authorgravatar for 77922942+expikr@users.noreply.github.comexpikr <77922942+expikr@users.noreply.github.com> 2024-05-30 03:58:05-06:00
committergravatar for andrew@ziglang.orgAndrew Kelley <andrew@ziglang.org> 2024-06-06 10:44:28-07:00
log0aeeff0d9434b37bb870e192091a563fc2a8dfce
tree81fc075f2c853f9850583257facc9968e081d644
parentce9d2eda731acf76fece8d720945ef63c36facba

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

3 files changed, 113 insertions(+), 144 deletions(-)

lib/std/math.zig+1
......@@ -52,6 +52,7 @@ pub const floatTrueMin = @import("math/float.zig").floatTrueMin;
5252pub const floatMin = @import("math/float.zig").floatMin;
5353pub const floatMax = @import("math/float.zig").floatMax;
5454pub const floatEps = @import("math/float.zig").floatEps;
55pub const floatEpsAt = @import("math/float.zig").floatEpsAt;
5556pub const inf = @import("math/float.zig").inf;
5657pub const nan = @import("math/float.zig").nan;
5758pub const snan = @import("math/float.zig").snan;
lib/std/math/float.zig+13
......@@ -94,6 +94,19 @@ pub inline fn floatEps(comptime T: type) T {
9494 return reconstructFloat(T, -floatFractionalBits(T), mantissaOne(T));
9595}
9696
97/// Returns the local epsilon of floating point type T.
98pub inline fn floatEpsAt(comptime T: type, x: T) T {
99 switch (@typeInfo(T)) {
100 .Float => |F| {
101 const U: type = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = F.bits } });
102 const u: U = @bitCast(x);
103 const y: T = @bitCast(u ^ 1);
104 return @abs(x - y);
105 },
106 else => @compileError("floatEpsAt only supports floats"),
107 }
108}
109
97110/// Returns the value inf for floating point type T.
98111pub inline fn inf(comptime T: type) T {
99112 return reconstructFloat(T, floatExponentMax(T) + 1, mantissaOne(T));
lib/std/math/hypot.zig+99-144
......@@ -1,13 +1,14 @@
1// Ported from musl, which is licensed under the MIT license:
2// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
3//
4// https://git.musl-libc.org/cgit/musl/tree/src/math/hypotf.c
5// https://git.musl-libc.org/cgit/musl/tree/src/math/hypot.c
6
71const std = @import("../std.zig");
82const math = std.math;
93const expect = std.testing.expect;
10const maxInt = std.math.maxInt;
4const isNan = math.isNan;
5const isInf = math.isInf;
6const inf = math.inf;
7const nan = math.nan;
8const floatEpsAt = math.floatEpsAt;
9const floatEps = math.floatEps;
10const floatMin = math.floatMin;
11const floatMax = math.floatMax;
1112
1213/// Returns sqrt(x * x + y * y), avoiding unnecessary overflow and underflow.
1314///
......@@ -15,162 +16,116 @@ const maxInt = std.math.maxInt;
1516///
1617/// | x | y | hypot |
1718/// |-------|-------|-------|
18/// | +inf | num | +inf |
19/// | num | +-inf | +inf |
20/// | nan | any | nan |
21/// | any | nan | nan |
19/// | +-inf | any | +inf |
20/// | any | +-inf | +inf |
21/// | nan | fin | nan |
22/// | fin | nan | nan |
2223pub fn hypot(x: anytype, y: anytype) @TypeOf(x, y) {
2324 const T = @TypeOf(x, y);
24 return switch (T) {
25 f32 => hypot32(x, y),
26 f64 => hypot64(x, y),
25 switch (@typeInfo(T)) {
26 .Float => {},
27 .ComptimeFloat => return @sqrt(x * x + y * y),
2728 else => @compileError("hypot not implemented for " ++ @typeName(T)),
28 };
29}
30
31fn hypot32(x: f32, y: f32) f32 {
32 var ux = @as(u32, @bitCast(x));
33 var uy = @as(u32, @bitCast(y));
34
35 ux &= maxInt(u32) >> 1;
36 uy &= maxInt(u32) >> 1;
37 if (ux < uy) {
38 const tmp = ux;
39 ux = uy;
40 uy = tmp;
4129 }
42
43 var xx = @as(f32, @bitCast(ux));
44 var yy = @as(f32, @bitCast(uy));
45 if (uy == 0xFF << 23) {
46 return yy;
47 }
48 if (ux >= 0xFF << 23 or uy == 0 or ux - uy >= (25 << 23)) {
49 return xx + yy;
50 }
51
52 var z: f32 = 1.0;
53 if (ux >= (0x7F + 60) << 23) {
54 z = 0x1.0p90;
55 xx *= 0x1.0p-90;
