mirror of
https://github.com/ziglang/zig.git
synced 2024-11-27 15:42:49 +00:00
327 lines
19 KiB
Zig
327 lines
19 KiB
Zig
const std = @import("../std.zig");
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const math = std.math;
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const assert = std.debug.assert;
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const expect = std.testing.expect;
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/// Returns the next representable value after `x` in the direction of `y`.
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///
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/// Special cases:
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///
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/// - If `x == y`, `y` is returned.
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/// - For floats, if either `x` or `y` is a NaN, a NaN is returned.
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/// - For floats, if `x == 0.0` and `@abs(y) > 0.0`, the smallest subnormal number with the sign of
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/// `y` is returned.
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///
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pub fn nextAfter(comptime T: type, x: T, y: T) T {
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return switch (@typeInfo(T)) {
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.Int, .ComptimeInt => nextAfterInt(T, x, y),
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.Float => nextAfterFloat(T, x, y),
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else => @compileError("expected int or non-comptime float, found '" ++ @typeName(T) ++ "'"),
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};
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}
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fn nextAfterInt(comptime T: type, x: T, y: T) T {
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comptime assert(@typeInfo(T) == .Int or @typeInfo(T) == .ComptimeInt);
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return if (@typeInfo(T) == .Int and @bitSizeOf(T) < 2)
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// Special case for `i0`, `u0`, `i1`, and `u1`.
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y
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else if (y > x)
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x + 1
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else if (y < x)
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x - 1
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else
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y;
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}
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// Based on nextafterf/nextafterl from mingw-w64 which are both public domain.
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// <https://github.com/mingw-w64/mingw-w64/blob/e89de847dd3e05bb8e46344378ce3e124f4e7d1c/mingw-w64-crt/math/nextafterf.c>
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// <https://github.com/mingw-w64/mingw-w64/blob/e89de847dd3e05bb8e46344378ce3e124f4e7d1c/mingw-w64-crt/math/nextafterl.c>
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fn nextAfterFloat(comptime T: type, x: T, y: T) T {
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comptime assert(@typeInfo(T) == .Float);
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if (x == y) {
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// Returning `y` ensures that (0.0, -0.0) returns -0.0 and that (-0.0, 0.0) returns 0.0.
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return y;
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}
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if (math.isNan(x) or math.isNan(y)) {
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return math.nan(T);
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}
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if (x == 0.0) {
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return if (y > 0.0)
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math.floatTrueMin(T)
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else
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-math.floatTrueMin(T);
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}
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if (@bitSizeOf(T) == 80) {
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// Unlike other floats, `f80` has an explicitly stored integer bit between the fractional
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// part and the exponent and thus requires special handling. This integer bit *must* be set
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// when the value is normal, an infinity or a NaN and *should* be cleared otherwise.
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const fractional_bits_mask = (1 << math.floatFractionalBits(f80)) - 1;
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const integer_bit_mask = 1 << math.floatFractionalBits(f80);
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const exponent_bits_mask = (1 << math.floatExponentBits(f80)) - 1;
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var x_parts = math.break_f80(x);
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// Bitwise increment/decrement the fractional part while also taking care to update the
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// exponent if we overflow the fractional part. This might flip the integer bit; this is
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// intentional.
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if ((x > 0.0) == (y > x)) {
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x_parts.fraction +%= 1;
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if (x_parts.fraction & fractional_bits_mask == 0) {
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x_parts.exp += 1;
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}
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} else {
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if (x_parts.fraction & fractional_bits_mask == 0) {
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x_parts.exp -= 1;
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}
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x_parts.fraction -%= 1;
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}
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// If the new value is normal or an infinity (indicated by at least one bit in the exponent
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// being set), the integer bit might have been cleared from an overflow, so we must ensure
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// that it remains set.
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if (x_parts.exp & exponent_bits_mask != 0) {
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x_parts.fraction |= integer_bit_mask;
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}
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// Otherwise, the new value is subnormal and the integer bit will have either flipped from
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// set to cleared (if the old value was normal) or remained cleared (if the old value was
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// subnormal), both of which are the outcomes we want.
