math/big: fix big.Exp and document better
- always return 1 for y <= 0
- document that the sign of m is ignored
- protect against div-0 panics by treating
m == 0 the same way as m == nil
- added extra tests
Fixes #4239.
R=agl, remyoudompheng, agl
CC=golang-dev
https://golang.org/cl/6724046
diff --git a/src/pkg/math/big/nat.go b/src/pkg/math/big/nat.go
index b2d6cd9..2e5c56d 100644
--- a/src/pkg/math/big/nat.go
+++ b/src/pkg/math/big/nat.go
@@ -1227,8 +1227,8 @@
return z.norm()
}
-// If m != nil, expNN calculates x**y mod m. Otherwise it calculates x**y. It
-// reuses the storage of z if possible.
+// If m != 0 (i.e., len(m) != 0), expNN sets z to x**y mod m;
+// otherwise it sets z to x**y. The result is the value of z.
func (z nat) expNN(x, y, m nat) nat {
if alias(z, x) || alias(z, y) {
// We cannot allow in-place modification of x or y.
@@ -1240,15 +1240,15 @@
z[0] = 1
return z
}
+ // y > 0
- if m != nil {
+ if len(m) != 0 {
// We likely end up being as long as the modulus.
z = z.make(len(m))
}
z = z.set(x)
- v := y[len(y)-1]
- // It's invalid for the most significant word to be zero, therefore we
- // will find a one bit.
+
+ v := y[len(y)-1] // v > 0 because y is normalized and y > 0
shift := leadingZeros(v) + 1
v <<= shift
var q nat
@@ -1272,7 +1272,7 @@
zz, z = z, zz
}
- if m != nil {
+ if len(m) != 0 {
zz, r = zz.div(r, z, m)
zz, r, q, z = q, z, zz, r
}
@@ -1292,7 +1292,7 @@
zz, z = z, zz
}
- if m != nil {
+ if len(m) != 0 {
zz, r = zz.div(r, z, m)
zz, r, q, z = q, z, zz, r
}
