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Diffstat (limited to 'libgo/go/math/big/int_test.go')
-rw-r--r-- | libgo/go/math/big/int_test.go | 1403 |
1 files changed, 1403 insertions, 0 deletions
diff --git a/libgo/go/math/big/int_test.go b/libgo/go/math/big/int_test.go new file mode 100644 index 0000000..163c662 --- /dev/null +++ b/libgo/go/math/big/int_test.go @@ -0,0 +1,1403 @@ +// Copyright 2009 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 big + +import ( + "bytes" + "encoding/gob" + "encoding/hex" + "fmt" + "testing" + "testing/quick" +) + +func isNormalized(x *Int) bool { + if len(x.abs) == 0 { + return !x.neg + } + // len(x.abs) > 0 + return x.abs[len(x.abs)-1] != 0 +} + +type funZZ func(z, x, y *Int) *Int +type argZZ struct { + z, x, y *Int +} + +var sumZZ = []argZZ{ + {NewInt(0), NewInt(0), NewInt(0)}, + {NewInt(1), NewInt(1), NewInt(0)}, + {NewInt(1111111110), NewInt(123456789), NewInt(987654321)}, + {NewInt(-1), NewInt(-1), NewInt(0)}, + {NewInt(864197532), NewInt(-123456789), NewInt(987654321)}, + {NewInt(-1111111110), NewInt(-123456789), NewInt(-987654321)}, +} + +var prodZZ = []argZZ{ + {NewInt(0), NewInt(0), NewInt(0)}, + {NewInt(0), NewInt(1), NewInt(0)}, + {NewInt(1), NewInt(1), NewInt(1)}, + {NewInt(-991 * 991), NewInt(991), NewInt(-991)}, + // TODO(gri) add larger products +} + +func TestSignZ(t *testing.T) { + var zero Int + for _, a := range sumZZ { + s := a.z.Sign() + e := a.z.Cmp(&zero) + if s != e { + t.Errorf("got %d; want %d for z = %v", s, e, a.z) + } + } +} + +func TestSetZ(t *testing.T) { + for _, a := range sumZZ { + var z Int + z.Set(a.z) + if !isNormalized(&z) { + t.Errorf("%v is not normalized", z) + } + if (&z).Cmp(a.z) != 0 { + t.Errorf("got z = %v; want %v", z, a.z) + } + } +} + +func TestAbsZ(t *testing.T) { + var zero Int + for _, a := range sumZZ { + var z Int + z.Abs(a.z) + var e Int + e.Set(a.z) + if e.Cmp(&zero) < 0 { + e.Sub(&zero, &e) + } + if z.Cmp(&e) != 0 { + t.Errorf("got z = %v; want %v", z, e) + } + } +} + +func testFunZZ(t *testing.T, msg string, f funZZ, a argZZ) { + var z Int + f(&z, a.x, a.y) + if !isNormalized(&z) { + t.Errorf("%s%v is not normalized", z, msg) + } + if (&z).Cmp(a.z) != 0 { + t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, &z, a.z) + } +} + +func TestSumZZ(t *testing.T) { + AddZZ := func(z, x, y *Int) *Int { return z.Add(x, y) } + SubZZ := func(z, x, y *Int) *Int { return z.Sub(x, y) } + for _, a := range sumZZ { + arg := a + testFunZZ(t, "AddZZ", AddZZ, arg) + + arg = argZZ{a.z, a.y, a.x} + testFunZZ(t, "AddZZ symmetric", AddZZ, arg) + + arg = argZZ{a.x, a.z, a.y} + testFunZZ(t, "SubZZ", SubZZ, arg) + + arg = argZZ{a.y, a.z, a.x} + testFunZZ(t, "SubZZ symmetric", SubZZ, arg) + } +} + +func TestProdZZ(t *testing.T) { + MulZZ := func(z, x, y *Int) *Int { return z.Mul(x, y) } + for _, a := range prodZZ { + arg := a + testFunZZ(t, "MulZZ", MulZZ, arg) + + arg = argZZ{a.z, a.y, a.x} + testFunZZ(t, "MulZZ symmetric", MulZZ, arg) + } +} + +// mulBytes returns x*y via grade school multiplication. Both inputs +// and the result are assumed to be in big-endian representation (to +// match the semantics of Int.Bytes and Int.SetBytes). +func mulBytes(x, y []byte) []byte { + z := make([]byte, len(x)+len(y)) + + // multiply + k0 := len(z) - 1 + for j := len(y) - 1; j >= 0; j-- { + d := int(y[j]) + if d != 0 { + k := k0 + carry := 0 + for i := len(x) - 1; i >= 0; i-- { + t := int(z[k]) + int(x[i])*d + carry + z[k], carry = byte(t), t>>8 + k-- + } + z[k] = byte(carry) + } + k0-- + } + + // normalize (remove leading 0's) + i := 0 + for i < len(z) && z[i] == 0 { + i++ + } + + return z[i:] +} + +func checkMul(a, b []byte) bool { + var x, y, z1 Int + x.SetBytes(a) + y.SetBytes(b) + z1.Mul(&x, &y) + + var z2 Int + z2.SetBytes(mulBytes(a, b)) + + return z1.Cmp(&z2) == 0 +} + +func TestMul(t *testing.T) { + if err := quick.Check(checkMul, nil); err != nil { + t.Error(err) + } +} + +var mulRangesZ = []struct { + a, b int64 + prod string +}{ + // entirely positive ranges are covered by mulRangesN + {-1, 1, "0"}, + {-2, -1, "2"}, + {-3, -2, "6"}, + {-3, -1, "-6"}, + {1, 3, "6"}, + {-10, -10, "-10"}, + {0, -1, "1"}, // empty range + {-1, -100, "1"}, // empty range + {-1, 1, "0"}, // range includes 0 + {-1e9, 0, "0"}, // range includes 0 + {-1e9, 