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-rw-r--r--src/math/big/arith_test.go673
1 files changed, 673 insertions, 0 deletions
diff --git a/src/math/big/arith_test.go b/src/math/big/arith_test.go
new file mode 100644
index 0000000..2aca0ef
--- /dev/null
+++ b/src/math/big/arith_test.go
@@ -0,0 +1,673 @@
+// 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 (
+ "fmt"
+ "internal/testenv"
+ "math/bits"
+ "math/rand"
+ "strings"
+ "testing"
+)
+
+var isRaceBuilder = strings.HasSuffix(testenv.Builder(), "-race")
+
+type funVV func(z, x, y []Word) (c Word)
+type argVV struct {
+ z, x, y nat
+ c Word
+}
+
+var sumVV = []argVV{
+ {},
+ {nat{0}, nat{0}, nat{0}, 0},
+ {nat{1}, nat{1}, nat{0}, 0},
+ {nat{0}, nat{_M}, nat{1}, 1},
+ {nat{80235}, nat{12345}, nat{67890}, 0},
+ {nat{_M - 1}, nat{_M}, nat{_M}, 1},
+ {nat{0, 0, 0, 0}, nat{_M, _M, _M, _M}, nat{1, 0, 0, 0}, 1},
+ {nat{0, 0, 0, _M}, nat{_M, _M, _M, _M - 1}, nat{1, 0, 0, 0}, 0},
+ {nat{0, 0, 0, 0}, nat{_M, 0, _M, 0}, nat{1, _M, 0, _M}, 1},
+}
+
+func testFunVV(t *testing.T, msg string, f funVV, a argVV) {
+ z := make(nat, len(a.z))
+ c := f(z, a.x, a.y)
+ for i, zi := range z {
+ if zi != a.z[i] {
+ t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i])
+ break
+ }
+ }
+ if c != a.c {
+ t.Errorf("%s%+v\n\tgot c = %#x; want %#x", msg, a, c, a.c)
+ }
+}
+
+func TestFunVV(t *testing.T) {
+ for _, a := range sumVV {
+ arg := a
+ testFunVV(t, "addVV_g", addVV_g, arg)
+ testFunVV(t, "addVV", addVV, arg)
+
+ arg = argVV{a.z, a.y, a.x, a.c}
+ testFunVV(t, "addVV_g symmetric", addVV_g, arg)
+ testFunVV(t, "addVV symmetric", addVV, arg)
+
+ arg = argVV{a.x, a.z, a.y, a.c}
+ testFunVV(t, "subVV_g", subVV_g, arg)
+ testFunVV(t, "subVV", subVV, arg)
+
+ arg = argVV{a.y, a.z, a.x, a.c}
+ testFunVV(t, "subVV_g symmetric", subVV_g, arg)
+ testFunVV(t, "subVV symmetric", subVV, arg)
+ }
+}
+
+// Always the same seed for reproducible results.
