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Code Editor : magic_test.go
// 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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