Use shift instead division (to support i2) and avoid overflow of temp results.

Author: two-horned

lib/std/math/egcd.zig

@@ -41,18 +41,19 @@ pub fn egcd(a: anytype, b: anytype) ExtendedGreatestCommonDivisor(@TypeOf(a, b))
     const toinv = @shrExact(other, @intCast(shift));
     const ctrl = @shrExact(odd, @intCast(shift)); // Invariant: |s|, |t|, |ctrl| < |MIN_OF(S)|
     const half_ctrl = 1 + @shrExact(ctrl - 1, 1);
+    const abs_ctrl = @abs(ctrl);
 
     var s: S = std.math.sign(toinv);
     var t: S = 0;
 
     var x = @abs(toinv);
-    var y = @abs(ctrl);
+    var y = abs_ctrl;
 
     {
         const xz = @ctz(x);
         x = @shrExact(x, @intCast(xz));
         for (0..xz) |_| {
-            const half_s = @divFloor(s, 2);
+            const half_s = s >> 1;
             if (s & 1 == 0)
                 s = half_s
             else
@@ -78,12 +79,14 @@ pub fn egcd(a: anytype, b: anytype) ExtendedGreatestCommonDivisor(@TypeOf(a, b))
         }
         x = @shrExact(x, @intCast(xz));
         for (0..xz) |_| {
-            const half_s = @divFloor(s, 2);
+            const half_s = s >> 1;
             if (s & 1 == 0)
                 s = half_s
             else
                 s = half_s + half_ctrl;
         }
+
+        if (s < 0) s = @intCast(abs_ctrl - @abs(s));
     }
 
     // Using integer widening is only a temporary solution.
@@ -98,6 +101,24 @@ pub fn egcd(a: anytype, b: anytype) ExtendedGreatestCommonDivisor(@TypeOf(a, b))
 }
 
 test {
+    {
+        const a: i2 = 0;
+        const b: i2 = 1;
+        const r = egcd(a, b);
+        const g = r.gcd;
+        const s: i2 = r.bezout_coeff_1;
+        const t: i2 = r.bezout_coeff_2;
+        try std.testing.expect(s * a + t * b == g);
+    }
+    {
+        const a: i8 = -128;
+        const b: i8 = 127;
+        const r = egcd(a, b);
+        const g = r.gcd;
+        const s: i16 = r.bezout_coeff_1;
+        const t: i16 = r.bezout_coeff_2;
+        try std.testing.expect(s * a + t * b == g);
+    }
     {
         const a: i16 = -32768;
         const b: i16 = -32768;