+var rnd = rand.New(rand.NewSource(0))
+
+func rndW() Word {
+ return Word(rnd.Int63()<<1 | rnd.Int63n(2))
+}
+
+func rndV(n int) []Word {
+ v := make([]Word, n)
+ for i := range v {
+ v[i] = rndW()
+ }
+ return v
+}
+
+var benchSizes = []int{1, 2, 3, 4, 5, 1e1, 1e2, 1e3, 1e4, 1e5}
+
+func BenchmarkAddVV(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ x := rndV(n)
+ y := rndV(n)
+ z := make([]Word, n)
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _W))
+ for i := 0; i < b.N; i++ {
+ addVV(z, x, y)
+ }
+ })
+ }
+}
+
+func BenchmarkSubVV(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ x := rndV(n)
+ y := rndV(n)
+ z := make([]Word, n)
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _W))
+ for i := 0; i < b.N; i++ {
+ subVV(z, x, y)
+ }
+ })
+ }
+}
+
+type funVW func(z, x []Word, y Word) (c Word)
+type argVW struct {
+ z, x nat
+ y Word
+ c Word
+}
+
+var sumVW = []argVW{
+ {},
+ {nil, nil, 2, 2},
+ {nat{0}, nat{0}, 0, 0},
+ {nat{1}, nat{0}, 1, 0},
+ {nat{1}, nat{1}, 0, 0},
+ {nat{0}, nat{_M}, 1, 1},
+ {nat{0, 0, 0, 0}, nat{_M, _M, _M, _M}, 1, 1},
+ {nat{585}, nat{314}, 271, 0},
+}
+
+var lshVW = []argVW{
+ {},
+ {nat{0}, nat{0}, 0, 0},
+ {nat{0}, nat{0}, 1, 0},
+ {nat{0}, nat{0}, 20, 0},
+
+ {nat{_M}, nat{_M}, 0, 0},
+ {nat{_M << 1 & _M}, nat{_M}, 1, 1},
+ {nat{_M << 20 & _M}, nat{_M}, 20, _M >> (_W - 20)},
+
+ {nat{_M, _M, _M}, nat{_M, _M, _M}, 0, 0},
+ {nat{_M << 1 & _M, _M, _M}, nat{_M, _M, _M}, 1, 1},
+ {nat{_M << 20 & _M, _M, _M}, nat{_M, _M, _M}, 20, _M >> (_W - 20)},
+}
+
+var rshVW = []argVW{
+ {},
+ {nat{0}, nat{0}, 0, 0},
+ {nat{0}, nat{0}, 1, 0},
+ {nat{0}, nat{0}, 20, 0},
+
+ {nat{_M}, nat{_M}, 0, 0},
+ {nat{_M >> 1}, nat{_M}, 1, _M << (_W - 1) & _M},
+ {nat{_M >> 20}, nat{_M}, 20, _M << (_W - 20) & _M},
+
+ {nat{_M, _M, _M}, nat{_M, _M, _M}, 0, 0},
+ {nat{_M, _M, _M >> 1}, nat{_M, _M, _M}, 1, _M << (_W - 1) & _M},
+ {nat{_M, _M, _M >> 20}, nat{_M, _M, _M}, 20, _M << (_W - 20) & _M},
+}
+
+func testFunVW(t *testing.T, msg string, f funVW, a argVW) {
+ z := make(nat, len(a.z))
+ c := f(z, a.x, a.y)
+ for i, zi := range z {
+ if zi != a.z[i] {
+ t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i])
+ break
+ }
+ }
+ if c != a.c {
+ t.Errorf("%s%+v\n\tgot c = %#x; want %#x", msg, a, c, a.c)
+ }
+}
+
+func testFunVWext(t *testing.T, msg string, f funVW, f_g funVW, a argVW) {
+ // using the result of addVW_g/subVW_g as golden
+ z_g := make(nat, len(a.z))
+ c_g := f_g(z_g, a.x, a.y)
+ c := f(a.z, a.x, a.y)
+
+ for i, zi := range a.z {
+ if zi != z_g[i] {
+ t.Errorf("%s\n\tgot z[%d] = %#x; want %#x", msg, i, zi, z_g[i])
+ break
+ }
+ }
+ if c != c_g {
+ t.Errorf("%s\n\tgot c = %#x; want %#x", msg, c, c_g)
+ }
+}
+
+func makeFunVW(f func(z, x []Word, s uint) (c Word)) funVW {
+ return func(z, x []Word, s Word) (c Word) {
+ return f(z, x, uint(s))
+ }
+}
+
+func TestFunVW(t *testing.T) {
+ for _, a := range sumVW {
+ arg := a
+ testFunVW(t, "addVW_g", addVW_g, arg)
+ testFunVW(t, "addVW", addVW, arg)
+
+ arg = argVW{a.x, a.z, a.y, a.c}
+ testFunVW(t, "subVW_g", subVW_g, arg)
+ testFunVW(t, "subVW", subVW, arg)
+ }
+
+ shlVW_g := makeFunVW(shlVU_g)
+ shlVW := makeFunVW(shlVU)
+ for _, a := range lshVW {
+ arg := a
+ testFunVW(t, "shlVU_g", shlVW_g, arg)
+ testFunVW(t, "shlVU", shlVW, arg)
+ }
+
+ shrVW_g := makeFunVW(shrVU_g)
+ shrVW := makeFunVW(shrVU)
+ for _, a := range rshVW {
+ arg := a
+ testFunVW(t, "shrVU_g", shrVW_g, arg)
+ testFunVW(t, "shrVU", shrVW, arg)
+ }
+}
+
+// Construct a vector comprising the same word, usually '0' or 'maximum uint'
+func makeWordVec(e Word, n int) []Word {
+ v := make([]Word, n)
+ for i := range v {
+ v[i] = e
+ }
+ return v
+}
+
+// Extended testing to addVW and subVW using various kinds of input data.