1e9, "0"}, // range includes 0 + {-10, -1, "3628800"}, // 10! + {-20, -2, "-2432902008176640000"}, // -20! + {-99, -1, + "-933262154439441526816992388562667004907159682643816214685929" + + "638952175999932299156089414639761565182862536979208272237582" + + "511852109168640000000000000000000000", // -99! + }, +} + +func TestMulRangeZ(t *testing.T) { + var tmp Int + // test entirely positive ranges + for i, r := range mulRangesN { + prod := tmp.MulRange(int64(r.a), int64(r.b)).String() + if prod != r.prod { + t.Errorf("#%da: got %s; want %s", i, prod, r.prod) + } + } + // test other ranges + for i, r := range mulRangesZ { + prod := tmp.MulRange(r.a, r.b).String() + if prod != r.prod { + t.Errorf("#%db: got %s; want %s", i, prod, r.prod) + } + } +} + +var stringTests = []struct { + in string + out string + base int + val int64 + ok bool +}{ + {in: "", ok: false}, + {in: "a", ok: false}, + {in: "z", ok: false}, + {in: "+", ok: false}, + {in: "-", ok: false}, + {in: "0b", ok: false}, + {in: "0x", ok: false}, + {in: "2", base: 2, ok: false}, + {in: "0b2", base: 0, ok: false}, + {in: "08", ok: false}, + {in: "8", base: 8, ok: false}, + {in: "0xg", base: 0, ok: false}, + {in: "g", base: 16, ok: false}, + {"0", "0", 0, 0, true}, + {"0", "0", 10, 0, true}, + {"0", "0", 16, 0, true}, + {"+0", "0", 0, 0, true}, + {"-0", "0", 0, 0, true}, + {"10", "10", 0, 10, true}, + {"10", "10", 10, 10, true}, + {"10", "10", 16, 16, true}, + {"-10", "-10", 16, -16, true}, + {"+10", "10", 16, 16, true}, + {"0x10", "16", 0, 16, true}, + {in: "0x10", base: 16, ok: false}, + {"-0x10", "-16", 0, -16, true}, + {"+0x10", "16", 0, 16, true}, + {"00", "0", 0, 0, true}, + {"0", "0", 8, 0, true}, + {"07", "7", 0, 7, true}, + {"7", "7", 8, 7, true}, + {"023", "19", 0, 19, true}, + {"23", "23", 8, 19, true}, + {"cafebabe", "cafebabe", 16, 0xcafebabe, true}, + {"0b0", "0", 0, 0, true}, + {"-111", "-111", 2, -7, true}, + {"-0b111", "-7", 0, -7, true}, + {"0b1001010111", "599", 0, 0x257, true}, + {"1001010111", "1001010111", 2, 0x257, true}, +} + +func format(base int) string { + switch base { + case 2: + return "%b" + case 8: + return "%o" + case 16: + return "%x" + } + return "%d" +} + +func TestGetString(t *testing.T) { + z := new(Int) + for i, test := range stringTests { + if !test.ok { + continue + } + z.SetInt64(test.val) + + if test.base == 10 { + s := z.String() + if s != test.out { + t.Errorf("#%da got %s; want %s", i, s, test.out) + } + } + + s := fmt.Sprintf(format(test.base), z) + if s != test.out { + t.Errorf("#%db got %s; want %s", i, s, test.out) + } + } +} + +func TestSetString(t *testing.T) { + tmp := new(Int) + for i, test := range stringTests { + // initialize to a non-zero value so that issues with parsing + // 0 are detected + tmp.SetInt64(1234567890) + n1, ok1 := new(Int).SetString(test.in, test.base) + n2, ok2 := tmp.SetString(test.in, test.base) + expected := NewInt(test.val) + if ok1 != test.ok || ok2 != test.ok { + t.Errorf("#%d (input '%s') ok incorrect (should be %t)", i, test.in, test.ok) + continue + } + if !ok1 { + if n1 != nil { + t.Errorf("#%d (input '%s') n1 != nil", i, test.in) + } + continue + } + if !ok2 { + if n2 != nil { + t.Errorf("#%d (input '%s') n2 != nil", i, test.in) + } + continue + } + + if ok1 && !isNormalized(n1) { + t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n1) + } + if ok2 && !isNormalized(n2) { + t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n2) + } + + if n1.Cmp(expected) != 0 { + t.Errorf("#%d (input '%s') got: %s want: %d", i, test.in, n1, test.val) + } + if n2.Cmp(expected) != 0 { + t.Errorf("#%d (input '%s') got: %s want: %d", i, test.in, n2, test.val) + } + } +} + +var formatTests = []struct { + input string + format string + output string +}{ + {"<nil>", "%x", "<nil>"}, + {"<nil>", "%#x", "<nil>"}, + {"<nil>", "%#y", "%!y(big.Int=<nil>)"}, + + {"10", "%b", "1010"}, + {"10", "%o", "12"}, + {"10", "%d", "10"}, + {"10", "%v", "10"}, + {"10", "%x", "a"}, + {"10", "%X", "A"}, + {"-10", "%X", "-A"}, + {"10", "%y", "%!y(big.Int=10)"}, + {"-10", "%y", "%!y(big.Int=-10)"}, + + {"10", "%#b", "1010"}, + {"10", "%#o", "012"}, + {"10", "%#d", "10"}, + {"10", "%#v", "10"}, + {"10", "%#x", "0xa"}, + {"10", "%#X", "0XA"}, + {"-10", "%#X", "-0XA"}, + {"10", "%#y", "%!y(big.Int=10)"}, + {"-10", "%#y", "%!y(big.Int=-10)"}, + + {"1234", "%d", "1234"}, + {"1234", "%3d", "1234"}, + {"1234", "%4d", "1234"}, + {"-1234", "%d", "-1234"}, + {"1234", "% 