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https://github.com/ziglang/zig.git
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41dd2beaac
* unify the logic for exporting math functions from compiler-rt,
with the appropriate suffixes and prefixes.
- add all missing f128 and f80 exports. Functions with missing
implementations call other functions and have TODO comments.
- also add f16 functions
* move math functions from freestanding libc to compiler-rt (#7265)
* enable all the f128 and f80 code in the stage2 compiler and behavior
tests (#11161).
* update std lib to use builtins rather than `std.math`.
135 lines
4.1 KiB
Zig
135 lines
4.1 KiB
Zig
// Ported from musl, which is licensed under the MIT license:
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// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
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//
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// https://git.musl-libc.org/cgit/musl/tree/src/math/coshf.c
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// https://git.musl-libc.org/cgit/musl/tree/src/math/cosh.c
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const std = @import("../std.zig");
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const math = std.math;
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const expo2 = @import("expo2.zig").expo2;
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const expect = std.testing.expect;
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const maxInt = std.math.maxInt;
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/// Returns the hyperbolic cosine of x.
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///
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/// Special Cases:
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/// - cosh(+-0) = 1
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/// - cosh(+-inf) = +inf
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/// - cosh(nan) = nan
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pub fn cosh(x: anytype) @TypeOf(x) {
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const T = @TypeOf(x);
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return switch (T) {
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f32 => cosh32(x),
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f64 => cosh64(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 cosh32(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 = @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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return expo2(ax);
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}
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fn cosh64(x: f64) f64 {
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const u = @bitCast(u64, x);
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const w = @intCast(u32, u >> 32) & (maxInt(u32) >> 1);
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const ax = @bitCast(f64, u & (maxInt(u64) >> 1));
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// TODO: Shouldn't need this explicit check.
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if (x == 0.0) {
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return 1.0;
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}
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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 = @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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return expo2(ax);
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}
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test "math.cosh" {
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try expect(cosh(@as(f32, 1.5)) == cosh32(1.5));
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try expect(cosh(@as(f64, 1.5)) == cosh64(1.5));
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}
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test "math.cosh32" {
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const epsilon = 0.000001;
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try expect(math.approxEqAbs(f32, cosh32(0.0), 1.0, epsilon));
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try expect(math.approxEqAbs(f32, cosh32(0.2), 1.020067, epsilon));
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try expect(math.approxEqAbs(f32, cosh32(0.8923), 1.425225, epsilon));
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try expect(math.approxEqAbs(f32, cosh32(1.5), 2.352410, epsilon));
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try expect(math.approxEqAbs(f32, cosh32(-0.0), 1.0, epsilon));
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try expect(math.approxEqAbs(f32, cosh32(-0.2), 1.020067, epsilon));
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try expect(math.approxEqAbs(f32, cosh32(-0.8923), 1.425225, epsilon));
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try expect(math.approxEqAbs(f32, cosh32(-1.5), 2.352410, epsilon));
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}
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test "math.cosh64" {
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const epsilon = 0.000001;
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try expect(math.approxEqAbs(f64, cosh64(0.0), 1.0, epsilon));
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try expect(math.approxEqAbs(f64, cosh64(0.2), 1.020067, epsilon));
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try expect(math.approxEqAbs(f64, cosh64(0.8923), 1.425225, epsilon));
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try expect(math.approxEqAbs(f64, cosh64(1.5), 2.352410, epsilon));
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try expect(math.approxEqAbs(f64, cosh64(-0.0), 1.0, epsilon));
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try expect(math.approxEqAbs(f64, cosh64(-0.2), 1.020067, epsilon));
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try expect(math.approxEqAbs(f64, cosh64(-0.8923), 1.425225, epsilon));
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try expect(math.approxEqAbs(f64, cosh64(-1.5), 2.352410, epsilon));
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}
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test "math.cosh32.special" {
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try expect(cosh32(0.0) == 1.0);
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try expect(cosh32(-0.0) == 1.0);
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try expect(math.isPositiveInf(cosh32(math.inf(f32))));
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try expect(math.isPositiveInf(cosh32(-math.inf(f32))));
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try expect(math.isNan(cosh32(math.nan(f32))));
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}
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test "math.cosh64.special" {
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try expect(cosh64(0.0) == 1.0);
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try expect(cosh64(-0.0) == 1.0);
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try expect(math.isPositiveInf(cosh64(math.inf(f64))));
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try expect(math.isPositiveInf(cosh64(-math.inf(f64))));
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try expect(math.isNan(cosh64(math.nan(f64))));
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}
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