// Convert attempts to convert the constant x to a given type.
// If the attempt is successful, the result is the new constant;
// otherwise the result is invalid.
func (x Const) Convert(typ *Type) Const {
// TODO(gri) implement this
switch x := x.Val.(type) {
//case bool:
case *big.Int:
switch Underlying(*typ) {
case Float32, Float64:
var z big.Rat
z.SetInt(x)
return Const{&z}
case String:
return Const{string(x.Int64())}
case Complex64, Complex128:
var z big.Rat
z.SetInt(x)
return Const{Cmplx{&z, &big.Rat{}}}
}
case *big.Rat:
switch Underlying(*typ) {
case Byte, Int, Uint, Int8, Uint8, Int16, Uint16, Int32, Uint32, Int64, Uint64:
// Convert to an integer. Remove the fractional component.
num, denom := x.Num(), x.Denom()
var z big.Int
z.Quo(num, denom)
return Const{&z}
}
//case Cmplx:
//case string:
}
//panic("unimplemented")
return x
}
func binaryFloatOp(x *big.Rat, op token.Token, y *big.Rat) interface{} {
var z big.Rat
switch op {
case token.ADD:
return z.Add(x, y)
case token.SUB:
return z.Sub(x, y)
case token.MUL:
return z.Mul(x, y)
case token.QUO:
return z.Quo(x, y)
case token.EQL:
return x.Cmp(y) == 0
case token.NEQ:
return x.Cmp(y) != 0
case token.LSS:
return x.Cmp(y) < 0
case token.LEQ:
return x.Cmp(y) <= 0
case token.GTR:
return x.Cmp(y) > 0
case token.GEQ:
return x.Cmp(y) >= 0
}
panic("unreachable")
}
func renderRat(img *image.RGBA) {
var yminR, ymaxMinR, heightR big.Rat
yminR.SetInt64(ymin)
ymaxMinR.SetInt64(ymax - ymin)
heightR.SetInt64(height)
var xminR, xmaxMinR, widthR big.Rat
xminR.SetInt64(xmin)
xmaxMinR.SetInt64(xmax - xmin)
widthR.SetInt64(width)
var y, x big.Rat
for py := int64(0); py < height; py++ {
// y := float64(py)/height*(ymax-ymin) + ymin
y.SetInt64(py)
y.Quo(&y, &heightR)
y.Mul(&y, &ymaxMinR)
y.Add(&y, &yminR)
for px := int64(0); px < width; px++ {
// x := float64(px)/width*(xmax-xmin) + xmin
x.SetInt64(px)
x.Quo(&x, &widthR)
x.Mul(&x, &xmaxMinR)
x.Add(&x, &xminR)
c := mandelbrotRat(&x, &y)
if c == nil {
c = color.Black
}
img.Set(int(px), int(py), c)
}
}
}
// Total returns the total of an Usage
func (u *Usage) Total() *big.Rat {
//return math.Min(u.Object.UnitPrice * u.BillableQuantity(), u.Object.UnitPriceCap)
total := new(big.Rat).Mul(u.BillableQuantity(), u.Object.UnitPrice)
total = total.Quo(total, u.Object.UnitQuantity)
return ratMin(total, u.Object.UnitPriceCap)
}
func String(v xdr.Int64) string {
var f, o, r big.Rat
f.SetInt64(int64(v))
o.SetInt64(One)
r.Quo(&f, &o)
return r.FloatString(7)
}
func GasPrice(bp, gl, ep *big.Int) *big.Int {
BP := new(big.Rat).SetInt(bp)
GL := new(big.Rat).SetInt(gl)
EP := new(big.Rat).SetInt(ep)
GP := new(big.Rat).Quo(BP, GL)
GP = GP.Quo(GP, EP)
return GP.Mul(GP, etherInWei).Num()
}
func tans(m []mTerm) *big.Rat {
if len(m) == 1 {
return tanEval(m[0].a, big.NewRat(m[0].n, m[0].d))
}
half := len(m) / 2
a := tans(m[:half])
b := tans(m[half:])
r := new(big.Rat)
return r.Quo(new(big.Rat).Add(a, b), r.Sub(one, r.Mul(a, b)))
}
// floatString returns the string representation for a
// numeric value v in normalized floating-point format.
func floatString(v exact.Value) string {
if exact.Sign(v) == 0 {
return "0.0"
}
// x != 0
// convert |v| into a big.Rat x
x := new(big.Rat).SetFrac(absInt(exact.Num(v)), absInt(exact.Denom(v)))
// normalize x and determine exponent e
// (This is not very efficient, but also not speed-critical.)
var e int
for x.Cmp(ten) >= 0 {
x.Quo(x, ten)
e++
}
for x.Cmp(one) < 0 {
x.Mul(x, ten)
e--
}
// TODO(gri) Values such as 1/2 are easier to read in form 0.5
// rather than 5.0e-1. Similarly, 1.0e1 is easier to read as
// 10.0. Fine-tune best exponent range for readability.
s := x.FloatString(100) // good-enough precision
// trim trailing 0's
i := len(s)
for i > 0 && s[i-1] == '0' {
i--
}
s = s[:i]
// add a 0 if the number ends in decimal point
if len(s) > 0 && s[len(s)-1] == '.' {
s += "0"
}
// add exponent and sign
if e != 0 {
s += fmt.Sprintf("e%+d", e)
}
if exact.Sign(v) < 0 {
s = "-" + s
}
// TODO(gri) If v is a "small" fraction (i.e., numerator and denominator
// are just a small number of decimal digits), add the exact fraction as
// a comment. For instance: 3.3333...e-1 /* = 1/3 */
return s
}
func sexToDec(deg, min, sec *big.Rat, dir string) *big.Rat {
// sexagesimal (base 60) to decimal
// https://imm.dtf.wa.gov.au/helpfiles/Latitude_Longitude_conversion_hlp.htm
deg.Add(deg, min.Quo(min, big.NewRat(60, 1)))
deg.Add(deg, sec.Quo(sec, big.NewRat(3600, 1)))
// N and E are the positive directions (like on an x,y axis)
if dir == "S" || dir == "W" {
deg.Neg(deg)
}
return deg
}
func tanEval(coef int64, f *big.Rat) *big.Rat {
if coef == 1 {
return f
}
if coef < 0 {
r := tanEval(-coef, f)
return r.Neg(r)
}
ca := coef / 2
cb := coef - ca
a := tanEval(ca, f)
b := tanEval(cb, f)
r := new(big.Rat)
return r.Quo(new(big.Rat).Add(a, b), r.Sub(one, r.Mul(a, b)))
}
func binaryCmplxOp(x cmplx, op token.Token, y cmplx) interface{} {
a, b := x.re, x.im
c, d := y.re, y.im
switch op {
case token.ADD:
// (a+c) + i(b+d)
var re, im big.Rat
re.Add(a, c)
im.Add(b, d)
return cmplx{&re, &im}
case token.SUB:
// (a-c) + i(b-d)
var re, im big.Rat
re.Sub(a, c)
im.Sub(b, d)
return cmplx{&re, &im}
case token.MUL:
// (ac-bd) + i(bc+ad)
var ac, bd, bc, ad big.Rat
ac.Mul(a, c)
bd.Mul(b, d)
bc.Mul(b, c)
ad.Mul(a, d)
var re, im big.Rat
re.Sub(&ac, &bd)
im.Add(&bc, &ad)
return cmplx{&re, &im}
case token.QUO:
// (ac+bd)/s + i(bc-ad)/s, with s = cc + dd
var ac, bd, bc, ad, s big.Rat
ac.Mul(a, c)
bd.Mul(b, d)
bc.Mul(b, c)
ad.Mul(a, d)
s.Add(c.Mul(c, c), d.Mul(d, d))
var re, im big.Rat
re.Add(&ac, &bd)
re.Quo(&re, &s)
im.Sub(&bc, &ad)
im.Quo(&im, &s)
return cmplx{&re, &im}
case token.EQL:
return a.Cmp(c) == 0 && b.Cmp(d) == 0
case token.NEQ:
return a.Cmp(c) != 0 || b.Cmp(d) != 0
}
panic("unreachable")
}
// ratScale multiplies x by 10**exp.
