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-rw-r--r--lib/std/math/ldexp.zig189
1 files changed, 123 insertions, 66 deletions
diff --git a/lib/std/math/ldexp.zig b/lib/std/math/ldexp.zig
index 57d8896c9c..d2fd8db9b7 100644
--- a/lib/std/math/ldexp.zig
+++ b/lib/std/math/ldexp.zig
@@ -1,91 +1,148 @@
-// 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/ldexpf.c
-// https://git.musl-libc.org/cgit/musl/tree/src/math/ldexp.c
-
const std = @import("std");
const math = std.math;
+const Log2Int = std.math.Log2Int;
const assert = std.debug.assert;
const expect = std.testing.expect;
/// Returns x * 2^n.
pub fn ldexp(x: anytype, n: i32) @TypeOf(x) {
- var base = x;
- var shift = n;
-
- const T = @TypeOf(base);
+ const T = @TypeOf(x);
const TBits = std.meta.Int(.unsigned, @typeInfo(T).Float.bits);
+ const exponent_bits = math.floatExponentBits(T);
const mantissa_bits = math.floatMantissaBits(T);
- const exponent_min = math.floatExponentMin(T);
- const exponent_max = math.floatExponentMax(T);
-
- const exponent_bias = exponent_max;
-
- // fix double rounding errors in subnormal ranges
- // https://git.musl-libc.org/cgit/musl/commit/src/math/ldexp.c?id=8c44a060243f04283ca68dad199aab90336141db
- const scale_min_expo = exponent_min + mantissa_bits + 1;
- const scale_min = @bitCast(T, @as(TBits, scale_min_expo + exponent_bias) << mantissa_bits);
- const scale_max = @bitCast(T, @intCast(TBits, exponent_max + exponent_bias) << mantissa_bits);
-
- // scale `shift` within floating point limits, if possible
- // second pass is possible due to subnormal range
- // third pass always results in +/-0.0 or +/-inf
- if (shift > exponent_max) {
- base *= scale_max;
- shift -= exponent_max;
- if (shift > exponent_max) {
- base *= scale_max;
- shift -= exponent_max;
- if (shift > exponent_max) shift = exponent_max;
+ const fractional_bits = math.floatFractionalBits(T);
+
+ const max_biased_exponent = 2 * math.floatExponentMax(T);
+ const mantissa_mask = @as(TBits, (1 << mantissa_bits) - 1);
+
+ const repr = @bitCast(TBits, x);
+ const sign_bit = repr & (1 << (exponent_bits + mantissa_bits));
+
+ if (math.isNan(x) or !math.isFinite(x))
+ return x;
+
+ var exponent: i32 = @intCast(i32, (repr << 1) >> (mantissa_bits + 1));
+ if (exponent == 0)
+ exponent += (@as(i32, exponent_bits) + @boolToInt(T == f80)) - @clz(repr << 1);
+
+ if (n >= 0) {
+ if (n > max_biased_exponent - exponent) {
+ // Overflow. Return +/- inf
+ return @bitCast(T, @bitCast(TBits, math.inf(T)) | sign_bit);
+ } else if (exponent + n <= 0) {
+ // Result is subnormal
+ return @bitCast(T, (repr << @intCast(Log2Int(TBits), n)) | sign_bit);
+ } else if (exponent <= 0) {
+ // Result is normal, but needs shifting
+ var result = @intCast(TBits, n + exponent) << mantissa_bits;
+ result |= (repr << @intCast(Log2Int(TBits), 1 - exponent)) & mantissa_mask;
+ return @bitCast(T, result | sign_bit);
}
- } else if (shift < exponent_min) {
- base *= scale_min;
- shift -= scale_min_expo;
- if (shift < exponent_min) {
- base *= scale_min;
- shift -= scale_min_expo;
- if (shift < exponent_min) shift = exponent_min;
+
+ // Result needs no shifting
+ return @bitCast(T, repr + (@intCast(TBits, n) << mantissa_bits));
+ } else {
+ if (n <= -exponent) {
+ if (n < -(mantissa_bits + exponent))
+ return @bitCast(T, sign_bit); // Severe underflow. Return +/- 0
+
+ // Result underflowed, we need to shift and round
+ const shift = @intCast(Log2Int(TBits), math.min(-n, -(exponent + n) + 1));
+ const exact_tie: bool = @ctz(repr) == shift - 1;
+ var result = repr & mantissa_mask;
+
+ if (T != f80) // Include integer bit
