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.
92 lines
2.4 KiB
Zig
92 lines
2.4 KiB
Zig
const math = @import("index.zig");
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const expo2 = @import("_expo2.zig").expo2;
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const assert = @import("../debug.zig").assert;
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pub fn cosh(x: var) -> @typeOf(x) {
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const T = @typeOf(x);
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switch (T) {
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f32 => @inlineCall(coshf, x),
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f64 => @inlineCall(coshd, x),
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else => @compileError("cosh not implemented for " ++ @typeName(T)),
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}
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}
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// cosh(x) = (exp(x) + 1 / exp(x)) / 2
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// = 1 + 0.5 * (exp(x) - 1) * (exp(x) - 1) / exp(x)
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// = 1 + (x * x) / 2 + o(x^4)
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fn coshf(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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// |x| < log(2)
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if (ux < 0x3F317217) {
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if (ux < 0x3F800000 - (12 << 23)) {
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math.raiseOverflow();
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return 1.0;
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}
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const t = math.expm1(ax);
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return 1 + t * t / (2 * (1 + t));
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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.exp(ax);
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return 0.5 * (t + 1 / t);
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}
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// |x| > log(FLT_MAX) or nan
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expo2(ax)
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}
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fn coshd(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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// |x| < log(2)
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if (w < 0x3FE62E42) {
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if (w < 0x3FF00000 - (26 << 20)) {
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if (x != 0) {
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math.raiseInexact();
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}
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return 1.0;
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}
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const t = math.expm1(ax);
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return 1 + t * t / (2 * (1 + t));
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}
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// |x| < log(DBL_MAX)
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if (w < 0x40862E42) {
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const t = math.exp(ax);
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// NOTE: If x > log(0x1p26) then 1/t is not required.
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return 0.5 * (t + 1 / t);
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}
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// |x| > log(CBL_MAX) or nan
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expo2(ax)
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}
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test "cosh" {
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assert(cosh(f32(1.5)) == coshf(1.5));
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assert(cosh(f64(1.5)) == coshd(1.5));
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}
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test "coshf" {
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const epsilon = 0.000001;
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assert(math.approxEq(f32, coshf(0.0), 1.0, epsilon));
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assert(math.approxEq(f32, coshf(0.2), 1.020067, epsilon));
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assert(math.approxEq(f32, coshf(0.8923), 1.425225, epsilon));
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assert(math.approxEq(f32, coshf(1.5), 2.352410, epsilon));
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}
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test "coshd" {
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const epsilon = 0.000001;
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assert(math.approxEq(f64, coshd(0.0), 1.0, epsilon));
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assert(math.approxEq(f64, coshd(0.2), 1.020067, epsilon));
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assert(math.approxEq(f64, coshd(0.8923), 1.425225, epsilon));
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assert(math.approxEq(f64, coshd(1.5), 2.352410, epsilon));
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}
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