func ratScale(x *big.Rat, exp int) {
if exp < 0 {
x.Inv(x)
ratScale(x, -exp)
x.Inv(x)
return
}
for exp >= 9 {
x.Quo(x, bigRatBillion)
exp -= 9
}
for exp >= 1 {
x.Quo(x, bigRatTen)
exp--
}
}
func sqrtFloat(x *big.Rat) *big.Rat {
t1 := new(big.Rat)
t2 := new(big.Rat)
t1.Set(x)
// Iterate.
// x{n} = (x{n-1}+x{0}/x{n-1}) / 2
for i := 0; i <= 4; i++ {
if t1.Cmp(zero) == 0 {
return t1
}
t2.Quo(x, t1)
t2.Add(t2, t1)
t1.Mul(half, t2)
}
return t1
}
// ratExponent returns the power of ten that x would display in scientific notation.
func ratExponent(x *big.Rat) int {
if x.Sign() < 0 {
x.Neg(x)
}
e := 0
invert := false
if x.Num().Cmp(x.Denom()) < 0 {
invert = true
x.Inv(x)
e++
}
for x.Cmp(bigRatBillion) >= 0 {
e += 9
x.Quo(x, bigRatBillion)
}
for x.Cmp(bigRatTen) > 0 {
e++
x.Quo(x, bigRatTen)
}
if invert {
return -e
}
return e
}
// binaryOpConst returns the result of the constant evaluation x op y;
// both operands must be of the same "kind" (boolean, numeric, or string).
// If intDiv is true, division (op == token.QUO) is using integer division
// (and the result is guaranteed to be integer) rather than floating-point
// division. Division by zero leads to a run-time panic.
//
func binaryOpConst(x, y interface{}, op token.Token, intDiv bool) interface{} {
x, y = matchConst(x, y)
switch x := x.(type) {
case bool:
y := y.(bool)
switch op {
case token.LAND:
return x && y
case token.LOR:
return x || y
default:
unreachable()
}
case int64:
y := y.(int64)
switch op {
case token.ADD:
// TODO(gri) can do better than this
if is63bit(x) && is63bit(y) {
return x + y
}
return normalizeIntConst(new(big.Int).Add(big.NewInt(x), big.NewInt(y)))
case token.SUB:
// TODO(gri) can do better than this
if is63bit(x) && is63bit(y) {
return x - y
}
return normalizeIntConst(new(big.Int).Sub(big.NewInt(x), big.NewInt(y)))
case token.MUL:
// TODO(gri) can do better than this
if is32bit(x) && is32bit(y) {
return x * y
}
return normalizeIntConst(new(big.Int).Mul(big.NewInt(x), big.NewInt(y)))
case token.REM:
return x % y
case token.QUO:
if intDiv {
return x / y
}
return normalizeRatConst(new(big.Rat).SetFrac(big.NewInt(x), big.NewInt(y)))
case token.AND:
return x & y
case token.OR:
return x | y
case token.XOR:
return x ^ y
case token.AND_NOT:
return x &^ y
default:
unreachable()
}
case *big.Int:
y := y.(*big.Int)
var z big.Int
switch op {
case token.ADD:
z.Add(x, y)
case token.SUB:
z.Sub(x, y)
case token.MUL:
z.Mul(x, y)
case token.REM:
z.Rem(x, y)
case token.QUO:
if intDiv {
z.Quo(x, y)
} else {
return normalizeRatConst(new(big.Rat).SetFrac(x, y))
}
case token.AND:
z.And(x, y)
case token.OR:
z.Or(x, y)
case token.XOR:
z.Xor(x, y)
case token.AND_NOT:
z.AndNot(x, y)
default:
unreachable()
}
return normalizeIntConst(&z)
case *big.Rat:
y := y.(*big.Rat)
var z big.Rat
switch op {
case token.ADD:
z.Add(x, y)
case token.SUB:
z.Sub(x, y)
case token.MUL:
z.Mul(x, y)
case token.QUO:
z.Quo(x, y)
default:
unreachable()
}
return normalizeRatConst(&z)
case complex:
y := y.(complex)
a, b := x.re, x.im
c, d := y.re, y.im
var re, im big.Rat
switch op {
case token.ADD:
// (a+c) + i(b+d)
re.Add(a, c)
im.Add(b, d)
case token.SUB:
// (a-c) + i(b-d)
re.Sub(a, c)
im.Sub(b, d)
case token.MUL:
// (ac-bd) + i(bc+ad)
var ac, bd, bc, ad big.Rat
ac.Mul(a, c)
bd.Mul(b, d)
bc.Mul(b, c)
ad.Mul(a, d)
re.Sub(&ac, &bd)
im.Add(&bc, &ad)
case token.QUO:
// (ac+bd)/s + i(bc-ad)/s, with s = cc + dd
var ac, bd, bc, ad, s big.Rat
ac.Mul(a, c)
bd.Mul(b, d)
bc.Mul(b, c)
ad.Mul(a, d)
s.Add(c.Mul(c, c), d.Mul(d, d))
re.Add(&ac, &bd)
re.Quo(&re, &s)
im.Sub(&bc, &ad)
im.Quo(&im, &s)
default:
unreachable()
}
return normalizeComplexConst(complex{&re, &im})
case string:
if op == token.ADD {
return x + y.(string)
}
}
unreachable()
return nil
}
func main() {
f, err := os.Create("/tmp/profile")
if err != nil {
log.Fatal(err)
}
pprof.StartCPUProfile(f)
defer pprof.StopCPUProfile()
p, _ := new(big.Int).SetString("233970423115425145524320034830162017933", 10)
a := big.NewInt(-95051)
b := big.NewInt(11279326)
G := dh.NewEllipticCurve(a, b, p)
gx := big.NewInt(182)
gy, _ := new(big.Int).SetString("85518893674295321206118380980485522083", 10)
g := dh.NewEllipticCurveElement(G, gx, gy)
q, _ := new(big.Int).SetString("29246302889428143187362802287225875743", 10)
