.gitignore

@@ -1,4 +1,3 @@
-bigint_go
-src
+
 *.wasm
 *.wat

src/base60.wa

@@ -0,0 +1,22 @@
+var (
+	天干 = []string{"甲", "乙", "丙", "丁", "戊", "己", "庚", "辛", "壬", "癸"}
+	地支 = []string{"子", "丑", "寅", "卯", "辰", "巳", "午", "未", "申", "酉", "戌", "亥"}
+)
+var base60Table = [64]string{}
+
+// var base60IndexTable = map[string]int{}
+
+func init() {
+	for i := 0; i < 64; i++ {
+		base60Table[i] = 天干[i%10] + 地支[i%12]
+		// base60IndexTable[base60Table[i]] = i
+	}
+}
+
+func base60Encode(buf: []byte) => string {
+	return ""
+}
+
+func base60Decode(s: string) => []byte {
+	return nil
+}

src/base60_test.wa

@@ -0,0 +1,92 @@
+import "base60/big"
+
+func Test_base60() {
+	println("Hello")
+	big.AAA()
+
+	// Output:
+	// Hello
+	// 32
+}
+
+func Test_Norm() {
+	big.Test_Norm()
+
+	// Output:
+	// NORM TEST PASS!
+}
+
+func Test_setWord {
+	big.Test_setWord()
+
+	// Output:
+	// set zero: 0
+	// set to 10: 10   10
+}
+
+func Test_set {
+	big.Test_set()
+
+	// Output:
+	// true
+	// item: 1 === 1
+	// item: 2 === 2
+	// item: 3 === 3
+	// item: 4 === 4
+}
+
+func Test_add_sub {
+	big.Test_add()
+
+	// Output:
+	// start test add
+}
+
+func Test_sub {
+	big.Test_sub()
+
+	// Output:
+	// start test sub
+}
+
+func Test_mul {
+	big.Test_mul()
+
+	// Output:
+	// start test mul
+}
+
+func Test_setString {
+	big.Test_setString()
+
+	// Output:
+	// 1796636465
+	// 5326
+}
+
+func Test_div {
+	big.Test_div()
+
+	// Output:
+	// ok div result
+	// ok div remainder result
+}
+
+func Test_int_set {
+	big.Test_Int_Set()
+
+	// Output:
+	// start test set
+}
+
+func Test_Int_Sum {
+	big.Test_Int_Sum()
+	// Output:
+	// start test int add and sub
+}
+
+func Test_Int_Quo {
+	big.Test_Quo()
+	// Output:
+	// start test int quo
+}

src/big/TestInt.wa

@@ -0,0 +1,93 @@
+// Author: TrueAbc
+// Note:
+//  The implementation refers to the go language "math/big" lib.
+
+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")},
+}
+
+func Test_Int_Set() {
+	println("start test set")
+	for _, a := range sumZZ {
+		z: Int
+		z.Set(a.z)
+		if (&z).Cmp(a.z) != 0 {
+			println("error for Int Set")
+		}
+	}
+}
+
+func testFunZZ(msg: string, f: funZZ, a: argZZ) {
+	z: Int
+	f(&z, a.x, a.y)
+	t := (&z).Cmp(a.z)
+	if t != 0 {
+		println(msg, " compute error ", t, ".")
+	}
+}
+
+func Test_Int_Sum() {
+	println("start test int add and sub")
+	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("AddZZ", AddZZ, arg)
+
+		arg = argZZ{a.z, a.y, a.x}
+		testFunZZ("AddZZ symmetric", AddZZ, arg)
+
+		arg = argZZ{a.x, a.z, a.y}
+		testFunZZ("SubZZ", SubZZ, arg)
+
+		arg = argZZ{a.y, a.z, a.x}
+		testFunZZ("SubZZ symmetric", SubZZ, arg)
+	}
+}
+
+var quoTests = []struct {
+	x, y: string
+	q, r: string
+}{
+	{
+		"476217953993950760840509444250624797097991362735329973741718102894495832294430498335824897858659711275234906400899559094370964723884706254265559534144986498357",
+		"9353930466774385905609975137998169297361893554149986716853295022578535724979483772383667534691121982974895531435241089241440253066816724367338287092081996",
+		"50911",
+		"1",
+	},
+	{
+		"11510768301994997771168",
+		"1328165573307167369775",
+		"8",
+		"885443715537658812968",
+	},
+}
+
+func Test_Quo() {
+	println("start test int quo")
+
+	for _, test := range quoTests {
+		x := NewInt(test.x)
+		y := NewInt(test.y)
+		expectedQ := NewInt(test.q)
+		expectedR := NewInt(test.r)
+
+		r := NewInt("0")
+		q, r := NewInt("0").QuoRem(x, y, r)
+
+		if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 {
+			println("error for Int quo")
+		}
+	}
+}

