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math.hypot: fix incorrect over/underflow behavior (#19472)

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expikr 2024-05-30 03:58:05 -06:00 committed by GitHub
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3 changed files with 114 additions and 145 deletions
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1
lib/std/math.zig
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@ -52,6 +52,7 @@ pub const floatTrueMin = @import("math/float.zig").floatTrueMin;
pub const floatMin = @import("math/float.zig").floatMin; pub const floatMin = @import("math/float.zig").floatMin;
pub const floatMax = @import("math/float.zig").floatMax; pub const floatMax = @import("math/float.zig").floatMax;
pub const floatEps = @import("math/float.zig").floatEps; pub const floatEps = @import("math/float.zig").floatEps;
pub const floatEpsAt = @import("math/float.zig").floatEpsAt;
pub const inf = @import("math/float.zig").inf; pub const inf = @import("math/float.zig").inf;
pub const nan = @import("math/float.zig").nan; pub const nan = @import("math/float.zig").nan;
pub const snan = @import("math/float.zig").snan; pub const snan = @import("math/float.zig").snan;

13
lib/std/math/float.zig
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@ -94,6 +94,19 @@ pub inline fn floatEps(comptime T: type) T {
return reconstructFloat(T, -floatFractionalBits(T), mantissaOne(T)); return reconstructFloat(T, -floatFractionalBits(T), mantissaOne(T));
} }
/// Returns the local epsilon of floating point type T.
pub inline fn floatEpsAt(comptime T: type, x: T) T {
switch (@typeInfo(T)) {
.Float => |F| {
const U: type = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = F.bits } });
const u: U = @bitCast(x);
const y: T = @bitCast(u ^ 1);
return @abs(x - y);
},
else => @compileError("floatEpsAt only supports floats"),
}
}
/// Returns the value inf for floating point type T. /// Returns the value inf for floating point type T.
pub inline fn inf(comptime T: type) T { pub inline fn inf(comptime T: type) T {
return reconstructFloat(T, floatExponentMax(T) + 1, mantissaOne(T)); return reconstructFloat(T, floatExponentMax(T) + 1, mantissaOne(T));

245
lib/std/math/hypot.zig
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@ -1,13 +1,14 @@
// Ported from musl, which is licensed under the MIT license:
// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
//
// https://git.musl-libc.org/cgit/musl/tree/src/math/hypotf.c
// https://git.musl-libc.org/cgit/musl/tree/src/math/hypot.c
const std = @import("../std.zig"); const std = @import("../std.zig");
const math = std.math; const math = std.math;
const expect = std.testing.expect; const expect = std.testing.expect;
const maxInt = std.math.maxInt; const isNan = math.isNan;
const isInf = math.isInf;
const inf = math.inf;
const nan = math.nan;
const floatEpsAt = math.floatEpsAt;
const floatEps = math.floatEps;
const floatMin = math.floatMin;
const floatMax = math.floatMax;
/// Returns sqrt(x * x + y * y), avoiding unnecessary overflow and underflow. /// Returns sqrt(x * x + y * y), avoiding unnecessary overflow and underflow.
/// ///
@ -15,162 +16,116 @@ const maxInt = std.math.maxInt;
/// ///
/// | x | y | hypot | /// | x | y | hypot |
/// |-------|-------|-------| /// |-------|-------|-------|
/// | +inf | num | +inf | /// | +-inf | any | +inf |
/// | num | +-inf | +inf | /// | any | +-inf | +inf |
/// | nan | any | nan | /// | nan | fin | nan |
/// | any | nan | nan | /// | fin | nan | nan |
pub fn hypot(x: anytype, y: anytype) @TypeOf(x, y) { pub fn hypot(x: anytype, y: anytype) @TypeOf(x, y) {
const T = @TypeOf(x, y); const T = @TypeOf(x, y);
return switch (T) { switch (@typeInfo(T)) {
f32 => hypot32(x, y), .Float => {},
f64 => hypot64(x, y), .ComptimeFloat => return @sqrt(x * x + y * y),
else => @compileError("hypot not implemented for " ++ @typeName(T)), else => @compileError("hypot not implemented for " ++ @typeName(T)),
}; }
const lower = @sqrt(floatMin(T));
const upper = @sqrt(floatMax(T) / 2);
const incre = @sqrt(floatEps(T) / 2);
const scale = floatEpsAt(T, incre);
const hypfn = if (emulateFma(T)) hypotUnfused else hypotFused;
var major: T = x;
var minor: T = y;
if (isInf(major) or isInf(minor)) return inf(T);
if (isNan(major) or isNan(minor)) return nan(T);
if (T == f16) return @floatCast(@sqrt(@mulAdd(f32, x, x, @as(f32, y) * y)));
if (T == f32) return @floatCast(@sqrt(@mulAdd(f64, x, x, @as(f64, y) * y)));
major = @abs(major);
minor = @abs(minor);
if (minor > major) {
const tempo = major;
major = minor;
minor = tempo;
}
if (major * incre >= minor) return major;
if (major > upper) return hypfn(T, major * scale, minor * scale) / scale;
if (minor < lower) return hypfn(T, major / scale, minor / scale) * scale;
return hypfn(T, major, minor);
} }
fn hypot32(x: f32, y: f32) f32 { inline fn emulateFma(comptime T: type) bool {
var ux = @as(u32, @bitCast(x)); // If @mulAdd lowers to the software implementation,
var uy = @as(u32, @bitCast(y)); // hypotUnfused should be used in place of hypotFused.
