Support MPFR floats in numkondo

Remove '-D' option (error tolerance) in numkondo

Changelog

@@ -0,0 +1,14 @@
+1.4:
+  * Support MPFR floats in numkondo.
+
+  * Remove '-D' option (error tolerance) in numkondo.
+
+
+1.3.1:
+  
+  * '-C' flag in meantools-derive:
+      allows to pipe the output of meantools-derive directly into numkondo.
+
+  * Fixed memory leak in meantools-derive.
+
+

INSTALL

@@ -6,6 +6,8 @@
 
 * meankondo should work on any POSIX compliant system, such as GNU/Linux or OSX.
 
+* meankondo is linked against the GNU MPFR and GNU GMP libraries.
+
 * Compiling:
   Run
     make

LGPL3

@@ -0,0 +1,165 @@
+                   GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+
+  This version of the GNU Lesser General Public License incorporates
+the terms and conditions of version 3 of the GNU General Public
+License, supplemented by the additional permissions listed below.
+
+  0. Additional Definitions.
+
+  As used herein, "this License" refers to version 3 of the GNU Lesser
+General Public License, and the "GNU GPL" refers to version 3 of the GNU
+General Public License.
+
+  "The Library" refers to a covered work governed by this License,
+other than an Application or a Combined Work as defined below.
+
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+by the Library, but which is not otherwise based on the Library.
+Defining a subclass of a class defined by the Library is deemed a mode
+of using an interface provided by the Library.
+
+  A "Combined Work" is a work produced by combining or linking an
+Application with the Library.  The particular version of the Library
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+
+  1. Exception to Section 3 of the GNU GPL.
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+  2. Conveying Modified Versions.
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+   on the Library, uncombined with any other library facilities,
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+   is a work based on the Library, and explaining where to find the
+   accompanying uncombined form of the same work.
+
+  6. Revised Versions of the GNU Lesser General Public License.
+
+  The Free Software Foundation may publish revised and/or new versions
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+received it does not specify a version number of the GNU Lesser
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+
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+Library.

Makefile

@@ -18,7 +18,7 @@
 #   if static=1 then link libkondo statically but other libraries dynamically
 STATIC=1
 
-VERSION=1.2
+VERSION=1.4
 
 # products of the compilation
 PROJECT_BINS= meankondo numkondo meantools kondo_preprocess meantools-convert
@@ -62,9 +62,9 @@ SRCDIR=./src
 OBJDIR=./objs
 
 # objects
-LIBKONDO_OBJS = $(addprefix $(OBJDIR)/,array.o cli_parser.o coefficient.o fields.o grouped_polynomial.o idtable.o istring.o number.o parse_file.o polynomial.o rational_float.o rational_int.o rcc.o tools.o)
+LIBKONDO_OBJS = $(addprefix $(OBJDIR)/,array.o cli_parser.o coefficient.o fields.o grouped_polynomial.o idtable.o istring.o number.o parse_file.o polynomial.o rational_float.o rational_int.o rcc.o rcc_mpfr.o tools.o)
 MEANKONDO_OBJS = $(addprefix $(OBJDIR)/,meankondo.o mean.o)
-NUMKONDO_OBJS = $(addprefix $(OBJDIR)/,numkondo.o flow.o)
+NUMKONDO_OBJS = $(addprefix $(OBJDIR)/,numkondo.o flow.o flow_mpfr.o)
 MEANTOOLS_OBJS = $(addprefix $(OBJDIR)/,meantools.o meantools_exp.o meantools_deriv.o meantools_eval.o)
 KONDO_PP_OBJS = $(addprefix $(OBJDIR)/,kondo_preprocess.o kondo.o)
 
@@ -78,8 +78,8 @@ XTRA_LIBS=
 ifeq ($(STATIC),1)
   # compile libkondo.a
   PREREQ=static
-  # libkondo is linked against libm
+  # libkondo is linked against libm, libmpfr and libgmp
-  XTRA_LIBS=-lm
+  XTRA_LIBS=-lm -lmpfr -lgmp
   # link binaries using the static library
   LIBKONDO_FLAG=-l:libkondo.a
   # install static lib
@@ -87,8 +87,8 @@ ifeq ($(STATIC),1)
 else ifeq ($(STATIC),2)
   # compile libkondo.a
   PREREQ=static
-  # libkondo is linked against libm
+  # libkondo is linked against libm, libmpfr and libgmp
-  XTRA_LIBS=-lm
+  XTRA_LIBS=-lm -lmpfr -lgmp
   # link binaries statically
   override LDFLAGS += -static
   INSTALLLIB=install-static
@@ -119,17 +119,17 @@ libkondo.a: $(LIBKONDO_OBJS)
 	$(AR) -rc $(BUILDDIR)/lib/$@ $^
 
