diff --git a/lib/std/math.zig b/lib/std/math.zig index f5ee7019cd..336007be57 100644 --- a/lib/std/math.zig +++ b/lib/std/math.zig @@ -223,6 +223,7 @@ pub const isInf = @import("math/isinf.zig").isInf; pub const isPositiveInf = @import("math/isinf.zig").isPositiveInf; pub const isNegativeInf = @import("math/isinf.zig").isNegativeInf; pub const isNormal = @import("math/isnormal.zig").isNormal; +pub const nextAfter = @import("math/nextafter.zig").nextAfter; pub const signbit = @import("math/signbit.zig").signbit; pub const scalbn = @import("math/scalbn.zig").scalbn; pub const ldexp = @import("math/ldexp.zig").ldexp; @@ -345,6 +346,7 @@ test { _ = isPositiveInf; _ = isNegativeInf; _ = isNormal; + _ = nextAfter; _ = signbit; _ = scalbn; _ = ldexp; diff --git a/lib/std/math/nextafter.zig b/lib/std/math/nextafter.zig new file mode 100644 index 0000000000..3a0b2d88a5 --- /dev/null +++ b/lib/std/math/nextafter.zig @@ -0,0 +1,327 @@ +const builtin = @import("builtin"); +const std = @import("../std.zig"); +const math = std.math; +const assert = std.debug.assert; +const expect = std.testing.expect; + +/// Returns the next representable value after `x` in the direction of `y`. +/// +/// Special cases: +/// +/// - If `x == y`, `y` is returned. +/// - For floats, if either `x` or `y` is a NaN, a NaN is returned. +/// - For floats, if `x == 0.0` and `@abs(y) > 0.0`, the smallest subnormal number with the sign of +/// `y` is returned. +/// +pub fn nextAfter(comptime T: type, x: T, y: T) T { + return switch (@typeInfo(T)) { + .Int, .ComptimeInt => nextAfterInt(T, x, y), + .Float => nextAfterFloat(T, x, y), + else => @compileError("expected int or non-comptime float, found '" ++ @typeName(T) ++ "'"), + }; +} + +fn nextAfterInt(comptime T: type, x: T, y: T) T { + comptime assert(@typeInfo(T) == .Int or @typeInfo(T) == .ComptimeInt); + return if (@typeInfo(T) == .Int and @bitSizeOf(T) < 2) + // Special case for `i0`, `u0`, `i1`, and `u1`. + y + else if (y > x) + x + 1 + else if (y < x) + x - 1 + else + y; +} + +// Based on nextafterf/nextafterl from mingw-w64 which are both public domain. +// +// + +fn nextAfterFloat(comptime T: type, x: T, y: T) T { + comptime assert(@typeInfo(T) == .Float); + if (x == y) { + // Returning `y` ensures that (0.0, -0.0) returns -0.0 and that (-0.0, 0.0) returns 0.0. + return y; + } + if (math.isNan(x) or math.isNan(y)) { + return math.nan(T); + } + if (x == 0.0) { + return if (y > 0.0) + math.floatTrueMin(T) + else + -math.floatTrueMin(T); + } + if (@bitSizeOf(T) == 80) { + // Unlike other floats, `f80` has an explicitly stored integer bit between the fractional + // part and the exponent and thus requires special handling. This integer bit *must* be set + // when the value is normal, an infinity or a NaN and *should* be cleared otherwise. + + const fractional_bits_mask = (1 << math.floatFractionalBits(f80)) - 1; + const integer_bit_mask = 1 << math.floatFractionalBits(f80); + const exponent_bits_mask = (1 << math.floatExponentBits(f80)) - 1; + + var x_parts = math.break_f80(x); + + // Bitwise increment/decrement