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90 lines
3.6 KiB
90 lines
3.6 KiB
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libmpdec
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========
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libmpdec is a fast C/C++ library for correctly-rounded arbitrary precision
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decimal floating point arithmetic. It is a complete implementation of
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Mike Cowlishaw/IBM's General Decimal Arithmetic Specification.
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Files required for the Python _decimal module
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=============================================
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Core files for small and medium precision arithmetic
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----------------------------------------------------
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basearith.{c,h} -> Core arithmetic in base 10**9 or 10**19.
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bits.h -> Portable detection of least/most significant one-bit.
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constants.{c,h} -> Constants that are used in multiple files.
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context.c -> Context functions.
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io.{c,h} -> Conversions between mpd_t and ASCII strings,
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mpd_t formatting (allows UTF-8 fill character).
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mpalloc.{c,h} -> Allocation handlers with overflow detection
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and functions for switching between static
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and dynamic mpd_t.
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mpdecimal.{c,h} -> All (quiet) functions of the specification.
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typearith.h -> Fast primitives for double word multiplication,
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division etc.
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Visual Studio only:
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~~~~~~~~~~~~~~~~~~~
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vccompat.h -> snprintf <==> sprintf_s and similar things.
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vcdiv64.asm -> Double word division used in typearith.h. VS 2008 does
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not allow inline asm for x64. Also, it does not provide
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an intrinsic for double word division.
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Files for bignum arithmetic:
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----------------------------
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The following files implement the Fast Number Theoretic Transform
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used for multiplying coefficients with more than 1024 words (see
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mpdecimal.c: _mpd_fntmul()).
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umodarith.h -> Fast low level routines for unsigned modular arithmetic.
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numbertheory.{c,h} -> Routines for setting up the Number Theoretic Transform.
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difradix2.{c,h} -> Decimation in frequency transform, used as the
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"base case" by the following three files:
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fnt.{c,h} -> Transform arrays up to 4096 words.
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sixstep.{c,h} -> Transform larger arrays of length 2**n.
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fourstep.{c,h} -> Transform larger arrays of length 3 * 2**n.
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convolute.{c,h} -> Fast convolution using one of the three transform
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functions.
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transpose.{c,h} -> Transpositions needed for the sixstep algorithm.
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crt.{c,h} -> Chinese Remainder Theorem: use information from three
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transforms modulo three different primes to get the
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final result.
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Pointers to literature, proofs and more
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=======================================
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literature/
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-----------
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REFERENCES.txt -> List of relevant papers.
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bignum.txt -> Explanation of the Fast Number Theoretic Transform (FNT).
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fnt.py -> Verify constants used in the FNT; Python demo for the
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O(N**2) discrete transform.
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matrix-transform.txt -> Proof for the Matrix Fourier Transform used in
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fourstep.c.
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six-step.txt -> Show that the algorithm used in sixstep.c is
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a variant of the Matrix Fourier Transform.
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mulmod-64.txt -> Proof for the mulmod64 algorithm from
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umodarith.h.
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mulmod-ppro.txt -> Proof for the x87 FPU modular multiplication
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from umodarith.h.
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umodarith.lisp -> ACL2 proofs for many functions from umodarith.h.
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Library Author
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==============
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Stefan Krah <skrah@bytereef.org>
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