 libkondo.so.$(VERSION): $(LIBKONDO_OBJS)
-	$(LD) -shared -lm $(LDFLAGS) -o $(BUILDDIR)/lib/$@ $^
+	$(LD) -shared -lm -lmpfr -lgmp $(LDFLAGS) -o $(BUILDDIR)/lib/$@ $^
 	ln -fs ./libkondo.so.$(VERSION) $(BUILDDIR)/lib/libkondo.so
 
 meankondo: $(MEANKONDO_OBJS)
 	$(LD) -L$(BUILDDIR)/lib $(LDFLAGS) -o $(BUILDDIR)/bin/$@ $^ $(LIBKONDO_FLAG) -lpthread $(XTRA_LIBS)
 
 numkondo: $(NUMKONDO_OBJS)
-	$(LD) -L$(BUILDDIR)/lib $(LDFLAGS) -o $(BUILDDIR)/bin/$@ $^ $(LIBKONDO_FLAG) -lm $(XTRA_LIBS)
+	$(LD) -L$(BUILDDIR)/lib $(LDFLAGS) -o $(BUILDDIR)/bin/$@ $^ $(LIBKONDO_FLAG) -lm -lmpfr -lgmp $(XTRA_LIBS)
 
 meantools: $(MEANTOOLS_OBJS)
-	$(LD) -L$(BUILDDIR)/lib $(LDFLAGS) -o $(BUILDDIR)/bin/$@ $^ $(LIBKONDO_FLAG) $(XTRA_LIBS)
+	$(LD) -L$(BUILDDIR)/lib $(LDFLAGS) -o $(BUILDDIR)/bin/$@ $^ $(LIBKONDO_FLAG) -lmpfr -lgmp $(XTRA_LIBS)
 
 meantools-convert:
 	cp scripts/meantools-convert $(BUILDDIR)/bin/

NOTICE

@@ -1,2 +1,15 @@
 meankondo
 Copyright 2015 Ian Jauslin
+
+The numerical values can be represented as multi-precision floats using
+the GNU MPFR library, which is licensed under the GNU Lesser General
+Public License (LGPL) version 3 (see LGPL3 for a copy of the license).
+See
+  http://www.mpfr.org/
+for details.
+
+The GNU MPFR library is based on the GNU GMP library, which is licensed
+under the GNU Lesser General Public License (LGPL) version 3 (see LGPL3
+for a copy of the license).  See
+  http://www.gmplib.org/
+for details.

doc/meankondo-doc.html

@@ -69,10 +69,10 @@
   </head>
 
   <body>
-    <h1 style="margin-bottom:50pt;">meankondo <span style="margin-left:10pt;font-size:18pt">v1.2</span></h1>
+    <h1 style="margin-bottom:50pt;">meankondo <span style="margin-left:10pt;font-size:18pt">v1.4</span></h1>
 
     <p>
-      This is the official documentation for <b>meankondo</b>, version 1.2. The aim of this document is not to give a technical description of how to use the various programs bundled with <b>meankondo</b>, nor is it to explain where hierarchical models come from and what their meaning is, but rather a conceptual overview of how <b>meankondo</b> approaches the computation of flow equations, and how its programs can be made to interact with one another to compute various quantities. For a more technical description, see the man pages included with the <b>meankondo</b> source code. For a more theoretical discussion of Fermionic hierarchical models, see [G.Benfatto, G.Gallavotti, I.Jauslin, 2015].
+      This is the official documentation for <b>meankondo</b>, version 1.4. The aim of this document is not to give a technical description of how to use the various programs bundled with <b>meankondo</b>, nor is it to explain where hierarchical models come from and what their meaning is, but rather a conceptual overview of how <b>meankondo</b> approaches the computation of flow equations, and how its programs can be made to interact with one another to compute various quantities. For a more technical description, see the man pages included with the <b>meankondo</b> source code. For a more theoretical discussion of Fermionic hierarchical models, see <a href="http://ian.jauslin.org/publications/15bgj">[G.Benfatto, G.Gallavotti, I.Jauslin, 2015]</a>.
     </p>
 