the fractional part while also taking care to update the + // exponent if we overflow the fractional part. This might flip the integer bit; this is + // intentional. + if ((x > 0.0) == (y > x)) { + x_parts.fraction +%= 1; + if (x_parts.fraction & fractional_bits_mask == 0) { + x_parts.exp += 1; + } + } else { + if (x_parts.fraction & fractional_bits_mask == 0) { + x_parts.exp -= 1; + } + x_parts.fraction -%= 1; + } + + // If the new value is normal or an infinity (indicated by at least one bit in the exponent + // being set), the integer bit might have been cleared from an overflow, so we must ensure + // that it remains set. + if (x_parts.exp & exponent_bits_mask != 0) { + x_parts.fraction |= integer_bit_mask; + } + // Otherwise, the new value is subnormal and the integer bit will have either flipped from + // set to cleared (if the old value was normal) or remained cleared (if the old value was + // subnormal), both of which are the outcomes we want. + + return math.make_f80(x_parts); + } else { + const Bits = std.meta.Int(.unsigned, @bitSizeOf(T)); + var x_bits: Bits = @bitCast(x); + if ((x > 0.0) == (y > x)) { + x_bits += 1; + } else { + x_bits -= 1; + } + return @bitCast(x_bits); + } +} + +test "math.nextAfter.int" { + try expect(nextAfter(i0, 0, 0) == 0); + try expect(nextAfter(u0, 0, 0) == 0); + try expect(nextAfter(i1, 0, 0) == 0); + try expect(nextAfter(i1, 0, -1) == -1); + try expect(nextAfter(i1, -1, -1) == -1); + try expect(nextAfter(i1, -1, 0) == 0); + try expect(nextAfter(u1, 0, 0) == 0); + try expect(nextAfter(u1, 0, 1) == 1); + try expect(nextAfter(u1, 1, 1) == 1); + try expect(nextAfter(u1, 1, 0) == 0); + inline for (.{ i8, i16, i32, i64, i128, i333 }) |T| { + try expect(nextAfter(T, 3, 7) == 4); + try expect(nextAfter(T, 3, -7) == 2); + try expect(nextAfter(T, -3, -7) == -4); + try expect(nextAfter(T, -3, 7) == -2); + try expect(nextAfter(T, 5, 5) == 5); + try expect(nextAfter(T, -5, -5) == -5); + try expect(nextAfter(T, 0, 0) == 0); + try expect(nextAfter(T, math.minInt(T), math.minInt(T)) == math.minInt(T)); + try expect(nextAfter(T, math.maxInt(T), math.maxInt(T)) == math.maxInt(T)); + } + inline for (.{ u8, u16, u32, u64, u128, u333 }) |T| { + try expect(nextAfter(T, 3, 7) == 4); + try expect(nextAfter(T, 7, 3) == 6); + try expect(nextAfter(T, 5, 5) == 5); + try expect(nextAfter(T, 0, 0) == 0); + try expect(nextAfter(T, math.minInt(T), math.minInt(T)) == math.minInt(T)); + try expect(nextAfter(T, math.maxInt(T), math.maxInt(T)) == math.maxInt(T)); + } + comptime { + try expect(nextAfter(comptime_int, 3, 7) == 4); + try expect(nextAfter(comptime_int, 3, -7) == 2); + try expect(nextAfter(comptime_int, -3, -7) == -4); + try expect(nextAfter(comptime_int, -3, 7) == -2); + try expect(nextAfter(comptime_int, 5, 5) == 5); + try expect(nextAfter(comptime_int, -5, -5) == -5); + try expect(nextAfter(comptime_int, 0, 0) == 0); + try expect(nextAfter(comptime_int, math.maxInt(u512), math.maxInt(u512)) == math.maxInt(u512)); + } +} + +test "math.nextAfter.float" { + @setEvalBranchQuota(2000); + + // normal -> normal + try expect(nextAfter(f16, 0x1.234p0, 2.0) == 0x1.238p0); + try expect(nextAfter(f16, 0x1.234p0, -2.0) == 0x1.230p0); + try expect(nextAfter(f16, 0x1.234p0, 0x1.234p0) == 0x1.234p0); + try expect(nextAfter(f16, -0x1.234p0, -2.0) == -0x1.238p0); + try expect(nextAfter(f16, -0x1.234p0, 2.0) == -0x1.230p0); + try expect(nextAfter(f16, -0x1.234p0, -0x1.234p0) == -0x1.234p0); + try expect(nextAfter(f32, 0x1.001234p0, 2.0) == 0x1.001236p0); + try expect(nextAfter(f32, 0x1.001234p0, -2.0) == 0x1.001232p0); + try expect(nextAfter(f32, 0x1.001234p0, 0x1.001234p0) == 0x1.001234p0); + try expect(nextAfter(f32, -0x1.001234p0, -2.0) == -0x1.001236p0); + try expect(nextAfter(f32, -0x1.001234p0, 2.0) == -0x1.001232p0); + try expect(nextAfter(f32, -0x1.001234p0, -0x1.001234p0) == -0x1.001234p0); + inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| { + try expect(nextAfter(T64, 0x1.0000000001234p0, 2.0) == 0x1.0000000001235p0); + try expect(nextAfter(T64, 0x1.0000000001234p0, -2.0) == 0x1.0000000001233p0); + try expect(nextAfter(T64, 0x1.0000000001234p0, 0x1.0000000001234p0) == 0x1.0000000001234p0); + try expect(nextAfter(T64, -0x1.0000000001234p0, -2.0) == -0x1.0000000001235p0); + try expect(nextAfter(T64, -0x1.0000000001234p0, 2.0) == -0x1.0000000001233p0); + try expect(nextAfter(T64, -0x1.0000000001234p0, -0x1.0000000001234p0) == -0x1.0000000001234p0); + } + inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| { + try expect(nextAfter(T80, 0x1.0000000000001234p0, 2.0) == 0x1.0000000000001236p0); + try expect(nextAfter(T80, 0x1.0000000000001234p0, -2.0) == 0x1.0000000000001232p0); + try expect(nextAfter(T80, 0x1.0000000000001234p0, 0x1.0000000000001234p0) == 0x1.0000000000001234p0); + try expect(nextAfter(T80, -0x1.0000000000001234p0, -2.0) == -0x1.0000000000001236p0); + try expect(nextAfter(T80, -0x1.0000000000001234p0, 2.0) == -0x1.0000000000001232p0); + try expect(nextAfter(T80, -0x1.0000000000001234p0, -0x1.0000000000001234p0) == -0x1.0000000000001234p0); + } + inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| { + try expect(nextAfter(T128, 0x1.0000000000000000000000001234p0, 2.0) == 0x1.0000000000000000000000001235p0); + try expect(nextAfter(T128, 0x1.0000000000000000000000001234p0, -2.0) == 0x1.0000000000000000000000001233p0); + try expect(nextAfter(T128, 0x1.0000000000000000000000001234p0, 0x1.0000000000000000000000001234p0) == 0x1.0000000000000000000000001234p0); + try expect(nextAfter(T128, -0x1.0000000000000000000000001234p0, -2.0) == -0x1.0000000000000000000000001235p0); + try expect(nextAfter(T128, -0x1.0000000000000000000000001234p0, 2.0) == -0x1.0000000000000000000000001233p0); + try expect(nextAfter(T128, -0x1.0000000000000000000000001234p0, -0x1.0000000000000000000000001234p0) == -0x1.0000000000000000000000001234p0); + } + + // subnormal -> subnormal + try expect(nextAfter(f16, 0x0.234p-14, 1.0) == 0x0.238p-14); + try expect(nextAfter(f16, 0x0.234p-14, -1.0) == 0x0.230p-14); + try expect(nextAfter(f16, 0x0.234p-14, 0x0.234p-14) == 0x0.234p-14); + try