+// We utilize the results of addVW_g and subVW_g as golden reference to check
+// correctness.
+func TestFunVWExt(t *testing.T) {
+ // 32 is the current threshold that triggers an optimized version of
+ // calculation for large-sized vector, ensure we have sizes around it tested.
+ var vwSizes = []int{0, 1, 3, 4, 5, 8, 9, 23, 31, 32, 33, 34, 35, 36, 50, 120}
+ for _, n := range vwSizes {
+ // vector of random numbers, using the result of addVW_g/subVW_g as golden
+ x := rndV(n)
+ y := rndW()
+ z := make(nat, n)
+ arg := argVW{z, x, y, 0}
+ testFunVWext(t, "addVW, random inputs", addVW, addVW_g, arg)
+ testFunVWext(t, "subVW, random inputs", subVW, subVW_g, arg)
+
+ // vector of random numbers, but make 'x' and 'z' share storage
+ arg = argVW{x, x, y, 0}
+ testFunVWext(t, "addVW, random inputs, sharing storage", addVW, addVW_g, arg)
+ testFunVWext(t, "subVW, random inputs, sharing storage", subVW, subVW_g, arg)
+
+ // vector of maximum uint, to force carry flag set in each 'add'
+ y = ^Word(0)
+ x = makeWordVec(y, n)
+ arg = argVW{z, x, y, 0}
+ testFunVWext(t, "addVW, vector of max uint", addVW, addVW_g, arg)
+
+ // vector of '0', to force carry flag set in each 'sub'
+ x = makeWordVec(0, n)
+ arg = argVW{z, x, 1, 0}
+ testFunVWext(t, "subVW, vector of zero", subVW, subVW_g, arg)
+ }
+}
+
+type argVU struct {
+ d []Word // d is a Word slice, the input parameters x and z come from this array.
+ l uint // l is the length of the input parameters x and z.
+ xp uint // xp is the starting position of the input parameter x, x := d[xp:xp+l].
+ zp uint // zp is the starting position of the input parameter z, z := d[zp:zp+l].
+ s uint // s is the shift number.
+ r []Word // r is the expected output result z.
+ c Word // c is the expected return value.
+ m string // message.
