Uncanonical display of Double

[daniel.is.fischer]

Prelude> 0.5 ^ 1030
0.8691694759794e-310

Should of course be 8.69...e-311, just to have it on record for now.

I'll take a look at the showing code one of the next days.

[augustss]

That code is pretty impenetrable. :)

My guess is that the log estimator doesn't do the right thing for negative exponents. Try (fixup (k0-1)).

[daniel.is.fischer]

For starters, a better approximation to logBase 10 2 fixes this,

     if b == 2 && base == 10 then
        -- logBase 10 2 is slightly bigger than 3/10 so
        -- the following will err on the low side.  Ignoring
        -- the fraction will make it err even more.
        -- Haskell promises that p-1 <= logBase b f < p.
        -- (p - 1 + e0) * 3 `div` 10
        (p - 1 + e0) * 21306 `quot` 70777

*FloatShow> let x :: Double; x = 0.5 ^ 1030
*FloatShow> floatToDigits 10 x
([8,6,9,1,6,9,4,7,5,9,7,9,4],-310)
*FloatShow> showFloat x ""
"8.691694759794e-311"

but I'd rather check the code carefully to see whether something else might need fixing (and maybe an earlier convergent of logBase 10 2 will suffice).

[daniel.is.fischer]

1. fix4383.dpatch fixes the issue, we no longer overestimate the base 10 logarithm
2. There was a typo (b instead of be) in the distance to the next smaller FP number for powers of floatRadix. I thought it ought to be b^e and verified it in the paper. This makes numrun012 fail because now 2 ^ 31 :: Float shows as "2.1474836e9" instead of "2.1474837e9" (and some other show values change too, e.g. 2.0 ^ 852 was "3.0030067315218801e256" is now "3.00300673152188e256").
3. Performance enhancement by using quot/quotRem instead of div/divMod and using the cache of powers of 2 instead of recomputing.
4. Further performance enhancement by adding a cache for powers of 10.
5. All of the above in one patch.

1. and 2. should be applied since they correct errors.
The performance enhancement isn't too bad, I think a few more percent could be squeezed out, but it doesn't solve the fundamental problem of the slowness of show for RealFloat values (cf.  http://www.haskell.org/pipermail/haskell-cafe/2009-June/062904.html). I plan to look into it for 7.2, not now.

[simonmar]

Thanks Daniel.

I presume we want the fixes in the 7.0 branch and the performance improvements in 7.2. Milestoning for 7.0.2 to get the fixes in initially.

[simonmar]

I pushed all these to HEAD. We want these two in 7.0.2:

Sun Oct 24 11:29:42 PDT 2010  Daniel Fischer <daniel.is.fischer@web.de>
  * FIX #4383
  Use a better approximation to logBase 10 2 to prevent leading zeros in floatToDigits.

Sun Oct 24 19:50:41 BST 2010  Daniel Fischer <daniel.is.fischer@web.de>
  * Fix typo in floatToDigits
  The mDn value for powers of 2 >= floatDigits x - 1 was typo'ed, leading to longer than necessary show results in a few cases (e.g. 2.0^852).
  Corrected in accordance with Burger and Dybvig's paper.

and these two should stay in HEAD only:

Sun Oct 24 20:07:07 BST 2010  Daniel Fischer <daniel.is.fischer@web.de>
  * Cache for powers of 10
  Add a cache for commonly needed powers of 10 to speed up floatToDigits.

Sun Oct 24 19:59:14 BST 2010  Daniel Fischer <daniel.is.fischer@web.de>
  * Performance enchancement for floatToDigits
  Use quot and quotRem instead of div and divMod for dividing positive Integers since that is a bit faster.

[igloo]

Both merged.