// currencyUnits converts a types.Currency to a string with human-readable
// units. The unit used will be the largest unit that results in a value
// greater than 1. The value is rounded to 4 significant digits.
func currencyUnits(c types.Currency) string {
pico := types.SiacoinPrecision.Div64(1e12)
if c.Cmp(pico) < 0 {
return c.String() + " H"
}
// iterate until we find a unit greater than c
mag := pico
unit := ""
for _, unit = range []string{"pS", "nS", "uS", "mS", "SC", "KS", "MS", "GS", "TS"} {
if c.Cmp(mag.Mul64(1e3)) < 0 {
break
} else if unit != "TS" {
// don't want to perform this multiply on the last iter; that
// would give us 1.235 TS instead of 1235 TS
mag = mag.Mul64(1e3)
}
}
num := new(big.Rat).SetInt(c.Big())
denom := new(big.Rat).SetInt(mag.Big())
res, _ := new(big.Rat).Mul(num, denom.Inv(denom)).Float64()
return fmt.Sprintf("%.4g %s", res, unit)
}
func (me *StatisticalAccumulator) Mean() *big.Rat {
mean := new(big.Rat)
mean.Inv(me.n)
mean.Mul(mean, me.sigmaXI)
return mean
}
// 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--
}
}
// Returns an approximate Birthday probability calculation
// based on the number of blocks given and the hash size.
//
// It uses the simplified calculation: p = k(k-1) / (2N)
//
// From http://preshing.com/20110504/hash-collision-probabilities/
func BirthdayProblem(blocks int) string {
k := big.NewInt(int64(blocks))
km1 := big.NewInt(int64(blocks - 1))
ksq := k.Mul(k, km1)
n := big.NewInt(0)
n = n.Exp(big.NewInt(2), big.NewInt(int64(HashSize)*8), nil)
twoN := n.Add(n, n)
var t, t2 big.Rat
var res *big.Rat
//
res = t.SetFrac(ksq, twoN)
f64, _ := res.Float64()
inv := t2.Inv(res).FloatString(0)
invs := fmt.Sprintf(" ~ 1/%s ~ %v", inv, f64)
return "Collision probability is" + invs
}
func (me *StatisticalAccumulator) Variance() *big.Rat {
variance := new(big.Rat)
variance.Inv(me.n)
variance.Mul(variance, me.sigmaXISquared)
temp := new(big.Rat)
temp.Mul(me.n, me.n)
temp.Inv(temp)
temp.Mul(temp, me.sigmaXI)
temp.Mul(temp, me.sigmaXI)
variance.Sub(variance, temp)
return variance
}
// 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
}
// How many fractions contain a numerator with more digits than the denominator?
func problem57() int {
sum := 0 // Number of fractions meeting the description.
const limit = 1000 // Given in problem description.
one := new(big.Rat).SetInt64(1)
two := new(big.Rat).SetInt64(2)
// result will be re-used each iteration to store the
// current value of the fractional expansion.
result := new(big.Rat)
// tail will be re-used each iteration to store the
// current value of the repeating component of the expansion.
// That component is 2, (2 + 1/2), (2 + 1/(2 + 1/2)), ...
tail := new(big.Rat).SetInt64(2)
for i := 0; i < limit; i++ {
temp := new(big.Rat)
tail.Add(two, temp.Inv(tail)) // tail = (2 + 1/tail)
result.Add(one, temp.Inv(tail)) // result = (1 + 1/tail)
if checkNumerator(result) {
sum++
}
}
return sum
}
// Mul multiplies the difficulty of a target by y. The product is defined by:
// y / x
func (x Target) MulDifficulty(y *big.Rat) (t Target) {
product := new(big.Rat).Mul(y, x.Inverse())
product = product.Inv(product)
return RatToTarget(product)
}
// Wrapper for dividing two values
func Div(x, y *big.Rat) *big.Rat {
yinv := y.Inv(y)
z := x.Mul(x, yinv)
return z
}