GG := dh.NewGeneratedGroup(G, g, *q)
var bias uint = 8
alice := dh.NewBiasedECDSA(GG, bias)
var msg = []byte("I was a fiend")
key, _ := new(big.Int).SetString("255bf9c75628ab469b45cced58755a3", 16)
d := new(big.Rat).SetInt(key)
numSigs := 22
B := dh.Matrix(make([]dh.Vector, numSigs+2))
zero := dh.Vector(make([]*big.Rat, numSigs+2))
for i, _ := range zero {
zero[i] = new(big.Rat)
}
for i, _ := range B {
B[i] = zero.Copy()
}
ct := big.NewRat(1, 1<<bias)
B[len(B)-2][len(B)-2].Set(ct)
cu := new(big.Rat).SetInt(q)
cu.Quo(cu, big.NewRat(1<<bias, 1))
B[len(B)-1][len(B)-1].Set(cu)
ts := make([]*big.Int, numSigs)
us := make([]*big.Int, numSigs)
for i := 0; i < numSigs; i++ {
B[i][i].SetInt(q)
r, s := alice.Sign(msg)
t, u := transform(msg, r, s, q, bias)
dt := new(big.Int).Mul(key, t)
temp := new(big.Int).Sub(u, dt)
temp.Mod(temp, q)
temp.Sub(q, temp)
log.Printf("\ndt: %x\nu: %x\nq-u-dt: %x\nq: %x", dt, u, temp, q)
ts[i] = t
us[i] = u
B[len(B)-2][i] = new(big.Rat).SetInt(t)
B[len(B)-1][i] = new(big.Rat).SetInt(u)
}
check := B[len(B)-1].Copy()
check.Sub(B[len(B)-2].Copy().Scale(d))
for i := 0; i < numSigs; i++ {
t := ts[i]
dt := new(big.Int).Mul(key, t)
m := new(big.Int).Div(dt, q)
check.Add(B[i].Copy().Scale(new(big.Rat).SetInt(m)))
}
log.Printf("check=%s", check)
B.LLL(big.NewRat(99, 100))
for _, v := range B {
if v[len(v)-1].Cmp(cu) == 0 {
log.Printf("%s", v)
d := new(big.Rat)
d.Sub(d, v[len(v)-2])
d.Mul(d, big.NewRat(1<<bias, 1))
guess := dh.Round(d).Num()
log.Printf("Recovered key: %x", guess)
log.Printf("Correct: %v", guess.Cmp(key) == 0)
}
}
}
// Contract evaluation is done here.
func (bm *BlockManager) ProcContract(tx *ethutil.Transaction, block *ethutil.Block, cb TxCallback) {
// Instruction pointer
pc := 0
blockInfo := bm.BlockInfo(block)
contract := block.GetContract(tx.Hash())
if contract == nil {
fmt.Println("Contract not found")
return
}
Pow256 := ethutil.BigPow(2, 256)
//fmt.Printf("# op arg\n")
out:
for {
// The base big int for all calculations. Use this for any results.
base := new(big.Int)
// XXX Should Instr return big int slice instead of string slice?
// Get the next instruction from the contract
//op, _, _ := Instr(contract.state.Get(string(Encode(uint32(pc)))))
nb := ethutil.NumberToBytes(uint64(pc), 32)
o, _, _ := ethutil.Instr(contract.State().Get(string(nb)))
op := OpCode(o)
if !cb(0) {
break
}
if Debug {
//fmt.Printf("%-3d %-4s\n", pc, op.String())
}
switch op {
case oSTOP:
break out
case oADD:
x, y := bm.stack.Popn()
// (x + y) % 2 ** 256
base.Add(x, y)
base.Mod(base, Pow256)
// Pop result back on the stack
bm.stack.Push(base)
case oSUB:
x, y := bm.stack.Popn()
// (x - y) % 2 ** 256
base.Sub(x, y)
base.Mod(base, Pow256)
// Pop result back on the stack
bm.stack.Push(base)
case oMUL:
x, y := bm.stack.Popn()
// (x * y) % 2 ** 256
base.Mul(x, y)
base.Mod(base, Pow256)
// Pop result back on the stack
bm.stack.Push(base)
case oDIV:
x, y := bm.stack.Popn()
// floor(x / y)
base.Div(x, y)
// Pop result back on the stack
bm.stack.Push(base)
case oSDIV:
x, y := bm.stack.Popn()
// n > 2**255
if x.Cmp(Pow256) > 0 {
x.Sub(Pow256, x)
}
if y.Cmp(Pow256) > 0 {
y.Sub(Pow256, y)
}
z := new(big.Int)
z.Div(x, y)
if z.Cmp(Pow256) > 0 {
z.Sub(Pow256, z)
}
// Push result on to the stack
bm.stack.Push(z)
case oMOD:
x, y := bm.stack.Popn()
base.Mod(x, y)
bm.stack.Push(base)
case oSMOD:
x, y := bm.stack.Popn()
// n > 2**255
if x.Cmp(Pow256) > 0 {
x.Sub(Pow256, x)
}
if y.Cmp(Pow256) > 0 {
y.Sub(Pow256, y)
}
z := new(big.Int)
z.Mod(x, y)
if z.Cmp(Pow256) > 0 {
z.Sub(Pow256, z)
}
// Push result on to the stack
bm.stack.Push(z)
case oEXP:
x, y := bm.stack.Popn()
base.Exp(x, y, Pow256)
bm.stack.Push(base)
case oNEG:
base.Sub(Pow256, bm.stack.Pop())
bm.stack.Push(base)
case oLT:
x, y := bm.stack.Popn()
// x < y
if x.Cmp(y) < 0 {
bm.stack.Push(ethutil.BigTrue)
} else {
bm.stack.Push(ethutil.BigFalse)
}
case oLE:
x, y := bm.stack.Popn()
// x <= y
if x.Cmp(y) < 1 {
bm.stack.Push(ethutil.BigTrue)
} else {
bm.stack.Push(ethutil.BigFalse)
}
case oGT:
x, y := bm.stack.Popn()
// x > y
if x.Cmp(y) > 0 {
bm.stack.Push(ethutil.BigTrue)
} else {
bm.stack.Push(ethutil.BigFalse)
}
case oGE:
x, y := bm.stack.Popn()
// x >= y
if x.Cmp(y) > -1 {
bm.stack.Push(ethutil.BigTrue)
} else {
bm.stack.Push(ethutil.BigFalse)
}
case oNOT:
x, y := bm.stack.Popn()
// x != y
if x.Cmp(y) != 0 {
bm.stack.Push(ethutil.BigTrue)
} else {
bm.stack.Push(ethutil.BigFalse)
}
// Please note that the following code contains some
// ugly string casting. This will have to change to big
// ints. TODO :)
case oMYADDRESS:
bm.stack.Push(ethutil.BigD(tx.Hash()))
case oTXSENDER:
bm.stack.Push(ethutil.BigD(tx.Sender()))
case oTXVALUE:
bm.stack.Push(tx.Value)
case oTXDATAN:
bm.stack.Push(big.NewInt(int64(len(tx.Data))))
case oTXDATA:
v := bm.stack.Pop()
// v >= len(data)
if v.Cmp(big.NewInt(int64(len(tx.Data)))) >= 0 {
bm.stack.Push(ethutil.Big("0"))
} else {
bm.stack.Push(ethutil.Big(tx.Data[v.Uint64()]))
}
case oBLK_PREVHASH:
bm.stack.Push(ethutil.Big(block.PrevHash))
case oBLK_COINBASE:
bm.stack.Push(ethutil.Big(block.Coinbase))
case oBLK_TIMESTAMP:
bm.stack.Push(big.NewInt(block.Time))
case oBLK_NUMBER:
bm.stack.Push(blockInfo.Number)
case oBLK_DIFFICULTY:
bm.stack.Push(block.Difficulty)
case oBASEFEE:
// e = 10^21
e := big.NewInt(0).Exp(big.NewInt(10), big.NewInt(21), big.NewInt(0))
d := new(big.Rat)
d.SetInt(block.Difficulty)
c := new(big.Rat)
c.SetFloat64(0.5)
// d = diff / 0.5
d.Quo(d, c)
// base = floor(d)
base.Div(d.Num(), d.Denom())
x := new(big.Int)
x.Div(e, base)
// x = floor(10^21 / floor(diff^0.5))
bm.stack.Push(x)
case oSHA256, oSHA3, oRIPEMD160:
// This is probably save
// ceil(pop / 32)
length := int(math.Ceil(float64(bm.stack.Pop().Uint64()) / 32.0))
// New buffer which will contain the concatenated popped items
data := new(bytes.Buffer)
for i := 0; i < length; i++ {
// Encode the number to bytes and have it 32bytes long
num := ethutil.NumberToBytes(bm.stack.Pop().Bytes(), 256)
data.WriteString(string(num))
}
if op == oSHA256 {
bm.stack.Push(base.SetBytes(ethutil.Sha256Bin(data.Bytes())))
} else if op == oSHA3 {
bm.stack.Push(base.SetBytes(ethutil.Sha3Bin(data.Bytes())))
} else {
bm.stack.Push(base.SetBytes(ethutil.Ripemd160(data.Bytes())))
}
case oECMUL:
y := bm.stack.Pop()
x := bm.stack.Pop()
//n := bm.stack.Pop()
//if ethutil.Big(x).Cmp(ethutil.Big(y)) {
data := new(bytes.Buffer)
data.WriteString(x.String())
data.WriteString(y.String())
if secp256k1.VerifyPubkeyValidity(data.Bytes()) == 1 {
// TODO
} else {
// Invalid, push infinity
bm.stack.Push(ethutil.Big("0"))
bm.stack.Push(ethutil.Big("0"))
}
//} else {
// // Invalid, push infinity
// bm.stack.Push("0")
// bm.stack.Push("0")
//}
case oECADD:
case oECSIGN:
case oECRECOVER:
case oECVALID:
case oPUSH:
pc++
bm.stack.Push(bm.mem[strconv.Itoa(pc)])
case oPOP:
// Pop current value of the stack
bm.stack.Pop()
case oDUP:
// Dup top stack
x := bm.stack.Pop()
bm.stack.Push(x)
bm.stack.Push(x)
case oSWAP:
// Swap two top most values
x, y := bm.stack.Popn()
bm.stack.Push(y)
bm.stack.Push(x)
case oMLOAD:
x := bm.stack.Pop()
bm.stack.Push(bm.mem[x.String()])
case oMSTORE:
x, y := bm.stack.Popn()
bm.mem[x.String()] = y
case oSLOAD:
// Load the value in storage and push it on the stack
x := bm.stack.Pop()
// decode the object as a big integer
decoder := ethutil.NewRlpDecoder([]byte(contract.State().Get(x.String())))
if !decoder.IsNil() {
bm.stack.Push(decoder.AsBigInt())
} else {
bm.stack.Push(ethutil.BigFalse)
}
case oSSTORE:
// Store Y at index X
x, y := bm.stack.Popn()
contract.State().Update(x.String(), string(ethutil.Encode(y)))
case oJMP:
x := int(bm.stack.Pop().Uint64())
// Set pc to x - 1 (minus one so the incrementing at the end won't effect it)
pc = x
pc--
case oJMPI:
x := bm.stack.Pop()
// Set pc to x if it's non zero
if x.Cmp(ethutil.BigFalse) != 0 {
pc = int(x.Uint64())
pc--
}
case oIND:
bm.stack.Push(big.NewInt(int64(pc)))
case oEXTRO:
memAddr := bm.stack.Pop()
contractAddr := bm.stack.Pop().Bytes()
// Push the contract's memory on to the stack
bm.stack.Push(getContractMemory(block, contractAddr, memAddr))
case oBALANCE:
// Pushes the balance of the popped value on to the stack
d := block.State().Get(bm.stack.Pop().String())
ether := ethutil.NewEtherFromData([]byte(d))
bm.stack.Push(ether.Amount)
case oMKTX:
value, addr := bm.stack.Popn()
from, length := bm.stack.Popn()
j := 0
dataItems := make([]string, int(length.Uint64()))
for i := from.Uint64(); i < length.Uint64(); i++ {
dataItems[j] = string(bm.mem[strconv.Itoa(int(i))].Bytes())
j++
}
// TODO sign it?