src/big/TestNat.wa

@@ -0,0 +1,144 @@
+// Author: TrueAbc
+// Note:
+//  The implementation refers to the go language "math/big" lib.
+
+// test好像并不执行该文件夹, 改为导出方法放在外层执行
+func Test_Norm {
+	t := nat{Data: []uint{1, 0, 0, 0}}
+	t = t.norm()
+	if len(t.Data) == 1 && t.Data[0] == 1 {
+		println("NORM TEST PASS!")
+	} else {
+		println("NORM TEST FAILED!")
+	}
+}
+
+func Test_setWord {
+	t := nat{Data: []uint{1, 2, 3, 4}}
+	z := t.setWord(0)
+	println("set zero:", len(z.Data))
+
+	z = t.setWord(10)
+	println("set to 10:", z.Data[0], " ", t.Data[0])
+}
+
+func Test_set {
+	t := nat{Data: []uint{1, 2, 3, 4}}
+	z := t.set(t)
+	println(len(z.Data) == len(t.Data))
+	for i := 0; i < len(z.Data); i++ {
+		println("item:", z.Data[i], "===", t.Data[i])
+	}
+}
+
+// 参考go单元测试的内容
+type funNN func(z: nat, x: nat, y: nat) => nat
+type argNN struct {
+	z: nat
+	x: nat
+	y: nat
+}
+
+var sumNN = []argNN{
+	{},
+	{z: nat{[]uint{1}}, x: nat{nil}, y: nat{[]uint{1}}},
+	{z: nat{[]uint{1111111110}}, x: nat{[]uint{123456789}}, y: nat{[]uint{987654321}}},
+	{z: nat{[]uint{0, 0, 0, 1}}, x: nat{nil}, y: nat{[]uint{0, 0, 0, 1}}},
+	{z: nat{[]uint{0, 0, 0, 1111111110}}, x: nat{[]uint{0, 0, 0, 123456789}}, y: nat{Data: []uint{0, 0, 0, 987654321}}},
+	{z: nat{[]uint{0, 0, 0, 1}}, x: nat{[]uint{0, 0, _M}}, y: nat{[]uint{0, 0, 1}}},
+}
+
+var prodNN = []argNN{
+	{},
+	{z: nat{nil}, x: nat{nil}, y: nat{nil}},
+	{z: nat{nil}, x: nat{[]uint{991}}, y: nat{nil}},
+	{z: nat{[]uint{991}}, x: nat{[]uint{991}}, y: nat{[]uint{1}}},
+	{z: nat{[]uint{991 * 991}}, x: nat{[]uint{991}}, y: nat{[]uint{991}}},
+	{z: nat{[]uint{0, 0, 991 * 991}}, x: nat{[]uint{0, 991}}, y: nat{[]uint{0, 991}}},
+	{z: nat{[]uint{1 * 991, 2 * 991, 3 * 991, 4 * 991}}, x: nat{[]uint{1, 2, 3, 4}}, y: nat{[]uint{991}}},
+	{z: nat{[]uint{4, 11, 20, 30, 20, 11, 4}}, x: nat{[]uint{1, 2, 3, 4}}, y: nat{[]uint{4, 3, 2, 1}}},
+	{
+		z: natFromString("11790184577738583171520872861412518665678211592275841109096961"),
+		x: natFromString("515377520732011331036461129765621272702107522001"),
+		y: natFromString("22876792454961"),
+	},
+}
+
+func testAdd(a: argNN) {
+	temp := &nat{Data: nil}
+	z := temp.add(a.x, a.y)
+	if z.cmp(a.z) != 0 {
+		println("Error for add result")
+	}
+}
+
+func testSub(a: argNN) {
+	temp := &nat{Data: nil}
+	z := temp.sub(a.x, a.y)
+	if z.cmp(a.z) != 0 {
+		println("Error for sub result")
+	}
+}
+
+func testMul(a: argNN) {
+	temp := &nat{Data: nil}
+	z := temp.mul(a.x, a.y)
+	if z.cmp(a.z) != 0 {
+		println("Error for mul result")
+	}
+}
+
+func Test_add {
+	println("start test add")
+	for _, a := range sumNN {
+		testAdd(a)
+	}
+}
+
+func Test_sub {
+	println("start test sub")
+	for _, a := range sumNN {
+		arg := argNN{a.x, a.z, a.y}
+		testSub(arg)
+	}
+}
+
+func Test_mul {
+	println("start test mul")
+	for _, a := range prodNN {
+		arg := a
+		testMul(arg)
+
+		arg = argNN{a.z, a.y, a.x}
+		testMul(arg)
+	}
+}
+
+func Test_div {
+	u := natFromString("11790184577738583171520872861412518665678211592275841109096961")
+	v := natFromString("515377520732011331036461129765621272702107522001")
+	w := natFromString("22876792454961") // 商
+	r := natFromString("0")              // 余数
+
+	q := &nat{nil}
+	q2, r2 := q.div(nat{nil}, u, v)
+
+	if q2.cmp(w) != 0 {
+		println("wrong div result")
+	} else {
+		println("ok div result")
+	}
+	if r2.cmp(r) != 0 {
+		println("wrong div remainder result")
+	} else {
+		println("ok div remainder result")
+	}
+
+}
+
+func Test_setString {
+	n := natFromString("22876792454961")
+	for _, i := range n.Data {
+		println(i)
+	}
+}