+}
+
+var argshlVUIn = []Word{1, 2, 4, 8, 16, 32, 64, 0, 0, 0}
+var argshlVUr0 = []Word{1, 2, 4, 8, 16, 32, 64}
+var argshlVUr1 = []Word{2, 4, 8, 16, 32, 64, 128}
+var argshlVUrWm1 = []Word{1 << (_W - 1), 0, 1, 2, 4, 8, 16}
+
+var argshlVU = []argVU{
+ // test cases for shlVU
+ {[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0}, 7, 0, 0, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "complete overlap of shlVU"},
+ {[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0, 0, 0, 0}, 7, 0, 3, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "partial overlap by half of shlVU"},
+ {[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0, 0, 0, 0, 0, 0, 0}, 7, 0, 6, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "partial overlap by 1 Word of shlVU"},
+ {[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0, 0, 0, 0, 0, 0, 0, 0}, 7, 0, 7, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "no overlap of shlVU"},
+ // additional test cases with shift values of 0, 1 and (_W-1)
+ {argshlVUIn, 7, 0, 0, 0, argshlVUr0, 0, "complete overlap of shlVU and shift of 0"},
+ {argshlVUIn, 7, 0, 0, 1, argshlVUr1, 0, "complete overlap of shlVU and shift of 1"},
+ {argshlVUIn, 7, 0, 0, _W - 1, argshlVUrWm1, 32, "complete overlap of shlVU and shift of _W - 1"},
+ {argshlVUIn, 7, 0, 1, 0, argshlVUr0, 0, "partial overlap by 6 Words of shlVU and shift of 0"},
+ {argshlVUIn, 7, 0, 1, 1, argshlVUr1, 0, "partial overlap by 6 Words of shlVU and shift of 1"},
+ {argshlVUIn, 7, 0, 1, _W - 1, argshlVUrWm1, 32, "partial overlap by 6 Words of shlVU and shift of _W - 1"},
+ {argshlVUIn, 7, 0, 2, 0, argshlVUr0, 0, "partial overlap by 5 Words of shlVU and shift of 0"},
+ {argshlVUIn, 7, 0, 2, 1, argshlVUr1, 0, "partial overlap by 5 Words of shlVU and shift of 1"},
+ {argshlVUIn, 7, 0, 2, _W - 1, argshlVUrWm1, 32, "partial overlap by 5 Words of shlVU abd shift of _W - 1"},
+ {argshlVUIn, 7, 0, 3, 0, argshlVUr0, 0, "partial overlap by 4 Words of shlVU and shift of 0"},
+ {argshlVUIn, 7, 0, 3, 1, argshlVUr1, 0, "partial overlap by 4 Words of shlVU and shift of 1"},
+ {argshlVUIn, 7, 0, 3, _W - 1, argshlVUrWm1, 32, "partial overlap by 4 Words of shlVU and shift of _W - 1"},
+}
+
+var argshrVUIn = []Word{0, 0, 0, 1, 2, 4, 8, 16, 32, 64}
+var argshrVUr0 = []Word{1, 2, 4, 8, 16, 32, 64}
+var argshrVUr1 = []Word{0, 1, 2, 4, 8, 16, 32}
+var argshrVUrWm1 = []Word{4, 8, 16, 32, 64, 128, 0}
+
+var argshrVU = []argVU{
+ // test cases for shrVU
+ {[]Word{0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 1, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "complete overlap of shrVU"},
+ {[]Word{0, 0, 0, 0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 4, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "partial overlap by half of shrVU"},
+ {[]Word{0, 0, 0, 0, 0, 0, 0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 7, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "partial overlap by 1 Word of shrVU"},
+ {[]Word{0, 0, 0, 0, 0, 0, 0, 0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 8, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "no overlap of shrVU"},
+ // additional test cases with shift values of 0, 1 and (_W-1)
+ {argshrVUIn, 7, 3, 3, 0, argshrVUr0, 0, "complete overlap of shrVU and shift of 0"},
+ {argshrVUIn, 7, 3, 3, 1, argshrVUr1, 1 << (_W - 1), "complete overlap of shrVU and shift of 1"},
+ {argshrVUIn, 7, 3, 3, _W - 1, argshrVUrWm1, 2, "complete overlap of shrVU and shift of _W - 1"},
+ {argshrVUIn, 7, 3, 2, 0, argshrVUr0, 0, "partial overlap by 6 Words of shrVU and shift of 0"},
+ {argshrVUIn, 7, 3, 2, 1, argshrVUr1, 1 << (_W - 1), "partial overlap by 6 Words of shrVU and shift of 1"},
+ {argshrVUIn, 7, 3, 2, _W - 1, argshrVUrWm1, 2, "partial overlap by 6 Words of shrVU and shift of _W - 1"},
+ {argshrVUIn, 7, 3, 1, 0, argshrVUr0, 0, "partial overlap by 5 Words of shrVU and shift of 0"},
+ {argshrVUIn, 7, 3, 1, 1, argshrVUr1, 1 << (_W - 1), "partial overlap by 5 Words of shrVU and shift of 1"},
+ {argshrVUIn, 7, 3, 1, _W - 1, argshrVUrWm1, 2, "partial overlap by 5 Words of shrVU and shift of _W - 1"},
+ {argshrVUIn, 7, 3, 0, 0, argshrVUr0, 0, "partial overlap by 4 Words of shrVU and shift of 0"},
+ {argshrVUIn, 7, 3, 0, 1, argshrVUr1, 1 << (_W - 1), "partial overlap by 4 Words of shrVU and shift of 1"},
+ {argshrVUIn, 7, 3, 0, _W - 1, argshrVUrWm1, 2, "partial overlap by 4 Words of shrVU and shift of _W - 1"},
+}
+
+func testShiftFunc(t *testing.T, f func(z, x []Word, s uint) Word, a argVU) {
+ // work on copy of a.d to preserve the original data.
