math/big: Allow non-prime modulus for ModInverse
The inverse is defined whenever the element and the
modulus are relatively prime. The code already handles
this situation, but the spec does not.
Test that it does indeed work.
Fixes #8875
LGTM=agl
R=agl
CC=golang-codereviews
https://golang.org/cl/155010043
diff --git a/src/math/big/int_test.go b/src/math/big/int_test.go
index ec05fbb..6070cf3 100644
--- a/src/math/big/int_test.go
+++ b/src/math/big/int_test.go
@@ -1448,24 +1448,40 @@
var modInverseTests = []struct {
element string
- prime string
+ modulus string
}{
- {"1", "7"},
- {"1", "13"},
+ {"1234567", "458948883992"},
{"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
}
func TestModInverse(t *testing.T) {
- var element, prime Int
+ var element, modulus, gcd, inverse Int
one := NewInt(1)
for i, test := range modInverseTests {
(&element).SetString(test.element, 10)
- (&prime).SetString(test.prime, 10)
- inverse := new(Int).ModInverse(&element, &prime)
- inverse.Mul(inverse, &element)
- inverse.Mod(inverse, &prime)
- if inverse.Cmp(one) != 0 {
- t.Errorf("#%d: failed (e·e^(-1)=%s)", i, inverse)
+ (&modulus).SetString(test.modulus, 10)
+ (&inverse).ModInverse(&element, &modulus)
+ (&inverse).Mul(&inverse, &element)
+ (&inverse).Mod(&inverse, &modulus)
+ if (&inverse).Cmp(one) != 0 {
+ t.Errorf("#%d: failed (e·e^(-1)=%s)", i, &inverse)
+ }
+ }
+ // exhaustive test for small values
+ for n := 2; n < 100; n++ {
+ (&modulus).SetInt64(int64(n))
+ for x := 1; x < n; x++ {
+ (&element).SetInt64(int64(x))
+ (&gcd).GCD(nil, nil, &element, &modulus)
+ if (&gcd).Cmp(one) != 0 {
+ continue
+ }
+ (&inverse).ModInverse(&element, &modulus)
+ (&inverse).Mul(&inverse, &element)
+ (&inverse).Mod(&inverse, &modulus)
+ if (&inverse).Cmp(one) != 0 {
+ t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse)
+ }
}
}
}
