Download or view e.frink in plain text format
/** Program to calculate e to arbitrary precision. This uses binary
splitting for speed.
You usually use this by calling E.getE[digits] which will return e
to the number of digits you specify.
This version has been updated to be fastest with
Frink: The Next Generation. Due to limitations in Java's BigDecimal
class, this is limited to a little over 101 million digits.
This differs from the basic algorithm in eBinarySplitting.frink
because when you ask for more digits of e than you previously had,
this *resumes* the calculation rather than starting from scratch.
See:
http://numbers.computation.free.fr/Constants/Algorithms/splitting.html
http://www.ginac.de/CLN/binsplit.pdf
*/
class E
{
class var largestDigits = -1
class var cacheE = undef
/** These variables help us resume the state of the binary-splitting
algorithm. */
class var largestP = 1
class var largestQ = 1
class var largestK = 1
class var logFactorial = 0.
/** This is the main public method to get the value of e to a certain
number of digits, calculating it if need be. If e has already been
calculated to a sufficient number of digits, this returns it from the
cache.
*/
class getE[digits = getPrecision[]] :=
{
origPrec = getPrecision[]
try
{
setPrecision[digits]
if (largestDigits >= digits)
return 1. * cacheE
else
return 1. * calcE[digits]
}
finally
setPrecision[origPrec]
}
/** This is an internal method that calculates the digits of e if
necessary. */
class calcE[digits] :=
{
origPrec = getPrecision[]
try
{
setPrecision[15]
// Find number of terms to calculate.
// ln[x!] = ln[1] + ln[2] + ... + ln[x]
logMax = digits * ln[10]
k = largestK
while (logFactorial < logMax)
{
logFactorial = logFactorial + ln[k]
k = k + 1
}
setPrecision[digits+3]
if largestK < k // We may have already calculated enough!
{
if (largestK == 1) // This is the first iteration
{
p = P[0,k]
q = Q[0,k]
} else
{
// Continuing iterations
pmb = P[largestK, k]
qmb = Q[largestK, k]
p = largestP qmb + pmb
q = largestQ qmb
}
// Store the biggest values back in the cache
largestP = p
largestQ = q
largestK = k
cacheE = 1 + (1. * p)/q
}
setPrecision[digits]
return 1. * cacheE
}
finally
setPrecision[origPrec]
}
/** Private method for binary splitting. */
class P[a,b] :=
{
if (b-a) == 1
return 1
m = (a+b) div 2
r = P[a,m] Q[m,b] + P[m,b]
return r
}
/** Private method for binary splitting. */
class Q[a,b] :=
{
if (b-a) == 1
return b
m = (a+b) div 2
return Q[a,m] Q[m,b]
}
}
Download or view e.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 19966 days, 10 hours, 34 minutes ago.