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// Special Cases:
//
// - log2(+inf) = +inf
// - log2(0) = -inf
// - log2(x) = nan if x < 0
// - log2(nan) = nan
const std = @import("../index.zig");
const math = std.math;
const assert = std.debug.assert;
const builtin = @import("builtin");
const TypeId = builtin.TypeId;
pub fn log2(x: var) -> @typeOf(x) {
const T = @typeOf(x);
switch (@typeId(T)) {
TypeId.FloatLiteral => {
return @typeOf(1.0)(log2_64(x));
},
TypeId.Float => {
return switch (T) {
f32 => log2_32(x),
f64 => log2_64(x),
else => @compileError("log2 not implemented for " ++ @typeName(T)),
};
},
TypeId.IntLiteral => comptime {
var result = 0;
var x_shifted = x;
while (b: {x_shifted >>= 1; break :b x_shifted != 0;}) : (result += 1) {}
return result;
},
TypeId.Int => {
return log2_int(T, x);
},
else => @compileError("log2 not implemented for " ++ @typeName(T)),
}
}
pub fn log2_int(comptime T: type, x: T) -> T {
assert(x != 0);
return T.bit_count - 1 - T(@clz(x));
}
pub fn log2_32(x_: f32) -> f32 {
const ivln2hi: f32 = 1.4428710938e+00;
const ivln2lo: f32 = -1.7605285393e-04;
const Lg1: f32 = 0xaaaaaa.0p-24;
const Lg2: f32 = 0xccce13.0p-25;
const Lg3: f32 = 0x91e9ee.0p-25;
const Lg4: f32 = 0xf89e26.0p-26;
var x = x_;
var u = @bitCast(u32, x);
var ix = u;
var k: i32 = 0;
// x < 2^(-126)
if (ix < 0x00800000 or ix >> 31 != 0) {
// log(+-0) = -inf
if (ix << 1 == 0) {
return -math.inf(f32);
}
// log(-#) = nan
if (ix >> 31 != 0) {
return math.nan(f32);
}
k -= 25;
x *= 0x1.0p25;
ix = @bitCast(u32, x);
} else if (ix >= 0x7F800000) {
return x;
} else if (ix == 0x3F800000) {
return 0;
}
// x into [sqrt(2) / 2, sqrt(2)]
ix += 0x3F800000 - 0x3F3504F3;
k += i32(ix >> 23) - 0x7F;
ix = (ix & 0x007FFFFF) + 0x3F3504F3;
x = @bitCast(f32, ix);
const f = x - 1.0;
const s = f / (2.0 + f);
const z = s * s;
const w = z * z;
const t1 = w * (Lg2 + w * Lg4);
const t2 = z * (Lg1 + w * Lg3);
const R = t2 + t1;
const hfsq = 0.5 * f * f;
var hi = f - hfsq;
u = @bitCast(u32, hi);
u &= 0xFFFFF000;
hi = @bitCast(f32, u);
const lo = f - hi - hfsq + s * (hfsq + R);
return (lo + hi) * ivln2lo + lo * ivln2hi + hi * ivln2hi + f32(k);
}
pub fn log2_64(x_: f64) -> f64 {
const ivln2hi: f64 = 1.44269504072144627571e+00;
const ivln2lo: f64 = 1.67517131648865118353e-10;
const Lg1: f64 = 6.666666666666735130e-01;
const Lg2: f64 = 3.999999999940941908e-01;
const Lg3: f64 = 2.857142874366239149e-01;
const Lg4: f64 = 2.222219843214978396e-01;
const Lg5: f64 = 1.818357216161805012e-01;
const Lg6: f64 = 1.531383769920937332e-01;
const Lg7: f64 = 1.479819860511658591e-01;
var x = x_;
var ix = @bitCast(u64, x);
var hx = u32(ix >> 32);
var k: i32 = 0;
if (hx < 0x00100000 or hx >> 31 != 0) {
// log(+-0) = -inf
if (ix << 1 == 0) {
return -math.inf(f64);
}
// log(-#) = nan
if (hx >> 31 != 0) {
return math.nan(f64);
}
// subnormal, scale x
k -= 54;
x *= 0x1.0p54;
hx = u32(@bitCast(u64, x) >> 32);
} else if (hx >= 0x7FF00000) {
return x;
} else if (hx == 0x3FF00000 and ix << 32 == 0) {
return 0;
}
// x into [sqrt(2) / 2, sqrt(2)]
hx += 0x3FF00000 - 0x3FE6A09E;
k += i32(hx >> 20) - 0x3FF;
hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
ix = (u64(hx) << 32) | (ix & 0xFFFFFFFF);
x = @bitCast(f64, ix);
const f = x - 1.0;
const hfsq = 0.5 * f * f;
const s = f / (2.0 + f);
const z = s * s;
const w = z * z;
const t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
const t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
const R = t2 + t1;
// hi + lo = f - hfsq + s * (hfsq + R) ~ log(1 + f)
var hi = f - hfsq;
var hii = @bitCast(u64, hi);
hii &= u64(@maxValue(u64)) << 32;
hi = @bitCast(f64, hii);
const lo = f - hi - hfsq + s * (hfsq + R);
var val_hi = hi * ivln2hi;
var val_lo = (lo + hi) * ivln2lo + lo * ivln2hi;
// spadd(val_hi, val_lo, y)
const y = f64(k);
const ww = y + val_hi;
val_lo += (y - ww) + val_hi;
val_hi = ww;
return val_lo + val_hi;
}
test "math.log2" {
if (builtin.os == builtin.Os.windows and builtin.arch == builtin.Arch.i386) {
// TODO get this test passing
// https://github.com/zig-lang/zig/issues/537
return;
}
assert(log2(f32(0.2)) == log2_32(0.2));
assert(log2(f64(0.2)) == log2_64(0.2));
}
test "math.log2_32" {
const epsilon = 0.000001;
assert(math.approxEq(f32, log2_32(0.2), -2.321928, epsilon));
assert(math.approxEq(f32, log2_32(0.8923), -0.164399, epsilon));
assert(math.approxEq(f32, log2_32(1.5), 0.584962, epsilon));
assert(math.approxEq(f32, log2_32(37.45), 5.226894, epsilon));
assert(math.approxEq(f32, log2_32(123123.234375), 16.909744, epsilon));
}
test "math.log2_64" {
const epsilon = 0.000001;
assert(math.approxEq(f64, log2_64(0.2), -2.321928, epsilon));
assert(math.approxEq(f64, log2_64(0.8923), -0.164399, epsilon));
assert(math.approxEq(f64, log2_64(1.5), 0.584962, epsilon));
assert(math.approxEq(f64, log2_64(37.45), 5.226894, epsilon));
assert(math.approxEq(f64, log2_64(123123.234375), 16.909744, epsilon));
}
test "math.log2_32.special" {
assert(math.isPositiveInf(log2_32(math.inf(f32))));
assert(math.isNegativeInf(log2_32(0.0)));
assert(math.isNan(log2_32(-1.0)));
assert(math.isNan(log2_32(math.nan(f32))));
}
test "math.log2_64.special" {
assert(math.isPositiveInf(log2_64(math.inf(f64))));
assert(math.isNegativeInf(log2_64(0.0)));
assert(math.isNan(log2_64(-1.0)));
assert(math.isNan(log2_64(math.nan(f64))));
}
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