+ result |= @as(TBits, @boolToInt(exponent > 0)) << fractional_bits;
+ result = @intCast(TBits, (result >> (shift - 1)));
+
+ // Round result, including round-to-even for exact ties
+ result = ((result + 1) >> 1) & ~@as(TBits, @boolToInt(exact_tie));
+ return @bitCast(T, result | sign_bit);
}
- }
- return base * @bitCast(T, @intCast(TBits, shift + exponent_bias) << mantissa_bits);
+ // Result is exact, and needs no shifting
+ return @bitCast(T, repr - (@intCast(TBits, -n) << mantissa_bits));
+ }
}
test "math.ldexp" {
- // TODO derive the various constants here with new maths API
-
- // basic usage
- try expect(ldexp(@as(f16, 1.5), 4) == 24.0);
- try expect(ldexp(@as(f32, 1.5), 4) == 24.0);
- try expect(ldexp(@as(f64, 1.5), 4) == 24.0);
- try expect(ldexp(@as(f128, 1.5), 4) == 24.0);
// subnormals
- try expect(math.isNormal(ldexp(@as(f16, 1.0), -14)));
- try expect(!math.isNormal(ldexp(@as(f16, 1.0), -15)));
- try expect(math.isNormal(ldexp(@as(f32, 1.0), -126)));
- try expect(!math.isNormal(ldexp(@as(f32, 1.0), -127)));
- try expect(math.isNormal(ldexp(@as(f64, 1.0), -1022)));
- try expect(!math.isNormal(ldexp(@as(f64, 1.0), -1023)));
- try expect(math.isNormal(ldexp(@as(f128, 1.0), -16382)));
- try expect(!math.isNormal(ldexp(@as(f128, 1.0), -16383)));
- // unreliable due to lack of native f16 support, see talk on PR #8733
- // try expect(ldexp(@as(f16, 0x1.1FFp-1), -14 - 9) == math.floatTrueMin(f16));
+ try expect(ldexp(@as(f16, 0x1.1FFp14), -14 - 9 - 15) == math.floatTrueMin(f16));
try expect(ldexp(@as(f32, 0x1.3FFFFFp-1), -126 - 22) == math.floatTrueMin(f32));
try expect(ldexp(@as(f64, 0x1.7FFFFFFFFFFFFp-1), -1022 - 51) == math.floatTrueMin(f64));
+ try expect(ldexp(@as(f80, 0x1.7FFFFFFFFFFFFFFEp-1), -16382 - 62) == math.floatTrueMin(f80));
try expect(ldexp(@as(f128, 0x1.7FFFFFFFFFFFFFFFFFFFFFFFFFFFp-1), -16382 - 111) == math.floatTrueMin(f128));
- // float limits
try expect(ldexp(math.floatMax(f32), -128 - 149) > 0.0);
try expect(ldexp(math.floatMax(f32), -128 - 149 - 1) == 0.0);
- try expect(!math.isPositiveInf(ldexp(math.floatTrueMin(f16), 15 + 24)));
- try expect(math.isPositiveInf(ldexp(math.floatTrueMin(f16), 15 + 24 + 1)));
- try expect(!math.isPositiveInf(ldexp(math.floatTrueMin(f32), 127 + 149)));
- try expect(math.isPositiveInf(ldexp(math.floatTrueMin(f32), 127 + 149 + 1)));
- try expect(!math.isPositiveInf(ldexp(math.floatTrueMin(f64), 1023 + 1074)));
- try expect(math.isPositiveInf(ldexp(math.floatTrueMin(f64), 1023 + 1074 + 1)));
- try expect(!math.isPositiveInf(ldexp(math.floatTrueMin(f128), 16383 + 16494)));
- try expect(math.isPositiveInf(ldexp(math.floatTrueMin(f128), 16383 + 16494 + 1)));
+
+ @setEvalBranchQuota(10_000);
+
+ inline for ([_]type{ f16, f32, f64, f80, f128 }) |T| {
+ const fractional_bits = math.floatFractionalBits(T);
+
+ const min_exponent = math.floatExponentMin(T);
+ const max_exponent = math.floatExponentMax(T);
+ const exponent_bias = max_exponent;
+
+ // basic usage
+ try expect(ldexp(@as(T, 1.5), 4) == 24.0);
+
+ // normals -> subnormals
+ try expect(math.isNormal(ldexp(@as(T, 1.0), min_exponent)));
+ try expect(!math.isNormal(ldexp(@as(T, 1.0), min_exponent - 1)));
+
+ // normals -> zero
+ try expect(ldexp(@as(T, 1.0), min_exponent - fractional_bits) > 0.0);
+ try expect(ldexp(@as(T, 1.0), min_exponent - fractional_bits - 1) == 0.0);
+
+ // subnormals -> zero
+ try expect(ldexp(math.floatTrueMin(T), 0) > 0.0);
+ try expect(ldexp(math.floatTrueMin(T), -1) == 0.0);
+
+ // Multiplications might flush the denormals to zero, esp. at
+ // runtime, so we manually construct the constants here instead.