src/big/arith.wa

@@ -0,0 +1,208 @@
+// Author: TrueAbc
+// Note:
+//  The implementation refers to the go language "math/big" lib.
+
+import "math/bits"
+
+func AAA {
+	println(bits.UintSize)
+}
+
+const (
+	_S = _W / 8 // 字宽（以字节为单位）
+
+	_W = bits.UintSize // 字宽（以位为单位）
+	_B = 1 << _W       // 基数
+	_M = _B - 1        // 基数掩码
+)
+
+// z1<<_W + z0 = x*y
+func mulWW(x, y: uint) => (z1, z0: uint) {
+	return bits.Mul(x, y)
+}
+
+// z1<<_W + z0 = x*y + c
+func mulAddWWW(x, y, c: uint) => (z1, z0: uint) {
+	hi, lo := bits.Mul(x, y)
+	cc: uint
+	lo, cc = bits.Add(lo, c, 0)
+	return hi + cc, lo
+}
+
+// nlz returns the number of leading zeros in x.
+// Wraps bits.LeadingZeros call for convenience.
+func nlz(x: uint) => uint {
+	return uint(bits.LeadingZeros(x))
+}
+
+// The resulting carry c is either 0 or 1.
+func addVV(z, x, y: []uint) => (c: uint) {
+	for i := 0; i < len(z) && i < len(x) && i < len(y); i++ {
+		zi, cc := bits.Add(x[i], y[i], c)
+		z[i] = zi
+		c = cc
+	}
+	return
+}
+
+// The resulting carry c is either 0 or 1.
+func subVV(z, x, y: []uint) => (c: uint) {
+	for i := 0; i < len(z) && i < len(x) && i < len(y); i++ {
+		zi, cc := bits.Sub(x[i], y[i], c)
+		z[i] = zi
+		c = cc
+	}
+	return
+}
+
+// The resulting carry c is either 0 or 1.
+func addVW(z, x: []uint, y: uint) => (c: uint) {
+	c = y
+	for i := 0; i < len(z) && i < len(x); i++ {
+		zi, cc := bits.Add(x[i], c, 0)
+		z[i] = zi
+		c = cc
+	}
+	return
+}
+
+func subVW(z, x: []uint, y: uint) => (c: uint) {
+	c = y
+	for i := 0; i < len(z) && i < len(x); i++ {
+		zi, cc := bits.Sub(x[i], c, 0)
+		z[i] = zi
+		c = cc
+	}
+	return
+}
+
+func shlVU(z, x: []uint, s: uint) => (c: uint) {
+	if s == 0 {
+		copy(z, x)
+		return
+	}
+	if len(z) == 0 {
+		return
+	}
+	s &= _W - 1 // hint to the compiler that shifts by s don't need guard code
+	ŝ := _W - s
+	ŝ &= _W - 1 // ditto
+	c = x[len(z)-1] >> ŝ
+	for i := len(z) - 1; i > 0; i-- {
+		z[i] = x[i]<<s | x[i-1]>>ŝ
+	}
+	z[0] = x[0] << s
+	return
+}
+
+func shrVU(z, x: []uint, s: uint) => (c: uint) {
+	if s == 0 {
+		copy(z, x)
+		return
+	}
+	if len(z) == 0 {
+		return
+	}
+	if len(x) != len(z) {
+		// This is an invariant guaranteed by the caller.
+		panic("len(x) != len(z)")
+	}
+	s &= _W - 1 // hint to the compiler that shifts by s don't need guard code
+	ŝ := _W - s
+	ŝ &= _W - 1 // ditto
+	c = x[0] << ŝ
+	for i := 1; i < len(z); i++ {
+		z[i-1] = x[i-1]>>s | x[i]<<ŝ
+	}
+	z[len(z)-1] = x[len(z)-1] >> s
+	return
+}
+
+func mulAddVWW(z, x: []uint, y, r: uint) => (c: uint) {
+	c = r
+	for i := 0; i < len(z) && i < len(x); i++ {
+		c, z[i] = mulAddWWW(x[i], y, c)
+	}
+	return
+}
+
+func addMulVVW(z, x: []uint, y: uint) => (c: uint) {
+	for i := 0; i < len(z) && i < len(x); i++ {
+		z1, z0 := mulAddWWW(x[i], y, z[i])
+		lo, cc := bits.Add(z0, c, 0)
+		c, z[i] = cc, lo
+		c += z1
+	}
+	return
+}
+
+// q = ( x1 << _W + x0 - r)/y. m = floor(( _B^2 - 1 ) / d - _B). Requiring x1<y.
+// An approximate reciprocal with a reference to "Improved Division by Invariant Integers
+// (IEEE Transactions on Computers, 11 Jun. 2010)"
+func divWW(x1, x0, y, m: uint) => (q, r: uint) {
+	s := nlz(y)
+	if s != 0 {
