// Copyright 2017 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package ssa
import (
"math/big"
"testing"
)
func TestMagicExhaustive8(t *testing.T) {
testMagicExhaustive(t, 8)
}
func TestMagicExhaustive8U(t *testing.T) {
testMagicExhaustiveU(t, 8)
}
func TestMagicExhaustive16(t *testing.T) {
if testing.Short() {
t.Skip("slow test; skipping")
}
testMagicExhaustive(t, 16)
}
func TestMagicExhaustive16U(t *testing.T) {
if testing.Short() {
t.Skip("slow test; skipping")
}
testMagicExhaustiveU(t, 16)
}
// exhaustive test of magic for n bits
func testMagicExhaustive(t *testing.T, n uint) {
min := -int64(1) << (n - 1)
max := int64(1) << (n - 1)
for c := int64(1); c < max; c++ {
if !smagicOK(n, int64(c)) {
continue
}
m := int64(smagic(n, c).m)
s := smagic(n, c).s
for i := min; i < max; i++ {
want := i / c
got := (i * m) >> (n + uint(s))
if i < 0 {
got++
}
if want != got {
t.Errorf("signed magic wrong for %d / %d: got %d, want %d (m=%d,s=%d)\n", i, c, got, want, m, s)
}
}
}
}
func testMagicExhaustiveU(t *testing.T, n uint) {
max := uint64(1) << n
for c := uint64(1); c < max; c++ {
if !umagicOK(n, int64(c)) {
continue
}
m := umagic(n, int64(c)).m
s := umagic(n, int64(c)).s
for i := uint64(0); i < max; i++ {
want := i / c
got := (i * (max + m)) >> (n + uint(s))
if want != got {
t.Errorf("unsigned magic wrong for %d / %d: got %d, want %d (m=%d,s=%d)\n", i, c, got, want, m, s)
}
}
}
}
func TestMagicUnsigned(t *testing.T) {
One := new(big.Int).SetUint64(1)
for _, n := range [...]uint{8, 16, 32, 64} {
TwoN := new(big.Int).Lsh(One, n)
Max := new(big.Int).Sub(TwoN, One)
for _, c := range [...]uint64{
3,
5,
6,
7,
9,
10,
11,
12,
13,
14,
15,
17,
1<<8 - 1,
1<<8 + 1,
1<<16 - 1,
1<<16 + 1,
1<<32 - 1,
1<<32 + 1,
1<<64 - 1,
} {
if c>>n != 0 {
continue // not appropriate for the given n.
}
if !umagicOK(n, int64(c)) {
t.Errorf("expected n=%d c=%d to pass\n", n, c)
}
m := umagic(n, int64(c)).m
s := umagic(n, int64(c)).s
C := new(big.Int).SetUint64(c)
M := new(big.Int).SetUint64(m)
M.Add(M, TwoN)
// Find largest multiple of c.
Mul := new(big.Int).Div(Max, C)
Mul.Mul(Mul, C)
mul := Mul.Uint64()
// Try some input values, mostly around multiples of c.
for _, x := range [...]uint64{0, 1,
c - 1, c, c + 1,
2*c - 1, 2 * c, 2*c + 1,
mul - 1, mul, mul + 1,
uint64(1)<<n - 1,
} {
X := new(big.Int).SetUint64(x)
if X.Cmp(Max) > 0 {
continue
}
Want := new(big.Int).Quo(X, C)
Got := new(big.Int).Mul(X, M)
Got.Rsh(Got, n+uint(s))
if Want.Cmp(Got) != 0 {
t.Errorf("umagic for %d/%d n=%d doesn't work, got=%s, want %s\n", x, c, n, Got, Want)
}
}
}
}
}
func TestMagicSigned(t *testing.T) {
One := new(big.Int).SetInt64(1)
for _, n := range [...]uint{8, 16, 32, 64} {
TwoNMinusOne := new(big.Int).Lsh(One, n-1)
Max := new(big.Int).Sub(TwoNMinusOne, One)
Min := new(big.Int).Neg(TwoNMinusOne)
for _, c := range [...]int64{
3,
5,
6,
7,
9,
10,
11,
12,
13,
14,
15,
17,
1<<7 - 1,
1<<7 + 1,
1<<15 - 1,
1<<15 + 1,
1<<31 - 1,
1<<31 + 1,
1<<63 - 1,
} {
if c>>(n-1) != 0 {
continue // not appropriate for the given n.