56 yy *= 0x1.0p-90;
57 } else if (uy < (0x7F - 60) << 23) {
58 z = 0x1.0p-90;
59 xx *= 0x1.0p-90;
60 yy *= 0x1.0p-90;
30 const lower = @sqrt(floatMin(T));
31 const upper = @sqrt(floatMax(T) / 2);
32 const incre = @sqrt(floatEps(T) / 2);
33 const scale = floatEpsAt(T, incre);
34 const hypfn = if (emulateFma(T)) hypotUnfused else hypotFused;
35 var major: T = x;
36 var minor: T = y;
37 if (isInf(major) or isInf(minor)) return inf(T);
38 if (isNan(major) or isNan(minor)) return nan(T);
39 if (T == f16) return @floatCast(@sqrt(@mulAdd(f32, x, x, @as(f32, y) * y)));
40 if (T == f32) return @floatCast(@sqrt(@mulAdd(f64, x, x, @as(f64, y) * y)));
41 major = @abs(major);
42 minor = @abs(minor);
43 if (minor > major) {
44 const tempo = major;
45 major = minor;
46 minor = tempo;
6147 }
62
63 return z * @sqrt(@as(f32, @floatCast(@as(f64, x) * x + @as(f64, y) * y)));
48 if (major * incre >= minor) return major;
49 if (major > upper) return hypfn(T, major * scale, minor * scale) / scale;
50 if (minor < lower) return hypfn(T, major / scale, minor / scale) * scale;
51 return hypfn(T, major, minor);
6452}
6553
66fn sq(hi: *f64, lo: *f64, x: f64) void {
67 const split: f64 = 0x1.0p27 + 1.0;
68 const xc = x * split;
69 const xh = x - xc + xc;
70 const xl = x - xh;
71 hi.* = x * x;
72 lo.* = xh * xh - hi.* + 2 * xh * xl + xl * xl;
54inline fn emulateFma(comptime T: type) bool {
55 // If @mulAdd lowers to the software implementation,
56 // hypotUnfused should be used in place of hypotFused.
57 // This takes an educated guess, but ideally we should
58 // properly detect at comptime when that fallback will
59 // occur.
60 return (T == f128 or T == f80);
7361}
7462
75fn hypot64(x: f64, y: f64) f64 {
76 var ux = @as(u64, @bitCast(x));
77 var uy = @as(u64, @bitCast(y));
78
79 ux &= maxInt(u64) >> 1;
80 uy &= maxInt(u64) >> 1;
81 if (ux < uy) {
82 const tmp = ux;
83 ux = uy;
84 uy = tmp;
85 }
86
87 const ex = ux >> 52;
88 const ey = uy >> 52;
89 var xx = @as(f64, @bitCast(ux));
90 var yy = @as(f64, @bitCast(uy));
91
92 // hypot(inf, nan) == inf
93 if (ey == 0x7FF) {
94 return yy;
95 }
96 if (ex == 0x7FF or uy == 0) {
97 return xx;
98 }
99
100 // hypot(x, y) ~= x + y * y / x / 2 with inexact for small y/x
101 if (ex - ey > 64) {
102 return xx + yy;
103 }
63inline fn hypotFused(comptime F: type, x: F, y: F) F {
64 const r = @sqrt(@mulAdd(F, x, x, y * y));
65 const rr = r * r;
66 const xx = x * x;
67 const z = @mulAdd(F, -y, y, rr - xx) + @mulAdd(F, r, r, -rr) - @mulAdd(F, x, x, -xx);
68 return r - z / (2 * r);
69}
10470
105 var z: f64 = 1;
106 if (ex > 0x3FF + 510) {
107 z = 0x1.0p700;
108 xx *= 0x1.0p-700;
109 yy *= 0x1.0p-700;
110 } else if (ey < 0x3FF - 450) {
111 z = 0x1.0p-700;
112 xx *= 0x1.0p700;
113 yy *= 0x1.0p700;
71inline fn hypotUnfused(comptime F: type, x: F, y: F) F {
72 const r = @sqrt(x * x + y * y);
73 if (r <= 2 * y) { // 30deg or steeper
74 const dx = r - y;
75 const z = x * (2 * dx - x) + (dx - 2 * (x - y)) * dx;
76 return r - z / (2 * r);
77 } else { // shallower than 30 deg
78 const dy = r - x;
79 const z = 2 * dy * (x - 2 * y) + (4 * dy - y) * y + dy * dy;
80 return r - z / (2 * r);
11481 }
115
116 var hx: f64 = undefined;
117 var lx: f64 = undefined;
118 var hy: f64 = undefined;
119 var ly: f64 = undefined;
120
121 sq(&hx, &lx, x);
122 sq(&hy, &ly, y);
123
124 return z * @sqrt(ly + lx + hy + hx);
12582}
12683
84const hypot_test_cases = .{
85 .{ 0.0, -1.2, 1.2 },
86 .{ 0.2, -0.34, 0.3944616584663203993612799816649560759946493601889826495362 },
87 .{ 0.8923, 2.636890, 2.7837722899152509525110650481670176852603253522923737962880 },
88 .{ 1.5, 5.25, 5.4600824169603887033229768686452745953332522619323580787836 },
89 .{ 37.45, 159.835, 164.16372840856167640478217141034363907565754072954443805164 },
