1 2 3libmpdec 4======== 5 6libmpdec is a fast C/C++ library for correctly-rounded arbitrary precision 7decimal floating point arithmetic. It is a complete implementation of 8Mike Cowlishaw/IBM's General Decimal Arithmetic Specification. 9 10 11Files required for the Python _decimal module 12============================================= 13 14 Core files for small and medium precision arithmetic 15 ---------------------------------------------------- 16 17 basearith.{c,h} -> Core arithmetic in base 10**9 or 10**19. 18 bits.h -> Portable detection of least/most significant one-bit. 19 constants.{c,h} -> Constants that are used in multiple files. 20 context.c -> Context functions. 21 io.{c,h} -> Conversions between mpd_t and ASCII strings, 22 mpd_t formatting (allows UTF-8 fill character). 23 memory.{c,h} -> Allocation handlers with overflow detection 24 and functions for switching between static 25 and dynamic mpd_t. 26 mpdecimal.{c,h} -> All (quiet) functions of the specification. 27 typearith.h -> Fast primitives for double word multiplication, 28 division etc. 29 30 Visual Studio only: 31 ~~~~~~~~~~~~~~~~~~~ 32 vccompat.h -> snprintf <==> sprintf_s and similar things. 33 vcstdint.h -> stdint.h (included in VS 2010 but not in VS 2008). 34 vcdiv64.asm -> Double word division used in typearith.h. VS 2008 does 35 not allow inline asm for x64. Also, it does not provide 36 an intrinsic for double word division. 37 38 Files for bignum arithmetic: 39 ---------------------------- 40 41 The following files implement the Fast Number Theoretic Transform 42 used for multiplying coefficients with more than 1024 words (see 43 mpdecimal.c: _mpd_fntmul()). 44 45 umodarith.h -> Fast low level routines for unsigned modular arithmetic. 46 numbertheory.{c,h} -> Routines for setting up the Number Theoretic Transform. 47 difradix2.{c,h} -> Decimation in frequency transform, used as the 48 "base case" by the following three files: 49 50 fnt.{c,h} -> Transform arrays up to 4096 words. 51 sixstep.{c,h} -> Transform larger arrays of length 2**n. 52 fourstep.{c,h} -> Transform larger arrays of length 3 * 2**n. 53 54 convolute.{c,h} -> Fast convolution using one of the three transform 55 functions. 56 transpose.{c,h} -> Transpositions needed for the sixstep algorithm. 57 crt.{c,h} -> Chinese Remainder Theorem: use information from three 58 transforms modulo three different primes to get the 59 final result. 60 61 62Pointers to literature, proofs and more 63======================================= 64 65 literature/ 66 ----------- 67 68 REFERENCES.txt -> List of relevant papers. 69 bignum.txt -> Explanation of the Fast Number Theoretic Transform (FNT). 70 fnt.py -> Verify constants used in the FNT; Python demo for the 71 O(N**2) discrete transform. 72 73 matrix-transform.txt -> Proof for the Matrix Fourier Transform used in 74 fourstep.c. 75 six-step.txt -> Show that the algorithm used in sixstep.c is 76 a variant of the Matrix Fourier Transform. 77 mulmod-64.txt -> Proof for the mulmod64 algorithm from 78 umodarith.h. 79 mulmod-ppro.txt -> Proof for the x87 FPU modular multiplication 80 from umodarith.h. 81 umodarith.lisp -> ACL2 proofs for many functions from umodarith.h. 82 83 84Library Author 85============== 86 87 Stefan Krah <skrah@bytereef.org> 88 89 90 91