func info(a *big.Int, n uint) {
dtrunc := int64(float64(a.BitLen())*.30103) - 10
var first, rest big.Int
rest.Exp(first.SetInt64(10), rest.SetInt64(dtrunc), nil)
first.Quo(a, &rest)
fstr := first.String()
fmt.Printf("%d! begins %s... and has %d digits.\n",
n, fstr, int64(len(fstr))+dtrunc)
}
func Factorial(n uint64) (r *big.Int) {
var oddFactNDiv2, oddFactNDiv4 big.Int
// closes on oddFactNDiv2, oddFactNDiv4
oddSwing := func(n uint64) (r *big.Int) {
if n < uint64(len(smallOddSwing)) {
return big.NewInt(smallOddSwing[n])
}
length := (n - 1) / 4
if n%4 != 2 {
length++
}
high := n - (n+1)&1
ndiv4 := n / 4
var oddFact big.Int
if ndiv4 < uint64(len(smallOddFactorial)) {
oddFact.SetInt64(smallOddFactorial[ndiv4])
r = &oddFact
} else {
r = &oddFactNDiv4
}
return oddFact.Quo(oddProduct(high, length), r)
}
// closes on oddFactNDiv2, oddFactNDiv4, oddSwing, and itself
var oddFactorial func(uint64) *big.Int
oddFactorial = func(n uint64) (oddFact *big.Int) {
if n < uint64(len(smallOddFactorial)) {
oddFact = big.NewInt(smallOddFactorial[n])
} else {
oddFact = oddFactorial(n / 2)
oddFact.Mul(oddFact.Mul(oddFact, oddFact), oddSwing(n))
}
oddFactNDiv4.Set(&oddFactNDiv2)
oddFactNDiv2.Set(oddFact)
return oddFact
}
oddFactNDiv2.SetInt64(1)
oddFactNDiv4.SetInt64(1)
r = oddFactorial(n)
exp := uint(n - uint64(xmath.BitCount64(n)))
return r.Lsh(r, exp)
}
func binaryIntOp(x *big.Int, op token.Token, y *big.Int) interface{} {
var z big.Int
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.REM:
return z.Rem(x, y)
case token.AND:
return z.And(x, y)
case token.OR:
return z.Or(x, y)
case token.XOR:
return z.Xor(x, y)
case token.AND_NOT:
return z.AndNot(x, y)
case token.SHL:
panic("unimplemented")
case token.SHR:
panic("unimplemented")
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 number_divide(x, y Obj) Obj {
xfx := (uintptr(unsafe.Pointer(x)) & fixnum_mask) == fixnum_tag
yfx := (uintptr(unsafe.Pointer(y)) & fixnum_mask) == fixnum_tag
if xfx && yfx {
i1 := int(uintptr(unsafe.Pointer(x))) >> fixnum_shift
i2 := int(uintptr(unsafe.Pointer(y))) >> fixnum_shift
// A good optimizer will combine the div and mod into
// one instruction.
r, m := i1/i2, i1%i2
if m == 0 && r > fixnum_min && r < fixnum_max {
return Make_fixnum(r)
} else {
return wrap(big.NewRat(int64(i1), int64(i2)))
}
}
if (!xfx && (uintptr(unsafe.Pointer(x))&heap_mask) != heap_tag) ||
(!yfx && (uintptr(unsafe.Pointer(y))&heap_mask) != heap_tag) {
panic("bad type")
}
if xfx {
x = wrap(big.NewInt(int64(fixnum_to_int(x))))
}
if yfx {
y = wrap(big.NewInt(int64(fixnum_to_int(y))))
//return wrap(z.Div(vx,vy))
}
switch vx := (*x).(type) {
case *big.Int:
var z *big.Int = big.NewInt(0)
switch vy := (*y).(type) {
case *big.Int:
return simpBig(z.Div(vx, vy))
case *big.Rat:
z := big.NewRat(1, 1)
z.SetInt(vx)
return simpRat(z.Quo(z, vy))
default:
panic("bad type")
}
case *big.Rat:
z := big.NewRat(1, 1)
switch vy := (*y).(type) {
case *big.Int:
z.SetInt(vy)
return simpRat(z.Quo(vx, z))
case *big.Rat:
return simpRat(z.Quo(vx, vy))
}
}
panic("bad type")
}