+ b := make([]Word, len(a.d))
+ copy(b, a.d)
+ z := b[a.zp : a.zp+a.l]
+ x := b[a.xp : a.xp+a.l]
+ c := f(z, x, a.s)
+ for i, zi := range z {
+ if zi != a.r[i] {
+ t.Errorf("d := %v, %s(d[%d:%d], d[%d:%d], %d)\n\tgot z[%d] = %#x; want %#x", a.d, a.m, a.zp, a.zp+a.l, a.xp, a.xp+a.l, a.s, i, zi, a.r[i])
+ break
+ }
+ }
+ if c != a.c {
+ t.Errorf("d := %v, %s(d[%d:%d], d[%d:%d], %d)\n\tgot c = %#x; want %#x", a.d, a.m, a.zp, a.zp+a.l, a.xp, a.xp+a.l, a.s, c, a.c)
+ }
+}
+
+func TestShiftOverlap(t *testing.T) {
+ for _, a := range argshlVU {
+ arg := a
+ testShiftFunc(t, shlVU, arg)
+ }
+
+ for _, a := range argshrVU {
+ arg := a
+ testShiftFunc(t, shrVU, arg)
+ }
+}
+
+func TestIssue31084(t *testing.T) {
+ // compute 10^n via 5^n << n.
+ const n = 165
+ p := nat(nil).expNN(nat{5}, nat{n}, nil)
+ p = p.shl(p, n)
+ got := string(p.utoa(10))
+ want := "1" + strings.Repeat("0", n)
+ if got != want {
+ t.Errorf("shl(%v, %v)\n\tgot %s\n\twant %s", p, n, got, want)
+ }
+}
+
+const issue42838Value = "159309191113245227702888039776771180559110455519261878607388585338616290151305816094308987472018268594098344692611135542392730712890625"
+
+func TestIssue42838(t *testing.T) {
+ const s = 192
+ z, _, _, _ := nat(nil).scan(strings.NewReader(issue42838Value), 0, false)
+ z = z.shl(z, s)
+ got := string(z.utoa(10))
+ want := "1" + strings.Repeat("0", s)
+ if got != want {
+ t.Errorf("shl(%v, %v)\n\tgot %s\n\twant %s", z, s, got, want)
+ }
+}
+
+func BenchmarkAddVW(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ x := rndV(n)
+ y := rndW()
+ z := make([]Word, n)
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _S))
+ for i := 0; i < b.N; i++ {
+ addVW(z, x, y)
+ }
+ })
+ }
+}
+
+// Benchmarking addVW using vector of maximum uint to force carry flag set
+func BenchmarkAddVWext(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ y := ^Word(0)
+ x := makeWordVec(y, n)
+ z := make([]Word, n)
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _S))
+ for i := 0; i < b.N; i++ {
+ addVW(z, x, y)
+ }
+ })
+ }
+}
+
+func BenchmarkSubVW(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ x := rndV(n)
+ y := rndW()
+ z := make([]Word, n)
