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Merge pull request 'std.math.pow: fix wrong answer for large even exponents' (#31537) from TemariVirus/zig:master into master

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Reviewed-on: https://codeberg.org/ziglang/zig/pulls/31537
Reviewed-by: Andrew Kelley <andrew@ziglang.org>
This commit is contained in:
Andrew Kelley
2026-03-16 23:40:43 +01:00
parent 8a8e4a1f04 e498550952
commit 2d237da50b
1 changed files with 80 additions and 33 deletions
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lib/std/math/pow.zig
+80 -33
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@@ -13,13 +13,13 @@ const expect = std.testing.expect;
/// - pow(x, +-0) = 1 for any x
/// - pow(1, y) = 1 for any y
/// - pow(x, 1) = x for any x
/// - pow(nan, y) = nan
/// - pow(x, nan) = nan
/// - pow(nan, y) = nan for any y != 0
/// - pow(x, nan) = nan for any x != 1
/// - pow(+-0, y) = +-inf for y an odd integer < 0
/// - pow(+-0, -inf) = +inf
/// - pow(+-0, +inf) = +0
/// - pow(+-0, y) = +inf for finite y < 0 and not an odd integer
/// - pow(+-0, y) = +-0 for y an odd integer > 0
/// - pow(+-0, y) = +-0 for finite y an odd integer > 0
/// - pow(+-0, y) = +0 for finite y > 0 and not an odd integer
/// - pow(-1, +-inf) = 1
/// - pow(x, +inf) = +inf for |x| > 1
@@ -39,20 +39,20 @@ pub fn pow(comptime T: type, x: T, y: T) T {
@compileError("pow not implemented for " ++ @typeName(T));
}
// pow(x, +-0) = 1 for all x
// pow(1, y) = 1 for all y
// pow(x, +-0) = 1 for any x
// pow(1, y) = 1 for any y
if (y == 0 or x == 1) {
return 1;
}
// pow(nan, y) = nan for all y
// pow(x, nan) = nan for all x
// pow(nan, y) = nan for any y != 0
// pow(x, nan) = nan for any x != 1
if (math.isNan(x) or math.isNan(y)) {
@branchHint(.unlikely);
return math.nan(T);
}
// pow(x, 1) = x for all x
// pow(x, 1) = x for any x
if (y == 1) {
return x;
}
@@ -77,7 +77,7 @@ pub fn pow(comptime T: type, x: T, y: T) T {
}
if (math.isInf(y)) {
// pow(-1, inf) = 1 for all x
// pow(-1, inf) = 1
if (x == -1) {
return 1.0;
}
@@ -124,7 +124,9 @@ pub fn pow(comptime T: type, x: T, y: T) T {
return math.nan(T);
}
if (yi >= 1 << (@typeInfo(T).float.bits - 1)) {
return @exp(y * @log(x));
// yi is a large even int, so the result is always positive
// and the sign of x doesn't matter
return @exp(y * @log(@abs(x)));
}
// a = a1 * 2^ae
@@ -208,6 +210,7 @@ test pow {
try expect(math.approxEqAbs(f32, pow(f32, 1.5, 3.3), 3.811546, epsilon));
try expect(math.approxEqAbs(f32, pow(f32, 37.45, 3.3), 155736.703125, epsilon));
try expect(math.approxEqAbs(f32, pow(f32, 89.123, 3.3), 2722489.5, epsilon));
try expect(math.approxEqAbs(f32, pow(f32, -1.0, 1e10), 1.0, epsilon));
try expect(math.approxEqAbs(f64, pow(f64, 0.0, 3.3), 0.0, epsilon));
try expect(math.approxEqAbs(f64, pow(f64, 0.8923, 3.3), 0.686572, epsilon));
@@ -215,48 +218,90 @@ test pow {
try expect(math.approxEqAbs(f64, pow(f64, 1.5, 3.3), 3.811546, epsilon));
