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math.hypot: fix incorrect over/underflow behavior (#19472)
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expikr
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@ -52,6 +52,7 @@ pub const floatTrueMin = @import("math/float.zig").floatTrueMin;
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pub const floatMin = @import("math/float.zig").floatMin;
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pub const floatMax = @import("math/float.zig").floatMax;
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pub const floatEps = @import("math/float.zig").floatEps;
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pub const floatEpsAt = @import("math/float.zig").floatEpsAt;
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pub const inf = @import("math/float.zig").inf;
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pub const nan = @import("math/float.zig").nan;
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pub const snan = @import("math/float.zig").snan;
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@ -94,6 +94,19 @@ pub inline fn floatEps(comptime T: type) T {
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return reconstructFloat(T, -floatFractionalBits(T), mantissaOne(T));
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}
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/// Returns the local epsilon of floating point type T.
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pub inline fn floatEpsAt(comptime T: type, x: T) T {
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switch (@typeInfo(T)) {
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.Float => |F| {
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const U: type = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = F.bits } });
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const u: U = @bitCast(x);
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const y: T = @bitCast(u ^ 1);
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return @abs(x - y);
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},
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else => @compileError("floatEpsAt only supports floats"),
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}
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}
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/// Returns the value inf for floating point type T.
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pub inline fn inf(comptime T: type) T {
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return reconstructFloat(T, floatExponentMax(T) + 1, mantissaOne(T));
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@ -1,13 +1,14 @@
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// Ported from musl, which is licensed under the MIT license:
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// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
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//
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// https://git.musl-libc.org/cgit/musl/tree/src/math/hypotf.c
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// https://git.musl-libc.org/cgit/musl/tree/src/math/hypot.c
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const std = @import("../std.zig");
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const math = std.math;
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const expect = std.testing.expect;
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const maxInt = std.math.maxInt;
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const isNan = math.isNan;
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const isInf = math.isInf;
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const inf = math.inf;
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const nan = math.nan;
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const floatEpsAt = math.floatEpsAt;
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const floatEps = math.floatEps;
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const floatMin = math.floatMin;
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const floatMax = math.floatMax;
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/// Returns sqrt(x * x + y * y), avoiding unnecessary overflow and underflow.
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///
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@ -15,162 +16,116 @@ const maxInt = std.math.maxInt;
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///
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/// | x | y | hypot |
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/// |-------|-------|-------|
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/// | +inf | num | +inf |
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/// | num | +-inf | +inf |
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/// | nan | any | nan |
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/// | any | nan | nan |
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/// | +-inf | any | +inf |
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/// | any | +-inf | +inf |
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/// | nan | fin | nan |
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/// | fin | nan | nan |
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pub fn hypot(x: anytype, y: anytype) @TypeOf(x, y) {
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const T = @TypeOf(x, y);
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return switch (T) {
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f32 => hypot32(x, y),
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f64 => hypot64(x, y),
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switch (@typeInfo(T)) {
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.Float => {},
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.ComptimeFloat => return @sqrt(x * x + y * y),
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else => @compileError("hypot not implemented for " ++ @typeName(T)),
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};
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}
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const lower = @sqrt(floatMin(T));
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const upper = @sqrt(floatMax(T) / 2);
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const incre = @sqrt(floatEps(T) / 2);
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const scale = floatEpsAt(T, incre);
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const hypfn = if (emulateFma(T)) hypotUnfused else hypotFused;
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var major: T = x;
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var minor: T = y;
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if (isInf(major) or isInf(minor)) return inf(T);
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if (isNan(major) or isNan(minor)) return nan(T);
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if (T == f16) return @floatCast(@sqrt(@mulAdd(f32, x, x, @as(f32, y) * y)));
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if (T == f32) return @floatCast(@sqrt(@mulAdd(f64, x, x, @as(f64, y) * y)));
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major = @abs(major);
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minor = @abs(minor);
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if (minor > major) {
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const tempo = major;
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major = minor;
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minor = tempo;
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}
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if (major * incre >= minor) return major;
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if (major > upper) return hypfn(T, major * scale, minor * scale) / scale;
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if (minor < lower) return hypfn(T, major / scale, minor / scale) * scale;
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return hypfn(T, major, minor);
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}
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fn hypot32(x: f32, y: f32) f32 {
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var ux = @as(u32, @bitCast(x));
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var uy = @as(u32, @bitCast(y));
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ux &= maxInt(u32) >> 1;
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uy &= maxInt(u32) >> 1;
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if (ux < uy) {
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const tmp = ux;
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ux = uy;
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uy = tmp;
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}
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var xx = @as(f32, @bitCast(ux));
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var yy = @as(f32, @bitCast(uy));
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if (uy == 0xFF << 23) {
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return yy;
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}
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if (ux >= 0xFF << 23 or uy == 0 or ux - uy >= (25 << 23)) {
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return xx + yy;
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}
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var z: f32 = 1.0;
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if (ux >= (0x7F + 60) << 23) {
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z = 0x1.0p90;
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xx *= 0x1.0p-90;
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yy *= 0x1.0p-90;
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} else if (uy < (0x7F - 60) << 23) {
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z = 0x1.0p-90;
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xx *= 0x1.0p-90;
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yy *= 0x1.0p-90;
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}
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return z * @sqrt(@as(f32, @floatCast(@as(f64, x) * x + @as(f64, y) * y)));
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inline fn emulateFma(comptime T: type) bool {
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// If @mulAdd lowers to the software implementation,
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// hypotUnfused should be used in place of hypotFused.
