));
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assert(math.approxEq(f32, asinhf(89.123), 5.183196, epsilon));
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assert(math.approxEq(f32, asinhf(123123.234375), 12.414088, epsilon));
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}
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test "asinhd" {
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const epsilon = 0.000001;
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assert(math.approxEq(f64, asinhd(0.0), 0.0, epsilon));
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assert(math.approxEq(f64, asinhd(0.2), 0.198690, epsilon));
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assert(math.approxEq(f64, asinhd(0.8923), 0.803133, epsilon));
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assert(math.approxEq(f64, asinhd(1.5), 1.194763, epsilon));
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assert(math.approxEq(f64, asinhd(37.45), 4.316332, epsilon));
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assert(math.approxEq(f64, asinhd(89.123), 5.183196, epsilon));
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assert(math.approxEq(f64, asinhd(123123.234375), 12.414088, epsilon));
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}
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