+		x1 = x1<<s | x0>>(_W-s)
+		x0 <<= s
+		y <<= s
+	}
+	d := y
+	// We know that
+	//   m = ⎣(B^2-1)/d⎦-B
+	//   ⎣(B^2-1)/d⎦ = m+B
+	//   (B^2-1)/d = m+B+delta1    0 <= delta1 <= (d-1)/d
+	//   B^2/d = m+B+delta2        0 <= delta2 <= 1
+	// The quotient we're trying to compute is
+	//   quotient = ⎣(x1*B+x0)/d⎦
+	//            = ⎣(x1*B*(B^2/d)+x0*(B^2/d))/B^2⎦
+	//            = ⎣(x1*B*(m+B+delta2)+x0*(m+B+delta2))/B^2⎦
+	//            = ⎣(x1*m+x1*B+x0)/B + x0*m/B^2 + delta2*(x1*B+x0)/B^2⎦
+	// The latter two terms of this three-term sum are between 0 and 1.
+	// So we can compute just the first term, and we will be low by at most 2.
+	t1, t0 := bits.Mul(m, x1)
+	_, c := bits.Add(t0, x0, 0)
+	t1, _ = bits.Add(t1, x1, c)
+	// The quotient is either t1, t1+1, or t1+2.
+	// We'll try t1 and adjust if needed.
+	qq := t1
+	// compute remainder r=x-d*q.
+	dq1, dq0 := bits.Mul(d, qq)
+	r0, b := bits.Sub(x0, dq0, 0)
+	r1, _ := bits.Sub(x1, dq1, b)
+	// The remainder we just computed is bounded above by B+d:
+	// r = x1*B + x0 - d*q.
+	//   = x1*B + x0 - d*⎣(x1*m+x1*B+x0)/B⎦
+	//   = x1*B + x0 - d*((x1*m+x1*B+x0)/B-alpha)                                   0 <= alpha < 1
+	//   = x1*B + x0 - x1*d/B*m                         - x1*d - x0*d/B + d*alpha
+	//   = x1*B + x0 - x1*d/B*⎣(B^2-1)/d-B⎦             - x1*d - x0*d/B + d*alpha
+	//   = x1*B + x0 - x1*d/B*⎣(B^2-1)/d-B⎦             - x1*d - x0*d/B + d*alpha
+	//   = x1*B + x0 - x1*d/B*((B^2-1)/d-B-beta)        - x1*d - x0*d/B + d*alpha   0 <= beta < 1
+	//   = x1*B + x0 - x1*B + x1/B + x1*d + x1*d/B*beta - x1*d - x0*d/B + d*alpha
+	//   =        x0        + x1/B        + x1*d/B*beta        - x0*d/B + d*alpha
+	//   = x0*(1-d/B) + x1*(1+d*beta)/B + d*alpha
+	//   <  B*(1-d/B) +  d*B/B          + d          because x0<B (and 1-d/B>0), x1<d, 1+d*beta<=B, alpha<1
+	//   =  B - d     +  d              + d
+	//   = B+d
+	// So r1 can only be 0 or 1. If r1 is 1, then we know q was too small.
+	// Add 1 to q and subtract d from r. That guarantees that r is <B, so
+	// we no longer need to keep track of r1.
+	if r1 != 0 {
+		qq++
+		r0 -= d
+	}
+	// If the remainder is still too large, increment q one more time.
+	if r0 >= d {
+		qq++
+		r0 -= d
+	}
+	return qq, r0 >> s
+}
+
+// reciprocalWord return the reciprocal of the divisor. rec = floor(( _B^2 - 1 ) / u - _B). u = d1 << nlz(d1).
+func reciprocalWord(d1: uint) => uint {
+	u := uint(d1 << nlz(d1))
+	x1 := ^u
+	x0 := uint(_M)
+	rec, _ := bits.Div(x1, x0, u) // (_B^2-1)/U-_B = (_B*(_M-C)+_M)/U
+	return uint(rec)
+}

src/big/binary.wa

@@ -0,0 +1,16 @@
+// Author: TrueAbc
+// Note:
+//  The implementation refers to the go language "math/big" lib.
+
+// 暂时把go的大端转换代码copy过来
+
+func Buf2Uint64(b: []byte) => uint64 {
+	_ = b[7] // bounds check hint to compiler; see golang.org/issue/14808
+	return uint64(b[7]) | uint64(b[6])<<8 | uint64(b[5])<<16 | uint64(b[4])<<24 |
+		uint64(b[3])<<32 | uint64(b[2])<<40 | uint64(b[1])<<48 | uint64(b[0])<<56
+}
+
+func Buf2Uint32(b: []byte) => uint32 {
+	_ = b[3] // bounds check hint to compiler; see golang.org/issue/14808
+	return uint32(b[0]) | uint32(b[1])<<8 | uint32(b[2])<<16 | uint32(b[3])<<24
+}