try expect(math.approxEqAbs(f64, pow(f64, 37.45, 3.3), 155736.7160616, epsilon));
try expect(math.approxEqAbs(f64, pow(f64, 89.123, 3.3), 2722490.231436, epsilon));
try expect(math.approxEqAbs(f64, pow(f64, -1.0, 1e20), 1.0, epsilon));
}
test "special" {
const epsilon = 0.000001;
// pow(x, +-0) = 1 for any x
try expect(pow(f32, 4, 0.0) == 1.0);
try expect(pow(f32, 7, -0.0) == 1.0);
try expect(pow(f32, math.nan(f32), -0.0) == 1.0);
// pow(1, y) = 1 for any y
try expect(pow(f32, 1.0, 4) == 1.0);
try expect(pow(f32, 1.0, 7) == 1.0);
try expect(pow(f32, 1.0, -math.inf(f32)) == 1.0);
try expect(pow(f32, 1.0, math.nan(f32)) == 1.0);
// pow(x, 1) = x for any x
try expect(pow(f32, 45, 1.0) == 45);
try expect(pow(f32, -45, 1.0) == -45);
try expect(math.isPositiveZero(pow(f32, 0.0, 1.0)));
try expect(math.isNegativeZero(pow(f32, -0.0, 1.0)));
try expect(math.isPositiveInf(pow(f32, math.inf(f32), 1.0)));
try expect(math.isNan(pow(f32, math.nan(f32), 1.0)));
// pow(nan, y) = nan for any y != 0
try expect(math.isNan(pow(f32, math.nan(f32), 5.0)));
try expect(math.isPositiveInf(pow(f32, -math.inf(f32), 0.5)));
try expect(math.isPositiveInf(pow(f32, -0.0, -0.5)));
try expect(pow(f32, -0.0, 0.5) == 0);
// pow(x, nan) = nan for any x != 1
try expect(math.isNan(pow(f32, 5.0, math.nan(f32))));
// pow(+-0, y) = +-inf for y an odd integer < 0
try expect(math.isPositiveInf(pow(f32, 0.0, -1.0)));
//expect(math.isNegativeInf(pow(f32, -0.0, -3.0))); TODO is this required?
try expect(math.isNegativeInf(pow(f32, -0.0, -5.0)));
// pow(+-0, -inf) = +inf
try expect(math.isPositiveInf(pow(f32, 0.0, -math.inf(f32))));
try expect(math.isPositiveInf(pow(f32, -0.0, -math.inf(f32))));
try expect(pow(f32, 0.0, math.inf(f32)) == 0.0);
try expect(pow(f32, -0.0, math.inf(f32)) == 0.0);
// pow(+-0, +inf) = +0
try expect(math.isPositiveZero(pow(f32, 0.0, math.inf(f32))));
try expect(math.isPositiveZero(pow(f32, -0.0, math.inf(f32))));
// pow(+-0, y) = +inf for finite y < 0 and not an odd integer
try expect(math.isPositiveInf(pow(f32, 0.0, -2.0)));
try expect(math.isPositiveInf(pow(f32, -0.0, -2.0)));
try expect(pow(f32, 0.0, 1.0) == 0.0);
try expect(pow(f32, -0.0, 1.0) == -0.0);
try expect(pow(f32, 0.0, 2.0) == 0.0);
try expect(pow(f32, -0.0, 2.0) == 0.0);
try expect(math.approxEqAbs(f32, pow(f32, -1.0, math.inf(f32)), 1.0, epsilon));
try expect(math.approxEqAbs(f32, pow(f32, -1.0, -math.inf(f32)), 1.0, epsilon));
try expect(math.isPositiveInf(pow(f32, 0.0, -5.2)));
try expect(math.isPositiveInf(pow(f32, -0.0, -0.5)));
// pow(+-0, y) = +-0 for finite y an odd integer > 0
try expect(math.isPositiveZero(pow(f32, 0.0, 3.0)));
try expect(math.isNegativeZero(pow(f32, -0.0, 5.0)));
// pow(+-0, y) = +0 for finite y > 0 and not an odd integer
try expect(math.isPositiveZero(pow(f32, 0.0, 2.0)));
try expect(math.isPositiveZero(pow(f32, -0.0, 2.0)));
try expect(math.isPositiveZero(pow(f32, 0.0, 5.2)));