     <h2 style="margin-top:50pt;">Table of contents</h2>
@@ -150,7 +150,7 @@
 	<li><b>external</b>: which are organized in pairs, and are denoted by \((\Psi_i^+,\Psi_i^-)\) for \(i\in\{1,\cdots,E\}\).
 	<li><b>super-external</b>: which denoted by \(H_i\) for \(i\in\{1,\cdots,X\}\) (the only difference with external fields is that super-external fields are not in pairs, which is a seemingly innocuous difference; but super-external fields are meant to be used for different purposes as external fields (see <a href="#flow_equation_definition">Definition</a> below)).
       </ul>
-      The fields are used as a basis for a complex algebra, so that we can take products and linear combinations of fields (in other words, the concept of <i>polynomials over the fields</i> is well defined). Some of the fields (<i>Fermions</i>) anti-commute with each other (two fields \(a\) and \(b\) are said to anti-commute if \(ab\equiv-ba\)), and the rest (<i>Bosons</i>) commute. Which fields are Fermions and which are Bosons is specified in the <code>#!fields</code> entry in the configuration file. <b>(Warning: As of version 1.2, all internal fields must be Fermions.)</b>
+      The fields are used as a basis for a complex algebra, so that we can take products and linear combinations of fields (in other words, the concept of <i>polynomials over the fields</i> is well defined). Some of the fields (<i>Fermions</i>) anti-commute with each other (two fields \(a\) and \(b\) are said to anti-commute if \(ab\equiv-ba\)), and the rest (<i>Bosons</i>) commute. Which fields are Fermions and which are Bosons is specified in the <code>#!fields</code> entry in the configuration file. <b>(Warning: As of version 1.4, all internal fields must be Fermions.)</b>
     </p>
     <p>
       In the configuration file of the <b>meankondo</b> program, the fields are specified in the <code>#!fields</code> entry.
@@ -286,7 +286,15 @@
       Numerical evaluations are not exact. The numbers manipulated <b>meankondo</b> are double precision floating point numbers ("doubles" for short), which are also system-dependent. On systems that follow the IEEE 754 standard, doubles have a precision of 53 bits, which implies they are accurate to 15 decimal places; and the absolute value of doubles is bounded above by \(2^{1024}-2^{1024-53}\) (that is the number whose binary expansion has \(1023\) digits and whose \(53\) left-most digits are \(1\) whereas the others are \(0\)) and below by \(2^{-1022}\).
     </p>-->
     <p>
-      Numerical evaluations are not exact. The numbers manipulated <b>meankondo</b> are "long doubles", which, when compiled for x86 processors, have a precision of 64 bits, which implies they are accurate to 19 decimal places; and the absolute value of doubles is bounded above by \(2^{16384}-2^{16384-64}\) (that is the number whose binary expansion has \(16383\) digits and whose \(64\) left-most digits are \(1\) whereas the others are \(0\)) and below by \(2^{-16382}\).
+      Numerical evaluations are not exact. The numbers manipulated <b>meankondo</b> are either "long doubles" or "MPFR floats", depending on the options passed to <b>numkondo</b> (see <code>man numkondo</code>).
+      <ul>
+	<li>
+	  Long doubles: when compiled for x86 processors, have a precision of 64 bits, which implies they are accurate to 19 decimal places; and the absolute value of doubles is bounded above by \(2^{16384}-2^{16384-64}\) (that is the number whose binary expansion has \(16383\) digits and whose \(64\) left-most digits are \(1\) whereas the others are \(0\)) and below by \(2^{-16382}\).
+	</li>
+	<li>
+	  MPFR floats: the precision and size of the exponent can be specified as options on the command line. The maximal precision and maximal value of the exponent are, on 64 bit systems, \(2^{63}\) bits and \(2^{62}\) respectively.
+	</li>
+      </ul>
     </p>
 