tx := ethutil.NewTransaction(string(addr.Bytes()), value, dataItems)
// Add the transaction to the tx pool
bm.server.txPool.QueueTransaction(tx)
case oSUICIDE:
//addr := bm.stack.Pop()
}
pc++
}
bm.stack.Print()
}
//export OFXTransactionCallback
func OFXTransactionCallback(transaction_data C.struct_OfxTransactionData, data unsafe.Pointer) C.int {
iobj := (*ImportObject)(data)
itl := iobj.TransactionList
transaction := new(Transaction)
if transaction_data.name_valid != 0 {
transaction.Description = C.GoString(&transaction_data.name[0])
}
// if transaction_data.reference_number_valid != 0 {
// fmt.Println("reference_number: ", C.GoString(&transaction_data.reference_number[0]))
// }
if transaction_data.date_posted_valid != 0 {
transaction.Date = time.Unix(int64(transaction_data.date_posted), 0)
} else if transaction_data.date_initiated_valid != 0 {
transaction.Date = time.Unix(int64(transaction_data.date_initiated), 0)
}
if transaction_data.fi_id_valid != 0 {
transaction.RemoteId = C.GoString(&transaction_data.fi_id[0])
}
if transaction_data.amount_valid != 0 {
split := new(Split)
r := new(big.Rat)
r.SetFloat64(float64(transaction_data.amount))
security, err := GetSecurity(itl.Account.SecurityId, itl.Account.UserId)
if err != nil {
if iobj.Error == nil {
iobj.Error = err
}
return 1
}
split.Amount = r.FloatString(security.Precision)
if transaction_data.memo_valid != 0 {
split.Memo = C.GoString(&transaction_data.memo[0])
}
if transaction_data.check_number_valid != 0 {
split.Number = C.GoString(&transaction_data.check_number[0])
}
split.SecurityId = -1
split.AccountId = itl.Account.AccountId
transaction.Splits = append(transaction.Splits, split)
} else {
if iobj.Error == nil {
iobj.Error = errors.New("OFX transaction amount invalid")
}
return 1
}
var security *Security
var err error
split := new(Split)
units := new(big.Rat)
if transaction_data.units_valid != 0 {
units.SetFloat64(float64(transaction_data.units))
if transaction_data.security_data_valid != 0 {
security_data := transaction_data.security_data_ptr
if security_data.ticker_valid != 0 {
s, err := GetSecurityByName(C.GoString(&security_data.ticker[0]))
if err != nil {
if iobj.Error == nil {
iobj.Error = errors.New("Failed to find OFX transaction security: " + C.GoString(&security_data.ticker[0]))
}
return 1
}
security = s
} else {
if iobj.Error == nil {
iobj.Error = errors.New("OFX security ticker invalid")
}
return 1
}
if security.Type == Stock && security_data.unique_id_valid != 0 && security_data.unique_id_type_valid != 0 && C.GoString(&security_data.unique_id_type[0]) == "CUSIP" {
// Validate the security CUSIP, if possible
if security.AlternateId != C.GoString(&security_data.unique_id[0]) {
if iobj.Error == nil {
iobj.Error = errors.New("OFX transaction security CUSIP failed to validate")
}
return 1
}
}
} else {
security, err = GetSecurity(itl.Account.SecurityId, itl.Account.UserId)
if err != nil {
if iobj.Error == nil {
iobj.Error = err
}
return 1
}
}
} else {
// Calculate units from other available fields if its not present
// units = - (amount + various fees) / unitprice
units.SetFloat64(float64(transaction_data.amount))
fees := new(big.Rat)
if transaction_data.fees_valid != 0 {
fees.SetFloat64(float64(-transaction_data.fees))
}
if transaction_data.commission_valid != 0 {
commission := new(big.Rat)
commission.SetFloat64(float64(-transaction_data.commission))
fees.Add(fees, commission)
}
units.Add(units, fees)
units.Neg(units)
if transaction_data.unitprice_valid != 0 && transaction_data.unitprice != 0 {
unitprice := new(big.Rat)
unitprice.SetFloat64(float64(transaction_data.unitprice))
units.Quo(units, unitprice)
}
// If 'units' wasn't present, assume we're using the account's security
security, err = GetSecurity(itl.Account.SecurityId, itl.Account.UserId)
if err != nil {
if iobj.Error == nil {
iobj.Error = err
}
return 1
}
}
split.Amount = units.FloatString(security.Precision)
split.SecurityId = security.SecurityId
split.AccountId = -1
transaction.Splits = append(transaction.Splits, split)
if transaction_data.fees_valid != 0 {
split := new(Split)
r := new(big.Rat)
r.SetFloat64(float64(-transaction_data.fees))
security, err := GetSecurity(itl.Account.SecurityId, itl.Account.UserId)
if err != nil {
if iobj.Error == nil {
iobj.Error = err
}
return 1
}
split.Amount = r.FloatString(security.Precision)
split.Memo = "fees"
split.SecurityId = itl.Account.SecurityId
split.AccountId = -1
transaction.Splits = append(transaction.Splits, split)
}
if transaction_data.commission_valid != 0 {
split := new(Split)
r := new(big.Rat)
r.SetFloat64(float64(-transaction_data.commission))
security, err := GetSecurity(itl.Account.SecurityId, itl.Account.UserId)
if err != nil {
if iobj.Error == nil {
iobj.Error = err
}
return 1
}
split.Amount = r.FloatString(security.Precision)
split.Memo = "commission"
split.SecurityId = itl.Account.SecurityId
split.AccountId = -1
transaction.Splits = append(transaction.Splits, split)
}
// if transaction_data.payee_id_valid != 0 {
// fmt.Println("payee_id: ", C.GoString(&transaction_data.payee_id[0]))
// }
transaction_list := append(*itl.Transactions, *transaction)
iobj.TransactionList.Transactions = &transaction_list
return 0
}
func (a *EqualSplitsAlgorithm) generateBoundaries() ([]tuple, error) {
// generateBoundaries should work for a split_column whose type is integral
// (both signed and unsigned) as well as for floating point values.
// We perform the calculation of the boundaries using precise big.Rat arithmetic and only
// truncate the result in the end if necessary.
// We do this since using float64 arithmetic does not have enough precision:
// for example, if max=math.MaxUint64 and min=math.MaxUint64-1000 then float64(min)==float64(max).
// On the other hand, using integer arithmetic for the case where the split_column is integral
// (i.e., rounding (max-min)/split_count to an integer) may cause very dissimilar interval
// lengths or a large deviation between split_count and the number of query-parts actually
// returned (consider min=0, max=9.5*10^6, and split_count=10^6).
// Note(erez): We can probably get away with using big.Float with ~64 bits of precision which
// will likely be more efficient. However, we defer optimizing this code until we see if this
// is a bottle-neck.
minValue, maxValue, err := a.executeMinMaxQuery()
if err != nil {
return nil, err
}
// If the table is empty, minValue and maxValue will be NULL.
if (minValue.IsNull() && !maxValue.IsNull()) ||
!minValue.IsNull() && maxValue.IsNull() {
panic(fmt.Sprintf("minValue and maxValue must both be NULL or both be non-NULL."+
" minValue: %v, maxValue: %v, splitParams.sql: %v",
minValue, maxValue, a.splitParams.sql))
}
if minValue.IsNull() {
log.Infof("Splitting an empty table. splitParams.sql: %v. Query will not be split.",
a.splitParams.sql)
return []tuple{}, nil
}
min, err := valueToBigRat(minValue)
if err != nil {
panic(fmt.Sprintf("Failed to convert min to a big.Rat: %v, min: %+v", err, min))
}
max, err := valueToBigRat(maxValue)
if err != nil {
panic(fmt.Sprintf("Failed to convert max to a big.Rat: %v, max: %+v", err, max))
}
minCmpMax := min.Cmp(max)
if minCmpMax > 0 {
panic(fmt.Sprintf("max(splitColumn) < min(splitColumn): max:%v, min:%v", max, min))
}
if minCmpMax == 0 {
log.Infof("max(%v)=min(%v)=%v. splitParams.sql: %v. Query will not be split.",
a.splitParams.splitColumns[0],
a.splitParams.splitColumns[0],
min,
a.splitParams.sql)
return []tuple{}, nil
}
// subIntervalSize = (max - min) / a.splitParams.splitCount
subIntervalSize := new(big.Rat)
subIntervalSize.Sub(max, min)
subIntervalSize.Quo(subIntervalSize, new(big.Rat).SetInt64(a.splitParams.splitCount))
boundary := new(big.Rat).Set(min) // Copy min into boundary.