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// This takes an educated guess, but ideally we should
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// properly detect at comptime when that fallback will
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// occur.
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return (T == f128 or T == f80);
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}
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fn sq(hi: *f64, lo: *f64, x: f64) void {
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const split: f64 = 0x1.0p27 + 1.0;
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const xc = x * split;
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const xh = x - xc + xc;
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const xl = x - xh;
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hi.* = x * x;
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lo.* = xh * xh - hi.* + 2 * xh * xl + xl * xl;
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inline fn hypotFused(comptime F: type, x: F, y: F) F {
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const r = @sqrt(@mulAdd(F, x, x, y * y));
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const rr = r * r;
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const xx = x * x;
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const z = @mulAdd(F, -y, y, rr - xx) + @mulAdd(F, r, r, -rr) - @mulAdd(F, x, x, -xx);
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return r - z / (2 * r);
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}
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fn hypot64(x: f64, y: f64) f64 {
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var ux = @as(u64, @bitCast(x));
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var uy = @as(u64, @bitCast(y));
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ux &= maxInt(u64) >> 1;
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uy &= maxInt(u64) >> 1;
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if (ux < uy) {
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const tmp = ux;
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ux = uy;
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uy = tmp;
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inline fn hypotUnfused(comptime F: type, x: F, y: F) F {
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const r = @sqrt(x * x + y * y);
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if (r <= 2 * y) { // 30deg or steeper
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const dx = r - y;
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const z = x * (2 * dx - x) + (dx - 2 * (x - y)) * dx;
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return r - z / (2 * r);
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} else { // shallower than 30 deg
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const dy = r - x;
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const z = 2 * dy * (x - 2 * y) + (4 * dy - y) * y + dy * dy;
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return r - z / (2 * r);
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}
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const ex = ux >> 52;
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const ey = uy >> 52;
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var xx = @as(f64, @bitCast(ux));
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var yy = @as(f64, @bitCast(uy));
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// hypot(inf, nan) == inf
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if (ey == 0x7FF) {
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return yy;
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}
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if (ex == 0x7FF or uy == 0) {
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return xx;
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}
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// hypot(x, y) ~= x + y * y / x / 2 with inexact for small y/x
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if (ex - ey > 64) {
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return xx + yy;
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}
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var z: f64 = 1;
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if (ex > 0x3FF + 510) {
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z = 0x1.0p700;
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xx *= 0x1.0p-700;
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yy *= 0x1.0p-700;
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} else if (ey < 0x3FF - 450) {
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z = 0x1.0p-700;
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xx *= 0x1.0p700;
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yy *= 0x1.0p700;
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}
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var hx: f64 = undefined;
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var lx: f64 = undefined;
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var hy: f64 = undefined;
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var ly: f64 = undefined;
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sq(&hx, &lx, x);
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sq(&hy, &ly, y);
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return z * @sqrt(ly + lx + hy + hx);
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}
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const hypot_test_cases = .{
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.{ 0.0, -1.2, 1.2 },
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.{ 0.2, -0.34, 0.3944616584663203993612799816649560759946493601889826495362 },
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.{ 0.8923, 2.636890, 2.7837722899152509525110650481670176852603253522923737962880 },
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.{ 1.5, 5.25, 5.4600824169603887033229768686452745953332522619323580787836 },
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.{ 37.45, 159.835, 164.16372840856167640478217141034363907565754072954443805164 },
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.{ 89.123, 382.028905, 392.28687638576315875933966414927490685367196874260165618371 },
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.{ 123123.234375, 529428.707813, 543556.88524707706887251269205923830745438413088753096759371 },
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};
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test hypot {
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const x32: f32 = 0.0;
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const y32: f32 = -1.2;