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _S))
+ for i := 0; i < b.N; i++ {
+ subVW(z, x, y)
+ }
+ })
+ }
+}
+
+// Benchmarking subVW using vector of zero to force carry flag set
+func BenchmarkSubVWext(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ x := makeWordVec(0, n)
+ y := Word(1)
+ z := make([]Word, n)
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _S))
+ for i := 0; i < b.N; i++ {
+ subVW(z, x, y)
+ }
+ })
+ }
+}
+
+type funVWW func(z, x []Word, y, r Word) (c Word)
+type argVWW struct {
+ z, x nat
+ y, r Word
+ c Word
+}
+
+var prodVWW = []argVWW{
+ {},
+ {nat{0}, nat{0}, 0, 0, 0},
+ {nat{991}, nat{0}, 0, 991, 0},
+ {nat{0}, nat{_M}, 0, 0, 0},
+ {nat{991}, nat{_M}, 0, 991, 0},
+ {nat{0}, nat{0}, _M, 0, 0},
+ {nat{991}, nat{0}, _M, 991, 0},
+ {nat{1}, nat{1}, 1, 0, 0},
+ {nat{992}, nat{1}, 1, 991, 0},
+ {nat{22793}, nat{991}, 23, 0, 0},
+ {nat{22800}, nat{991}, 23, 7, 0},
+ {nat{0, 0, 0, 22793}, nat{0, 0, 0, 991}, 23, 0, 0},
+ {nat{7, 0, 0, 22793}, nat{0, 0, 0, 991}, 23, 7, 0},
+ {nat{0, 0, 0, 0}, nat{7893475, 7395495, 798547395, 68943}, 0, 0, 0},
+ {nat{991, 0, 0, 0}, nat{7893475, 7395495, 798547395, 68943}, 0, 991, 0},
+ {nat{0, 0, 0, 0}, nat{0, 0, 0, 0}, 894375984, 0, 0},
+ {nat{991, 0, 0, 0}, nat{0, 0, 0, 0}, 894375984, 991, 0},
+ {nat{_M << 1 & _M}, nat{_M}, 1 << 1, 0, _M >> (_W - 1)},
+ {nat{_M<<1&_M + 1}, nat{_M}, 1 << 1, 1, _M >> (_W - 1)},
+ {nat{_M << 7 & _M}, nat{_M}, 1 << 7, 0, _M >> (_W - 7)},
+ {nat{_M<<7&_M + 1<<6}, nat{_M}, 1 << 7, 1 << 6, _M >> (_W - 7)},
+ {nat{_M << 7 & _M, _M, _M, _M}, nat{_M, _M, _M, _M}, 1 << 7, 0, _M >> (_W - 7)},
+ {nat{_M<<7&_M + 1<<6, _M, _M, _M}, nat{_M, _M, _M, _M}, 1 << 7, 1 << 6, _M >> (_W - 7)},
+}
+
+func testFunVWW(t *testing.T, msg string, f funVWW, a argVWW) {
+ z := make(nat, len(a.z))
+ c := f(z, a.x, a.y, a.r)
+ for i, zi := range z {
+ if zi != a.z[i] {
+ t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i])
+ break
+ }
+ }
+ if c != a.c {
+ t.Errorf("%s%+v\n\tgot c = %#x; want %#x", msg, a, c, a.c)
+ }
+}
+
+// TODO(gri) mulAddVWW and divWVW are symmetric operations but
+// their signature is not symmetric. Try to unify.