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return math.make_f80(x_parts);
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} else {
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const Bits = std.meta.Int(.unsigned, @bitSizeOf(T));
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var x_bits: Bits = @bitCast(x);
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if ((x > 0.0) == (y > x)) {
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x_bits += 1;
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} else {
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x_bits -= 1;
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}
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return @bitCast(x_bits);
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}
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}
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test "int" {
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try expect(nextAfter(i0, 0, 0) == 0);
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try expect(nextAfter(u0, 0, 0) == 0);
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try expect(nextAfter(i1, 0, 0) == 0);
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try expect(nextAfter(i1, 0, -1) == -1);
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try expect(nextAfter(i1, -1, -1) == -1);
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try expect(nextAfter(i1, -1, 0) == 0);
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try expect(nextAfter(u1, 0, 0) == 0);
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try expect(nextAfter(u1, 0, 1) == 1);
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try expect(nextAfter(u1, 1, 1) == 1);
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try expect(nextAfter(u1, 1, 0) == 0);
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inline for (.{ i8, i16, i32, i64, i128, i333 }) |T| {
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try expect(nextAfter(T, 3, 7) == 4);
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try expect(nextAfter(T, 3, -7) == 2);
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try expect(nextAfter(T, -3, -7) == -4);
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try expect(nextAfter(T, -3, 7) == -2);
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try expect(nextAfter(T, 5, 5) == 5);
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try expect(nextAfter(T, -5, -5) == -5);
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try expect(nextAfter(T, 0, 0) == 0);
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try expect(nextAfter(T, math.minInt(T), math.minInt(T)) == math.minInt(T));
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try expect(nextAfter(T, math.maxInt(T), math.maxInt(T)) == math.maxInt(T));
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}
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inline for (.{ u8, u16, u32, u64, u128, u333 }) |T| {
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try expect(nextAfter(T, 3, 7) == 4);
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try expect(nextAfter(T, 7, 3) == 6);
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try expect(nextAfter(T, 5, 5) == 5);
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try expect(nextAfter(T, 0, 0) == 0);
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try expect(nextAfter(T, math.minInt(T), math.minInt(T)) == math.minInt(T));
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try expect(nextAfter(T, math.maxInt(T), math.maxInt(T)) == math.maxInt(T));
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}
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comptime {
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try expect(nextAfter(comptime_int, 3, 7) == 4);
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try expect(nextAfter(comptime_int, 3, -7) == 2);
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try expect(nextAfter(comptime_int, -3, -7) == -4);
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try expect(nextAfter(comptime_int, -3, 7) == -2);
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try expect(nextAfter(comptime_int, 5, 5) == 5);
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try expect(nextAfter(comptime_int, -5, -5) == -5);
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try expect(nextAfter(comptime_int, 0, 0) == 0);
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try expect(nextAfter(comptime_int, math.maxInt(u512), math.maxInt(u512)) == math.maxInt(u512));
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}
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}
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test "float" {
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@setEvalBranchQuota(3000);
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// normal -> normal
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try expect(nextAfter(f16, 0x1.234p0, 2.0) == 0x1.238p0);
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try expect(nextAfter(f16, 0x1.234p0, -2.0) == 0x1.230p0);
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try expect(nextAfter(f16, 0x1.234p0, 0x1.234p0) == 0x1.234p0);
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try expect(nextAfter(f16, -0x1.234p0, -2.0) == -0x1.238p0);
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try expect(nextAfter(f16, -0x1.234p0, 2.0) == -0x1.230p0);
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try expect(nextAfter(f16, -0x1.234p0, -0x1.234p0) == -0x1.234p0);