expect(nextAfter(f16, -0x0.234p-14, -1.0) == -0x0.238p-14); + try expect(nextAfter(f16, -0x0.234p-14, 1.0) == -0x0.230p-14); + try expect(nextAfter(f16, -0x0.234p-14, -0x0.234p-14) == -0x0.234p-14); + try expect(nextAfter(f32, 0x0.001234p-126, 1.0) == 0x0.001236p-126); + try expect(nextAfter(f32, 0x0.001234p-126, -1.0) == 0x0.001232p-126); + try expect(nextAfter(f32, 0x0.001234p-126, 0x0.001234p-126) == 0x0.001234p-126); + try expect(nextAfter(f32, -0x0.001234p-126, -1.0) == -0x0.001236p-126); + try expect(nextAfter(f32, -0x0.001234p-126, 1.0) == -0x0.001232p-126); + try expect(nextAfter(f32, -0x0.001234p-126, -0x0.001234p-126) == -0x0.001234p-126); + inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| { + try expect(nextAfter(T64, 0x0.0000000001234p-1022, 1.0) == 0x0.0000000001235p-1022); + try expect(nextAfter(T64, 0x0.0000000001234p-1022, -1.0) == 0x0.0000000001233p-1022); + try expect(nextAfter(T64, 0x0.0000000001234p-1022, 0x0.0000000001234p-1022) == 0x0.0000000001234p-1022); + try expect(nextAfter(T64, -0x0.0000000001234p-1022, -1.0) == -0x0.0000000001235p-1022); + try expect(nextAfter(T64, -0x0.0000000001234p-1022, 1.0) == -0x0.0000000001233p-1022); + try expect(nextAfter(T64, -0x0.0000000001234p-1022, -0x0.0000000001234p-1022) == -0x0.0000000001234p-1022); + } + inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| { + try expect(nextAfter(T80, 0x0.0000000000001234p-16382, 1.0) == 0x0.0000000000001236p-16382); + try expect(nextAfter(T80, 0x0.0000000000001234p-16382, -1.0) == 0x0.0000000000001232p-16382); + try expect(nextAfter(T80, 0x0.0000000000001234p-16382, 0x0.0000000000001234p-16382) == 0x0.0000000000001234p-16382); + try expect(nextAfter(T80, -0x0.0000000000001234p-16382, -1.0) == -0x0.0000000000001236p-16382); + try expect(nextAfter(T80, -0x0.0000000000001234p-16382, 1.0) == -0x0.0000000000001232p-16382); + try expect(nextAfter(T80, -0x0.0000000000001234p-16382, -0x0.0000000000001234p-16382) == -0x0.0000000000001234p-16382); + } + inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| { + try expect(nextAfter(T128, 0x0.0000000000000000000000001234p-16382, 1.0) == 0x0.0000000000000000000000001235p-16382); + try expect(nextAfter(T128, 0x0.0000000000000000000000001234p-16382, -1.0) == 0x0.0000000000000000000000001233p-16382); + try expect(nextAfter(T128, 0x0.0000000000000000000000001234p-16382, 0x0.0000000000000000000000001234p-16382) == 0x0.0000000000000000000000001234p-16382); + try expect(nextAfter(T128, -0x0.0000000000000000000000001234p-16382, -1.0) == -0x0.0000000000000000000000001235p-16382); + try expect(nextAfter(T128, -0x0.0000000000000000000000001234p-16382, 1.0) == -0x0.0000000000000000000000001233p-16382); + try expect(nextAfter(T128, -0x0.0000000000000000000000001234p-16382, -0x0.0000000000000000000000001234p-16382) == -0x0.0000000000000000000000001234p-16382); + } + + // normal -> normal (change in exponent) + try expect(nextAfter(f16, 0x1.FFCp3, math.inf(f16)) == 0x1p4); + try expect(nextAfter(f16, 0x1p4, -math.inf(f16)) == 0x1.FFCp3); + try expect(nextAfter(f16, -0x1.FFCp3, -math.inf(f16)) == -0x1p4); + try