src/big/int.wa

@@ -0,0 +1,247 @@
+// Author: TrueAbc
+// Note:
+//  The implementation refers to the go language "math/big" lib.
+
+type Int struct {
+	neg: bool // sign
+	abs: nat  // absolute value of the integer
+}
+
+var intOne = &Int{false, natOne}
+
+// 测试用
+func NewInt(x: string) => *Int {
+	t := new(Int)
+	neg := false
+	if x[0] == '-' {
+		neg = true
+		x = x[1:]
+	}
+	t.abs = natFromString(x)
+	t.neg = neg
+
+	return t
+}
+
+// Sign returns:
+//
+//	-1 if x <  0
+//	 0 if x == 0
+//	+1 if x >  0
+//
+func Int.Sign() => int {
+	if len(this.abs.Data) == 0 {
+		return 0
+	}
+	if this.neg {
+		return -1
+	}
+	return 1
+}
+
+// Set sets z to x and returns z.
+func Int.Set(x: *Int) => *Int {
+	if this != x {
+		this.abs = this.abs.set(x.abs)
+		this.neg = x.neg
+	}
+	return this
+}
+
+// Bits provides raw (unchecked but fast) access to x by returning its
+// absolute value as a little-endian Word slice. The result and x share
+// the same underlying array.
+// Bits is intended to support implementation of missing low-level Int
+// functionality outside this package; it should be avoided otherwise.
+func Int.Bits() => []uint {
+	return this.abs.Data
+}
+
+// SetBits provides raw (unchecked but fast) access to z by setting its
+// value to abs, interpreted as a little-endian Word slice, and returning
+// z. The result and abs share the same underlying array.
+// SetBits is intended to support implementation of missing low-level Int
+// functionality outside this package; it should be avoided otherwise.
+func Int.SetBits(abs: []uint) => *Int {
+	temp := &nat{abs}
+	this.abs = temp.norm()
+	this.neg = false
+	return this
+}
+
+// Abs sets z to |x| (the absolute value of x) and returns z.
+func Int.Abs(x: *Int) => *Int {
+	this.Set(x)
+	this.neg = false
+	return this
+}
+
+// Neg sets z to -x and returns z.
+func Int.Neg(x: *Int) => *Int {
+	this.Set(x)
+	this.neg = len(this.abs.Data) > 0 && !this.neg // 0 has no sign
+	return this
+}
+
+// Add sets z to the sum x+y and returns z.
+func Int.Add(x, y: *Int) => *Int {
+	neg := x.neg
+	if x.neg == y.neg {
+		// x + y == x + y
+		// (-x) + (-y) == -(x + y)
+		this.abs = this.abs.add(x.abs, y.abs)
+	} else {
+		// x + (-y) == x - y == -(y - x)
+		// (-x) + y == y - x == -(x - y)
+		if x.abs.cmp(y.abs) >= 0 {
+			this.abs = this.abs.sub(x.abs, y.abs)
+		} else {
+			neg = !neg
+			this.abs = this.abs.sub(y.abs, x.abs)
+		}
+	}
+	this.neg = len(this.abs.Data) > 0 && neg // 0 has no sign
+	return this
+}
+
+// Sub sets z to the difference x-y and returns z.
+func Int.Sub(x, y: *Int) => *Int {
+	neg := x.neg
+	if x.neg != y.neg {
+		// x - (-y) == x + y
+		// (-x) - y == -(x + y)
+		this.abs = this.abs.add(x.abs, y.abs)
+	} else {
+		// x - y == x - y == -(y - x)
+		// (-x) - (-y) == y - x == -(x - y)
+		if x.abs.cmp(y.abs) >= 0 {
+			this.abs = this.abs.sub(x.abs, y.abs)
+		} else {
+			neg = !neg
+			this.abs = this.abs.sub(y.abs, x.abs)
+		}
+	}
+	this.neg = len(this.abs.Data) > 0 && neg // 0 has no sign
+	return this
+}
+
+// Mul sets z to the product x*y and returns z.
+func Int.Mul(x, y: *Int) => *Int {
+	// x * y == x * y
+	// x * (-y) == -(x * y)
+	// (-x) * y == -(x * y)
+	// (-x) * (-y) == x * y
+	this.abs = this.abs.mul(x.abs, y.abs)
+	this.neg = len(this.abs.Data) > 0 && this.neg != this.neg // 0 has no sign
+	return this
+}
+
+// QuoRem sets z to the quotient x/y and r to the remainder x%y
+// and returns the pair (z, r) for y != 0.
+// If y == 0, a division-by-zero run-time panic occurs.
+//
+// QuoRem implements T-division and modulus (like Go):
+//
+//	q = x/y      with the result truncated to zero
+//	r = x - y*q
+//
+// (See Daan Leijen, ``Division and Modulus for Computer Scientists''.)
+// See DivMod for Euclidean division and modulus (unlike Go).
+//
+func Int.QuoRem(x, y, r: *Int) => (*Int, *Int) {
+	this.abs, r.abs = this.abs.div(r.abs, x.abs, y.abs)
+	this.neg, r.neg = len(this.abs.Data) > 0 && x.neg != y.neg, len(r.abs.Data) > 0 && x.neg // 0 has no sign
+	return this, r
+}
+
+// DivMod sets z to the quotient x div y and m to the modulus x mod y
+// and returns the pair (z, m) for y != 0.
+// If y == 0, a division-by-zero run-time panic occurs.
+//
+// DivMod implements Euclidean division and modulus (unlike Go):
+//
+//	q = x div y  such that
+//	m = x - y*q  with 0 <= m < |y|
+//
+// (See Raymond T. Boute, ``The Euclidean definition of the functions
+// div and mod''. ACM Transactions on Programming Languages and
+// Systems (TOPLAS), 14(2):127-144, New York, NY, USA, 4/1992.
+// ACM press.)
+// See QuoRem for T-division and modulus (like Go).
+//
+func Int.DivMod(x, y, m: *Int) => (*Int, *Int) {
+	y0 := y // save y
+	if this == y || alias(this.abs, y.abs) {
+		y0 = new(Int).Set(y)
+	}
+	this.QuoRem(x, y, m)
+	if m.neg {
+		if y0.neg {
+			this.Add(this, intOne)
+			m.Sub(m, y0)
+		} else {
+			this.Sub(this, intOne)
+			m.Add(m, y0)
+		}
+	}
+	return this, m
+}
+
+// Cmp compares x and y and returns:
+//
+//   -1 if x <  y
+//    0 if x == y
+//   +1 if x >  y
+//
+func Int.Cmp(y: *Int) => (r: int) {
+	// x cmp y == x cmp y
+	// x cmp (-y) == x
+	// (-x) cmp y == y
+	// (-x) cmp (-y) == -(x cmp y)
+	switch {
+	case this == y:
+		// nothing to do
+	case this.neg == y.neg:
+		r = this.abs.cmp(y.abs)
+		if this.neg {
+			r = -r
+		}
+	case this.neg:
+		r = -1
+	default:
+		r = 1
+	}
+	return
+}
+
+// CmpAbs compares the absolute values of x and y and returns:
+//
+//   -1 if |x| <  |y|
+//    0 if |x| == |y|
+//   +1 if |x| >  |y|
+//
+func Int.CmpAbs(y: *Int) => int {
+	return this.abs.cmp(y.abs)
+}
+
+// SetBytes interprets buf as the bytes of a big-endian unsigned
+// integer, sets z to that value, and returns z.
+func Int.SetBytes(buf: []byte) => *Int {
+	this.abs = this.abs.setBytes(buf)
+	this.neg = false
+	return this
+}
+
+// Bytes returns the absolute value of x as a big-endian byte slice.
+//
+// To use a fixed length slice, or a preallocated one, use FillBytes.
+func Int.Bytes() => []byte {
+	buf := make([]byte, len(this.abs.Data)*_S)
+	return buf[this.abs.bytes(buf):]
+}
+
+// BitLen returns the length of the absolute value of x in bits.
+// The bit length of 0 is 0.
+func Int.BitLen() => int {
+	return this.abs.bitLen()
+}