}
if !smagicOK(n, int64(c)) {
t.Errorf("expected n=%d c=%d to pass\n", n, c)
}
m := smagic(n, int64(c)).m
s := smagic(n, int64(c)).s
C := new(big.Int).SetInt64(c)
M := new(big.Int).SetUint64(m)
// Find largest multiple of c.
Mul := new(big.Int).Div(Max, C)
Mul.Mul(Mul, C)
mul := Mul.Int64()
// Try some input values, mostly around multiples of c.
for _, x := range [...]int64{
-1, 1,
-c - 1, -c, -c + 1, c - 1, c, c + 1,
-2*c - 1, -2 * c, -2*c + 1, 2*c - 1, 2 * c, 2*c + 1,
-mul - 1, -mul, -mul + 1, mul - 1, mul, mul + 1,
int64(1)<<(n-1) - 1, -int64(1) << (n - 1),
} {
X := new(big.Int).SetInt64(x)
if X.Cmp(Min) < 0 || X.Cmp(Max) > 0 {
continue
}
Want := new(big.Int).Quo(X, C)
Got := new(big.Int).Mul(X, M)
Got.Rsh(Got, n+uint(s))
if x < 0 {
Got.Add(Got, One)
}
if Want.Cmp(Got) != 0 {
t.Errorf("smagic for %d/%d n=%d doesn't work, got=%s, want %s\n", x, c, n, Got, Want)
}
}
}
}
}
func testDivisibleExhaustiveU(t *testing.T, n uint) {
maxU := uint64(1) << n
for c := uint64(1); c < maxU; c++ {
if !udivisibleOK(n, int64(c)) {
continue
}
k := udivisible(n, int64(c)).k
m := udivisible(n, int64(c)).m
max := udivisible(n, int64(c)).max
mask := ^uint64(0) >> (64 - n)
for i := uint64(0); i < maxU; i++ {
want := i%c == 0
mul := (i * m) & mask
rot := (mul>>uint(k) | mul<<(n-uint(k))) & mask
got := rot <= max
if want != got {
t.Errorf("unsigned divisible wrong for %d %% %d == 0: got %v, want %v (k=%d,m=%d,max=%d)\n", i, c, got, want, k, m, max)
}
}
}
}
func TestDivisibleExhaustive8U(t *testing.T) {
testDivisibleExhaustiveU(t, 8)
}
func TestDivisibleExhaustive16U(t *testing.T) {
if testing.Short() {
t.Skip("slow test; skipping")
}
testDivisibleExhaustiveU(t, 16)
}
func TestDivisibleUnsigned(t *testing.T) {
One := new(big.Int).SetUint64(1)
for _, n := range [...]uint{8, 16, 32, 64} {
TwoN := new(big.Int).Lsh(One, n)
Max := new(big.Int).Sub(TwoN, One)
for _, c := range [...]uint64{
3,
5,
6,
7,
9,
10,
11,
12,
13,
14,
15,
17,
1<<8 - 1,
1<<8 + 1,
1<<16 - 1,
1<<16 + 1,
1<<32 - 1,
1<<32 + 1,
1<<64 - 1,
} {
if c>>n != 0 {
continue // c too large for the given n.
}
if !udivisibleOK(n, int64(c)) {
t.Errorf("expected n=%d c=%d to pass\n", n, c)
}
k := udivisible(n, int64(c)).k
m := udivisible(n, int64(c)).m
max := udivisible(n, int64(c)).max
mask := ^uint64(0) >> (64 - n)
C := new(big.Int).SetUint64(c)
// Find largest multiple of c.
