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package bigfft
import (
"fmt"
. "math/big"
"testing"
)
// parseHex reads an hex-formatted number modulo 2^bits+1.
func parseHex(s string, bits int) fermat {
z := new(Int)
z, ok := z.SetString(s, 0)
if !ok {
panic(s)
}
f := fermat(z.Bits())
for len(f)*_W <= bits {
f = append(f, 0)
}
return f
}
func compare(t *testing.T, prefix string, a, b fermat) {
var x, y Int
x.SetBits(a)
y.SetBits(b)
if x.Cmp(&y) != 0 {
t.Errorf("%s: %x != %x", prefix, &x, &y)
}
}
func TestFermatShift(t *testing.T) {
const n = 4
f := make(fermat, n+1)
for i := 0; i < n; i++ {
f[i] = Word(rnd.Int63())
}
b := NewInt(1)
b = b.Lsh(b, uint(n*_W))
b = b.Add(b, NewInt(1))
z := make(fermat, len(f)) // Test with uninitialized z.
for shift := -2048; shift < 2048; shift++ {
z.Shift(f, shift)
z2 := new(Int)
z2.SetBits(f)
if shift < 0 {
s2 := (-shift) % (2 * n * _W)
z2 = z2.Lsh(z2, uint(2*n*_W-s2))
} else {
z2 = z2.Lsh(z2, uint(shift))
}
z2 = z2.Mod(z2, b)
compare(t, fmt.Sprintf("shift %d", shift), z, z2.Bits())
}
}
func TestFermatShiftHalf(t *testing.T) {
const n = 3
f := make(fermat, n+1)
for i := 0; i < n; i++ {
f[i] = ^Word(0)
}
b := NewInt(1)
b = b.Lsh(b, uint(n*_W))
b = b.Add(b, NewInt(1))
z := make(fermat, len(f)) // Test with uninitialized z.
tmp := make(fermat, len(f))
tmp2 := make(fermat, len(f))
for shift := 0; shift < 16384; shift++ {
// Shift twice by shift/2
z.ShiftHalf(f, shift, tmp)
copy(tmp, z)
z.ShiftHalf(tmp, shift, tmp2)
z2 := new(Int)
z2 = z2.Lsh(new(Int).SetBits(f), uint(shift))
z2 = z2.Mod(z2, b)
compare(t, fmt.Sprintf("shift %d", shift), z, z2.Bits())
}
}
type test struct{ a, b, c fermat }
// addTests is a series of mod 2^256+1 tests.
var addTests = []test{
{
parseHex("0x5555555555555555555555555555555555555555555555555555555555555555", 256),
parseHex("0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaab", 256),
parseHex("0x10000000000000000000000000000000000000000000000000000000000000000", 256),
},
{
parseHex("0x5555555555555555555555555555555555555555555555555555555555555555", 256),
parseHex("0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", 256),
parseHex("0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", 256),
},
{
parseHex("0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", 256),
parseHex("0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", 256),
parseHex("0x5555555555555555555555555555555555555555555555555555555555555553", 256),
},
}
func TestFermatAdd(t *testing.T) {
for i, item := range addTests {
z := make(fermat, len(item.a))
z = z.Add(item.a, item.b)
compare(t, fmt.Sprintf("addTests[%d]", i), z, item.c)
}
}
var mulTests = []test{
{ // 3^400 = 3^200 * 3^200
parseHex("0xc21a937a76f3432ffd73d97e447606b683ecf6f6e4a7ae223c2578e26c486a03", 256),
parseHex("0xc21a937a76f3432ffd73d97e447606b683ecf6f6e4a7ae223c2578e26c486a03", 256),
parseHex("0x0e65f4d3508036eaca8faa2b8194ace009c863e44bdc040c459a7127bf8bcc62", 256),
},
{ // 2^256 * 2^256 mod (2^256+1) = 1.
parseHex("0x10000000000000000000000000000000000000000000000000000000000000000", 256),
parseHex("0x10000000000000000000000000000000000000000000000000000000000000000", 256),
parseHex("0x1", 256),
},
{ // (2^256-1) * (2^256-1) mod (2^256+1) = 4.
parseHex("0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", 256),
parseHex("0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", 256),
parseHex("0x4", 256),
},
{ // 1<<(64W) * 1<<(64W) mod (1<<64W+1) = 1
fermat{64: 1},
fermat{64: 1},
fermat{0: 1},
},
{
// Test case from issue 1. One of the squares of the Fourier
// transforms was miscomputed.
// The input number is made of 18 words, but we are working modulo 2^1280+1
parseHex("0xfffffffffffffffffffffffeffffffffffffffffffffffffffffffffffff00000000000000000000000100000000000000000000000000000000000000000000000000000000fffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff000100000000000000000000000100000000000000000000000000000000fffefffffffffffffffffffd", 1280),
parseHex("0xfffffffffffffffffffffffeffffffffffffffffffffffffffffffffffff00000000000000000000000100000000000000000000000000000000000000000000000000000000fffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff000100000000000000000000000100000000000000000000000000000000fffefffffffffffffffffffd", 1280),
parseHex("0xfffe00000003fffc0000000000000000fff40003000000000000000000060001fffffffd0001fffffffffffffffe000dfffbfffffffffffffffffffafffe0000000200000000000000000002fff60002fffffffffffffffa00060001ffffffff0000000000000000fffc0007fffe0000000000000007fff8fffdfffffffffffffffffffa00000004fffa0000fffffffffffffff600080000000000000000000a", 1280),
},
}
func TestFermatMul(t *testing.T) {
for i, item := range mulTests {
z := make(fermat, 3*len(item.a))
z = z.Mul(item.a, item.b)
compare(t, fmt.Sprintf("mulTests[%d]", i), z, item.c)
}
}
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