Here are my comments on the code so far. It's not very much, since I only got through a few files. I'll try to expand on this as I have time, but no promises.
Many thanks Steven.
concepts/mp_number_architypes.hpp:
* The file name is misspelled. It should be "archetypes."
Indeed, fixed in my local copy.
* The #includes aren't quite right. The file does not use trunc, and does use fpclassify.
* line 28: mpl::list requires #include <boost/mpl/list.hpp> * line 79: stringstream requires #include <sstream>
Fixed in my local copy.
depricated:
* Should be deprecated.
Will go away if the library is accepted anyway (just contains bits and bobs not in the submission that I didn't want to delete just yet).
detail/functions/constants.hpp:
* line 12: typedef typename has_enough_bits<...> pred_type; If you're going to go through all this trouble to make sure that you have a type with enough bits, you shouldn't assume that unsigned has enough. IIRC, the standard only guarantees 16 bits for unsigned.
Nod. There's some new code that simplifies all that as well, simplified and fixed in my local copy.
* line 38: if(digits < 3640) Ugh. I'm assuming that digits means binary digits and 3640 = floor(log_2 10^1100)
Comments to that effect throughout.
* line 51: I would appreciate a brief description of the formula. This code isn't very readable.
Nod. Added locally: // // We calculate log2 from using the formula: // // ln(2) = 3/4 SUM[n>=0] ((-1)^n * N!^2 / (2^n(2n+1)!)) // // Numerator and denominator are calculated separately and then // divided at the end, we also precalculate the terms up to n = 5 // since these fit in a 32-bit integer anyway. // // See Gourdon, X., and Sebah, P. The logarithmic constant: log 2, Jan. 2004. // Also http://www.mpfr.org/algorithms.pdf. // Also spotted a missing optimisation in the arithmetic.
* line 105: It looks like this is using the formula e \approx \sum_0^n{\frac{1}{i!}} = (\sum_0^n\frac{n!}{i!})/n! and induction using the rule: \sum_0^n\frac{n!}{i!} = (\sum_0^(n-1)\frac{(n-1)!}{i!}) * n + 1
Please explain the math or point to somewhere that explains it.
Nod adding locally: // // Standard evaluation from the definition of e: http://functions.wolfram.com/Constants/E/02/ //
* line 147: ditto for pi
Nod. Adding locally: // // This algorithm is from: // Schonhage, A., Grotefeld, A. F. W., and Vetter, E. Fast Algorithms: A Multitape Turing // Machine Implementation. BI Wissenschaftverlag, 1994. // Also described in MPFR's algorithm guide: http://www.mpfr.org/algorithms.pdf. // // Let: // a[0] = A[0] = 1 // B[0] = 1/2 // D[0] = 1/4 // Then: // S[k+1] = (A[k]+B[k]) / 4 // b[k] = sqrt(B[k]) // a[k+1] = a[k]^2 // B[k+1] = 2(A[k+1]-S[k+1]) // D[k+1] = D[k] - 2^k(A[k+1]-B[k+1]) // Stop when |A[k]-B[k]| <= 2^(k-p) // and PI = B[k]/D[k] Currently testing those changes before moving on to the other comments, Thanks again, John.