var result []tuple
for i := int64(1); i < a.splitParams.splitCount; i++ {
boundary.Add(boundary, subIntervalSize)
// Here boundary=min+i*subIntervalSize
boundaryValue := bigRatToValue(boundary, a.splitParams.splitColumnTypes[0])
result = append(result, tuple{boundaryValue})
}
return result, nil
}
s.fatalf("cannot convert %q to int", p)
}
s.pushX(i)
}},
},
// rational literal
{
regex(floatPat + "/" + floatPat),
genericOp{0, 1, func(s *stack, p string) {
i := strings.Index(p, "/")
r0, ok0 := new(big.Rat).SetString(p[0:i])
r1, ok1 := new(big.Rat).SetString(p[i+1:])
if !ok0 || !ok1 {
s.fatalf("bad rational %q", p)
}
s.pushX(r0.Quo(r0, r1))
}},
},
// float literal
{
regex(floatPat),
genericOp{0, 1, func(s *stack, p string) {
v, err := strconv.ParseFloat(p, 64)
if err != nil {
s.fatalf("bad float number %q", p)
}
s.pushX(v)
}},
},
// rune literal
{
func (vm *Vm) Process(contract *Contract, state *State, vars RuntimeVars) {
vm.mem = make(map[string]*big.Int)
vm.stack = NewStack()
addr := vars.address // tx.Hash()[12:]
// Instruction pointer
pc := 0
if contract == nil {
fmt.Println("Contract not found")
return
}
Pow256 := ethutil.BigPow(2, 256)
if ethutil.Config.Debug {
ethutil.Config.Log.Debugf("# op\n")
}
stepcount := 0
totalFee := new(big.Int)
out:
for {
stepcount++
// The base big int for all calculations. Use this for any results.
base := new(big.Int)
val := contract.GetMem(pc)
//fmt.Printf("%x = %d, %v %x\n", r, len(r), v, nb)
op := OpCode(val.Uint())
var fee *big.Int = new(big.Int)
var fee2 *big.Int = new(big.Int)
if stepcount > 16 {
fee.Add(fee, StepFee)
}
// Calculate the fees
switch op {
case oSSTORE:
y, x := vm.stack.Peekn()
val := contract.Addr(ethutil.BigToBytes(x, 256))
if val.IsEmpty() && len(y.Bytes()) > 0 {
fee2.Add(DataFee, StoreFee)
} else {
fee2.Sub(DataFee, StoreFee)
}
case oSLOAD:
fee.Add(fee, StoreFee)
case oEXTRO, oBALANCE:
fee.Add(fee, ExtroFee)
case oSHA256, oRIPEMD160, oECMUL, oECADD, oECSIGN, oECRECOVER, oECVALID:
fee.Add(fee, CryptoFee)
case oMKTX:
fee.Add(fee, ContractFee)
}
tf := new(big.Int).Add(fee, fee2)
if contract.Amount.Cmp(tf) < 0 {
fmt.Println("Insufficient fees to continue running the contract", tf, contract.Amount)
break
}
// Add the fee to the total fee. It's subtracted when we're done looping
totalFee.Add(totalFee, tf)
if ethutil.Config.Debug {
ethutil.Config.Log.Debugf("%-3d %-4s", pc, op.String())
}
switch op {
case oSTOP:
fmt.Println("")
break out
case oADD:
x, y := vm.stack.Popn()
// (x + y) % 2 ** 256
base.Add(x, y)
base.Mod(base, Pow256)
// Pop result back on the stack
vm.stack.Push(base)
case oSUB:
x, y := vm.stack.Popn()
// (x - y) % 2 ** 256
base.Sub(x, y)
base.Mod(base, Pow256)
// Pop result back on the stack
vm.stack.Push(base)
case oMUL:
x, y := vm.stack.Popn()
// (x * y) % 2 ** 256
base.Mul(x, y)
base.Mod(base, Pow256)
// Pop result back on the stack
vm.stack.Push(base)
case oDIV:
x, y := vm.stack.Popn()
// floor(x / y)
base.Div(x, y)
// Pop result back on the stack
vm.stack.Push(base)
case oSDIV:
x, y := vm.stack.Popn()
// n > 2**255
if x.Cmp(Pow256) > 0 {
x.Sub(Pow256, x)
}
if y.Cmp(Pow256) > 0 {
y.Sub(Pow256, y)
}
z := new(big.Int)
z.Div(x, y)
if z.Cmp(Pow256) > 0 {
z.Sub(Pow256, z)
}
// Push result on to the stack
vm.stack.Push(z)
case oMOD:
x, y := vm.stack.Popn()
base.Mod(x, y)
vm.stack.Push(base)
case oSMOD:
x, y := vm.stack.Popn()
// n > 2**255
if x.Cmp(Pow256) > 0 {
x.Sub(Pow256, x)
}
if y.Cmp(Pow256) > 0 {
y.Sub(Pow256, y)
}
z := new(big.Int)
z.Mod(x, y)
if z.Cmp(Pow256) > 0 {
z.Sub(Pow256, z)
}
// Push result on to the stack
vm.stack.Push(z)
case oEXP:
x, y := vm.stack.Popn()
base.Exp(x, y, Pow256)
vm.stack.Push(base)
case oNEG:
base.Sub(Pow256, vm.stack.Pop())
vm.stack.Push(base)
case oLT:
x, y := vm.stack.Popn()
// x < y
if x.Cmp(y) < 0 {
vm.stack.Push(ethutil.BigTrue)
} else {
vm.stack.Push(ethutil.BigFalse)
}
case oLE:
x, y := vm.stack.Popn()
// x <= y
if x.Cmp(y) < 1 {
vm.stack.Push(ethutil.BigTrue)
} else {
vm.stack.Push(ethutil.BigFalse)
}
case oGT:
x, y := vm.stack.Popn()
// x > y
if x.Cmp(y) > 0 {
vm.stack.Push(ethutil.BigTrue)
} else {
vm.stack.Push(ethutil.BigFalse)
}
case oGE:
x, y := vm.stack.Popn()
// x >= y
if x.Cmp(y) > -1 {
vm.stack.Push(ethutil.BigTrue)
} else {
vm.stack.Push(ethutil.BigFalse)
}
case oNOT:
x, y := vm.stack.Popn()
// x != y
if x.Cmp(y) != 0 {
vm.stack.Push(ethutil.BigTrue)
} else {
vm.stack.Push(ethutil.BigFalse)
}
case oMYADDRESS:
vm.stack.Push(ethutil.BigD(addr))
case oTXSENDER:
vm.stack.Push(ethutil.BigD(vars.sender))
case oTXVALUE:
vm.stack.Push(vars.txValue)
case oTXDATAN:
vm.stack.Push(big.NewInt(int64(len(vars.txData))))
case oTXDATA:
v := vm.stack.Pop()
// v >= len(data)
if v.Cmp(big.NewInt(int64(len(vars.txData)))) >= 0 {
vm.stack.Push(ethutil.Big("0"))
} else {
vm.stack.Push(ethutil.Big(vars.txData[v.Uint64()]))
}
case oBLK_PREVHASH:
vm.stack.Push(ethutil.BigD(vars.prevHash))
case oBLK_COINBASE:
vm.stack.Push(ethutil.BigD(vars.coinbase))
case oBLK_TIMESTAMP:
vm.stack.Push(big.NewInt(vars.time))
case oBLK_NUMBER:
vm.stack.Push(big.NewInt(int64(vars.blockNumber)))
case oBLK_DIFFICULTY:
vm.stack.Push(vars.diff)
case oBASEFEE:
// e = 10^21
e := big.NewInt(0).Exp(big.NewInt(10), big.NewInt(21), big.NewInt(0))
d := new(big.Rat)
d.SetInt(vars.diff)
c := new(big.Rat)
c.SetFloat64(0.5)
// d = diff / 0.5
d.Quo(d, c)
// base = floor(d)