 

man/kondo_preprocess.1

@@ -1,5 +1,5 @@
-.Dd $Mdocdate: April 14 2015 $
+.Dd $Mdocdate: September 22 2015 $
-.Dt kondo_preprocess 1.2
+.Dt kondo_preprocess 1.4
 .Os
 .Sh NAME
 .Nm kondo_preprocess
@@ -94,6 +94,30 @@ defines external fields for A and B, denoted by a and b. They can be used as fie
 .D1 <axb.h>
 .Pp
 .It
+Scalar products of A's and B's may also be specified using the '<#.#>' syntax:
+.D1 <An.An>
+.D1 <Bn.Bn>
+.D1 <An.Bn>
+.D1 <An.h>
+.D1 <Bn.h>
+.Pp
+The difference between '[f #.#]' and '<#.#>' is that the former corresponds to a '#!symbols' entry whereas the latter is replaced by its corresponding polynomial when
+.Nm
+reads it (see
+.Sx meankondo Ns (1)).
+.Pp
+.It
+A vector 't=(t1,t2,t3)' of Pauli matrices (satisfying the Pauli commutation relations [ti,tj]=\\delta_{i,j}1+\\epsilon_{i,j,k}tk) is introduced as a non-commuting object. It can be used in scalar producs:
+.D1 <An.t>
+.D1 <Bn.t>
+.D1 <t.h>
+.D1 <a.t>
+.D1 <b.t>
+.Pp
+Note that the '<#,#>' must be used since these scalar products do not commute whereas '#!symbols' entries must commute (see
+.Sx meankondo Ns (1)).
+.Pp
+.It
 Furthermore, in order to simplify writing products of polynomials over each box index, if the polynomial contains a '%', then
 .Nm
 multiplies the polynomial by itself as many times as there are boxes (2^dimension times), replacing '%' with the appropriate box index. For example, if dimension=1
@@ -118,6 +142,9 @@ in which the polynomial can use the fields
 .D1 <a.h>
 .D1 <b.h>
 .D1 <axb.h>
+.D1 <t.h>
+.D1 <a.t>
+.D1 <b.t>
 defined above.
 .Pp
 Example:

man/meankondo.1

@@ -1,5 +1,5 @@
-.Dd $Mdocdate: April 13 2015 $
+.Dd $Mdocdate: September 22 2015 $
-.Dt meankondo 1.2
+.Dt meankondo 1.4
 .Os
 .Sh NAME
 .Nm meankondo
@@ -44,7 +44,7 @@ as well as the following pre-processors, which generate configuration files for
 .It Fl t Ar threads
 The number of threads to use for the computation.
 .It Fl C
-Format the ouptput so it can be piped to
+Format the output so it can be piped to
 .Sy numkondo ,
 that is, instead of printing the flow equation, print a full configuration file containing the flow equation as well as all the other entries of the configuration file that do not pertain to the computation of the flow equation.
 .It Fl v
@@ -67,7 +67,7 @@ recognizes the following entries (unless explicitly mentioned, the entries below
 .It Sy #!fields
 A list of the fields of the model.
 .Pp
-The fields entry contains 4 lines which start with 'i:', 'x:', 'h:' and 'f:'. Each of these is followed by a ',' separated list of field indices, which are positive integers.
+The fields entry contains 5 lines which start with 'i:', 'x:', 'h:', 'f:' and 'a:'. Each of these is followed by a ',' separated list of field indices, which are positive integers.
 .Bl -bullet
 .It
 The indices following 'i' correspond to internal fields, which are integrated out using the Wick rule and the propagator provided in the '#!propagator' entry. Each internal field is associated a conjugate field, whose index is the opposite of the field's index (e.g. 'i:101' defines a field whose index is -101)
@@ -77,6 +77,10 @@ The indices following 'x' correspond to external fields that are associated conj
 The indices following 'h' correspond to external fields that are not associated a conjugate field. External indices may not appear as internal indices.
 .It
 The 'f' line specifies which of the internal and external indices are Fermions, i.e. which fields anti-commute. The fields appearing in the 'f' line should also either appear in the 'i' or 'x' line. WARNING: for the moment, only cases in which all of the internal fields are Fermions are supported.
+.It
+The 'a' line specifies a list of external fields listed in the 'h' entry that do not commute with each other. Specifying fields in this entry will prevent
+.Nm
+from sorting them. These fields may not be in the 'i', 'x' or 'f' entries. This entry can be used to treat cases in which the coefficients of the input polynomial are operators that do not commute. Their commutation relations may be specified in the '#!identities' entries (see below).
 .El
 .Pp
 .Em Line breaks are not ignored in this entry.
@@ -84,8 +88,9 @@ The 'f' line specifies which of the internal and external indices are Fermions,
 Example:
 .D1 i:101,102,201,202
 .D1 x:100,200
-.D1 h:301,302,303
+.D1 h:301,302,303,401,402,403
 .D1 f:100,101,102
+.D1 a:401,402,403
 .It Sy #!propagator
 The propagator of the model.
 .Pp
@@ -98,31 +103,41 @@ just as easily as propagators with symbolic entries. Such an entry means that
 .Pp
 Example:
 .D1 101;102: 1 , 102;101: -1 , 201;202: s{-1} + (-1)[l10] , 202;201: (-1)s{-1} + [l10]
-.It Sy #!symbols
-Symbolic variables used as shortcuts for more complicated expressions (optional entry).
-.Pp
-In order to simplify long expressions, symbolic variables can be defined in this entry. Each variable is assigned an index, which is a positive integer that must be different from any of the internel and external indices defined in the '#!fields' entry.
-.Pp
-The symbols entry is a ',' separated list, whose elements are of the form
-.D1 index= polynomial
-where index is the index of the variable and polynomial is the expression it stands for (see the POLYNOMIALS section below for information on how to format polynomials). Note that polynomial can contain other symbolic variables. There is no safeguard against self-referencing definitions that may cause infinite loops.
-.Pp
-Example:
-.D1 1001= (-1)[f-100][f100] + (-1)[f-101][f101] , 2001=[f-100][f100] + [f-201][f201]
-.Pp
-This entry is optional.
 .Pp
 .It Sy #!identities
 Identities satisfied by some of the fields (optional entry).
 .Pp
-In some cases, some of the quantities involved in a model will satisfy an identity (e.g. a vector may be of unit-norm), which should simplified out from the flow equation.
+In some cases, some of the quantities involved in a model will satisfy an identity (e.g. a vector may be of unit-norm, or non-commuting objects may satisfy non-trivial commutation relations), which should be simplified out from the flow equation.
 .Pp
 The identities entry is a ',' separated list, whose elements are of the form
 .D1 monomial=polynomial
 where monomial represents the left side of the identity and is a sequence of field indices of the form '[f index1][f index2]...' and polynomial represents the right side of the identity (see the POLYNOMIALS section below for information on how to format polynomials).
 .Pp
 Example:
-.D1 [f301][f301]=(1)+(-1)[f302][f302]+(-1)[f303][f303]
+.D1 [f301][f301]=(1)+(-1)[f302][f302]+(-1)[f303][f303],
+.D1 [f401][f401]=(1),
+.D1 [f401][f402]=(s{-1})[f403],
+.D1 [f401][f403]=((-1)s{-1})[f402]
+.Pp
+This entry is optional.
+.Pp
+.It Sy #!symbols
+Symbolic variables used as shortcuts for more complicated expressions (optional entry).
+.Pp
+In order to simplify long expressions, symbolic variables can be defined in this entry. Each variable is assigned an index, which is a positive integer that must be different from any of the internal and external indices defined in the '#!fields' entry.
+.Pp
+Seemingly similar functionality can be achieved using an '#!identity' entry (see above), though symbols are handled differently from identities. Indeed, while identities are simplified out of the polynomials as soon as they occur, symbols are only resolved when
+.Nm
+computes the mean of the input polynomial. Using symbols can thereby be a lot faster than using identities. However, as is mentioned below, symbols must commute with each other and all other fields, whereas identities can be made to be fermionic or non-commuting.
+.Pp
+The symbols entry is a ',' separated list, whose elements are of the form
+.D1 index= polynomial
+where index is the index of the variable and polynomial is the expression it stands for (see the POLYNOMIALS section below for information on how to format polynomials). Note that polynomial can contain other symbolic variables. There is no safeguard against self-referencing definitions that may cause infinite loops.
+.Pp
+WARNING: Symbols are assumed to commute with each other and all other Fermions. They should therefore not represent quantities that do not commute (e.g. odd monomials of fermions or non-commuting objects specified in the 'a:' entry in the '#!fields' entry).
+.Pp
+Example:
+.D1 1001= (-1)[f-100][f100] + (-1)[f-101][f101] , 2001=[f-100][f100] + [f-201][f201]
 .Pp
 This entry is optional.
 .Pp
@@ -157,16 +172,16 @@ computes the mean of a monomial containing elements of different groups, it fact
 .Nm
 does not repeatedly try to pair independent fields.
 .Pp
+WARNING:
+.Nm
+assumes that the symbols and fields in each group are independent but does not check that they are. If symbols or fields that are not independent are put in different groups, or if some are in a group while others are not in any group, then the resulting flow equation may be wrong.
+.Pp
 The groups entry is a list of collections of fields or symbols of the following form
 .D1 (index1,index2,...)
 .Pp
 Example:
 .D1 (1001,1002) (2001,2002)
 .Pp
-.Em Warning:
-.Nm
-does not check that the fields in different groups are truly independent, so cases in which fields in different group have a non-vanishing propagator entry may give unexpected results.
-.Pp
 This entry is optional.
 .El
 .Pp

