mirror of
https://github.com/ziglang/zig.git
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218 lines
6.4 KiB
Zig
218 lines
6.4 KiB
Zig
// SPDX-License-Identifier: MIT
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// Copyright (c) 2015-2021 Zig Contributors
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// This file is part of [zig](https://ziglang.org/), which is MIT licensed.
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// The MIT license requires this copyright notice to be included in all copies
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// and substantial portions of the software.
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// 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/log2f.c
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// https://git.musl-libc.org/cgit/musl/tree/src/math/log2.c
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const std = @import("../std.zig");
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const math = std.math;
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const expect = std.testing.expect;
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const maxInt = std.math.maxInt;
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/// Returns the base-2 logarithm of x.
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///
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/// Special Cases:
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/// - log2(+inf) = +inf
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/// - log2(0) = -inf
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/// - log2(x) = nan if x < 0
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/// - log2(nan) = nan
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pub fn log2(x: anytype) @TypeOf(x) {
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const T = @TypeOf(x);
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switch (@typeInfo(T)) {
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.ComptimeFloat => {
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return @as(comptime_float, log2_64(x));
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},
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.Float => {
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return switch (T) {
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f32 => log2_32(x),
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f64 => log2_64(x),
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else => @compileError("log2 not implemented for " ++ @typeName(T)),
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};
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},
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.ComptimeInt => comptime {
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var result = 0;
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var x_shifted = x;
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while (b: {
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x_shifted >>= 1;
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break :b x_shifted != 0;
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}) : (result += 1) {}
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return result;
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},
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.Int => {
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return math.log2_int(T, x);
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},
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else => @compileError("log2 not implemented for " ++ @typeName(T)),
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}
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}
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pub fn log2_32(x_: f32) f32 {
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const ivln2hi: f32 = 1.4428710938e+00;
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const ivln2lo: f32 = -1.7605285393e-04;
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const Lg1: f32 = 0xaaaaaa.0p-24;
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const Lg2: f32 = 0xccce13.0p-25;
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const Lg3: f32 = 0x91e9ee.0p-25;
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const Lg4: f32 = 0xf89e26.0p-26;
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var x = x_;
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var u = @bitCast(u32, x);
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var ix = u;
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var k: i32 = 0;
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// x < 2^(-126)
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if (ix < 0x00800000 or ix >> 31 != 0) {
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// log(+-0) = -inf
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if (ix << 1 == 0) {
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return -math.inf(f32);
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}
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// log(-#) = nan
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if (ix >> 31 != 0) {
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return math.nan(f32);
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}
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k -= 25;
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x *= 0x1.0p25;
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ix = @bitCast(u32, x);
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} else if (ix >= 0x7F800000) {
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return x;
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} else if (ix == 0x3F800000) {
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return 0;
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}
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// x into [sqrt(2) / 2, sqrt(2)]
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ix += 0x3F800000 - 0x3F3504F3;
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k += @intCast(i32, ix >> 23) - 0x7F;
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ix = (ix & 0x007FFFFF) + 0x3F3504F3;
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x = @bitCast(f32, ix);
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const f = x - 1.0;
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const s = f / (2.0 + f);
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const z = s * s;
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const w = z * z;
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const t1 = w * (Lg2 + w * Lg4);
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const t2 = z * (Lg1 + w * Lg3);
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const R = t2 + t1;
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const hfsq = 0.5 * f * f;
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var hi = f - hfsq;
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u = @bitCast(u32, hi);
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u &= 0xFFFFF000;
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hi = @bitCast(f32, u);
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const lo = f - hi - hfsq + s * (hfsq + R);
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return (lo + hi) * ivln2lo + lo * ivln2hi + hi * ivln2hi + @intToFloat(f32, k);
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}
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pub fn log2_64(x_: f64) f64 {
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const ivln2hi: f64 = 1.44269504072144627571e+00;
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const ivln2lo: f64 = 1.67517131648865118353e-10;