base.Div(d.Num(), d.Denom())
x := new(big.Int)
x.Div(e, base)
// x = floor(10^21 / floor(diff^0.5))
vm.stack.Push(x)
case oSHA256, oSHA3, oRIPEMD160:
// This is probably save
// ceil(pop / 32)
length := int(math.Ceil(float64(vm.stack.Pop().Uint64()) / 32.0))
// New buffer which will contain the concatenated popped items
data := new(bytes.Buffer)
for i := 0; i < length; i++ {
// Encode the number to bytes and have it 32bytes long
num := ethutil.NumberToBytes(vm.stack.Pop().Bytes(), 256)
data.WriteString(string(num))
}
if op == oSHA256 {
vm.stack.Push(base.SetBytes(ethutil.Sha256Bin(data.Bytes())))
} else if op == oSHA3 {
vm.stack.Push(base.SetBytes(ethutil.Sha3Bin(data.Bytes())))
} else {
vm.stack.Push(base.SetBytes(ethutil.Ripemd160(data.Bytes())))
}
case oECMUL:
y := vm.stack.Pop()
x := vm.stack.Pop()
//n := vm.stack.Pop()
//if ethutil.Big(x).Cmp(ethutil.Big(y)) {
data := new(bytes.Buffer)
data.WriteString(x.String())
data.WriteString(y.String())
if secp256k1.VerifyPubkeyValidity(data.Bytes()) == 1 {
// TODO
} else {
// Invalid, push infinity
vm.stack.Push(ethutil.Big("0"))
vm.stack.Push(ethutil.Big("0"))
}
//} else {
// // Invalid, push infinity
// vm.stack.Push("0")
// vm.stack.Push("0")
//}
case oECADD:
case oECSIGN:
case oECRECOVER:
case oECVALID:
case oPUSH:
pc++
vm.stack.Push(contract.GetMem(pc).BigInt())
case oPOP:
// Pop current value of the stack
vm.stack.Pop()
case oDUP:
// Dup top stack
x := vm.stack.Pop()
vm.stack.Push(x)
vm.stack.Push(x)
case oSWAP:
// Swap two top most values
x, y := vm.stack.Popn()
vm.stack.Push(y)
vm.stack.Push(x)
case oMLOAD:
x := vm.stack.Pop()
vm.stack.Push(vm.mem[x.String()])
case oMSTORE:
x, y := vm.stack.Popn()
vm.mem[x.String()] = y
case oSLOAD:
// Load the value in storage and push it on the stack
x := vm.stack.Pop()
// decode the object as a big integer
decoder := contract.Addr(x.Bytes())
if !decoder.IsNil() {
vm.stack.Push(decoder.BigInt())
} else {
vm.stack.Push(ethutil.BigFalse)
}
case oSSTORE:
// Store Y at index X
y, x := vm.stack.Popn()
addr := ethutil.BigToBytes(x, 256)
fmt.Printf(" => %x (%v) @ %v", y.Bytes(), y, ethutil.BigD(addr))
contract.SetAddr(addr, y)
//contract.State().Update(string(idx), string(y))
case oJMP:
x := int(vm.stack.Pop().Uint64())
// Set pc to x - 1 (minus one so the incrementing at the end won't effect it)
pc = x
pc--
case oJMPI:
x := vm.stack.Pop()
// Set pc to x if it's non zero
if x.Cmp(ethutil.BigFalse) != 0 {
pc = int(x.Uint64())
pc--
}
case oIND:
vm.stack.Push(big.NewInt(int64(pc)))
case oEXTRO:
memAddr := vm.stack.Pop()
contractAddr := vm.stack.Pop().Bytes()
// Push the contract's memory on to the stack
vm.stack.Push(contractMemory(state, contractAddr, memAddr))
case oBALANCE:
// Pushes the balance of the popped value on to the stack
account := state.GetAccount(vm.stack.Pop().Bytes())
vm.stack.Push(account.Amount)
case oMKTX:
addr, value := vm.stack.Popn()
from, length := vm.stack.Popn()
makeInlineTx(addr.Bytes(), value, from, length, contract, state)
case oSUICIDE:
recAddr := vm.stack.Pop().Bytes()
// Purge all memory
deletedMemory := contract.state.Purge()
// Add refunds to the pop'ed address
refund := new(big.Int).Mul(StoreFee, big.NewInt(int64(deletedMemory)))
account := state.GetAccount(recAddr)
account.Amount.Add(account.Amount, refund)
// Update the refunding address
state.UpdateAccount(recAddr, account)
// Delete the contract
state.trie.Update(string(addr), "")
ethutil.Config.Log.Debugf("(%d) => %x\n", deletedMemory, recAddr)
break out
default:
fmt.Printf("Invalid OPCODE: %x\n", op)
}
ethutil.Config.Log.Debugln("")
//vm.stack.Print()
pc++
}
state.UpdateContract(addr, contract)
}
// evaluatePostfix takes a postfix expression and evaluates it
func evaluatePostfix(postfix []string) (*big.Rat, error) {
var stack stack.Stack
result := new(big.Rat) // note: a new(big.Rat) has value "0/1" ie zero
for _, token := range postfix {
if isOperand(token) {
bigrat := new(big.Rat)
if _, err := fmt.Sscan(token, bigrat); err != nil {
return nil, fmt.Errorf("unable to scan %s", token)
}
stack.Push(bigrat)
} else if isOperator(token) {
op2, err2 := stack.Pop()
if err2 != nil {
return nil, err2
}
var op1 interface{}
if token != "@" {
var err1 error
if op1, err1 = stack.Pop(); err1 != nil {
return nil, err1
}
}
dummy := new(big.Rat)
switch token {
case "**":
float1 := BigratToFloat(op1.(*big.Rat))
float2 := BigratToFloat(op2.(*big.Rat))
float_result := math.Pow(float1, float2)
stack.Push(FloatToBigrat(float_result))
case "*":
result := dummy.Mul(op1.(*big.Rat), op2.(*big.Rat))
stack.Push(result)
case "/":
result := dummy.Quo(op1.(*big.Rat), op2.(*big.Rat))
stack.Push(result)
case "+":
result = dummy.Add(op1.(*big.Rat), op2.(*big.Rat))
stack.Push(result)
case "-":
result = dummy.Sub(op1.(*big.Rat), op2.(*big.Rat))
stack.Push(result)
case "<":
if op1.(*big.Rat).Cmp(op2.(*big.Rat)) <= -1 {
stack.Push(big.NewRat(1, 1))
} else {
stack.Push(new(big.Rat))
}
case ">":
if op1.(*big.Rat).Cmp(op2.(*big.Rat)) >= 1 {
stack.Push(big.NewRat(1, 1))
} else {
stack.Push(new(big.Rat))
}
case "@":
result := dummy.Mul(big.NewRat(-1, 1), op2.(*big.Rat))
stack.Push(result)
}
} else {
return nil, fmt.Errorf("unknown token %v", token)
}
}
retval, err := stack.Pop()
if err != nil {
return nil, err
}
return retval.(*big.Rat), nil
}
// BinaryOp returns the result of the binary expression x op y.
