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Source file src/math/big/arith_test.go

Documentation: math/big

  // 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/rand"
  	"strings"
  	"testing"
  )
  
  var isRaceBuilder = strings.HasSuffix(testenv.Builder(), "-race")
  
  type funWW func(x, y, c Word) (z1, z0 Word)
  type argWW struct {
  	x, y, c, z1, z0 Word
  }
  
  var sumWW = []argWW{
  	{0, 0, 0, 0, 0},
  	{0, 1, 0, 0, 1},
  	{0, 0, 1, 0, 1},
  	{0, 1, 1, 0, 2},
  	{12345, 67890, 0, 0, 80235},
  	{12345, 67890, 1, 0, 80236},
  	{_M, 1, 0, 1, 0},
  	{_M, 0, 1, 1, 0},
  	{_M, 1, 1, 1, 1},
  	{_M, _M, 0, 1, _M - 1},
  	{_M, _M, 1, 1, _M},
  }
  
  func testFunWW(t *testing.T, msg string, f funWW, a argWW) {
  	z1, z0 := f(a.x, a.y, a.c)
  	if z1 != a.z1 || z0 != a.z0 {
  		t.Errorf("%s%+v\n\tgot z1:z0 = %#x:%#x; want %#x:%#x", msg, a, z1, z0, a.z1, a.z0)
  	}
  }
  
  func TestFunWW(t *testing.T) {
  	for _, a := range sumWW {
  		arg := a
  		testFunWW(t, "addWW_g", addWW_g, arg)
  
  		arg = argWW{a.y, a.x, a.c, a.z1, a.z0}
  		testFunWW(t, "addWW_g symmetric", addWW_g, arg)
  
  		arg = argWW{a.z0, a.x, a.c, a.z1, a.y}
  		testFunWW(t, "subWW_g", subWW_g, arg)
  
  		arg = argWW{a.z0, a.y, a.c, a.z1, a.x}
  		testFunWW(t, "subWW_g symmetric", subWW_g, arg)
  	}
  }
  
  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)
  			}
  		})
  	}
  }
  
  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 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)
  	}
  }
  
  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)
  			}
  		})
  	}
  }
  
  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_g", divWVW_g, arg)
  			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)
  		}
  	}
  }
  
  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)
  			}
  		})
  	}
  }
  

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