5d", " 1234"}, + {"1234", "%+5d", "+1234"}, + {"1234", "%-5d", "1234 "}, + {"1234", "%x", "4d2"}, + {"1234", "%X", "4D2"}, + {"-1234", "%3x", "-4d2"}, + {"-1234", "%4x", "-4d2"}, + {"-1234", "%5x", " -4d2"}, + {"-1234", "%-5x", "-4d2 "}, + {"1234", "%03d", "1234"}, + {"1234", "%04d", "1234"}, + {"1234", "%05d", "01234"}, + {"1234", "%06d", "001234"}, + {"-1234", "%06d", "-01234"}, + {"1234", "%+06d", "+01234"}, + {"1234", "% 06d", " 01234"}, + {"1234", "%-6d", "1234 "}, + {"1234", "%-06d", "1234 "}, + {"-1234", "%-06d", "-1234 "}, + + {"1234", "%.3d", "1234"}, + {"1234", "%.4d", "1234"}, + {"1234", "%.5d", "01234"}, + {"1234", "%.6d", "001234"}, + {"-1234", "%.3d", "-1234"}, + {"-1234", "%.4d", "-1234"}, + {"-1234", "%.5d", "-01234"}, + {"-1234", "%.6d", "-001234"}, + + {"1234", "%8.3d", " 1234"}, + {"1234", "%8.4d", " 1234"}, + {"1234", "%8.5d", " 01234"}, + {"1234", "%8.6d", " 001234"}, + {"-1234", "%8.3d", " -1234"}, + {"-1234", "%8.4d", " -1234"}, + {"-1234", "%8.5d", " -01234"}, + {"-1234", "%8.6d", " -001234"}, + + {"1234", "%+8.3d", " +1234"}, + {"1234", "%+8.4d", " +1234"}, + {"1234", "%+8.5d", " +01234"}, + {"1234", "%+8.6d", " +001234"}, + {"-1234", "%+8.3d", " -1234"}, + {"-1234", "%+8.4d", " -1234"}, + {"-1234", "%+8.5d", " -01234"}, + {"-1234", "%+8.6d", " -001234"}, + + {"1234", "% 8.3d", " 1234"}, + {"1234", "% 8.4d", " 1234"}, + {"1234", "% 8.5d", " 01234"}, + {"1234", "% 8.6d", " 001234"}, + {"-1234", "% 8.3d", " -1234"}, + {"-1234", "% 8.4d", " -1234"}, + {"-1234", "% 8.5d", " -01234"}, + {"-1234", "% 8.6d", " -001234"}, + + {"1234", "%.3x", "4d2"}, + {"1234", "%.4x", "04d2"}, + {"1234", "%.5x", "004d2"}, + {"1234", "%.6x", "0004d2"}, + {"-1234", "%.3x", "-4d2"}, + {"-1234", "%.4x", "-04d2"}, + {"-1234", "%.5x", "-004d2"}, + {"-1234", "%.6x", "-0004d2"}, + + {"1234", "%8.3x", " 4d2"}, + {"1234", "%8.4x", " 04d2"}, + {"1234", "%8.5x", " 004d2"}, + {"1234", "%8.6x", " 0004d2"}, + {"-1234", "%8.3x", " -4d2"}, + {"-1234", "%8.4x", " -04d2"}, + {"-1234", "%8.5x", " -004d2"}, + {"-1234", "%8.6x", " -0004d2"}, + + {"1234", "%+8.3x", " +4d2"}, + {"1234", "%+8.4x", " +04d2"}, + {"1234", "%+8.5x", " +004d2"}, + {"1234", "%+8.6x", " +0004d2"}, + {"-1234", "%+8.3x", " -4d2"}, + {"-1234", "%+8.4x", " -04d2"}, + {"-1234", "%+8.5x", " -004d2"}, + {"-1234", "%+8.6x", " -0004d2"}, + + {"1234", "% 8.3x", " 4d2"}, + {"1234", "% 8.4x", " 04d2"}, + {"1234", "% 8.5x", " 004d2"}, + {"1234", "% 8.6x", " 0004d2"}, + {"1234", "% 8.7x", " 00004d2"}, + {"1234", "% 8.8x", " 000004d2"}, + {"-1234", "% 8.3x", " -4d2"}, + {"-1234", "% 8.4x", " -04d2"}, + {"-1234", "% 8.5x", " -004d2"}, + {"-1234", "% 8.6x", " -0004d2"}, + {"-1234", "% 8.7x", "-00004d2"}, + {"-1234", "% 8.8x", "-000004d2"}, + + {"1234", "%-8.3d", "1234 "}, + {"1234", "%-8.4d", "1234 "}, + {"1234", "%-8.5d", "01234 "}, + {"1234", "%-8.6d", "001234 "}, + {"1234", "%-8.7d", "0001234 "}, + {"1234", "%-8.8d", "00001234"}, + {"-1234", "%-8.3d", "-1234 "}, + {"-1234", "%-8.4d", "-1234 "}, + {"-1234", "%-8.5d", "-01234 "}, + {"-1234", "%-8.6d", "-001234 "}, + {"-1234", "%-8.7d", "-0001234"}, + {"-1234", "%-8.8d", "-00001234"}, + + {"16777215", "%b", "111111111111111111111111"}, // 2**24 - 1 + + {"0", "%.d", ""}, + {"0", "%.0d", ""}, + {"0", "%3.d", ""}, +} + +func TestFormat(t *testing.T) { + for i, test := range formatTests { + var x *Int + if test.input != "<nil>" { + var ok bool + x, ok = new(Int).SetString(test.input, 0) + if !ok { + t.Errorf("#%d failed reading input %s", i, test.input) + } + } + output := fmt.Sprintf(test.format, x) + if output != test.output { + t.Errorf("#%d got %q; want %q, {%q, %q, %q}", i, output, test.output, test.input, test.format, test.output) + } + } +} + +var scanTests = []struct { + input string + format string + output string + remaining int +}{ + {"1010", "%b", "10", 0}, + {"0b1010", "%v", "10", 0}, + {"12", "%o", "10", 0}, + {"012", "%v", "10", 0}, + {"10", "%d", "10", 0}, + {"10", "%v", "10", 0}, + {"a", "%x", "10", 0}, + {"0xa", "%v", "10", 0}, + {"A", "%X", "10", 0}, + {"-A", "%X", "-10", 0}, + {"+0b1011001", "%v", "89", 0}, + {"0xA", "%v", "10", 0}, + {"0 ", "%v", "0", 