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|
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, .comptime_int => 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) == .comptime_int);
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.
// <https://github.com/mingw-w64/mingw-w64/blob/e89de847dd3e05bb8e46344378ce3e124f4e7d1c/mingw-w64-crt/math/nextafterf.c>
// <https://github.com/mingw-w64/mingw-w64/blob/e89de847dd3e05bb8e46344378ce3e124f4e7d1c/mingw-w64-crt/math/nextafterl.c>
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.F80.fromFloat(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 x_parts.toFloat();
} 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 "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 "float" {
@setEvalBranchQuota(4000);
// 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));
}
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