expect(nextAfter(f16, -0x1p4, math.inf(f16)) == -0x1.FFCp3); + try expect(nextAfter(f32, 0x1.FFFFFEp3, math.inf(f32)) == 0x1p4); + try expect(nextAfter(f32, 0x1p4, -math.inf(f32)) == 0x1.FFFFFEp3); + try expect(nextAfter(f32, -0x1.FFFFFEp3, -math.inf(f32)) == -0x1p4); + try expect(nextAfter(f32, -0x1p4, math.inf(f32)) == -0x1.FFFFFEp3); + inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| { + try expect(nextAfter(T64, 0x1.FFFFFFFFFFFFFp3, math.inf(T64)) == 0x1p4); + try expect(nextAfter(T64, 0x1p4, -math.inf(T64)) == 0x1.FFFFFFFFFFFFFp3); + try expect(nextAfter(T64, -0x1.FFFFFFFFFFFFFp3, -math.inf(T64)) == -0x1p4); + try expect(nextAfter(T64, -0x1p4, math.inf(T64)) == -0x1.FFFFFFFFFFFFFp3); + } + inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| { + try expect(nextAfter(T80, 0x1.FFFFFFFFFFFFFFFEp3, math.inf(T80)) == 0x1p4); + try expect(nextAfter(T80, 0x1p4, -math.inf(T80)) == 0x1.FFFFFFFFFFFFFFFEp3); + try expect(nextAfter(T80, -0x1.FFFFFFFFFFFFFFFEp3, -math.inf(T80)) == -0x1p4); + try expect(nextAfter(T80, -0x1p4, math.inf(T80)) == -0x1.FFFFFFFFFFFFFFFEp3); + } + inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| { + try expect(nextAfter(T128, 0x1.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp3, math.inf(T128)) == 0x1p4); + try expect(nextAfter(T128, 0x1p4, -math.inf(T128)) == 0x1.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp3); + try expect(nextAfter(T128, -0x1.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp3, -math.inf(T128)) == -0x1p4); + try expect(nextAfter(T128, -0x1p4, math.inf(T128)) == -0x1.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp3); + } + + // normal -> subnormal + try expect(nextAfter(f16, 0x1p-14, -math.inf(f16)) == 0x0.FFCp-14); + try expect(nextAfter(f16, -0x1p-14, math.inf(f16)) == -0x0.FFCp-14); + try expect(nextAfter(f32, 0x1p-126, -math.inf(f32)) == 0x0.FFFFFEp-126); + try expect(nextAfter(f32, -0x1p-126, math.inf(f32)) == -0x0.FFFFFEp-126); + inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| { + try expect(nextAfter(T64, 0x1p-1022, -math.inf(T64)) == 0x0.FFFFFFFFFFFFFp-1022); + try expect(nextAfter(T64, -0x1p-1022, math.inf(T64)) == -0x0.FFFFFFFFFFFFFp-1022); + } + inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| { + try expect(nextAfter(T80, 0x1p-16382, -math.inf(T80)) == 0x0.FFFFFFFFFFFFFFFEp-16382); + try expect(nextAfter(T80, -0x1p-16382, math.inf(T80)) == -0x0.FFFFFFFFFFFFFFFEp-16382); + } + inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| { + try expect(nextAfter(T128, 0x1p-16382, -math.inf(T128)) == 0x0.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp-16382); + try expect(nextAfter(T128, -0x1p-16382, math.inf(T128)) == -0x0.