src/big/nat.wa

@@ -0,0 +1,317 @@
+// Author: TrueAbc
+// Note:
+//  The implementation refers to the go language "math/big" lib.
+
+import (
+	"math/bits"
+)
+
+type nat struct {
+	Data: []uint
+}
+
+func natFromString(s: string) => nat {
+	temp := &nat{nil}
+	return temp.setString(s)
+}
+
+// 这个方法是临时使用的, 用于部分内容的测试
+func nat.setString(s: string) => nat {
+	// 长度应该是超过的
+	z := this.make((len(s) + _S - 1) / _S)
+	val: uint = 0
+	for i := 0; i < len(s); i++ {
+		if s[i] < '0' || s[i] > '9' {
+			println("bad big integer:", s[i])
+		}
+		val = uint(s[i] - '0')
+		z = z.mulAddWW(z, 10, val)
+		val = 0
+	}
+
+	return z.norm()
+}
+
+func nat.clear() {
+	for i := range this.Data {
+		this.Data[i] = 0
+	}
+}
+
+var (
+	natOne = nat{Data: []uint{1}}
+)
+
+func nat.raw_print() {
+	print("raw_nat: {")
+	for i := range this.Data {
+		print(this.Data[i])
+		if i != len(this.Data)-1 {
+			print(",")
+		}
+	}
+	println("}")
+}
+
+func nat.norm() => nat {
+	i := len(this.Data)
+	for i > 0 && this.Data[i-1] == 0 {
+		i--
+	}
+	return nat{Data: this.Data[0:i]}
+}
+
+func nat.make(n: int) => nat {
+	if n <= cap(this.Data) {
+		return nat{Data: this.Data[:n]} // reuse this.Data
+	}
+	if n == 1 {
+		// Most nats start small and stay that way; don't over-allocate.
+		return nat{Data: make([]uint, 1)}
+	}
+	// Choosing a good value for e has significant performance impact
+	// because it increases the chance that a value can be reused.
+	const e = 4 // extra capacity
+	return nat{Data: make([]uint, n, n+e)}
+}
+
+func nat.setWord(x: uint) => nat {
+	if x == 0 {
+		return nat{Data: this.Data[:0]}
+	}
+	z := this.make(1)
+	z.Data[0] = x
+	return z
+}
+
+func nat.set(x: nat) => nat {
+	z := this.make(len(x.Data))
+	copy(z.Data, x.Data)
+
+	return z
+}
+
+func nat.add(x, y: nat) => nat {
+	m := len(x.Data)
+	n := len(y.Data)
+
+	switch {
+	case m < n:
+		return this.add(y, x)
+	case m == 0:
+		// n == 0 because m >= n; result is 0
+		return nat{Data: this.Data[:0]}
+	case n == 0:
+		// result is x
+		return this.set(x)
+	}
+	// m > 0
+	z := this.make(m + 1)
+	c := addVV(z.Data[0:n], x.Data, y.Data)
+	if m > n {
+		c = addVW(z.Data[n:m], x.Data[n:], c)
+	}
+	z.Data[m] = c
+
+	return z.norm()
+}
+
+func nat.sub(x, y: nat) => nat {
+	m := len(x.Data)
+	n := len(y.Data)
+	switch {
+	case m < n:
+		panic("underflow")
+	case m == 0:
+		// n == 0 because m >= n; result is 0
+		return nat{Data: this.Data[:0]}
+	case n == 0:
+		// result is x
+		return this.set(x)
+	}
+	// m > 0
+	z := this.make(m)
+	c := subVV(z.Data[0:n], x.Data, y.Data)
+	if m > n {
+		c = subVW(z.Data[n:], x.Data[n:], c)
+	}
+	if c != 0 {
+		panic("underflow")
+	}
+	return z.norm()
+}
+
+func nat.cmp(y: nat) => int {
+	r := 0
+	m := len(this.Data)
+	n := len(y.Data)
+	if m != n || m == 0 {
+		switch {
+		case m < n:
+			r = -1
+		case m > n:
+			r = 1
+		}
+		return r
+	}
+	i := m - 1
+	for i > 0 && this.Data[i] == y.Data[i] {
+		i--
+	}
+	switch {
+	case this.Data[i] < y.Data[i]:
+		r = -1
+	case this.Data[i] > y.Data[i]:
+		r = 1
+	}
+	return r
+}
+
+func nat.mulAddWW(x: nat, y, r: uint) => nat {
+	m := len(x.Data)
+	if m == 0 || y == 0 {
+		return this.setWord(r) // result is r
+	}
+	// m > 0
+
+	z := this.make(m + 1)
+	z.Data[m] = mulAddVWW(z.Data[:m], x.Data, y, r)
+	return z.norm()
+}
+
+// basicMul multiplies x and y and leaves the result in z.
+// The (non-normalized) result is placed in z[0 : len(x) + len(y)].
+func basicMul(z, x, y: nat) {
+	// z.Data[:len(x.Data)+len(y.Data)].clear()
+	// initialize z
+	t := nat{Data: z.Data[:len(x.Data)+len(y.Data)]}
+	t.clear()
+
+	for i, d := range y.Data {
+		if d != 0 {
+			z.Data[len(x.Data)+i] = addMulVVW(z.Data[i:i+len(x.Data)], x.Data, d)
+		}
+	}
+}
+
+// alias reports whether x and y share the same base array.
+// Note: alias assumes that the capacity of underlying arrays
+//       is never changed for nat values; i.e. that there are
+//       no 3-operand slice expressions in this code (or worse,
+//       reflect-based operations to the same effect).
+func alias(x, y: nat) => bool {
+	x_cap := cap(x.Data)
+	y_cap := cap(y.Data)
+	return x_cap > 0 && y_cap > 0 && &x.Data[:x_cap][x_cap-1] == &y.Data[:y_cap][y_cap-1]
+}
+
+// addAt implements z += x<<(_W*i); z must be long enough.
+// (we don't use nat.add because we need z to stay the same
+// slice, and we don't need to normalize z after each addition)
+func addAt(z, x: nat, i: int) {
+	if n := len(x.Data); n > 0 {
+		if c := addVV(z.Data[i:i+n], z.Data[i:], x.Data); c != 0 {
+			j := i + n
+			if j < len(z.Data) {
+				addVW(z.Data[j:], z.Data[j:], c)
+			}
+		}
+	}
+}
+
+func nat.mul(x, y: nat) => nat {
+	m := len(x.Data)
+	n := len(y.Data)
+	switch {
+	case m < n:
+		return this.mul(y, x)
+	case m == 0 || n == 0:
+		return nat{Data: this.Data[:0]}
+	case n == 1:
+		return this.mulAddWW(x, y.Data[0], 0)
+	}
+	// m >= n > 1
+
+	// determine if z can be reused
+	if alias(*this, x) || alias(*this, y) {
+		// 空指针操作
+		this = nil // z is an alias for x or y - cannot reuse
+	}
+
+	z := this.make(m + n)
+	basicMul(z, x, y)
+	return z.norm()
+}
+
+func getNat(n: int) => *nat {
+	r := (&nat{}).make(n)
+	return &r
+}
+
+func putNat(x: *nat) {
+	// panic("todo")
+}
+
+func nat.bitLen() => int {
+	if i := len(this.Data) - 1; i >= 0 {
+		return i*_W + bits.Len(uint(this.Data[i]))
+	}
+	return 0
+}
+
+// bytes writes the value of z into buf using big-endian encoding.
+// The value of z is encoded in the slice buf[i:]. If the value of z
+// cannot be represented in buf, bytes panics. The number i of unused
+// bytes at the beginning of buf is returned as result.
+func nat.bytes(buf: []byte) => int {
+	i := len(buf)
+	for _, d := range this.Data {
+		for j := 0; j < _S; j++ {
+			i--
+			if i >= 0 {
+				buf[i] = byte(d)
+			} else if byte(d) != 0 {
+				panic("math/big: buffer too small to fit value")
+			}
+			d >>= 8
+		}
+	}
+
+	if i < 0 {
+		i = 0
+	}
+	for i < len(buf) && buf[i] == 0 {
+		i++
+	}
+	return i
+}
+
+// bigEndianWord returns the contents of buf interpreted as a big-endian encoded Word value.
+func bigEndianWord(buf: []byte) => uint {
+	if _W == 64 {
+		return uint(Buf2Uint64(buf))
+	}
+	return uint(Buf2Uint64(buf))
+}
+
+// setBytes interprets buf as the bytes of a big-endian unsigned
+// integer, sets z to that value, and returns z.
+func nat.setBytes(buf: []byte) => nat {
+	z := this.make((len(buf) + _S - 1) / _S)
+	i := len(buf)
+	for k := 0; i >= _S; k++ {
+		z.Data[k] = bigEndianWord(buf[i-_S : i])
+		i -= _S
+	}
+
+	if i > 0 {
+		d: uint = 0
+		for s := uint(0); i > 0; s += 8 {
+			d |= uint(buf[i-1]) << s
+			i--
+		}
+		z.Data[len(z.Data)-1] = d
+	}
+
+	return z.norm()
+}