Mul := new(big.Int).Div(Max, C)
Mul.Mul(Mul, C)
mul := Mul.Uint64()
// Try some input values, mostly around multiples of c.
for _, x := range [...]uint64{0, 1,
c - 1, c, c + 1,
2*c - 1, 2 * c, 2*c + 1,
mul - 1, mul, mul + 1,
uint64(1)<<n - 1,
} {
X := new(big.Int).SetUint64(x)
if X.Cmp(Max) > 0 {
continue
}
want := x%c == 0
mul := (x * m) & mask
rot := (mul>>uint(k) | mul<<(n-uint(k))) & mask
got := rot <= max
if want != got {
t.Errorf("unsigned divisible wrong for %d %% %d == 0: got %v, want %v (k=%d,m=%d,max=%d)\n", x, c, got, want, k, m, max)
}
}
}
}
}
func testDivisibleExhaustive(t *testing.T, n uint) {
minI := -int64(1) << (n - 1)
maxI := int64(1) << (n - 1)
for c := int64(1); c < maxI; c++ {
if !sdivisibleOK(n, int64(c)) {
continue
}
k := sdivisible(n, int64(c)).k
m := sdivisible(n, int64(c)).m
a := sdivisible(n, int64(c)).a
max := sdivisible(n, int64(c)).max
mask := ^uint64(0) >> (64 - n)
for i := minI; i < maxI; i++ {
want := i%c == 0
mul := (uint64(i)*m + a) & mask
rot := (mul>>uint(k) | mul<<(n-uint(k))) & mask
got := rot <= max
if want != got {
t.Errorf("signed divisible wrong for %d %% %d == 0: got %v, want %v (k=%d,m=%d,a=%d,max=%d)\n", i, c, got, want, k, m, a, max)
}
}
}
}
func TestDivisibleExhaustive8(t *testing.T) {
testDivisibleExhaustive(t, 8)
}
func TestDivisibleExhaustive16(t *testing.T) {
if testing.Short() {
t.Skip("slow test; skipping")
}
testDivisibleExhaustive(t, 16)
}
func TestDivisibleSigned(t *testing.T) {
One := new(big.Int).SetInt64(1)
for _, n := range [...]uint{8, 16, 32, 64} {
TwoNMinusOne := new(big.Int).Lsh(One, n-1)
Max := new(big.Int).Sub(TwoNMinusOne, One)
Min := new(big.Int).Neg(TwoNMinusOne)
for _, c := range [...]int64{
3,
5,
6,
7,
9,
10,
11,
12,
13,
14,
15,
17,
1<<7 - 1,
1<<7 + 1,
1<<15 - 1,
1<<15 + 1,
1<<31 - 1,
1<<31 + 1,
1<<63 - 1,
} {
if c>>(n-1) != 0 {
continue // not appropriate for the given n.
}
if !sdivisibleOK(n, int64(c)) {
t.Errorf("expected n=%d c=%d to pass\n", n, c)
}
k := sdivisible(n, int64(c)).k
m := sdivisible(n, int64(c)).m
a := sdivisible(n, int64(c)).a
max := sdivisible(n, int64(c)).max
mask := ^uint64(0) >> (64 - n)
C := new(big.Int).SetInt64(c)
// Find largest multiple of c.
Mul := new(big.Int).Div(Max, C)
Mul.Mul(Mul, C)
mul := Mul.Int64()
// Try some input values, mostly around multiples of c.
for _, x := range [...]int64{
-1, 1,
-c - 1, -c, -c + 1, c - 1, c, c + 1,
-2*c - 1, -2 * c, -2*c + 1, 2*c - 1, 2 * c, 2*c + 1,
-mul - 1, -mul, -mul + 1, mul - 1, mul, mul + 1,
int64(1)<<(n-1) - 1, -int64(1) << (n - 1),
} {
X := new(big.Int).SetInt64(x)
if X.Cmp(Min) < 0 || X.Cmp(Max) > 0 {
continue
}
want := x%c == 0
mul := (uint64(x)*m + a) & mask
rot := (mul>>uint(k) | mul<<(n-uint(k))) & mask
got := rot <= max
if want != got {
t.Errorf("signed divisible wrong for %d %% %d == 0: got %v, want %v (k=%d,m=%d,a=%d,max=%d)\n", x, c, got, want, k, m, a, max)
}
}
}
}
}
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