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const Lg1: f64 = 6.666666666666735130e-01;
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const Lg2: f64 = 3.999999999940941908e-01;
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const Lg3: f64 = 2.857142874366239149e-01;
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const Lg4: f64 = 2.222219843214978396e-01;
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const Lg5: f64 = 1.818357216161805012e-01;
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const Lg6: f64 = 1.531383769920937332e-01;
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const Lg7: f64 = 1.479819860511658591e-01;
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var x = x_;
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var ix = @bitCast(u64, x);
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var hx = @intCast(u32, ix >> 32);
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var k: i32 = 0;
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if (hx < 0x00100000 or hx >> 31 != 0) {
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// log(+-0) = -inf
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if (ix << 1 == 0) {
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return -math.inf(f64);
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}
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// log(-#) = nan
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if (hx >> 31 != 0) {
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return math.nan(f64);
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}
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// subnormal, scale x
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k -= 54;
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x *= 0x1.0p54;
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hx = @intCast(u32, @bitCast(u64, x) >> 32);
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} else if (hx >= 0x7FF00000) {
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return x;
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} else if (hx == 0x3FF00000 and ix << 32 == 0) {
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return 0;
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}
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// x into [sqrt(2) / 2, sqrt(2)]
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hx += 0x3FF00000 - 0x3FE6A09E;
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k += @intCast(i32, hx >> 20) - 0x3FF;
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hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
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ix = (@as(u64, hx) << 32) | (ix & 0xFFFFFFFF);
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x = @bitCast(f64, ix);
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const f = x - 1.0;
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const hfsq = 0.5 * f * f;
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const s = f / (2.0 + f);
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const z = s * s;
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const w = z * z;
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const t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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const t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
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const R = t2 + t1;
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// hi + lo = f - hfsq + s * (hfsq + R) ~ log(1 + f)
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var hi = f - hfsq;
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var hii = @bitCast(u64, hi);
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hii &= @as(u64, maxInt(u64)) << 32;
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hi = @bitCast(f64, hii);
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const lo = f - hi - hfsq + s * (hfsq + R);
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var val_hi = hi * ivln2hi;
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var val_lo = (lo + hi) * ivln2lo + lo * ivln2hi;
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// spadd(val_hi, val_lo, y)
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const y = @intToFloat(f64, k);
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const ww = y + val_hi;
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val_lo += (y - ww) + val_hi;
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val_hi = ww;
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return val_lo + val_hi;
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}
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test "math.log2" {
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expect(log2(@as(f32, 0.2)) == log2_32(0.2));
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expect(log2(@as(f64, 0.2)) == log2_64(0.2));
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}
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test "math.log2_32" {
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const epsilon = 0.000001;
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expect(math.approxEqAbs(f32, log2_32(0.2), -2.321928, epsilon));
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expect(math.approxEqAbs(f32, log2_32(0.8923), -0.164399, epsilon));
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expect(math.approxEqAbs(f32, log2_32(1.5), 0.584962, epsilon));
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expect(math.approxEqAbs(f32, log2_32(37.45), 5.226894, epsilon));
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expect(math.approxEqAbs(f32, log2_32(123123.234375), 16.909744, epsilon));
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}
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test "math.log2_64" {
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const epsilon = 0.000001;
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expect(math.approxEqAbs(f64, log2_64(0.2), -2.321928, epsilon));
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expect(math.approxEqAbs(f64, log2_64(0.8923), -0.164399, epsilon));
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expect(math.approxEqAbs(f64, log2_64(1.5), 0.584962, epsilon));
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expect(math.approxEqAbs(f64, log2_64(37.45), 5.226894, epsilon));
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expect(math.approxEqAbs(f64, log2_64(123123.234375), 16.909744, epsilon));
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}
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test "math.log2_32.special" {
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expect(math.isPositiveInf(log2_32(math.inf(f32))));
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expect(math.isNegativeInf(log2_32(0.0)));
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expect(math.isNan(log2_32(-1.0)));
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expect(math.isNan(log2_32(math.nan(f32))));
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}
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test "math.log2_64.special" {
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expect(math.isPositiveInf(log2_64(math.inf(f64))));
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expect(math.isNegativeInf(log2_64(0.0)));
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expect(math.isNan(log2_64(-1.0)));
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expect(math.isNan(log2_64(math.nan(f64))));
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}
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