man/meantools-convert.1

@@ -1,5 +1,5 @@
-.Dd $Mdocdate: June 12 2015 $
+.Dd $Mdocdate: September 22 2015 $
-.Dt meantools-convert 1.2
+.Dt meantools-convert 1.4
 .Os
 .Sh NAME
 .Nm meantools-convert

man/meantools.1

@@ -1,5 +1,5 @@
-.Dd $Mdocdate: April 14 2015 $
+.Dd $Mdocdate: September 22 2015 $
-.Dt meantools 1.2
+.Dt meantools 1.4
 .Os
 .Sh NAME
 .Nm meantools
@@ -13,11 +13,14 @@
 .Sy derive
 .Op Fl d Ar nderivs
 .Op Fl V Ar variables
+.Op Fl C
 .Op Ar config_file
 .Pp
 .Nm
 .Sy eval
 .Op Fl R Ar values
+.Op Fl P Ar precision
+.Op Fl E Ar max_exponent
 .Op Ar config_file
 .Pp
 .Sh DESCRIPTION
@@ -95,6 +98,10 @@ The variables that depend on the extra virtual parameter (defaults to all) (WARN
 would interpret the argument as being a flag, for example, write '-V "0,-1"' instead of '-V "-1,0"').
 .Pp
 Can either be a ',' separated list if indices or 'all' to derive with respect to all available variables.
+.It Fl C
+Format the output so it can be piped to
+.Sy numkondo ,
+that is, instead of printing the flow equation, print a full configuration file containing the flow equation as well as all the other entries of the configuration file that do not pertain to the computation of the flow equation.
 .El
 .Pp
 .Sy Configuration file:
@@ -131,6 +138,12 @@ The values of the rccs with which to evaluate the flow equation.
 .Ar values
 is formatted like an initial_condition (see
 .Sx numkondo Ns (1) ) .
+.It Fl P Ar precision
+Number of bits used for the significand of numerical values (see 
+.Sx numkondo Ns (1) ) .
+.It Fl E Ar max_exponent
+Largest allowed value for the exponent of numerical values (see
+.Sx numkondo Ns (1) ) .
 .El
 .Pp
 .Sy Configuration file:

man/numkondo.1

@@ -1,5 +1,5 @@
-.Dd $Mdocdate: April 14 2015 $
+.Dd $Mdocdate: September 22 2015 $
-.Dt numkondo 1.2
+.Dt numkondo 1.4
 .Os
 .Sh NAME
 .Nm numkondo
@@ -8,8 +8,9 @@
 .Nm
 .Op Fl F
 .Op Fl N Ar niter
-.Op Fl D Ar tolerance
 .Op Fl I Ar initial_condition
+.Op Fl P Ar precision
+.Op Fl E Ar max_exponent
 .Op Ar config_file
 .Pp
 .Nm
@@ -44,12 +45,12 @@ as well as the following pre-processors, which generate configuration files for
 Number of iterations
 .It Fl F
 Only print the last step of the computation, with full precision. The output can be used as an initial condition for further iterations.
-.It Fl D Ar tolerance
-If this option is provided, any number smaller than
-.Ar tolerance
-is set to 0.
 .It Fl I Ar initial_condition
 Set the initial condition from the command-line (overrides the initial condition in the configuration file). The format is the same as the '#!initial_configuration' entry, see below.
+.It Fl P Ar precision
+Number of bits used for the significand of numerical values (see the NUMERICAL PRECISION section). If this option is specified, then numerical values are represented as MPFR floats instead of long doubles, which requires more computating time.
+.It Fl E Ar max_exponent
+Largest allowed value for the exponent of numerical values (see the NUMERICAL PRECISION section). If this option is specified, then numerical values are represented as MPFR floats instead of long doubles, which requires more computating time.
 .It Fl v
 Print version information and exit.
 .El
@@ -145,6 +146,19 @@ If the '-F' flag is provided,
 .Nm
 prints the last step of the iteration to stdout in a format that can be re-used as an initial condition for subsequent iterations.
 .Pp
+.Sh NUMERICAL PRECISION
+Numerical values are represented as floating point numbers, which consist in a significand (or mantissa) and an exponent. The number is given by
+.D1 significand * 2^exponent
+.Pp
+If neither the '-P' nor the '-E' flags are specified, then numerical values are implemented using the 'long double' type, which allocates 64 bits to the significand and 15 to the exponent (this may change depending on the implementation of the C compiler used to compile
+.Nm ) .
+Numbers are therefore accurate to 19 decimal places, and the exponent must be in the interval [-16382 , 16383].
+.Pp
+If one of the '-P' or '-E' flags are specified, then numerical values are implemented using the GNU MPFR library. The number of bits allocated to the significand and exponent can be set by the '-P' and '-E' flags, within the limits set by the MPFR library. These values depend on the implementation of the library. On 64-bit systems, the maximal precision and maximal value of the exponent should be of the order of 2^63 and 2^62 respectively.
+.Pp
+Note that using MPFR floats increases the computing time required to run
+.Nm
+.Pp
 .Sh RETURN CODE
 .Nm
 returns 0 on success and -1 on error.