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try expect(nextAfter(f32, 0x1.001234p0, 2.0) == 0x1.001236p0);
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try expect(nextAfter(f32, 0x1.001234p0, -2.0) == 0x1.001232p0);
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try expect(nextAfter(f32, 0x1.001234p0, 0x1.001234p0) == 0x1.001234p0);
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try expect(nextAfter(f32, -0x1.001234p0, -2.0) == -0x1.001236p0);
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try expect(nextAfter(f32, -0x1.001234p0, 2.0) == -0x1.001232p0);
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try expect(nextAfter(f32, -0x1.001234p0, -0x1.001234p0) == -0x1.001234p0);
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inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| {
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try expect(nextAfter(T64, 0x1.0000000001234p0, 2.0) == 0x1.0000000001235p0);
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try expect(nextAfter(T64, 0x1.0000000001234p0, -2.0) == 0x1.0000000001233p0);
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try expect(nextAfter(T64, 0x1.0000000001234p0, 0x1.0000000001234p0) == 0x1.0000000001234p0);
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try expect(nextAfter(T64, -0x1.0000000001234p0, -2.0) == -0x1.0000000001235p0);
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try expect(nextAfter(T64, -0x1.0000000001234p0, 2.0) == -0x1.0000000001233p0);
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try expect(nextAfter(T64, -0x1.0000000001234p0, -0x1.0000000001234p0) == -0x1.0000000001234p0);
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}
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inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| {
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try expect(nextAfter(T80, 0x1.0000000000001234p0, 2.0) == 0x1.0000000000001236p0);
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try expect(nextAfter(T80, 0x1.0000000000001234p0, -2.0) == 0x1.0000000000001232p0);
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try expect(nextAfter(T80, 0x1.0000000000001234p0, 0x1.0000000000001234p0) == 0x1.0000000000001234p0);
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try expect(nextAfter(T80, -0x1.0000000000001234p0, -2.0) == -0x1.0000000000001236p0);
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try expect(nextAfter(T80, -0x1.0000000000001234p0, 2.0) == -0x1.0000000000001232p0);
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try expect(nextAfter(T80, -0x1.0000000000001234p0, -0x1.0000000000001234p0) == -0x1.0000000000001234p0);
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}
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inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| {
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try expect(nextAfter(T128, 0x1.0000000000000000000000001234p0, 2.0) == 0x1.0000000000000000000000001235p0);
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try expect(nextAfter(T128, 0x1.0000000000000000000000001234p0, -2.0) == 0x1.0000000000000000000000001233p0);
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try expect(nextAfter(T128, 0x1.0000000000000000000000001234p0, 0x1.0000000000000000000000001234p0) == 0x1.0000000000000000000000001234p0);
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try expect(nextAfter(T128, -0x1.0000000000000000000000001234p0, -2.0) == -0x1.0000000000000000000000001235p0);
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try expect(nextAfter(T128, -0x1.0000000000000000000000001234p0, 2.0) == -0x1.0000000000000000000000001233p0);
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try expect(nextAfter(T128, -0x1.0000000000000000000000001234p0, -0x1.0000000000000000000000001234p0) == -0x1.0000000000000000000000001234p0);
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}
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// subnormal -> subnormal
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try expect(nextAfter(f16, 0x0.234p-14, 1.0) == 0x0.238p-14);
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try expect(nextAfter(f16, 0x0.234p-14, -1.0) == 0x0.230p-14);
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try expect(nextAfter(f16, 0x0.234p-14, 0x0.234p-14) == 0x0.234p-14);
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try expect(nextAfter(f16, -0x0.234p-14, -1.0) == -0x0.238p-14);
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try expect(nextAfter(f16, -0x0.234p-14, 1.0) == -0x0.230p-14);
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try expect(nextAfter(f16, -0x0.234p-14, -0x0.234p-14) == -0x0.234p-14);
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try expect(nextAfter(f32, 0x0.001234p-126, 1.0) == 0x0.001236p-126);
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try expect(nextAfter(f32, 0x0.001234p-126, -1.0) == 0x0.001232p-126);
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try expect(nextAfter(f32, 0x0.001234p-126, 0x0.001234p-126) == 0x0.001234p-126);
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try expect(nextAfter(f32, -0x0.001234p-126, -1.0) == -0x0.001236p-126);
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try expect(nextAfter(f32, -0x0.001234p-126, 1.0) == -0x0.001232p-126);
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try expect(nextAfter(f32, -0x0.001234p-126, -0x0.001234p-126) == -0x0.001234p-126);
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inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| {