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const x64: f64 = 0.0;
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const y64: f64 = -1.2;
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try expect(hypot(x32, y32) == hypot32(0.0, -1.2));
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try expect(hypot(x64, y64) == hypot64(0.0, -1.2));
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try expect(hypot(0.3, 0.4) == 0.5);
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}
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test hypot32 {
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const epsilon = 0.000001;
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try expect(math.approxEqAbs(f32, hypot32(0.0, -1.2), 1.2, epsilon));
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try expect(math.approxEqAbs(f32, hypot32(0.2, -0.34), 0.394462, epsilon));
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try expect(math.approxEqAbs(f32, hypot32(0.8923, 2.636890), 2.783772, epsilon));
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try expect(math.approxEqAbs(f32, hypot32(1.5, 5.25), 5.460083, epsilon));
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try expect(math.approxEqAbs(f32, hypot32(37.45, 159.835), 164.163742, epsilon));
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try expect(math.approxEqAbs(f32, hypot32(89.123, 382.028905), 392.286865, epsilon));
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try expect(math.approxEqAbs(f32, hypot32(123123.234375, 529428.707813), 543556.875, epsilon));
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test "hypot.correct" {
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inline for (.{ f16, f32, f64, f128 }) |T| {
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inline for (hypot_test_cases) |v| {
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const a: T, const b: T, const c: T = v;
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try expect(math.approxEqRel(T, hypot(a, b), c, @sqrt(floatEps(T))));
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}
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}
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}
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test hypot64 {
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const epsilon = 0.000001;
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try expect(math.approxEqAbs(f64, hypot64(0.0, -1.2), 1.2, epsilon));
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try expect(math.approxEqAbs(f64, hypot64(0.2, -0.34), 0.394462, epsilon));
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try expect(math.approxEqAbs(f64, hypot64(0.8923, 2.636890), 2.783772, epsilon));
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try expect(math.approxEqAbs(f64, hypot64(1.5, 5.25), 5.460082, epsilon));
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try expect(math.approxEqAbs(f64, hypot64(37.45, 159.835), 164.163728, epsilon));
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try expect(math.approxEqAbs(f64, hypot64(89.123, 382.028905), 392.286876, epsilon));
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try expect(math.approxEqAbs(f64, hypot64(123123.234375, 529428.707813), 543556.885247, epsilon));
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test "hypot.precise" {
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inline for (.{ f16, f32, f64 }) |T| { // f128 seems to be 5 ulp
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inline for (hypot_test_cases) |v| {
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const a: T, const b: T, const c: T = v;
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try expect(math.approxEqRel(T, hypot(a, b), c, floatEps(T)));
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}
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}
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}
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test "hypot32.special" {
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try expect(math.isPositiveInf(hypot32(math.inf(f32), 0.0)));
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try expect(math.isPositiveInf(hypot32(-math.inf(f32), 0.0)));
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try expect(math.isPositiveInf(hypot32(0.0, math.inf(f32))));
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try expect(math.isPositiveInf(hypot32(0.0, -math.inf(f32))));
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try expect(math.isNan(hypot32(math.nan(f32), 0.0)));
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try expect(math.isNan(hypot32(0.0, math.nan(f32))));
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}
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test "hypot.special" {
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inline for (.{ f16, f32, f64, f128 }) |T| {
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try expect(math.isNan(hypot(nan(T), 0.0)));
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try expect(math.isNan(hypot(0.0, nan(T))));
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test "hypot64.special" {
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try expect(math.isPositiveInf(hypot64(math.inf(f64), 0.0)));
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try expect(math.isPositiveInf(hypot64(-math.inf(f64), 0.0)));
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try expect(math.isPositiveInf(hypot64(0.0, math.inf(f64))));
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try expect(math.isPositiveInf(hypot64(0.0, -math.inf(f64))));
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try expect(math.isNan(hypot64(math.nan(f64), 0.0)));
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try expect(math.isNan(hypot64(0.0, math.nan(f64))));
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try expect(math.isPositiveInf(hypot(inf(T), 0.0)));
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try expect(math.isPositiveInf(hypot(0.0, inf(T))));
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try expect(math.isPositiveInf(hypot(inf(T), nan(T))));
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try expect(math.isPositiveInf(hypot(nan(T), inf(T))));
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try expect(math.isPositiveInf(hypot(-inf(T), 0.0)));
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try expect(math.isPositiveInf(hypot(0.0, -inf(T))));
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try expect(math.isPositiveInf(hypot(-inf(T), nan(T))));
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try expect(math.isPositiveInf(hypot(nan(T), -inf(T))));
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}
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}
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