scripts/meantools-convert

@@ -105,7 +105,7 @@ def latex_engine(argv,text):
             oneline=0
             i=i+1
 
-    return(convert_latex(text,lsym,Lsym,Csym,oneline,columns))
+    return(convert_latex(text,lsym,Lsym,Csym,oneline))
 
 # convert to C format
 def convert_C(text, lsym, Lsym, Csym, oneline):
@@ -160,7 +160,7 @@ def convert_C(text, lsym, Lsym, Csym, oneline):
     return(text+';')
 
 # convert to LaTeX format
-def convert_latex(text, lsym, Lsym, Csym, oneline, columns):
+def convert_latex(text, lsym, Lsym, Csym, oneline):
     # remove newlines
     if (oneline==0):
         text=text.replace('\n','\\\\\n')

src/coefficient.c

@@ -18,6 +18,10 @@ limitations under the License.
 
 #include <stdio.h>
 #include <stdlib.h>
+#include <stdarg.h>
+// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
+#define MPFR_USE_VA_LIST
+#include <mpfr.h>
 #include "definitions.cpp"
 #include "rational.h"
 #include "istring.h"
@@ -721,7 +725,7 @@ int evalcoef(RCC rccs, Coefficient coef, long double* out){
   int i,j;
   long double num_factor;
 
-  *out=0;
+  *out=0.;
 
   // for each monomial
   for(i=0;i<coef.length;i++){
@@ -737,3 +741,44 @@ int evalcoef(RCC rccs, Coefficient coef, long double* out){
   }
   return(0);
 }
+
+// evaluate a coefficient on a vector (using mpfr floats)
+int evalcoef_mpfr(RCC_mpfr rccs, Coefficient coef, mpfr_t out){
+  int i,j;
+  mpfr_t num_factor;
+  // tmp number (do not initialize Z)
+  mpfr_t x, y, Z;
+
+  // init numbers
+  mpfr_inits(num_factor, x, y, (mpfr_ptr) NULL);
+
+  mpfr_init(out);
+  mpfr_set_zero(out, 1);
+
+  // for each monomial
+  for(i=0;i<coef.length;i++){
+    // product of factors
+    mpfr_set_flt(num_factor, 1., MPFR_RNDN);
+    for(j=0;j<coef.factors[i].length;j++){
+      mpfr_mul(x,num_factor,rccs.values[intlist_find_err(rccs.indices,rccs.length,coef.factors[i].values[j])], MPFR_RNDN);
+      mpfr_set(num_factor,x, MPFR_RNDN);
+    }
+    // denominator
+    if(coef.denoms[i].power>0){
+      mpfr_pow_si(y, rccs.values[intlist_find_err(rccs.indices,rccs.length,coef.denoms[i].index)], coef.denoms[i].power, MPFR_RNDN);
+      mpfr_div(x, num_factor, y, MPFR_RNDN);
+      mpfr_set(num_factor, x, MPFR_RNDN);
+    }
+
+    number_mpfr_val(Z, coef.nums[i]);
+    mpfr_mul(x, num_factor, Z, MPFR_RNDN);
+    mpfr_add(y, x, out, MPFR_RNDN);
+    mpfr_set(out, y, MPFR_RNDN);
+    mpfr_clear(Z);
+  }
+
+  // free numbers
+  mpfr_clears(num_factor, x, y, (mpfr_ptr)NULL);
+
+  return(0);
+}

src/coefficient.h

@@ -74,5 +74,7 @@ int coef_denom_cmp(coef_denom denom1, coef_denom denom2);
 