+
+type funWVW func(z []Word, xn Word, x []Word, y Word) (r Word)
+type argWVW struct {
+ z nat
+ xn Word
+ x nat
+ y Word
+ r Word
+}
+
+func testFunWVW(t *testing.T, msg string, f funWVW, a argWVW) {
+ z := make(nat, len(a.z))
+ r := f(z, a.xn, a.x, a.y)
+ for i, zi := range z {
+ if zi != a.z[i] {
+ t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i])
+ break
+ }
+ }
+ if r != a.r {
+ t.Errorf("%s%+v\n\tgot r = %#x; want %#x", msg, a, r, a.r)
+ }
+}
+
+func TestFunVWW(t *testing.T) {
+ for _, a := range prodVWW {
+ arg := a
+ testFunVWW(t, "mulAddVWW_g", mulAddVWW_g, arg)
+ testFunVWW(t, "mulAddVWW", mulAddVWW, arg)
+
+ if a.y != 0 && a.r < a.y {
+ arg := argWVW{a.x, a.c, a.z, a.y, a.r}
+ testFunWVW(t, "divWVW", divWVW, arg)
+ }
+ }
+}
+
+var mulWWTests = []struct {
+ x, y Word
+ q, r Word
+}{
+ {_M, _M, _M - 1, 1},
+ // 32 bit only: {0xc47dfa8c, 50911, 0x98a4, 0x998587f4},
+}
+
+func TestMulWW(t *testing.T) {
+ for i, test := range mulWWTests {
+ q, r := mulWW_g(test.x, test.y)
+ if q != test.q || r != test.r {
+ t.Errorf("#%d got (%x, %x) want (%x, %x)", i, q, r, test.q, test.r)
+ }
+ }
+}
+
+var mulAddWWWTests = []struct {
+ x, y, c Word
+ q, r Word
+}{
+ // TODO(agl): These will only work on 64-bit platforms.
+ // {15064310297182388543, 0xe7df04d2d35d5d80, 13537600649892366549, 13644450054494335067, 10832252001440893781},
+ // {15064310297182388543, 0xdab2f18048baa68d, 13644450054494335067, 12869334219691522700, 14233854684711418382},
+ {_M, _M, 0, _M - 1, 1},
+ {_M, _M, _M, _M, 0},
+}
+
+func TestMulAddWWW(t *testing.T) {
+ for i, test := range mulAddWWWTests {
+ q, r := mulAddWWW_g(test.x, test.y, test.c)
+ if q != test.q || r != test.r {
+ t.Errorf("#%d got (%x, %x) want (%x, %x)", i, q, r, test.q, test.r)
+ }
+ }
+}
+
+var divWWTests = []struct {
+ x1, x0, y Word
+ q, r Word
+}{
+ {_M >> 1, 0, _M, _M >> 1, _M >> 1},
+ {_M - (1 << (_W - 2)), _M, 3 << (_W - 2), _M, _M - (1 << (_W - 2))},
+}
+
+const testsNumber = 1 << 16
+
+func TestDivWW(t *testing.T) {
+ i := 0
+ for i, test := range divWWTests {
+ rec := reciprocalWord(test.y)
+ q, r := divWW(test.x1, test.x0, test.y, rec)
+ if q != test.q || r != test.r {
+ t.Errorf("#%d got (%x, %x) want (%x, %x)", i, q, r, test.q, test.r)
+ }
+ }
+ //random tests
+ for ; i < testsNumber; i++ {
+ x1 := rndW()
+ x0 := rndW()
+ y := rndW()
+ if x1 >= y {
+ continue
+ }
+ rec := reciprocalWord(y)
+ qGot, rGot := divWW(x1, x0, y, rec)
+ qWant, rWant := bits.Div(uint(x1), uint(x0), uint(y))
+ if uint(qGot) != qWant || uint(rGot) != rWant {
+ t.Errorf("#%d got (%x, %x) want (%x, %x)", i, qGot, rGot, qWant, rWant)
+ }
+ }
+}
+
+func BenchmarkMulAddVWW(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ z := make([]Word, n+1)
+ x := rndV(n)
+ y := rndW()
+ r := rndW()
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _W))
+ for i := 0; i < b.N; i++ {
+ mulAddVWW(z, x, y, r)
+ }
+ })
+ }
+}
+
+func BenchmarkAddMulVVW(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ x := rndV(n)
+ y := rndW()
+ z := make([]Word, n)
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _W))
+ for i := 0; i < b.N; i++ {
+ addMulVVW(z, x, y)
+ }
+ })
+ }
+}
+func BenchmarkDivWVW(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ x := rndV(n)
+ y := rndW()
+ z := make([]Word, n)
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _W))
+ for i := 0; i < b.N; i++ {
+ divWVW(z, 0, x, y)
+ }
+ })
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-15 09:12:08 +0000