Thanks everybody! It turns out WolframAlpha will do the computation for me. (It won't let me copy the digits, so I have to transcribe them by hand, but given how much time I'm spending reviewing the notes anyway, that is a small part of the overall labor cost.)

On Fri, Dec 18, 2015 at 4:31 AM, Olaf Klinke <olf@aatal-apotheke.de> wrote:

As it happens, I am just studying a presentation [1] Martin Escardo gave to students at the University of Birmingham. It contains Haskell code for exact real number computation. Among other things, there is a function that computes a signed digit representation of pi/32. It computes several thousand digits in a few seconds.
I did not try it yet, but many irrational numbers are fixed points of simple arithmetical expressions. For example, the golden ratio is the fixed point of \x -> 1+1/x. Infinite streams of digits should be a type where such a fixed point is computable. Or you could use a sufficiently precise rational approximation and convert that do decimal in the usual way.

import Data.Ratio
import Data.List (iterate)

-- one step of Heron's algorithm for sqrt(a)
heron :: (Fractional a) => a -> a -> a
heron a x = (x+a/x)/2

-- infinite stream of approximations to sqrt(a)
approx :: (Fractional a) => a -> [a]
approx a = iterate (heron a) 1

-- Find an interval with rational end-points
-- for a signed-digit real number
type SDReal = [Int] -- use digits [-1,0,1]
interval :: Int -> SDReal -> (Rational,Rational)
interval precision x = let
  f = foldr (\d g -> (a d).g) id (take precision x))
  a d = \x -> ((fromIntegral d)+x)/2
  in (f(-1),f(1))

Cheers,
Olaf

[1] www.cs.bham.ac.uk/~mhe/.talks/phdopen2013/realreals.lhs

--

Jeffrey Benjamin Brown

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