Commit eac1e613be

@@ -15,175 +15,157 @@ const minInt = std.math.minInt;
 ///
 /// Special Cases:
 ///  - ilogb(+-inf) = maxInt(i32)
-///  - ilogb(0)     = maxInt(i32)
-///  - ilogb(nan)   = maxInt(i32)
+///  - ilogb(+-0)   = minInt(i32)
+///  - ilogb(nan)   = minInt(i32)
 pub fn ilogb(x: anytype) i32 {
     const T = @TypeOf(x);
-    return switch (T) {
-        f32 => ilogb32(x),
-        f64 => ilogb64(x),
-        f128 => ilogb128(x),
-        else => @compileError("ilogb not implemented for " ++ @typeName(T)),
-    };
+    return ilogbX(T, x);
 }
 
-// TODO: unify these implementations with generics
+pub const fp_ilogbnan = minInt(i32);
+pub const fp_ilogb0 = minInt(i32);
 
-// NOTE: Should these be exposed publicly?
-const fp_ilogbnan = -1 - @as(i32, maxInt(u32) >> 1);
-const fp_ilogb0 = fp_ilogbnan;
+fn ilogbX(comptime T: type, x: T) i32 {
+    const typeWidth = @typeInfo(T).Float.bits;
+    const significandBits = math.floatMantissaBits(T);
+    const exponentBits = math.floatExponentBits(T);
 
-fn ilogb32(x: f32) i32 {
-    var u = @bitCast(u32, x);
-    var e = @intCast(i32, (u >> 23) & 0xFF);
+    const Z = std.meta.Int(.unsigned, typeWidth);
 
-    // TODO: We should be able to merge this with the lower check.
-    if (math.isNan(x)) {
-        return maxInt(i32);
-    }
+    const signBit = (@as(Z, 1) << (significandBits + exponentBits));
+    const maxExponent = ((1 << exponentBits) - 1);
+    const exponentBias = (maxExponent >> 1);
 
-    if (e == 0) {
-        u <<= 9;
-        if (u == 0) {
-            math.raiseInvalid();
-            return fp_ilogb0;
-        }
+    const absMask = signBit - 1;
 
-        // subnormal
-        e = -0x7F;
-        while (u >> 31 == 0) : (u <<= 1) {
-            e -= 1;
-        }
-        return e;
-    }
-
-    if (e == 0xFF) {
-        math.raiseInvalid();
-        if (u << 9 != 0) {
-            return fp_ilogbnan;
-        } else {
-            return maxInt(i32);
-        }
-    }
-
-    return e - 0x7F;
-}
-
-fn ilogb64(x: f64) i32 {
-    var u = @bitCast(u64, x);
-    var e = @intCast(i32, (u >> 52) & 0x7FF);
-
-    if (math.isNan(x)) {
-        return maxInt(i32);
-    }
+    var u = @bitCast(Z, x) & absMask;
+    var e = @intCast(i32, u >> significandBits);
 
     if (e == 0) {
-        u <<= 12;
         if (u == 0) {
             math.raiseInvalid();
             return fp_ilogb0;
         }
 
-        // subnormal
-        e = -0x3FF;
-        while (u >> 63 == 0) : (u <<= 1) {
-            e -= 1;
-        }
-        return e;
+        // offset sign bit, exponent bits, and integer bit (if present) + bias
+        const offset = 1 + exponentBits + @boolToInt(T == f80) - exponentBias;
+        return offset - @intCast(i32, @clz(u));
     }
 
-    if (e == 0x7FF) {
+    if (e == maxExponent) {
         math.raiseInvalid();
-        if (u << 12 != 0) {
-            return fp_ilogbnan;
-        } else {
-            return maxInt(i32);
-        }
+        if (u > @bitCast(Z, math.inf(T))) {
+            return fp_ilogbnan; // u is a NaN
+        } else return maxInt(i32);
     }
 