1}, + {"2+3", "%v", "2", 2}, + {"0XABC 12", "%v", "2748", 3}, +} + +func TestScan(t *testing.T) { + var buf bytes.Buffer + for i, test := range scanTests { + x := new(Int) + buf.Reset() + buf.WriteString(test.input) + if _, err := fmt.Fscanf(&buf, test.format, x); err != nil { + t.Errorf("#%d error: %s", i, err) + } + if x.String() != test.output { + t.Errorf("#%d got %s; want %s", i, x.String(), test.output) + } + if buf.Len() != test.remaining { + t.Errorf("#%d got %d bytes remaining; want %d", i, buf.Len(), test.remaining) + } + } +} + +// Examples from the Go Language Spec, section "Arithmetic operators" +var divisionSignsTests = []struct { + x, y int64 + q, r int64 // T-division + d, m int64 // Euclidian division +}{ + {5, 3, 1, 2, 1, 2}, + {-5, 3, -1, -2, -2, 1}, + {5, -3, -1, 2, -1, 2}, + {-5, -3, 1, -2, 2, 1}, + {1, 2, 0, 1, 0, 1}, + {8, 4, 2, 0, 2, 0}, +} + +func TestDivisionSigns(t *testing.T) { + for i, test := range divisionSignsTests { + x := NewInt(test.x) + y := NewInt(test.y) + q := NewInt(test.q) + r := NewInt(test.r) + d := NewInt(test.d) + m := NewInt(test.m) + + q1 := new(Int).Quo(x, y) + r1 := new(Int).Rem(x, y) + if !isNormalized(q1) { + t.Errorf("#%d Quo: %v is not normalized", i, *q1) + } + if !isNormalized(r1) { + t.Errorf("#%d Rem: %v is not normalized", i, *r1) + } + if q1.Cmp(q) != 0 || r1.Cmp(r) != 0 { + t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q1, r1, q, r) + } + + q2, r2 := new(Int).QuoRem(x, y, new(Int)) + if !isNormalized(q2) { + t.Errorf("#%d Quo: %v is not normalized", i, *q2) + } + if !isNormalized(r2) { + t.Errorf("#%d Rem: %v is not normalized", i, *r2) + } + if q2.Cmp(q) != 0 || r2.Cmp(r) != 0 { + t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q2, r2, q, r) + } + + d1 := new(Int).Div(x, y) + m1 := new(Int).Mod(x, y) + if !isNormalized(d1) { + t.Errorf("#%d Div: %v is not normalized", i, *d1) + } + if !isNormalized(m1) { + t.Errorf("#%d Mod: %v is not normalized", i, *m1) + } + if d1.Cmp(d) != 0 || m1.Cmp(m) != 0 { + t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d1, m1, d, m) + } + + d2, m2 := new(Int).DivMod(x, y, new(Int)) + if !isNormalized(d2) { + t.Errorf("#%d Div: %v is not normalized", i, *d2) + } + if !isNormalized(m2) { + t.Errorf("#%d Mod: %v is not normalized", i, *m2) + } + if d2.Cmp(d) != 0 || m2.Cmp(m) != 0 { + t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d2, m2, d, m) + } + } +} + +func checkSetBytes(b []byte) bool { + hex1 := hex.EncodeToString(new(Int).SetBytes(b).Bytes()) + hex2 := hex.EncodeToString(b) + + for len(hex1) < len(hex2) { + hex1 = "0" + hex1 + } + + for len(hex1) > len(hex2) { + hex2 = "0" + hex2 + } + + return hex1 == hex2 +} + +func TestSetBytes(t *testing.T) { + if err := quick.Check(checkSetBytes, nil); err != nil { + t.Error(err) + } +} + +func checkBytes(b []byte) bool { + b2 := new(Int).SetBytes(b).Bytes() + return bytes.Compare(b, b2) == 0 +} + +func TestBytes(t *testing.T) { + if err := quick.Check(checkSetBytes, nil); err != nil { + t.Error(err) + } +} + +func checkQuo(x, y []byte) bool { + u := new(Int).SetBytes(x) + v := new(Int).SetBytes(y) + + if len(v.abs) == 0 { + return true + } + + r := new(Int) + q, r := new(Int).QuoRem(u, v, r) + + if r.Cmp(v) >= 0 { + return false + } + + uprime := new(Int).Set(q) + uprime.Mul(uprime, v) + uprime.Add(uprime, r) + + return uprime.Cmp(u) == 0 +} + +var quoTests = []struct { + x, y string + q, r string +}{ + { + "476217953993950760840509444250624797097991362735329973741718102894495832294430498335824897858659711275234906400899559094370964723884706254265559534144986498357", + "9353930466774385905609975137998169297361893554149986716853295022578535724979483772383667534691121982974895531435241089241440253066816724367338287092081996", + "50911", + "1", + }, + { + "11510768301994997771168", + "1328165573307167369775", + "8", + "885443715537658812968", + }, +} + +func TestQuo(t *testing.T) { + if err := quick.Check(checkQuo, nil); err != nil { + t.Error(err) + } + + for i, test := range quoTests { + x, _ := new(Int).SetString(test.x, 10) + y, _ := new(Int).SetString(test.y, 10) + expectedQ, _ := new(Int).SetString(test.q, 10) + expectedR, _ := new(Int).SetString(test.r, 10) + + r := new(Int) + q, r := new(Int).QuoRem(x, y, r) + + if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 { + t.Errorf("#%d got (%s, %s) want (%s, %s)", i, q, r, expectedQ, expectedR) + } + } +} + +func TestQuoStepD6(t *testing.T) { + // See Knuth, Volume 2, section 4.3.1, exercise 21. This code exercises + // a code path which only triggers 1 in 10^{-19} cases. + + u := &Int{false, nat{0, 0, 1 + 1<<(_W-1), _M ^ (1 << (_W - 1))}} + v := &Int{false, nat{5, 2 + 1<<(_W-1), 1 << (_W - 1)}} + + r := new(Int) + q, r := new(Int).QuoRem(u, v, r) + const expectedQ64 = "18446744073709551613" + const expectedR64 = "3138550867693340382088035895064302439801311770021610913807" + const expectedQ32 = "4294967293" + const expectedR32 = "39614081266355540837921718287" + if q.String() != expectedQ64 && q.String() != expectedQ32 || + r.String() != expectedR64 && r.String() != expectedR32 { + t.Errorf("got (%s, %s) want (%s, %s) or (%s, %s)", q, r, expectedQ64, expectedR64, expectedQ32, expectedR32) + } +} + +var bitLenTests = []struct { + in string + out int +}{ + {"-1", 1}, + {"0", 0}, + {"1", 1}, + {"2", 2}, + {"4", 3}, + {"0xabc", 12}, + {"0x8000", 16}, + {"0x80000000", 32}, + {"0x800000000000", 48}, + {"0x8000000000000000", 64}, + {"0x80000000000000000000", 80}, + {"-0x4000000000000000000000", 87}, +} + +func TestBitLen(t *testing.T) { + for i, test := range bitLenTests { + x, ok := new(Int).SetString(test.in, 0) + if !ok { + t.Errorf("#%d test input invalid: %s", i, test.in) + continue + } + + if n := x.BitLen(); n != test.out { + t.Errorf("#%d got %d want %d", i, n, test.out) + } + } +} + +var expTests = []struct { + x, y, m string + out string +}{ + {"5", "0", "", "1"}, + {"-5", "0", "", "-1"}, + {"5", "1", "", "5"}, + {"-5", "1", "", "-5"}, + {"-2", "3", "2", "0"}, + {"5", "2", "", "25"}, + {"1", "65537", "2", "1"}, + {"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"}, + {"0x8000000000000000", "2", "6719", "4944"}, + {"0x8000000000000000", "3", "6719", "5447"}, + {"0x8000000000000000", "1000", "6719", "1603"}, + {"0x8000000000000000", "1000000", "6719", "3199"}, + { + "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347", + "298472983472983471903246121093472394872319615612417471234712061", + "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464", + "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291", + }, +} + +func TestExp(t *testing.T) { + for i, test := range expTests { + x, ok1 := new(Int).SetString(test.x, 0) + y, ok2 := new(Int).SetString(test.y, 0) + out, ok3 := new(Int).SetString(test.out, 0) + + var ok4 bool + var m *Int + + if len(test.m) == 0 { + m, ok4 = nil, true + } else { + m, ok4 = new(Int).SetString(test.m, 0) + } + + if !ok1 || !ok2 || !ok3 || !ok4 { + t.Errorf("#%d: error in input", i) + continue + } + + z := y.Exp(x, y, m) + if !isNormalized(z) { + t.Errorf("#%d: %v is not normalized", i, *z) + } + if z.Cmp(out) != 0 { + t.Errorf("#%d: got %s want %s", i, z, out) + } + } +} + +func checkGcd(aBytes, bBytes []byte) bool { + a := new(Int).SetBytes(aBytes) + b := new(Int).SetBytes(bBytes) + + x := new(Int) + y := new(Int) + d := new(Int) + + GcdInt(d, x, y, a, b) + x.Mul(x, a) + y.Mul(y, b) + x.Add(x, y) + + return x.Cmp(d) == 0 +} + +var gcdTests = []struct { + a, b int64 + d, x, y int64 +}{ + {120, 23, 1, -9, 47}, +} + +func TestGcd(t *testing.T) { + for i, test := range gcdTests { + a := NewInt(test.a) + b := NewInt(test.b) + + x := new(Int) + y := new(Int) + d := new(Int) + + expectedX := NewInt(test.x) + expectedY := NewInt(test.y) + expectedD := NewInt(test.d) + + GcdInt(d, x, y, a, b) + + if expectedX.Cmp(x) != 0 || + expectedY.Cmp(y) != 0 || + expectedD.Cmp(d) != 0 { + t.Errorf("#%d got (%s %s %s) want (%s %s %s)", i, x, y, d, expectedX, expectedY, expectedD) + } + } + + quick.Check(checkGcd, nil) +} + +var primes = []string{ + "2", + "3", + "5", + "7", + "11", + + "13756265695458089029", + "13496181268022124907", + "10953742525620032441", + "17908251027575790097", + + // http://code.google.com/p/go/issues/detail?id=638 + "18699199384836356663", + + "98920366548084643601728869055592650835572950932266967461790948584315647051443", + "94560208308847015747498523884063394671606671904944666360068158221458669711639", + + // http://primes.utm.edu/lists/small/small3.html + "449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163", + "230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593", + "5521712099665906221540423207019333379125265462121169655563495403888449493493629943498064604536961775110765377745550377067893607246020694972959780839151452457728855382113555867743022746090187341871655890805971735385789993", + "203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123", +} + +var composites = []string{ + "21284175091214687912771199898307297748211672914763848041968395774954376176754", + "6084766654921918907427900243509372380954290099172559290432744450051395395951", + "84594350493221918389213352992032324280367711247940675652888030554255915464401", + "82793403787388584738507275144194252681", +} + +func TestProbablyPrime(t *testing.T) { + nreps := 20 + if testing.Short() { + nreps = 1 + } + for i, s := range primes { + p, _ := new(Int).SetString(s, 10) + if !ProbablyPrime(p, nreps) { + t.Errorf("#%d prime found to be non-prime (%s)", i, s) + } + } + + for i, s := range composites { + c, _ := new(Int).SetString(s, 10) + if ProbablyPrime(c, nreps) { + t.Errorf("#%d composite found to be prime (%s)", i, s) + } + if testing.Short() { + break + } + } +} + +type intShiftTest struct { + in string + shift uint + out string +} + +var rshTests = []intShiftTest{ + {"0", 0, "0"}, + {"-0", 0, "0"}, + {"0", 1, "0"}, + {"0", 2, "0"}, + {"1", 0, "1"}, + {"1", 1, "0"}, + {"1", 2, "0"}, + {"2", 0, "2"}, + {"2", 1, "1"}, + {"-1", 0, "-1"}, + {"-1", 1, "-1"}, + {"-1", 10, "-1"}, + {"-100", 2, "-25"}, + {"-100", 3, "-13"}, + {"-100", 100, "-1"}, + {"4294967296", 0, "4294967296"}, + {"4294967296", 1, "2147483648"}, + {"4294967296", 2, "1073741824"}, + {"18446744073709551616", 0, "18446744073709551616"}, + {"18446744073709551616", 1, "9223372036854775808"}, + {"18446744073709551616", 2, "4611686018427387904"}, + {"18446744073709551616", 64, "1"}, + {"340282366920938463463374607431768211456", 64, "18446744073709551616"}, + {"340282366920938463463374607431768211456", 128, "1"}, +} + +func TestRsh(t *testing.T) { + for i, test := range rshTests { + in, _ := new(Int).SetString(test.in, 10) + expected, _ := new(Int).SetString(test.out, 10) + out := new(Int).Rsh(in, test.shift) + + if !isNormalized(out) { + t.Errorf("#%d: %v is not normalized", i, *out) + } + if out.Cmp(expected) != 0 { + t.Errorf("#%d: got %s want %s", i, out, expected) + } + } +} + +func TestRshSelf(t *testing.T) { + for i, test := range rshTests { + z, _ := new(Int).SetString(test.in, 10) + expected, _ := new(Int).SetString(test.out, 10) + z.Rsh(z, test.shift) + + if !isNormalized(z) { + t.Errorf("#%d: %v is not normalized", i, *z) + } + if z.Cmp(expected) != 0 { + t.Errorf("#%d: got %s want %s", i, z, expected) + } + } +} + +var lshTests = []intShiftTest{ + {"0", 0, "0"}, + {"0", 1, "0"}, + {"0", 2, "0"}, + {"1", 0, "1"}, + {"1", 1, "2"}, + {"1", 2, "4"}, + {"2", 0, "2"}, + {"2", 1, "4"}, + {"2", 2, "8"}, + {"-87", 1, "-174"}, + {"4294967296", 0, "4294967296"}, + {"4294967296", 1, "8589934592"}, + {"4294967296", 2, "17179869184"}, + {"18446744073709551616", 0, "18446744073709551616"}, + {"9223372036854775808", 1, "18446744073709551616"}, + {"4611686018427387904", 2, "18446744073709551616"}, + {"1", 64, "18446744073709551616"}, + {"18446744073709551616", 64, "340282366920938463463374607431768211456"}, + {"1", 128, "340282366920938463463374607431768211456"}, +} + +func TestLsh(t *testing.T) { + for i, test := range lshTests { + in, _ := new(Int).SetString(test.in, 10) + expected, _ := new(Int).SetString(test.out, 10) + out := new(Int).Lsh(in, test.shift) + + if !isNormalized(out) { + t.Errorf("#%d: %v is not normalized", i, *out) + } + if out.Cmp(expected) != 0 { + t.Errorf("#%d: got %s want %s", i, out, expected) + } + } +} + +func TestLshSelf(t *testing.T) { + for i, test := range lshTests { + z, _ := new(Int).SetString(test.in, 10) + expected, _ := new(Int).SetString(test.out, 10) + z.Lsh(z, test.shift) + + if !isNormalized(z) { + t.Errorf("#%d: %v is not normalized", i, *z) + } + if z.Cmp(expected) != 0 { + t.Errorf("#%d: got %s want %s", i, z, expected) + } + } +} + +func TestLshRsh(t *testing.T) { + for i, test := range rshTests { + in, _ := new(Int).SetString(test.in, 10) + out := new(Int).Lsh(in, test.shift) + out = out.Rsh(out, test.shift) + + if !isNormalized(out) { + t.Errorf("#%d: %v is not normalized", i, *out) + } + if in.Cmp(out) != 