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// Ported from musl, which is licensed under the MIT license:
// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
//
// https://git.musl-libc.org/cgit/musl/tree/src/math/lnf.c
// https://git.musl-libc.org/cgit/musl/tree/src/math/ln.c
const std = @import("../std.zig");
const math = std.math;
const expect = std.testing.expect;
const builtin = @import("builtin");
const TypeId = builtin.TypeId;
/// Returns the natural logarithm of x.
///
/// Special Cases:
/// - ln(+inf) = +inf
/// - ln(0) = -inf
/// - ln(x) = nan if x < 0
/// - ln(nan) = nan
pub fn ln(x: var) @typeOf(x) {
const T = @typeOf(x);
switch (@typeId(T)) {
TypeId.ComptimeFloat => {
return @typeOf(1.0)(ln_64(x));
},
TypeId.Float => {
return switch (T) {
f32 => ln_32(x),
f64 => ln_64(x),
else => @compileError("ln not implemented for " ++ @typeName(T)),
};
},
TypeId.ComptimeInt => {
return @typeOf(1)(math.floor(ln_64(f64(x))));
},
TypeId.Int => {
return T(math.floor(ln_64(f64(x))));
},
else => @compileError("ln not implemented for " ++ @typeName(T)),
}
}
pub fn ln_32(x_: f32) f32 {
const ln2_hi: f32 = 6.9313812256e-01;
const ln2_lo: f32 = 9.0580006145e-06;
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 ix = @bitCast(u32, x);
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);
}
// subnormal, scale x
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 += @intCast(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;
const dk = @intToFloat(f32, k);
return s * (hfsq + R) + dk * ln2_lo - hfsq + f + dk * ln2_hi;
}
pub fn ln_64(x_: f64) f64 {
const ln2_hi: f64 = 6.93147180369123816490e-01;
const ln2_lo: f64 = 1.90821492927058770002e-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 = @intCast(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 = @intCast(u32, @bitCast(u64, ix) >> 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 += @intCast(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;
const dk = @intToFloat(f64, k);
return s * (hfsq + R) + dk * ln2_lo - hfsq + f + dk * ln2_hi;
}
test "math.ln" {
expect(ln(f32(0.2)) == ln_32(0.2));
expect(ln(f64(0.2)) == ln_64(0.2));
}
test "math.ln32" {
const epsilon = 0.000001;
expect(math.approxEq(f32, ln_32(0.2), -1.609438, epsilon));
expect(math.approxEq(f32, ln_32(0.8923), -0.113953, epsilon));
expect(math.approxEq(f32, ln_32(1.5), 0.405465, epsilon));
expect(math.approxEq(f32, ln_32(37.45), 3.623007, epsilon));
expect(math.approxEq(f32, ln_32(89.123), 4.490017, epsilon));
expect(math.approxEq(f32, ln_32(123123.234375), 11.720941, epsilon));
}
test "math.ln64" {
const epsilon = 0.000001;
expect(math.approxEq(f64, ln_64(0.2), -1.609438, epsilon));
expect(math.approxEq(f64, ln_64(0.8923), -0.113953, epsilon));
expect(math.approxEq(f64, ln_64(1.5), 0.405465, epsilon));
expect(math.approxEq(f64, ln_64(37.45), 3.623007, epsilon));
expect(math.approxEq(f64, ln_64(89.123), 4.490017, epsilon));
expect(math.approxEq(f64, ln_64(123123.234375), 11.720941, epsilon));
}
test "math.ln32.special" {
expect(math.isPositiveInf(ln_32(math.inf(f32))));
expect(math.isNegativeInf(ln_32(0.0)));
expect(math.isNan(ln_32(-1.0)));
expect(math.isNan(ln_32(math.nan(f32))));
}
test "math.ln64.special" {
expect(math.isPositiveInf(ln_64(math.inf(f64))));
expect(math.isNegativeInf(ln_64(0.0)));
expect(math.isNan(ln_64(-1.0)));
expect(math.isNan(ln_64(math.nan(f64))));
}
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