use @assume_effects :terminates_locally on bezout, similarly to `…

…gcdx`

- also flip output order to align with `gcdx`'s

.vendor/SmithNormalForm/src/bezout.jl

@@ -4,30 +4,30 @@ Calculates Bézout coefficients.
 This is analogous to `gcdx`, and solves the same problem, but does not necessarily return
 identical solutions.
 """
-function bezout(a::R, b::R) where {R}
+Base.@assume_effects :terminates_locally function bezout(a::R, b::R) where {R}
     rev = a < b
     x, y = rev ? (a,b) : (b,a)
 
     s0, s1 = oneunit(R), zero(R)
     t0, t1 = zero(R), oneunit(R)
 
-    while y != zero(R)
-        q = div(x, y)
-        x, y = y, x - y * q
+    while !iszero(y)
+        q, r = divrem(x, y)
+        x, y = y, r
         s0, s1 = s1, s0 - q * s1
         t0, t1 = t1, t0 - q * t1
     end
 
     s, t = rev ? (s0, t0) : (t0, s0)
     g = x
 
-    if g == a
+    if g == a # differs from `gcdx` here (also in `rev` clauses above)
         s = one(R)
         t = zero(R)
     elseif g == -a
         s = -one(R)
         t = zero(R)
     end
 
-    return s, t, g
+    return g, s, t
 end

.vendor/SmithNormalForm/src/snf.jl

@@ -84,7 +84,7 @@ function rowpivot(U::AbstractArray{R,2},
         (iszero(b) || i == k) && continue
         a = D[i,j]
 
-        s, t, g = bezout(a, b)
+        g, s, t = bezout(a, b)
         x = divide(a, g)
         y = divide(b, g)
 
@@ -103,7 +103,7 @@ function colpivot(V::AbstractArray{R,2},
         (iszero(b) || j == k) && continue
         a = D[i,j]
 
-        s, t, g = bezout(a, b)
+        g, s, t = bezout(a, b)
         x = divide(a, g)
         y = divide(b, g)
 

.vendor/SmithNormalForm/test/runtests.jl

@@ -7,12 +7,12 @@ using SmithNormalForm
     a = 12
     b = 42
 
-    s,t,g = SmithNormalForm.bezout(a,b)
+    g,s,t = SmithNormalForm.bezout(a,b)
     @test s*a + t*b == g
     g,s,t = gcdx(a,b)
     @test s*a + t*b == g
 
-    s,t,g = SmithNormalForm.bezout(b,a)
+    g,s,t = SmithNormalForm.bezout(b,a)
     @test s*b + t*a == g
     g,s,t = gcdx(b,a)
     @test s*b + t*a == g