Internals: Adding a Library for Interval Arithmetic

This documents a way to add mpfi to the arsenal of M2. Perhaps also arb.

mpfi

Dan Grayson's talk summary

We can work by analogy with mpfr. Before starting, check the license compatibility: some version of GPL is usually OK.

• Modify M2/INSTALL.
• M2/configure.ac
  • Get mpfi on LIBLIST
  • Check that mpfi.h is in order: search for AC_CHECK_HEADER and mpfr to see an example. (The libraries appear in order of dependency: more dependent first, more independent last. So -lmpfi should be go before -lmpfr.)
• Create M2/libraries/mpfi/Makefile.in (modify a copy of M2/libraries/mpfr/Makefile.in)
• Make sure you run make in M2/ after modifying configure.ac and any of the Makefile.in files.
• grep -r mpfr M2/Macaulay2/* to see where in source code mpfr is used.
  • e.g. d/version.dd has "mpfr version" => Ccode(constcharstar,"mpfr_version")
• dichotomy in memory allocation (native vs. garbage collected): see d/gmp.d for comment starting with --We introduce to types...
• Create something analogous to RRcell (see parse.d)

What makes RR_100 tick? (This may make RRi tick.)

• Compare raw RR_100 and raw RR_53 (53=standard precision)
• rawRR in interface.dd wraps IM2_Ring_RRR --- make something like that: e.g. create rawRRi that wraps rawRingRRi
• IM2_Ring_RRR is in engine.h and x-relem.cpp. Inspect the code in the latter.
• Look at aring-RRR.hpp
  • Engine's ARings are fast implementations of "coefficient rings". (A polynomial ring is not an ARing. See aring.hpp for DummyRing --- all methods mentioned there need to be implemented.)
  • Create aring-RRi.hpp --- this will house ARingRRi.
  • In aring.hpp, add ring_RRi and set ring_top = 17
  • No worries about memory allocation --- assume all memory is getting allocated without GC, unless gmp_RR gets involved.
• Look at aring-glue.hpp (no need to make changes here --- just be aware that this is a place where ARings get used).
  • ring_elem operations are handled here (at the moment, ring_elem is GC-ed).

autotools

The summary of this commit:

• add 1 line to config/files
• in configure.ac mention mpfi in help for --enable-build-libraries options
• write libraries/mpfi/Makefile.in

cmake

Detailed instructions are here.

• ExternalProject_Add is what we need to add mpfi (modify the corresponding block in cmake/build-libraries.cmake for mpfr).
  • There are several steps in setting up an external project: e.g. CONFIGURE_COMMAND controls the "configure" step, BUILD_COMMAND the building, etc.
  • _ADD_COMPONENT_DEPENDENCY to declare mpfi dependencies.
• Modify cmake/check-libraries.cmake and cmake/FindMPFI.cmake accordingly.

Front end

(Michael Burr and Anton Leykin)

• changes in d/ involve classes.dd,expr.d,actors2.dd, equality.dd, parse.d, gmp.d, gmp_aux.[h,c]
  • introduce RRi, RRimutable, RRiClass
  • copy-paste RR versions of methods (with minimal edits) whenever errors pop up during a build.
• gmp.d handling RRi, RRimutable:
  • leftRR and rightRR get the left/right ends of the interval
  • input methods
  • arithmetic operations
  • comparison operations
• util.d
  • toExpr
• gmp1.d
  • tostringRRi
• interface.dd
  • rawToRRi (is it used anywhere? see. toRRi)
• actors.d
  • arithmetic on the level of Expr
• actors3.d
  • round0(e:Expr):Expr
• actors4.d
  • interval (constructor)
  • toRRi, toRR, toCC, etc. (for Expr)
• real.m2 handles the InexactField called RRi
• exports.m2 exports RRi, RRi', toRRi, interval

Promote and lift

• raw rings/elements (general): m2/engine.m2
• single (raw/front) ring elements: m2/reals.m2
• matrices/lists (general): m2/modules.m2, uses rawPromote

General questions:

• How should promote and lift work for intervals?
  • What is the philosophy for RR_*?
• What is the expected behavior of new ... from ... ?

Testing

• Macaulay2/normal/RRi.m2
• Should there be any g-tests?
• What tests get executed when building M2?