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try expect(nextAfter(T64, 0x0.0000000001234p-1022, 1.0) == 0x0.0000000001235p-1022);
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try expect(nextAfter(T64, 0x0.0000000001234p-1022, -1.0) == 0x0.0000000001233p-1022);
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try expect(nextAfter(T64, 0x0.0000000001234p-1022, 0x0.0000000001234p-1022) == 0x0.0000000001234p-1022);
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try expect(nextAfter(T64, -0x0.0000000001234p-1022, -1.0) == -0x0.0000000001235p-1022);
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try expect(nextAfter(T64, -0x0.0000000001234p-1022, 1.0) == -0x0.0000000001233p-1022);
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try expect(nextAfter(T64, -0x0.0000000001234p-1022, -0x0.0000000001234p-1022) == -0x0.0000000001234p-1022);
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}
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inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| {
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try expect(nextAfter(T80, 0x0.0000000000001234p-16382, 1.0) == 0x0.0000000000001236p-16382);
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try expect(nextAfter(T80, 0x0.0000000000001234p-16382, -1.0) == 0x0.0000000000001232p-16382);
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try expect(nextAfter(T80, 0x0.0000000000001234p-16382, 0x0.0000000000001234p-16382) == 0x0.0000000000001234p-16382);
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try expect(nextAfter(T80, -0x0.0000000000001234p-16382, -1.0) == -0x0.0000000000001236p-16382);
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try expect(nextAfter(T80, -0x0.0000000000001234p-16382, 1.0) == -0x0.0000000000001232p-16382);
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try expect(nextAfter(T80, -0x0.0000000000001234p-16382, -0x0.0000000000001234p-16382) == -0x0.0000000000001234p-16382);
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}
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inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| {
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try expect(nextAfter(T128, 0x0.0000000000000000000000001234p-16382, 1.0) == 0x0.0000000000000000000000001235p-16382);
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try expect(nextAfter(T128, 0x0.0000000000000000000000001234p-16382, -1.0) == 0x0.0000000000000000000000001233p-16382);
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try expect(nextAfter(T128, 0x0.0000000000000000000000001234p-16382, 0x0.0000000000000000000000001234p-16382) == 0x0.0000000000000000000000001234p-16382);
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try expect(nextAfter(T128, -0x0.0000000000000000000000001234p-16382, -1.0) == -0x0.0000000000000000000000001235p-16382);
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try expect(nextAfter(T128, -0x0.0000000000000000000000001234p-16382, 1.0) == -0x0.0000000000000000000000001233p-16382);
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try expect(nextAfter(T128, -0x0.0000000000000000000000001234p-16382, -0x0.0000000000000000000000001234p-16382) == -0x0.0000000000000000000000001234p-16382);
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}
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// normal -> normal (change in exponent)
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try expect(nextAfter(f16, 0x1.FFCp3, math.inf(f16)) == 0x1p4);
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try expect(nextAfter(f16, 0x1p4, -math.inf(f16)) == 0x1.FFCp3);
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try expect(nextAfter(f16, -0x1.FFCp3, -math.inf(f16)) == -0x1p4);
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try expect(nextAfter(f16, -0x1p4, math.inf(f16)) == -0x1.FFCp3);
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try expect(nextAfter(f32, 0x1.FFFFFEp3, math.inf(f32)) == 0x1p4);
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try expect(nextAfter(f32, 0x1p4, -math.inf(f32)) == 0x1.FFFFFEp3);
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try expect(nextAfter(f32, -0x1.FFFFFEp3, -math.inf(f32)) == -0x1p4);
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try expect(nextAfter(f32, -0x1p4, math.inf(f32)) == -0x1.FFFFFEp3);
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inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| {
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try expect(nextAfter(T64, 0x1.FFFFFFFFFFFFFp3, math.inf(T64)) == 0x1p4);
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try expect(nextAfter(T64, 0x1p4, -math.inf(T64)) == 0x1.FFFFFFFFFFFFFp3);
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try expect(nextAfter(T64, -0x1.FFFFFFFFFFFFFp3, -math.inf(T64)) == -0x1p4);
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try expect(nextAfter(T64, -0x1p4, math.inf(T64)) == -0x1.FFFFFFFFFFFFFp3);
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}
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inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| {
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try expect(nextAfter(T80, 0x1.FFFFFFFFFFFFFFFEp3, math.inf(T80)) == 0x1p4);
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try expect(nextAfter(T80, 0x1p4, -math.inf(T80)) == 0x1.FFFFFFFFFFFFFFFEp3);
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try expect(nextAfter(T80, -0x1.FFFFFFFFFFFFFFFEp3, -math.inf(T80)) == -0x1p4);
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try expect(nextAfter(T80, -0x1p4, math.inf(T80)) == -0x1.FFFFFFFFFFFFFFFEp3);