src/big/natdiv.wa

@@ -0,0 +1,375 @@
+// Author: TrueAbc
+// Note:
+//  The implementation refers to the go language "math/big" lib.
+
+import "math/bits"
+
+// div returns q, r such that q = ⌊u/v⌋ and r = u%v = u - q·v.
+// It uses z and z2 as the storage for q and r.
+func nat.div(z2, u, v: nat) => (q: nat, r: nat) {
+	if len(v.Data) == 0 {
+		panic("division by zero")
+	}
+
+	if u.cmp(v) < 0 {
+		q.Data = this.Data[:0]
+		r = z2.set(u)
+		return
+	}
+	if len(v.Data) == 1 {
+		// Short division: long optimized for a single-word divisor.
+		// In that case, the 2-by-1 guess is all we need at each step.
+		r2: uint
+		q, r2 = this.divW(u, v.Data[0])
+		r = z2.setWord(r2)
+		return
+	}
+	q, r = this.divLarge(z2, u, v)
+	return
+}
+
+func nat.divW(x: nat, y: uint) => (q: nat, r: uint) {
+	m := len(x.Data)
+	switch {
+	case y == 0:
+		panic("division by zero")
+	case y == 1:
+		q = this.set(x) // result is x
+		return
+	case m == 0:
+		q.Data = this.Data[:0] // result is 0
+		return
+	}
+	// m > 0
+	z := this.make(m)
+	r = divWVW(z.Data, 0, x.Data, y)
+	q = z.norm()
+	return
+}
+
+// divWVW overwrites z with ⌊x/y⌋, returning the remainder r.
+// The caller must ensure that len(z) = len(x).
+func divWVW(z: []uint, xn: uint, x: []uint, y: uint) => (r: uint) {
+	r = xn
+	if len(x) == 1 {
+		qq, rr := bits.Div(uint(r), uint(x[0]), uint(y))
+		z[0] = uint(qq)
+		return uint(rr)
+	}
+
+	rec := reciprocalWord(y)
+	for i := len(z) - 1; i >= 0; i-- {
+		z[i], r = divWW(r, x[i], y, rec)
+	}
+	return r
+}
+
+// div returns q, r such that q = ⌊uIn/vIn⌋ and r = uIn%vIn = uIn - q·vIn.
+// It uses z and u as the storage for q and r.
+// The caller must ensure that len(vIn) ≥ 2 (use divW otherwise)
+// and that len(uIn) ≥ len(vIn) (the answer is 0, uIn otherwise).
+func nat.divLarge(u, uIn, vIn: nat) => (q: nat, r: nat) {
+	z := *this
+	n := len(vIn.Data)
+	m := len(uIn.Data) - n
+	// Scale the inputs so vIn's top bit is 1 (see “Scaling Inputs” above).
+	// vIn is treated as a read-only input (it may be in use by another
+	// goroutine), so we must make a copy.
+	shift := nlz(vIn.Data[n-1])
+	vp := getNat(n)
+	v := *vp
+	shlVU(v.Data, vIn.Data, shift)
+	u = u.make(len(uIn.Data) + 1)
+	u.Data[len(uIn.Data)] = shlVU(u.Data[0:len(uIn.Data)], uIn.Data, shift)
+
+	// The caller should not pass aliased z and u, since those are
+	// the two different outputs, but correct just in case.
+	if alias(z, u) {
+		z.Data = nil
+	}
+	q = z.make(m + 1)
+
+	// Use basic or recursive long division depending on size.
+	if n < divRecursiveThreshold {
+		q.divBasic(u, v)
+	} else {
+		q.divRecursive(u, v)
+	}
+	putNat(vp)
+
+	q = q.norm()
+
+	// Undo scaling of remainder.
+	shrVU(u.Data, u.Data, shift)
+	r = u.norm()
+
+	return q, r
+}
+
+// divBasic implements long division as described above.
+// It overwrites q with ⌊u/v⌋ and overwrites u with the remainder r.
+// q must be large enough to hold ⌊u/v⌋.
+func nat.divBasic(u, v: nat) {
+	n := len(v.Data)
+	m := len(u.Data) - n
+
+	qhatvp := getNat(n + 1)
+	qhatv := *qhatvp
+
+	// Set up for divWW below, precomputing reciprocal argument.
+	vn1 := v.Data[n-1]
+	rec := reciprocalWord(vn1)
+
+	// Compute each digit of quotient.
+	for j := m; j >= 0; j-- {
+		// Compute the 2-by-1 guess q̂.
+		// The first iteration must invent a leading 0 for u.
+		qhat := uint(_M)
+		ujn: uint
+		if j+n < len(u.Data) {
+			ujn = u.Data[j+n]
+		}
+
+		// ujn ≤ vn1, or else q̂ would be more than one digit.
+		// For ujn == vn1, we set q̂ to the max digit M above.
+		// Otherwise, we compute the 2-by-1 guess.
+		if ujn != vn1 {
+			rhat: uint
+			qhat, rhat = divWW(ujn, u.Data[j+n-1], vn1, rec)
+
+			// Refine q̂ to a 3-by-2 guess. See “Refining Guesses” above.
+			vn2 := v.Data[n-2]
+			x1, x2 := mulWW(qhat, vn2)
+			ujn2 := u.Data[j+n-2]
+			for greaterThan(x1, x2, rhat, ujn2) {
+				qhat--
+				prevRhat := rhat
+				rhat += vn1
+				// If r̂  overflows, then
+				// r̂ u[j+n-2]v[n-1] is now definitely > x1 x2.
+				if rhat < prevRhat {
+					break
+				}
+				// TODO(rsc): No need for a full mulWW.
+				// x2 += vn2; if x2 overflows, x1++
+				x1, x2 = mulWW(qhat, vn2)
+			}
+		}
+
+		// Compute q̂·v.
+		qhatv.Data[n] = mulAddVWW(qhatv.Data[0:n], v.Data, qhat, 0)
+		qhl := len(qhatv.Data)
+		if j+qhl > len(u.Data) && qhatv.Data[n] == 0 {
+			qhl--
+		}
+
+		// Subtract q̂·v from the current section of u.
+		// If it underflows, q̂·v > u, which we fix up
+		// by decrementing q̂ and adding v back.
+		c := subVV(u.Data[j:j+qhl], u.Data[j:], qhatv.Data)
+		if c != 0 {
+			c := addVV(u.Data[j:j+n], u.Data[j:], v.Data)
+			// If n == qhl, the carry from subVV and the carry from addVV
+			// cancel out and don't affect u[j+n].
+			if n < qhl {
+				u.Data[j+n] += c
+			}
+			qhat--
+		}
+
+		// Save quotient digit.
+		// Caller may know the top digit is zero and not leave room for it.
+		if j == m && m == len(this.Data) && qhat == 0 {
+			continue
+		}
+		this.Data[j] = qhat
+	}
+
+	putNat(qhatvp)
+}
+
+// greaterThan reports whether the two digit numbers x1 x2 > y1 y2.
+// TODO(rsc): In contradiction to most of this file, x1 is the high
+// digit and x2 is the low digit. This should be fixed.
+func greaterThan(x1, x2, y1, y2: uint) => bool {
+	return x1 > y1 || x1 == y1 && x2 > y2
+}
+
+// divRecursiveThreshold is the number of divisor digits
+// at which point divRecursive is faster than divBasic.
+const divRecursiveThreshold = 100
+
+// divRecursive implements recursive division as described above.
+// It overwrites z with ⌊u/v⌋ and overwrites u with the remainder r.
+// z must be large enough to hold ⌊u/v⌋.
+// This function is just for allocating and freeing temporaries
+// around divRecursiveStep, the real implementation.
+func nat.divRecursive(u, v: nat) {
+	// Recursion depth is (much) less than 2 log₂(len(v)).
+	// Allocate a slice of temporaries to be reused across recursion,