try expect(math.isPositiveZero(pow(f32, -0.0, 0.5)));
// pow(-1, +-inf) = 1
try expect(pow(f32, -1.0, math.inf(f32)) == 1.0);
try expect(pow(f32, -1.0, -math.inf(f32)) == 1.0);
// pow(x, +inf) = +inf for |x| > 1
try expect(math.isPositiveInf(pow(f32, 1.2, math.inf(f32))));
try expect(math.isPositiveInf(pow(f32, -1.2, math.inf(f32))));
try expect(pow(f32, 1.2, -math.inf(f32)) == 0.0);
try expect(pow(f32, -1.2, -math.inf(f32)) == 0.0);
try expect(pow(f32, 0.2, math.inf(f32)) == 0.0);
try expect(pow(f32, -0.2, math.inf(f32)) == 0.0);
// pow(x, -inf) = +0 for |x| > 1
try expect(math.isPositiveZero(pow(f32, 1.2, -math.inf(f32))));
try expect(math.isPositiveZero(pow(f32, -1.2, -math.inf(f32))));
// pow(x, +inf) = +0 for |x| < 1
try expect(math.isPositiveZero(pow(f32, 0.2, math.inf(f32))));
try expect(math.isPositiveZero(pow(f32, -0.2, math.inf(f32))));
// pow(x, -inf) = +inf for |x| < 1
try expect(math.isPositiveInf(pow(f32, 0.2, -math.inf(f32))));
try expect(math.isPositiveInf(pow(f32, -0.2, -math.inf(f32))));
try expect(math.isPositiveInf(pow(f32, math.inf(f32), 1.0)));
try expect(pow(f32, math.inf(f32), -1.0) == 0.0);
//expect(pow(f32, -math.inf(f32), 5.0) == pow(f32, -0.0, -5.0)); TODO support negative 0?
try expect(pow(f32, -math.inf(f32), -5.2) == pow(f32, -0.0, 5.2));
// pow(+inf, y) = +inf for y > 0
try expect(math.isPositiveInf(pow(f32, math.inf(f32), 2.0)));
try expect(math.isPositiveInf(pow(f32, math.inf(f32), 0.2)));
// pow(+inf, y) = +0 for y < 0
try expect(math.isPositiveZero(pow(f32, math.inf(f32), -2.0)));
try expect(math.isPositiveZero(pow(f32, math.inf(f32), -0.2)));
// pow(-inf, y) = -inf for y an odd integer > 0
try expect(math.isNegativeInf(pow(f32, -math.inf(f32), 5.0)));
// pow(-inf, +inf) = +inf
try expect(math.isPositiveInf(pow(f32, -math.inf(f32), math.inf(f32))));
// pow(-inf, -inf) = +0
try expect(math.isPositiveZero(pow(f32, -math.inf(f32), -math.inf(f32))));
// pow(-inf, y) = +inf for finite y > 0 and not an odd integer
try expect(math.isPositiveInf(pow(f32, -math.inf(f32), 4.0)));
try expect(math.isPositiveInf(pow(f32, -math.inf(f32), 0.5)));
// pow(-inf, y) = -0 for finite y an odd integer < 0
try expect(math.isNegativeZero(pow(f32, -math.inf(f32), -3.0)));
// pow(-inf, y) = +0 for finite y < 0 and not an odd integer
try expect(math.isPositiveZero(pow(f32, -math.inf(f32), -2.0)));
try expect(math.isPositiveZero(pow(f32, -math.inf(f32), -5.2)));
// pow(x, y) = nan for finite x < 0 and finite non-integer y
try expect(math.isNan(pow(f32, -1.0, 1.2)));
try expect(math.isNan(pow(f32, -12.4, 78.5)));
try expect(math.isNan(pow(f32, -12.4, -78.5)));
}
test "overflow" {
@@ -265,4 +310,6 @@ test "overflow" {
try expect(math.isNegativeInf(pow(f64, -2, (1 << 32) + 1)));
try expect(pow(f64, 0.5, 1 << 45) == 0);
try expect(math.isPositiveInf(pow(f64, 0.5, -(1 << 45))));
try expect(math.isPositiveInf(pow(f64, -2, 1 << 64)));
try expect(pow(f64, 0.5, 1 << 64) == 0);
}