90 .{ 89.123, 382.028905, 392.28687638576315875933966414927490685367196874260165618371 },
91 .{ 123123.234375, 529428.707813, 543556.88524707706887251269205923830745438413088753096759371 },
92};
93
12794test hypot {
128 const x32: f32 = 0.0;
129 const y32: f32 = -1.2;
130 const x64: f64 = 0.0;
131 const y64: f64 = -1.2;
132 try expect(hypot(x32, y32) == hypot32(0.0, -1.2));
133 try expect(hypot(x64, y64) == hypot64(0.0, -1.2));
95 try expect(hypot(0.3, 0.4) == 0.5);
13496}
13597
136test hypot32 {
137 const epsilon = 0.000001;
138
139 try expect(math.approxEqAbs(f32, hypot32(0.0, -1.2), 1.2, epsilon));
140 try expect(math.approxEqAbs(f32, hypot32(0.2, -0.34), 0.394462, epsilon));
141 try expect(math.approxEqAbs(f32, hypot32(0.8923, 2.636890), 2.783772, epsilon));
142 try expect(math.approxEqAbs(f32, hypot32(1.5, 5.25), 5.460083, epsilon));
143 try expect(math.approxEqAbs(f32, hypot32(37.45, 159.835), 164.163742, epsilon));
144 try expect(math.approxEqAbs(f32, hypot32(89.123, 382.028905), 392.286865, epsilon));
145 try expect(math.approxEqAbs(f32, hypot32(123123.234375, 529428.707813), 543556.875, epsilon));
98test "hypot.correct" {
99 inline for (.{ f16, f32, f64, f128 }) |T| {
100 inline for (hypot_test_cases) |v| {
101 const a: T, const b: T, const c: T = v;
102 try expect(math.approxEqRel(T, hypot(a, b), c, @sqrt(floatEps(T))));
103 }
104 }
146105}
147106
148test hypot64 {
149 const epsilon = 0.000001;
150
151 try expect(math.approxEqAbs(f64, hypot64(0.0, -1.2), 1.2, epsilon));
152 try expect(math.approxEqAbs(f64, hypot64(0.2, -0.34), 0.394462, epsilon));
153 try expect(math.approxEqAbs(f64, hypot64(0.8923, 2.636890), 2.783772, epsilon));
154 try expect(math.approxEqAbs(f64, hypot64(1.5, 5.25), 5.460082, epsilon));
155 try expect(math.approxEqAbs(f64, hypot64(37.45, 159.835), 164.163728, epsilon));
156 try expect(math.approxEqAbs(f64, hypot64(89.123, 382.028905), 392.286876, epsilon));
157 try expect(math.approxEqAbs(f64, hypot64(123123.234375, 529428.707813), 543556.885247, epsilon));
107test "hypot.precise" {
108 inline for (.{ f16, f32, f64 }) |T| { // f128 seems to be 5 ulp
109 inline for (hypot_test_cases) |v| {
110 const a: T, const b: T, const c: T = v;
111 try expect(math.approxEqRel(T, hypot(a, b), c, floatEps(T)));
112 }
113 }
158114}
159115
160test "hypot32.special" {
161 try expect(math.isPositiveInf(hypot32(math.inf(f32), 0.0)));
162 try expect(math.isPositiveInf(hypot32(-math.inf(f32), 0.0)));
163 try expect(math.isPositiveInf(hypot32(0.0, math.inf(f32))));
164 try expect(math.isPositiveInf(hypot32(0.0, -math.inf(f32))));
165 try expect(math.isNan(hypot32(math.nan(f32), 0.0)));
166 try expect(math.isNan(hypot32(0.0, math.nan(f32))));
167}
116test "hypot.special" {
117 inline for (.{ f16, f32, f64, f128 }) |T| {
118 try expect(math.isNan(hypot(nan(T), 0.0)));
119 try expect(math.isNan(hypot(0.0, nan(T))));
120
121 try expect(math.isPositiveInf(hypot(inf(T), 0.0)));
122 try expect(math.isPositiveInf(hypot(0.0, inf(T))));
123 try expect(math.isPositiveInf(hypot(inf(T), nan(T))));
124 try expect(math.isPositiveInf(hypot(nan(T), inf(T))));
168125
169test "hypot64.special" {
170 try expect(math.isPositiveInf(hypot64(math.inf(f64), 0.0)));
171 try expect(math.isPositiveInf(hypot64(-math.inf(f64), 0.0)));
172 try expect(math.isPositiveInf(hypot64(0.0, math.inf(f64))));
173 try expect(math.isPositiveInf(hypot64(0.0, -math.inf(f64))));
174 try expect(math.isNan(hypot64(math.nan(f64), 0.0)));
175 try expect(math.isNan(hypot64(0.0, math.nan(f64))));
126 try expect(math.isPositiveInf(hypot(-inf(T), 0.0)));
127 try expect(math.isPositiveInf(hypot(0.0, -inf(T))));
128 try expect(math.isPositiveInf(hypot(-inf(T), nan(T))));
129 try expect(math.isPositiveInf(hypot(nan(T), -inf(T))));
130 }
176131}