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp-16382); + } + + // subnormal -> normal + try expect(nextAfter(f16, 0x0.FFCp-14, math.inf(f16)) == 0x1p-14); + try expect(nextAfter(f16, -0x0.FFCp-14, -math.inf(f16)) == -0x1p-14); + try expect(nextAfter(f32, 0x0.FFFFFEp-126, math.inf(f32)) == 0x1p-126); + try expect(nextAfter(f32, -0x0.FFFFFEp-126, -math.inf(f32)) == -0x1p-126); + inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| { + try expect(nextAfter(T64, 0x0.FFFFFFFFFFFFFp-1022, math.inf(T64)) == 0x1p-1022); + try expect(nextAfter(T64, -0x0.FFFFFFFFFFFFFp-1022, -math.inf(T64)) == -0x1p-1022); + } + inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| { + try expect(nextAfter(T80, 0x0.FFFFFFFFFFFFFFFEp-16382, math.inf(T80)) == 0x1p-16382); + try expect(nextAfter(T80, -0x0.FFFFFFFFFFFFFFFEp-16382, -math.inf(T80)) == -0x1p-16382); + } + inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| { + try expect(nextAfter(T128, 0x0.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp-16382, math.inf(T128)) == 0x1p-16382); + try expect(nextAfter(T128, -0x0.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp-16382, -math.inf(T128)) == -0x1p-16382); + } + + // special values + inline for (.{ f16, f32, f64, f80, f128, c_longdouble }) |T| { + try expect(bitwiseEqual(T, nextAfter(T, 0.0, 0.0), 0.0)); + try expect(bitwiseEqual(T, nextAfter(T, 0.0, -0.0), -0.0)); + try expect(bitwiseEqual(T, nextAfter(T, -0.0, -0.0), -0.0)); + try expect(bitwiseEqual(T, nextAfter(T, -0.0, 0.0), 0.0)); + try expect(nextAfter(T, 0.0, math.inf(T)) == math.floatTrueMin(T)); + try expect(nextAfter(T, 0.0, -math.inf(T)) == -math.floatTrueMin(T)); + try expect(nextAfter(T, -0.0, -math.inf(T)) == -math.floatTrueMin(T)); + try expect(nextAfter(T, -0.0, math.inf(T)) == math.floatTrueMin(T)); + try expect(bitwiseEqual(T, nextAfter(T, math.floatTrueMin(T), 0.0), 0.0)); + try expect(bitwiseEqual(T, nextAfter(T, math.floatTrueMin(T), -0.0), 0.0)); + try expect(bitwiseEqual(T, nextAfter(T, math.floatTrueMin(T), -math.inf(T)), 0.0)); + try expect(bitwiseEqual(T, nextAfter(T, -math.floatTrueMin(T), -0.0), -0.0)); + try expect(bitwiseEqual(T, nextAfter(T, -math.floatTrueMin(T), 0.0), -0.0)); + try expect(bitwiseEqual(T, nextAfter(T, -math.floatTrueMin(T), math.inf(T)), -0.0)); + try expect(nextAfter(T, math.inf(T), math.inf(T)) == math.inf(T)); + try expect(nextAfter(T, math.inf(T), -math.inf(T)) == math.floatMax(T)); + try expect(nextAfter(T, math.floatMax(T), math.inf(T)) == math.inf(T)); + try expect(nextAfter(T, -math.inf(T), -math.inf(T)) == -math.inf(T)); + try expect(nextAfter(T, -math.inf(T), math.inf(T)) == -math.floatMax(T)); + try expect(nextAfter(T, -math.floatMax(T), -math.inf(T)) == -math.inf(T)); + try expect(math.isNan(nextAfter(T, 1.0, math.nan(T)))); + try expect(math.isNan(nextAfter(T, math.nan(T), 1.0))); + try expect(math.isNan(nextAfter(T, math.nan(T), math.nan(T)))); + try expect(math.isNan(nextAfter(T, math.inf(T), math.nan(T)))); + try expect(math.isNan(nextAfter(T, -math.inf(T), math.nan(T)))); + try expect(math.isNan(nextAfter(T, math.nan(T), math.inf(T)))); + try expect(math.isNan(nextAfter(T, math.nan(T), -math.inf(T)))); + } +} + +/// Helps ensure that 0.0 doesn't compare equal to -0.0. +fn bitwiseEqual(comptime T: type, x: T, y: T) bool { + comptime assert(@typeInfo(T) == .Float); + const Bits = std.meta.Int(.unsigned, @bitSizeOf(T)); + return @as(Bits, @bitCast(x)) == @as(Bits, @bitCast(y)); +}