0 { + t.Errorf("#%d: got %s want %s", i, out, in) + } + } + for i, test := range lshTests { + in, _ := new(Int).SetString(test.in, 10) + out := new(Int).Lsh(in, test.shift) + out.Rsh(out, test.shift) + + if !isNormalized(out) { + t.Errorf("#%d: %v is not normalized", i, *out) + } + if in.Cmp(out) != 0 { + t.Errorf("#%d: got %s want %s", i, out, in) + } + } +} + +var int64Tests = []int64{ + 0, + 1, + -1, + 4294967295, + -4294967295, + 4294967296, + -4294967296, + 9223372036854775807, + -9223372036854775807, + -9223372036854775808, +} + +func TestInt64(t *testing.T) { + for i, testVal := range int64Tests { + in := NewInt(testVal) + out := in.Int64() + + if out != testVal { + t.Errorf("#%d got %d want %d", i, out, testVal) + } + } +} + +var bitwiseTests = []struct { + x, y string + and, or, xor, andNot string +}{ + {"0x00", "0x00", "0x00", "0x00", "0x00", "0x00"}, + {"0x00", "0x01", "0x00", "0x01", "0x01", "0x00"}, + {"0x01", "0x00", "0x00", "0x01", "0x01", "0x01"}, + {"-0x01", "0x00", "0x00", "-0x01", "-0x01", "-0x01"}, + {"-0xaf", "-0x50", "-0xf0", "-0x0f", "0xe1", "0x41"}, + {"0x00", "-0x01", "0x00", "-0x01", "-0x01", "0x00"}, + {"0x01", "0x01", "0x01", "0x01", "0x00", "0x00"}, + {"-0x01", "-0x01", "-0x01", "-0x01", "0x00", "0x00"}, + {"0x07", "0x08", "0x00", "0x0f", "0x0f", "0x07"}, + {"0x05", "0x0f", "0x05", "0x0f", "0x0a", "0x00"}, + {"0x013ff6", "0x9a4e", "0x1a46", "0x01bffe", "0x01a5b8", "0x0125b0"}, + {"-0x013ff6", "0x9a4e", "0x800a", "-0x0125b2", "-0x01a5bc", "-0x01c000"}, + {"-0x013ff6", "-0x9a4e", "-0x01bffe", "-0x1a46", "0x01a5b8", "0x8008"}, + { + "0x1000009dc6e3d9822cba04129bcbe3401", + "0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd", + "0x1000001186210100001000009048c2001", + "0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd", + "0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc", + "0x8c40c2d8822caa04120b8321400", + }, + { + "0x1000009dc6e3d9822cba04129bcbe3401", + "-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd", + "0x8c40c2d8822caa04120b8321401", + "-0xb9bd7d543685789d57ca918e82229142459020483cd2014001fd", + "-0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fe", + "0x1000001186210100001000009048c2000", + }, + { + "-0x1000009dc6e3d9822cba04129bcbe3401", + "-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd", + "-0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd", + "-0x1000001186210100001000009048c2001", + "0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc", + "0xb9bd7d543685789d57ca918e82229142459020483cd2014001fc", + }, +} + +type bitFun func(z, x, y *Int) *Int + +func testBitFun(t *testing.T, msg string, f bitFun, x, y *Int, exp string) { + expected := new(Int) + expected.SetString(exp, 0) + + out := f(new(Int), x, y) + if out.Cmp(expected) != 0 { + t.Errorf("%s: got %s want %s", msg, out, expected) + } +} + +func testBitFunSelf(t *testing.T, msg string, f bitFun, x, y *Int, exp string) { + self := new(Int) + self.Set(x) + expected := new(Int) + expected.SetString(exp, 0) + + self = f(self, self, y) + if self.Cmp(expected) != 0 { + t.Errorf("%s: got %s want %s", msg, self, expected) + } +} + +func altBit(x *Int, i int) uint { + z := new(Int).Rsh(x, uint(i)) + z = z.And(z, NewInt(1)) + if z.Cmp(new(Int)) != 0 { + return 1 + } + return 0 +} + +func altSetBit(z *Int, x *Int, i int, b uint) *Int { + one := NewInt(1) + m := one.Lsh(one, uint(i)) + switch b { + case 1: + return z.Or(x, m) + case 0: + return z.AndNot(x, m) + } + panic("set bit is not 0 or 1") +} + +func testBitset(t *testing.T, x *Int) { + n := x.BitLen() + z := new(Int).Set(x) + z1 := new(Int).Set(x) + for i := 0; i < n+10; i++ { + old := z.Bit(i) + old1 := altBit(z1, i) + if old != old1 { + t.Errorf("bitset: inconsistent value for Bit(%s, %d), got %v want %v", z1, i, old, old1) + } + z := new(Int).SetBit(z, i, 1) + z1 := altSetBit(new(Int), z1, i, 1) + if z.Bit(i) == 0 { + t.Errorf("bitset: bit %d of %s got 0 want 1", i, x) + } + if z.Cmp(z1) != 0 { + t.Errorf("bitset: inconsistent value after SetBit 1, got %s want %s", z, z1) + } + z.SetBit(z, i, 0) + altSetBit(z1, z1, i, 0) + if z.Bit(i) != 0 { + t.Errorf("bitset: bit %d of %s got 1 want 0", i, x) + } + if z.Cmp(z1) != 0 { + t.Errorf("bitset: inconsistent value after SetBit 0, got %s want %s", z, z1) + } + altSetBit(z1, z1, i, old) + z.SetBit(z, i, old) + if z.Cmp(z1) != 0 { + t.Errorf("bitset: inconsistent value after SetBit old, got %s want %s", z, z1) + } + } + if z.Cmp(x) != 0 { + t.Errorf("bitset: got %s want %s", z, x) + } +} + +var bitsetTests = []struct { + x string + i int + b uint +}{ + {"0", 0, 0}, + {"0", 200, 0}, + {"1", 0, 1}, + {"1", 1, 0}, + {"-1", 0, 1}, + {"-1", 200, 1}, + {"0x2000000000000000000000000000", 108, 0}, + {"0x2000000000000000000000000000", 109, 1}, + {"0x2000000000000000000000000000", 110, 0}, + {"-0x2000000000000000000000000001", 108, 1}, + {"-0x2000000000000000000000000001", 109, 0}, + {"-0x2000000000000000000000000001", 110, 1}, +} + +func TestBitSet(t *testing.T) { + for _, test := range bitwiseTests { + x := new(Int) + x.SetString(test.x, 0) + testBitset(t, x) + x = new(Int) + x.SetString(test.y, 0) + testBitset(t, x) + } + for i, test := range bitsetTests { + x := new(Int) + x.SetString(test.x, 0) + b := x.Bit(test.i) + if b != test.b { + + t.Errorf("#%d want %v got %v", i, test.b, b) + } + } +} + +func BenchmarkBitset(b *testing.B) { + z := new(Int) + z.SetBit(z, 512, 1) + b.ResetTimer() + b.StartTimer() + for i := b.N - 1; i >= 0; i-- { + z.SetBit(z, i&512, 1) + } +} + +func BenchmarkBitsetNeg(b *testing.B) { + z := NewInt(-1) + z.SetBit(z, 512, 0) + b.ResetTimer() + b.StartTimer() + for i := b.N - 1; i >= 0; i-- { + z.SetBit(z, i&512, 0) + } +} + +func BenchmarkBitsetOrig(b *testing.B) { + z := new(Int) + altSetBit(z, z, 512, 1) + b.ResetTimer() + b.StartTimer() + for i := b.N - 1; i >= 0; i-- { + altSetBit(z, z, i&512, 1) + } +} + +func BenchmarkBitsetNegOrig(b *testing.B) { + z := NewInt(-1) + altSetBit(z, z, 512, 0) + b.ResetTimer() + b.StartTimer() + for i := b.N - 1; i >= 0; i-- { + altSetBit(z, z, i&512, 0) + } +} + +func TestBitwise(t *testing.T) { + x := new(Int) + y := new(Int) + for _, test := range bitwiseTests { + x.SetString(test.x, 0) + y.SetString(test.y, 0) + + testBitFun(t, "and", (*Int).And, x, y, test.and) + testBitFunSelf(t, "and", (*Int).And, x, y, test.and) + testBitFun(t, "andNot", (*Int).AndNot, x, y, test.andNot) + testBitFunSelf(t, "andNot", (*Int).AndNot, x, y, test.andNot) + testBitFun(t, "or", (*Int).Or, x, y, test.or) + testBitFunSelf(t, "or", (*Int).Or, x, y, test.or) + testBitFun(t, "xor", (*Int).Xor, x, y, test.xor) + testBitFunSelf(t, "xor", (*Int).Xor, x, y, test.xor) + } +} + +var notTests = []struct { + in string + out string +}{ + {"0", "-1"}, + {"1", "-2"}, + {"7", "-8"}, + {"0", "-1"}, + {"-81910", "81909"}, + { + "298472983472983471903246121093472394872319615612417471234712061", + "-298472983472983471903246121093472394872319615612417471234712062", + }, +} + +func TestNot(t *testing.T) { + in := new(Int) + out := new(Int) + expected := new(Int) + for i, test := range notTests { + in.SetString(test.in, 10) + expected.SetString(test.out, 10) + out = out.Not(in) + if out.Cmp(expected) != 0 { + t.Errorf("#%d: got %s want %s", i, out, expected) + } + out = out.Not(out) + if out.Cmp(in) != 0 { + t.Errorf("#%d: got %s want %s", i, out, in) + } + } +} + +var modInverseTests = []struct { + element string + prime string +}{ + {"1", "7"}, + {"1", "13"}, + {"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"}, +} + +func TestModInverse(t *testing.T) { + var element, prime 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) + } + } +} + +// used by TestIntGobEncoding and TestRatGobEncoding +var gobEncodingTests = []string{ + "0", + "1", + "2", + "10", + "42", + "1234567890", + "298472983472983471903246121093472394872319615612417471234712061", +} + +func TestIntGobEncoding(t *testing.T) { + var medium bytes.Buffer + enc := gob.NewEncoder(&medium) + dec := gob.NewDecoder(&medium) + for i, test := range gobEncodingTests { + for j := 0; j < 2; j++ { + medium.Reset() // empty buffer for each test case (in case of failures) + stest := test + if j != 0 { + // negative numbers + stest = "-" + test + } + var tx Int + tx.SetString(stest, 10) + if err := enc.Encode(&tx); err != nil { + t.Errorf("#%d%c: encoding failed: %s", i, 'a'+j, err) + } + var rx Int + if err := dec.Decode(&rx); err != nil { + t.Errorf("#%d%c: decoding failed: %s", i, 'a'+j, err) + } + if rx.Cmp(&tx) != 0 { + t.Errorf("#%d%c: transmission failed: got %s want %s", i, 'a'+j, &rx, &tx) + } + } + } +} |