// This takes an educated guess, but ideally we should
ux &= maxInt(u32) >> 1; // properly detect at comptime when that fallback will
uy &= maxInt(u32) >> 1; // occur.
if (ux < uy) { return (T == f128 or T == f80);
const tmp = ux;
ux = uy;
uy = tmp;
}
var xx = @as(f32, @bitCast(ux));
var yy = @as(f32, @bitCast(uy));
if (uy == 0xFF << 23) {
return yy;
}
if (ux >= 0xFF << 23 or uy == 0 or ux - uy >= (25 << 23)) {
return xx + yy;
}
var z: f32 = 1.0;
if (ux >= (0x7F + 60) << 23) {
z = 0x1.0p90;
xx *= 0x1.0p-90;
yy *= 0x1.0p-90;
} else if (uy < (0x7F - 60) << 23) {
z = 0x1.0p-90;
xx *= 0x1.0p-90;
yy *= 0x1.0p-90;
}
return z * @sqrt(@as(f32, @floatCast(@as(f64, x) * x + @as(f64, y) * y)));
} }
fn sq(hi: *f64, lo: *f64, x: f64) void { inline fn hypotFused(comptime F: type, x: F, y: F) F {
const split: f64 = 0x1.0p27 + 1.0; const r = @sqrt(@mulAdd(F, x, x, y * y));
const xc = x * split; const rr = r * r;
const xh = x - xc + xc; const xx = x * x;
const xl = x - xh; const z = @mulAdd(F, -y, y, rr - xx) + @mulAdd(F, r, r, -rr) - @mulAdd(F, x, x, -xx);
hi.* = x * x; return r - z / (2 * r);
lo.* = xh * xh - hi.* + 2 * xh * xl + xl * xl;
} }
fn hypot64(x: f64, y: f64) f64 { inline fn hypotUnfused(comptime F: type, x: F, y: F) F {
var ux = @as(u64, @bitCast(x)); const r = @sqrt(x * x + y * y);
var uy = @as(u64, @bitCast(y)); if (r <= 2 * y) { // 30deg or steeper
const dx = r - y;
ux &= maxInt(u64) >> 1; const z = x * (2 * dx - x) + (dx - 2 * (x - y)) * dx;
uy &= maxInt(u64) >> 1; return r - z / (2 * r);
if (ux < uy) { } else { // shallower than 30 deg
const tmp = ux; const dy = r - x;
ux = uy; const z = 2 * dy * (x - 2 * y) + (4 * dy - y) * y + dy * dy;
uy = tmp; return r - z / (2 * r);
} }
const ex = ux >> 52;
const ey = uy >> 52;
var xx = @as(f64, @bitCast(ux));
var yy = @as(f64, @bitCast(uy));
// hypot(inf, nan) == inf
if (ey == 0x7FF) {
return yy;
}
if (ex == 0x7FF or uy == 0) {
return xx;
}
// hypot(x, y) ~= x + y * y / x / 2 with inexact for small y/x
if (ex - ey > 64) {
return xx + yy;
}
var z: f64 = 1;
if (ex > 0x3FF + 510) {
z = 0x1.0p700;
xx *= 0x1.0p-700;
yy *= 0x1.0p-700;
} else if (ey < 0x3FF - 450) {
z = 0x1.0p-700;
xx *= 0x1.0p700;
yy *= 0x1.0p700;
}
var hx: f64 = undefined;
var lx: f64 = undefined;
var hy: f64 = undefined;
var ly: f64 = undefined;
sq(&hx, &lx, x);
sq(&hy, &ly, y);
return z * @sqrt(ly + lx + hy + hx);
} }
const hypot_test_cases = .{
.{ 0.0, -1.2, 1.2 },
.{ 0.2, -0.34, 0.3944616584663203993612799816649560759946493601889826495362 },
.{ 0.8923, 2.636890, 2.7837722899152509525110650481670176852603253522923737962880 },
.{ 1.5, 5.25, 5.4600824169603887033229768686452745953332522619323580787836 },
.{ 37.45, 159.835, 164.16372840856167640478217141034363907565754072954443805164 },
.{ 89.123, 382.028905, 392.28687638576315875933966414927490685367196874260165618371 },
.{ 123123.234375, 529428.707813, 543556.88524707706887251269205923830745438413088753096759371 },
};
test hypot { test hypot {
const x32: f32 = 0.0; try expect(hypot(0.3, 0.4) == 0.5);
const y32: f32 = -1.2;
const x64: f64 = 0.0;
const y64: f64 = -1.2;