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}
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inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| {
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try expect(nextAfter(T128, 0x1.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp3, math.inf(T128)) == 0x1p4);
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try expect(nextAfter(T128, 0x1p4, -math.inf(T128)) == 0x1.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp3);
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try expect(nextAfter(T128, -0x1.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp3, -math.inf(T128)) == -0x1p4);
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try expect(nextAfter(T128, -0x1p4, math.inf(T128)) == -0x1.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp3);
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}
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// normal -> subnormal
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try expect(nextAfter(f16, 0x1p-14, -math.inf(f16)) == 0x0.FFCp-14);
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try expect(nextAfter(f16, -0x1p-14, math.inf(f16)) == -0x0.FFCp-14);
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try expect(nextAfter(f32, 0x1p-126, -math.inf(f32)) == 0x0.FFFFFEp-126);
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try expect(nextAfter(f32, -0x1p-126, math.inf(f32)) == -0x0.FFFFFEp-126);
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inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| {
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try expect(nextAfter(T64, 0x1p-1022, -math.inf(T64)) == 0x0.FFFFFFFFFFFFFp-1022);
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try expect(nextAfter(T64, -0x1p-1022, math.inf(T64)) == -0x0.FFFFFFFFFFFFFp-1022);
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}
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inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| {
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try expect(nextAfter(T80, 0x1p-16382, -math.inf(T80)) == 0x0.FFFFFFFFFFFFFFFEp-16382);
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try expect(nextAfter(T80, -0x1p-16382, math.inf(T80)) == -0x0.FFFFFFFFFFFFFFFEp-16382);
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}
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inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| {
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try expect(nextAfter(T128, 0x1p-16382, -math.inf(T128)) == 0x0.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp-16382);
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try expect(nextAfter(T128, -0x1p-16382, math.inf(T128)) == -0x0.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp-16382);
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}
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// subnormal -> normal
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try expect(nextAfter(f16, 0x0.FFCp-14, math.inf(f16)) == 0x1p-14);
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try expect(nextAfter(f16, -0x0.FFCp-14, -math.inf(f16)) == -0x1p-14);
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try expect(nextAfter(f32, 0x0.FFFFFEp-126, math.inf(f32)) == 0x1p-126);
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try expect(nextAfter(f32, -0x0.FFFFFEp-126, -math.inf(f32)) == -0x1p-126);
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inline for (.{f64} ++ if (@bitSizeOf(c_longdouble) == 64) .{c_longdouble} else .{}) |T64| {
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try expect(nextAfter(T64, 0x0.FFFFFFFFFFFFFp-1022, math.inf(T64)) == 0x1p-1022);
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try expect(nextAfter(T64, -0x0.FFFFFFFFFFFFFp-1022, -math.inf(T64)) == -0x1p-1022);
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}
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inline for (.{f80} ++ if (@bitSizeOf(c_longdouble) == 80) .{c_longdouble} else .{}) |T80| {
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try expect(nextAfter(T80, 0x0.FFFFFFFFFFFFFFFEp-16382, math.inf(T80)) == 0x1p-16382);
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try expect(nextAfter(T80, -0x0.FFFFFFFFFFFFFFFEp-16382, -math.inf(T80)) == -0x1p-16382);
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}
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inline for (.{f128} ++ if (@bitSizeOf(c_longdouble) == 128) .{c_longdouble} else .{}) |T128| {
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|
try expect(nextAfter(T128, 0x0.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp-16382, math.inf(T128)) == 0x1p-16382);
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try expect(nextAfter(T128, -0x0.FFFFFFFFFFFFFFFFFFFFFFFFFFFFp-16382, -math.inf(T128)) == -0x1p-16382);
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|
}
|
|
|
|
// special values
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inline for (.{ f16, f32, f64, f80, f128, c_longdouble }) |T| {
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|
try expect(bitwiseEqual(T, nextAfter(T, 0.0, 0.0), 0.0));
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try expect(bitwiseEqual(T, nextAfter(T, 0.0, -0.0), -0.0));
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|
try expect(bitwiseEqual(T, nextAfter(T, -0.0, -0.0), -0.0));
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|
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));
|
|
}
|