-    return e - 0x3FF;
+    return e - exponentBias;
 }
 
-fn ilogb128(x: f128) i32 {
-    var u = @bitCast(u128, x);
-    var e = @intCast(i32, (u >> 112) & 0x7FFF);
-
-    if (math.isNan(x)) {
-        return maxInt(i32);
-    }
-
-    if (e == 0) {
-        u <<= 16;
-        if (u == 0) {
-            math.raiseInvalid();
-            return fp_ilogb0;
-        }
-
-        // subnormal x
-        return ilogb128(x * 0x1p120) - 120;
-    }
-
-    if (e == 0x7FFF) {
-        math.raiseInvalid();
-        if (u << 16 != 0) {
-            return fp_ilogbnan;
-        } else {
-            return maxInt(i32);
-        }
-    }
-
-    return e - 0x3FFF;
+test "type dispatch" {
+    try expect(ilogb(@as(f32, 0.2)) == ilogbX(f32, 0.2));
+    try expect(ilogb(@as(f64, 0.2)) == ilogbX(f64, 0.2));
 }
 
-test "type dispatch" {
-    try expect(ilogb(@as(f32, 0.2)) == ilogb32(0.2));
-    try expect(ilogb(@as(f64, 0.2)) == ilogb64(0.2));
+test "16" {
+    try expect(ilogbX(f16, 0.0) == fp_ilogb0);
+    try expect(ilogbX(f16, 0.5) == -1);
+    try expect(ilogbX(f16, 0.8923) == -1);
+    try expect(ilogbX(f16, 10.0) == 3);
+    try expect(ilogbX(f16, -65504) == 15);
+    try expect(ilogbX(f16, 2398.23) == 11);
+
+    try expect(ilogbX(f16, 0x1p-1) == -1);
+    try expect(ilogbX(f16, 0x1p-17) == -17);
+    try expect(ilogbX(f16, 0x1p-24) == -24);
 }
 
 test "32" {
-    try expect(ilogb32(0.0) == fp_ilogb0);
-    try expect(ilogb32(0.5) == -1);
-    try expect(ilogb32(0.8923) == -1);
-    try expect(ilogb32(10.0) == 3);
-    try expect(ilogb32(-123984) == 16);
-    try expect(ilogb32(2398.23) == 11);
+    try expect(ilogbX(f32, 0.0) == fp_ilogb0);
+    try expect(ilogbX(f32, 0.5) == -1);
+    try expect(ilogbX(f32, 0.8923) == -1);
+    try expect(ilogbX(f32, 10.0) == 3);
+    try expect(ilogbX(f32, -123984) == 16);
+    try expect(ilogbX(f32, 2398.23) == 11);
+
+    try expect(ilogbX(f32, 0x1p-1) == -1);
+    try expect(ilogbX(f32, 0x1p-122) == -122);
+    try expect(ilogbX(f32, 0x1p-127) == -127);
 }
 
 test "64" {
-    try expect(ilogb64(0.0) == fp_ilogb0);
-    try expect(ilogb64(0.5) == -1);
-    try expect(ilogb64(0.8923) == -1);
-    try expect(ilogb64(10.0) == 3);
-    try expect(ilogb64(-123984) == 16);
-    try expect(ilogb64(2398.23) == 11);
+    try expect(ilogbX(f64, 0.0) == fp_ilogb0);
+    try expect(ilogbX(f64, 0.5) == -1);
+    try expect(ilogbX(f64, 0.8923) == -1);
+    try expect(ilogbX(f64, 10.0) == 3);
+    try expect(ilogbX(f64, -123984) == 16);
+    try expect(ilogbX(f64, 2398.23) == 11);
+
+    try expect(ilogbX(f64, 0x1p-1) == -1);
+    try expect(ilogbX(f64, 0x1p-127) == -127);
+    try expect(ilogbX(f64, 0x1p-1012) == -1012);
+    try expect(ilogbX(f64, 0x1p-1023) == -1023);
+}
+
+test "80" {
+    try expect(ilogbX(f80, 0.0) == fp_ilogb0);
+    try expect(ilogbX(f80, 0.5) == -1);
+    try expect(ilogbX(f80, 0.8923) == -1);
+    try expect(ilogbX(f80, 10.0) == 3);
+    try expect(ilogbX(f80, -123984) == 16);
+    try expect(ilogbX(f80, 2398.23) == 11);
+
+    try expect(ilogbX(f80, 0x1p-1) == -1);
+    try expect(ilogbX(f80, 0x1p-127) == -127);
+    try expect(ilogbX(f80, 0x1p-1023) == -1023);
+    try expect(ilogbX(f80, 0x1p-16383) == -16383);
 }
 