+	// plus one extra temporary not live across the recursion.
+	recDepth := 2 * bits.Len(uint(len(v.Data)))
+	tmp := getNat(3 * len(v.Data))
+
+	temps := make([]*nat, recDepth)
+
+	this.clear()
+	this.divRecursiveStep(u, v, 0, tmp, temps)
+	// Free temporaries.
+	for _, n := range temps {
+		if n != nil {
+			putNat(n)
+		}
+	}
+	putNat(tmp)
+}
+
+// divRecursiveStep is the actual implementation of recursive division.
+// It adds ⌊u/v⌋ to z and overwrites u with the remainder r.
+// z must be large enough to hold ⌊u/v⌋.
+// It uses temps[depth] (allocating if needed) as a temporary live across
+// the recursive call. It also uses tmp, but not live across the recursion.
+func nat.divRecursiveStep(u, v: nat, depth: int, tmp: *nat, temps: []*nat) {
+	// u is a subsection of the original and may have leading zeros.
+	// TODO(rsc): The v = v.norm() is useless and should be removed.
+	// We know (and require) that v's top digit is ≥ B/2.
+	u = u.norm()
+	v = v.norm()
+	if len(u.Data) == 0 {
+		this.clear()
+		return
+	}
+
+	// Fall back to basic division if the problem is now small enough.
+	n := len(v.Data)
+	if n < divRecursiveThreshold {
+		this.divBasic(u, v)
+		return
+	}
+
+	// Nothing to do if u is shorter than v (implies u < v).
+	m := len(u.Data) - n
+	if m < 0 {
+		return
+	}
+	// We consider B digits in a row as a single wide digit.
+	// (See “Recursive Division” above.)
+	//
+	// TODO(rsc): rename B to Wide, to avoid confusion with _B,
+	// which is something entirely different.
+	// TODO(rsc): Look into whether using ⌈n/2⌉ is better than ⌊n/2⌋.
+	B := n / 2
+
+	// Allocate a nat for qhat below.
+	if temps[depth] == nil {
+		temps[depth] = getNat(n) // TODO(rsc): Can be just B+1.
+	} else {
+		*temps[depth] = temps[depth].make(B + 1)
+	}
+
+	// Compute each wide digit of the quotient.
+	//
+	// TODO(rsc): Change the loop to be
+	//	for j := (m+B-1)/B*B; j > 0; j -= B {
+	// which will make the final step a regular step, letting us
+	// delete what amounts to an extra copy of the loop body below.
+	j := m
+
+	for j > B {
+		// Divide u[j-B:j+n] (3 wide digits) by v (2 wide digits).
+		// First make the 2-by-1-wide-digit guess using a recursive call.
+		// Then extend the guess to the full 3-by-2 (see “Refining Guesses”).
+		//
+		// For the 2-by-1-wide-digit guess, instead of doing 2B-by-B-digit,
+		// we use a (2B+1)-by-(B+1) digit, which handles the possibility that
+		// the result has an extra leading 1 digit as well as guaranteeing
+		// that the computed q̂ will be off by at most 1 instead of 2.
+
+		// s is the number of digits to drop from the 3B- and 2B-digit chunks.
+		// We drop B-1 to be left with 2B+1 and B+1.
+		s := (B - 1)
+
+		// uu is the up-to-3B-digit section of u we are working on.
+		uu := nat{u.Data[j-B:]}
+
+		// Compute the 2-by-1 guess q̂, leaving r̂ in uu[s:B+n].
+		qhat := *temps[depth]
+		qhat.clear()
+		qhat.divRecursiveStep(nat{uu.Data[s : B+n]}, nat{v.Data[s:]}, depth+1, tmp, temps)
+		qhat = qhat.norm()
+
+		// Extend to a 3-by-2 quotient and remainder.
+		// Because divRecursiveStep overwrote the top part of uu with
+		// the remainder r̂, the full uu already contains the equivalent
+		// of r̂·B + uₙ₋₂ from the “Refining Guesses” discussion.
+		// Subtracting q̂·vₙ₋₂ from it will compute the full-length remainder.
+		// If that subtraction underflows, q̂·v > u, which we fix up
+		// by decrementing q̂ and adding v back, same as in long division.
+
+		// TODO(rsc): Instead of subtract and fix-up, this code is computing
+		// q̂·vₙ₋₂ and decrementing q̂ until that product is ≤ u.
+		// But we can do the subtraction directly, as in the comment above
+		// and in long division, because we know that q̂ is wrong by at most one.
+		qhatv := tmp.make(3 * n)
+		qhatv.clear()
+		qhatv = qhatv.mul(qhat, nat{v.Data[:s]})
+		for i := 0; i < 2; i++ {
+			e := qhatv.cmp(uu.norm())
+			if e <= 0 {
+				break
+			}
+			subVW(qhat.Data, qhat.Data, 1)
+			c := subVV(qhatv.Data[:s], qhatv.Data[:s], v.Data[:s])
+			if len(qhatv.Data) > s {
+				subVW(qhatv.Data[s:], qhatv.Data[s:], c)
+			}
+			addAt(nat{uu.Data[s:]}, nat{v.Data[s:]}, 0)
+		}
+		if qhatv.cmp(uu.norm()) > 0 {
+			panic("impossible")
+		}
+		c := subVV(uu.Data[:len(qhatv.Data)], uu.Data[:len(qhatv.Data)], qhatv.Data)
+		if c > 0 {
+			subVW(uu.Data[len(qhatv.Data):], uu.Data[len(qhatv.Data):], c)
+		}
+		addAt(*this, qhat, j-B)
+		j -= B
+	}
+
+	// TODO(rsc): Rewrite loop as described above and delete all this code.
+
+	// Now u < (v<<B), compute lower bits in the same way.
+	// Choose shift = B-1 again.
+	s := B - 1
+	qhat := *temps[depth]
+	qhat.clear()
+	temp_u := &nat{u.Data[s:]}
+	qhat.divRecursiveStep(temp_u.norm(), nat{v.Data[s:]}, depth+1, tmp, temps)
+	qhat = qhat.norm()
+	qhatv := tmp.make(3 * n)
+	qhatv.clear()
+	qhatv = qhatv.mul(qhat, nat{v.Data[:s]})
+	// Set the correct remainder as before.
+	for i := 0; i < 2; i++ {
+		if e := qhatv.cmp(u.norm()); e > 0 {
+			subVW(qhat.Data, qhat.Data, 1)
+			c := subVV(qhatv.Data[:s], qhatv.Data[:s], v.Data[:s])
+			if len(qhatv.Data) > s {
+				subVW(qhatv.Data[s:], qhatv.Data[s:], c)
+			}
+			addAt(nat{u.Data[s:]}, nat{v.Data[s:]}, 0)
+		}
+	}
+	if qhatv.cmp(u.norm()) > 0 {
+		panic("impossible")
+	}
+	c := subVV(u.Data[0:len(qhatv.Data)], u.Data[0:len(qhatv.Data)], qhatv.Data)
+	if c > 0 {
+		c = subVW(u.Data[len(qhatv.Data):], u.Data[len(qhatv.Data):], c)
+	}
+	if c > 0 {
+		panic("impossible")
+	}
+	// Done!
+	addAt(*this, qhat.norm(), 0)
+}

src/main.wa

@@ -0,0 +1,7 @@
+import "base60/big" //当前目录的包路径为'base60'(在wa.mod.json中配置)，因此导入当前目录下的包应添加'base60/'路径前缀
+
+func main {
+	println("Base60 主程序入口")
+
+	big.AAA()
+}

wa.mod.json

@@ -1,6 +1,6 @@
 {
-	"name": "wa_bigint_std",
-	"pkgpath": "myapp",
+	"name": "base60",
+	"pkgpath": "base60",
 	"version": "0.0.1",
 	"authors": ["author", "author2"],
 	"description": "module description",