try expect(hypot(x32, y32) == hypot32(0.0, -1.2));
try expect(hypot(x64, y64) == hypot64(0.0, -1.2));
} }
test hypot32 { test "hypot.correct" {
const epsilon = 0.000001; inline for (.{ f16, f32, f64, f128 }) |T| {
inline for (hypot_test_cases) |v| {
try expect(math.approxEqAbs(f32, hypot32(0.0, -1.2), 1.2, epsilon)); const a: T, const b: T, const c: T = v;
try expect(math.approxEqAbs(f32, hypot32(0.2, -0.34), 0.394462, epsilon)); try expect(math.approxEqRel(T, hypot(a, b), c, @sqrt(floatEps(T))));
try expect(math.approxEqAbs(f32, hypot32(0.8923, 2.636890), 2.783772, epsilon)); }
try expect(math.approxEqAbs(f32, hypot32(1.5, 5.25), 5.460083, epsilon)); }
try expect(math.approxEqAbs(f32, hypot32(37.45, 159.835), 164.163742, epsilon));
try expect(math.approxEqAbs(f32, hypot32(89.123, 382.028905), 392.286865, epsilon));
try expect(math.approxEqAbs(f32, hypot32(123123.234375, 529428.707813), 543556.875, epsilon));
} }
test hypot64 { test "hypot.precise" {
const epsilon = 0.000001; inline for (.{ f16, f32, f64 }) |T| { // f128 seems to be 5 ulp
inline for (hypot_test_cases) |v| {
try expect(math.approxEqAbs(f64, hypot64(0.0, -1.2), 1.2, epsilon)); const a: T, const b: T, const c: T = v;
try expect(math.approxEqAbs(f64, hypot64(0.2, -0.34), 0.394462, epsilon)); try expect(math.approxEqRel(T, hypot(a, b), c, floatEps(T)));
try expect(math.approxEqAbs(f64, hypot64(0.8923, 2.636890), 2.783772, epsilon)); }
try expect(math.approxEqAbs(f64, hypot64(1.5, 5.25), 5.460082, epsilon)); }
try expect(math.approxEqAbs(f64, hypot64(37.45, 159.835), 164.163728, epsilon));
try expect(math.approxEqAbs(f64, hypot64(89.123, 382.028905), 392.286876, epsilon));
try expect(math.approxEqAbs(f64, hypot64(123123.234375, 529428.707813), 543556.885247, epsilon));
} }
test "hypot32.special" { test "hypot.special" {
try expect(math.isPositiveInf(hypot32(math.inf(f32), 0.0))); inline for (.{ f16, f32, f64, f128 }) |T| {
try expect(math.isPositiveInf(hypot32(-math.inf(f32), 0.0))); try expect(math.isNan(hypot(nan(T), 0.0)));
try expect(math.isPositiveInf(hypot32(0.0, math.inf(f32)))); try expect(math.isNan(hypot(0.0, nan(T))));
try expect(math.isPositiveInf(hypot32(0.0, -math.inf(f32))));
try expect(math.isNan(hypot32(math.nan(f32), 0.0)));
try expect(math.isNan(hypot32(0.0, math.nan(f32))));
}
test "hypot64.special" { try expect(math.isPositiveInf(hypot(inf(T), 0.0)));
try expect(math.isPositiveInf(hypot64(math.inf(f64), 0.0))); try expect(math.isPositiveInf(hypot(0.0, inf(T))));
try expect(math.isPositiveInf(hypot64(-math.inf(f64), 0.0))); try expect(math.isPositiveInf(hypot(inf(T), nan(T))));
try expect(math.isPositiveInf(hypot64(0.0, math.inf(f64)))); try expect(math.isPositiveInf(hypot(nan(T), inf(T))));
try expect(math.isPositiveInf(hypot64(0.0, -math.inf(f64))));
try expect(math.isNan(hypot64(math.nan(f64), 0.0))); try expect(math.isPositiveInf(hypot(-inf(T), 0.0)));
try expect(math.isNan(hypot64(0.0, math.nan(f64)))); try expect(math.isPositiveInf(hypot(0.0, -inf(T))));
try expect(math.isPositiveInf(hypot(-inf(T), nan(T))));
try expect(math.isPositiveInf(hypot(nan(T), -inf(T))));
}
} }