// The operation must be defined for the operands.
// To force integer division of Int operands, use op == token.QUO_ASSIGN
// instead of token.QUO; the result is guaranteed to be Int in this case.
// Division by zero leads to a run-time panic.
//
func BinaryOp(x Value, op token.Token, y Value) Value {
x, y = match(x, y)
switch x := x.(type) {
case unknownVal:
return x
case boolVal:
y := y.(boolVal)
switch op {
case token.LAND:
return x && y
case token.LOR:
return x || y
}
case int64Val:
a := int64(x)
b := int64(y.(int64Val))
var c int64
switch op {
case token.ADD:
if !is63bit(a) || !is63bit(b) {
return normInt(new(big.Int).Add(big.NewInt(a), big.NewInt(b)))
}
c = a + b
case token.SUB:
if !is63bit(a) || !is63bit(b) {
return normInt(new(big.Int).Sub(big.NewInt(a), big.NewInt(b)))
}
c = a - b
case token.MUL:
if !is32bit(a) || !is32bit(b) {
return normInt(new(big.Int).Mul(big.NewInt(a), big.NewInt(b)))
}
c = a * b
case token.QUO:
return normFloat(new(big.Rat).SetFrac(big.NewInt(a), big.NewInt(b)))
case token.QUO_ASSIGN: // force integer division
c = a / b
case token.REM:
c = a % b
case token.AND:
c = a & b
case token.OR:
c = a | b
case token.XOR:
c = a ^ b
case token.AND_NOT:
c = a &^ b
default:
goto Error
}
return int64Val(c)
case intVal:
a := x.val
b := y.(intVal).val
var c big.Int
switch op {
case token.ADD:
c.Add(a, b)
case token.SUB:
c.Sub(a, b)
case token.MUL:
c.Mul(a, b)
case token.QUO:
return normFloat(new(big.Rat).SetFrac(a, b))
case token.QUO_ASSIGN: // force integer division
c.Quo(a, b)
case token.REM:
c.Rem(a, b)
case token.AND:
c.And(a, b)
case token.OR:
c.Or(a, b)
case token.XOR:
c.Xor(a, b)
case token.AND_NOT:
c.AndNot(a, b)
default:
goto Error
}
return normInt(&c)
case floatVal:
a := x.val
b := y.(floatVal).val
var c big.Rat
switch op {
case token.ADD:
c.Add(a, b)
case token.SUB:
c.Sub(a, b)
case token.MUL:
c.Mul(a, b)
case token.QUO:
c.Quo(a, b)
default:
goto Error
}
return normFloat(&c)
case complexVal:
y := y.(complexVal)
a, b := x.re, x.im
c, d := y.re, y.im
var re, im big.Rat
switch op {
case token.ADD:
// (a+c) + i(b+d)
re.Add(a, c)
im.Add(b, d)
case token.SUB:
// (a-c) + i(b-d)
re.Sub(a, c)
im.Sub(b, d)
case token.MUL:
// (ac-bd) + i(bc+ad)
var ac, bd, bc, ad big.Rat
ac.Mul(a, c)
bd.Mul(b, d)
bc.Mul(b, c)
ad.Mul(a, d)
re.Sub(&ac, &bd)
im.Add(&bc, &ad)
case token.QUO:
// (ac+bd)/s + i(bc-ad)/s, with s = cc + dd
var ac, bd, bc, ad, s, cc, dd big.Rat
ac.Mul(a, c)
bd.Mul(b, d)
bc.Mul(b, c)
ad.Mul(a, d)
cc.Mul(c, c)
dd.Mul(d, d)
s.Add(&cc, &dd)
re.Add(&ac, &bd)
re.Quo(&re, &s)
im.Sub(&bc, &ad)
im.Quo(&im, &s)
default:
goto Error
}
return normComplex(&re, &im)
case stringVal:
if op == token.ADD {
return x + y.(stringVal)
}
}
Error:
panic(fmt.Sprintf("invalid binary operation %v %s %v", x, op, y))
}
func Quotient(a, b *big.Rat) big.Rat {
var q big.Rat
return Minus(*q.Quo(a, b))
}
func backsub(m Matrix) (Vector, error) {
if len(m) == 0 || len(m[0]) < 2 {
return Vector{}, nil
}
coeffs := make(Vector, len(m[0])-1)
cnts := make([]int, len(m))
for i := range cnts {
cnts[i] = -1
}
zero := new(big.Rat)
for i := range m {
nz := 0
l := len(m[i]) - 1
for j := range m[i][:l] {
if m[i][j].Cmp(zero) != 0 {
nz++
}
}
if l-nz == l {
return nil, fmt.Errorf("contains a zero row")
}
cnts[i] = nz
}
z := make([]index, len(cnts))
for i := range z {
z[i].r = i
z[i].n = cnts[i]
}
sort.Sort(indexSlice(z))
for i := range z {
r := m[z[i].r]
l := len(r) - 1
w := new(big.Rat).Set(r[l])
var v *big.Rat
for j := range r[:l] {
if r[j].Cmp(zero) == 0 {
continue
}
if coeffs[j] != nil {
u := new(big.Rat).Set(coeffs[j])
u.Mul(u, r[j])
w.Sub(w, u)
} else if v != nil {
return nil, fmt.Errorf("matrix not in rref form")
} else {
v = new(big.Rat).Set(r[j])
}
}
if v.Cmp(zero) == 0 {
return nil, fmt.Errorf("matrix not in rref form")
}
coeffs[z[i].r] = w.Quo(w, v)
}
return coeffs, nil
}