 test "128" {
-    try expect(ilogb128(0.0) == fp_ilogb0);
-    try expect(ilogb128(0.5) == -1);
-    try expect(ilogb128(0.8923) == -1);
-    try expect(ilogb128(10.0) == 3);
-    try expect(ilogb128(-123984) == 16);
-    try expect(ilogb128(2398.23) == 11);
+    try expect(ilogbX(f128, 0.0) == fp_ilogb0);
+    try expect(ilogbX(f128, 0.5) == -1);
+    try expect(ilogbX(f128, 0.8923) == -1);
+    try expect(ilogbX(f128, 10.0) == 3);
+    try expect(ilogbX(f128, -123984) == 16);
+    try expect(ilogbX(f128, 2398.23) == 11);
+
+    try expect(ilogbX(f128, 0x1p-1) == -1);
+    try expect(ilogbX(f128, 0x1p-127) == -127);
+    try expect(ilogbX(f128, 0x1p-1023) == -1023);
+    try expect(ilogbX(f128, 0x1p-16383) == -16383);
+}
+
+test "16 special" {
+    try expect(ilogbX(f16, math.inf(f16)) == maxInt(i32));
+    try expect(ilogbX(f16, -math.inf(f16)) == maxInt(i32));
+    try expect(ilogbX(f16, 0.0) == minInt(i32));
+    try expect(ilogbX(f16, math.nan(f16)) == fp_ilogbnan);
 }
 
 test "32 special" {
-    try expect(ilogb32(math.inf(f32)) == maxInt(i32));
-    try expect(ilogb32(-math.inf(f32)) == maxInt(i32));
-    try expect(ilogb32(0.0) == minInt(i32));
-    try expect(ilogb32(math.nan(f32)) == maxInt(i32));
+    try expect(ilogbX(f32, math.inf(f32)) == maxInt(i32));
+    try expect(ilogbX(f32, -math.inf(f32)) == maxInt(i32));
+    try expect(ilogbX(f32, 0.0) == minInt(i32));
+    try expect(ilogbX(f32, math.nan(f32)) == fp_ilogbnan);
 }
 
 test "64 special" {
-    try expect(ilogb64(math.inf(f64)) == maxInt(i32));
-    try expect(ilogb64(-math.inf(f64)) == maxInt(i32));
-    try expect(ilogb64(0.0) == minInt(i32));
-    try expect(ilogb64(math.nan(f64)) == maxInt(i32));
+    try expect(ilogbX(f64, math.inf(f64)) == maxInt(i32));
+    try expect(ilogbX(f64, -math.inf(f64)) == maxInt(i32));
+    try expect(ilogbX(f64, 0.0) == minInt(i32));
+    try expect(ilogbX(f64, math.nan(f64)) == fp_ilogbnan);
+}
+
+test "80 special" {
+    try expect(ilogbX(f80, math.inf(f80)) == maxInt(i32));
+    try expect(ilogbX(f80, -math.inf(f80)) == maxInt(i32));
+    try expect(ilogbX(f80, 0.0) == minInt(i32));
+    try expect(ilogbX(f80, math.nan(f80)) == fp_ilogbnan);
 }
 
 test "128 special" {
-    try expect(ilogb128(math.inf(f128)) == maxInt(i32));
-    try expect(ilogb128(-math.inf(f128)) == maxInt(i32));
-    try expect(ilogb128(0.0) == minInt(i32));
-    try expect(ilogb128(math.nan(f128)) == maxInt(i32));
+    try expect(ilogbX(f128, math.inf(f128)) == maxInt(i32));
+    try expect(ilogbX(f128, -math.inf(f128)) == maxInt(i32));
+    try expect(ilogbX(f128, 0.0) == minInt(i32));
+    try expect(ilogbX(f128, math.nan(f128)) == fp_ilogbnan);
 }

@@ -1,91 +1,142 @@
-// 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);
+
+        // subnormals -> subnormals
+        try expect(ldexp(math.floatTrueMin(T), 3) == math.floatTrueMin(T) * 8);
+        try expect(ldexp(math.floatTrueMin(T) * 8, -2) == math.floatTrueMin(T) * 2);
+        try expect(ldexp(math.floatTrueMin(T) * 8, -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);
+    }
 }