+ const Z = std.meta.Int(.unsigned, @bitSizeOf(T));
+ const EightTimesTrueMin = @bitCast(T, @as(Z, 8));
+ const TwoTimesTrueMin = @bitCast(T, @as(Z, 2));
+
+ // subnormals -> subnormals
+ try expect(ldexp(math.floatTrueMin(T), 3) == EightTimesTrueMin);
+ try expect(ldexp(EightTimesTrueMin, -2) == TwoTimesTrueMin);
+ try expect(ldexp(EightTimesTrueMin, -3) == math.floatTrueMin(T));
+
+ // subnormals -> normals (+)
+ try expect(ldexp(math.floatTrueMin(T), fractional_bits) == math.floatMin(T));
+ try expect(ldexp(math.floatTrueMin(T), fractional_bits - 1) == math.floatMin(T) * 0.5);
+
+ // subnormals -> normals (-)
+ try expect(ldexp(-math.floatTrueMin(T), fractional_bits) == -math.floatMin(T));
+ try expect(ldexp(-math.floatTrueMin(T), fractional_bits - 1) == -math.floatMin(T) * 0.5);
+
+ // subnormals -> float limits (+inf)
+ try expect(math.isFinite(ldexp(math.floatTrueMin(T), max_exponent + exponent_bias + fractional_bits - 1)));
+ try expect(ldexp(math.floatTrueMin(T), max_exponent + exponent_bias + fractional_bits) == math.inf(T));
+
+ // subnormals -> float limits (-inf)
+ try expect(math.isFinite(ldexp(-math.floatTrueMin(T), max_exponent + exponent_bias + fractional_bits - 1)));
+ try expect(ldexp(-math.floatTrueMin(T), max_exponent + exponent_bias + fractional_bits) == -math.inf(T));
+
+ // infinity -> infinity
+ try expect(ldexp(math.inf(T), math.maxInt(i32)) == math.inf(T));
+ try expect(ldexp(math.inf(T), math.minInt(i32)) == math.inf(T));
+ try expect(ldexp(math.inf(T), max_exponent) == math.inf(T));
+ try expect(ldexp(math.inf(T), min_exponent) == math.inf(T));
+ try expect(ldexp(-math.inf(T), math.maxInt(i32)) == -math.inf(T));
+ try expect(ldexp(-math.inf(T), math.minInt(i32)) == -math.inf(T));
+
+ // extremely large n
+ try expect(ldexp(math.floatMax(T), math.maxInt(i32)) == math.inf(T));
+ try expect(ldexp(math.floatMax(T), -math.maxInt(i32)) == 0.0);
+ try expect(ldexp(math.floatMax(T), math.minInt(i32)) == 0.0);
+ try expect(ldexp(math.floatTrueMin(T), math.maxInt(i32)) == math.inf(T));
+ try expect(ldexp(math.floatTrueMin(T), -math.maxInt(i32)) == 0.0);
+ try expect(ldexp(math.floatTrueMin(T), math.minInt(i32)) == 0.0);
+ }
}
generated by cgit v1.2.3 (git 2.39.1) at 2025-12-28 07:49:53 +0000