 // evaluate a coefficient on a vector
 int evalcoef(RCC rccs, Coefficient coef, long double* out);
+// evaluate a coefficient on a vector (using mpfr floats)
+int evalcoef_mpfr(RCC_mpfr rccs, Coefficient coef, mpfr_t out);
 
 #endif

src/definitions.cpp

@@ -17,7 +17,7 @@ limitations under the License.
 #ifndef DEFINITIONS_GCC
 #define DEFINITIONS_GCC
 
-#define VERSION "1.2"
+#define VERSION "1.4"
 
 // number of entries in a configuration file
 #define ARG_COUNT 10

src/fields.c

@@ -32,6 +32,7 @@ int init_Fields_Table(Fields_Table* fields){
   init_Identities(&((*fields).ids), FIELDS_SIZE);
   init_Symbols(&((*fields).symbols), FIELDS_SIZE);
   init_Int_Array(&((*fields).fermions),FIELDS_SIZE);
+  init_Int_Array(&((*fields).noncommuting),FIELDS_SIZE);
   return(0);
 }
 int free_Fields_Table(Fields_Table fields){
@@ -41,6 +42,7 @@ int free_Fields_Table(Fields_Table fields){
   free_Identities(fields.ids);
   free_Symbols(fields.symbols);
   free_Int_Array(fields.fermions);
+  free_Int_Array(fields.noncommuting);
   return(0);
 }
 
@@ -73,6 +75,16 @@ int is_fermion(int index, Fields_Table fields){
   }
 }
 
+// check whether a field is non-commuting
+int is_noncommuting(int index, Fields_Table fields){
+  if(int_array_find(abs(index), fields.noncommuting)>=0){
+    return(1);
+  }
+  else{
+    return(0);
+  }
+}
+
 
 // ------------------ Identities --------------------
 
@@ -180,13 +192,16 @@ int identities_concat(Identities input, Identities* output){
 
 // resolve the identities
 // requires both the monomials in polynomial and the ids in fields to be sorted
+// IMPORTANT: the sorting must be such that noncommuting fields must come before the other fields
 int resolve_ids(Polynomial* polynomial, Fields_Table fields){
   int i,j,k,l;
   int sign;
   int fermion_count;
+  int first_field;
   int at_least_one;
   int security;
-  Int_Array monomial;
+  Int_Array pre_monomial;
+  Int_Array post_monomial;
   Number num;
   Number tmp_num;
 
@@ -207,29 +222,38 @@ int resolve_ids(Polynomial* polynomial, Fields_Table fields){
 
       // loop over ids
       for(j=0;j<fields.ids.length;j++){
+
 	// check whether the monomial matches the id
-	if(int_array_is_subarray_ordered(fields.ids.lhs[j],(*polynomial).monomials[i])==1){
+	first_field=int_array_is_subarray_noncommuting(fields.ids.lhs[j],(*polynomial).monomials[i],fields);
-	  init_Int_Array(&monomial, (*polynomial).monomials[i].length);
+	if(first_field>=0){
-	  
+	  init_Int_Array(&pre_monomial, (*polynomial).monomials[i].length);
-	  // remove lhs from monomial
+	  init_Int_Array(&post_monomial, (*polynomial).monomials[i].length);
-	  // sign from moving the fields out of the monomial
+
+	  // add whatever is before the first field to pre
+	  for(k=0;k<first_field;k++){
+	    int_array_append((*polynomial).monomials[i].values[k],&pre_monomial);
+	  }
+
+	  // find others and move them together
+	  // sign from moving the fields
 	  sign=1;
-	  // number of Fermions to remove from the monomial
+	  // number of Fermions to jump over
 	  fermion_count=0;
-	  for(k=0,l=0;k<(*polynomial).monomials[i].length;k++){
+	  for(l=1,k=first_field+1;k<(*polynomial).monomials[i].length;k++){
 	    // check whether the field is identical to the "current" one in the id
 	    // if l is too large, then keep the field
 	    if(l>=fields.ids.lhs[j].length || (*polynomial).monomials[i].values[k]!=fields.ids.lhs[j].values[l]){
-	      int_array_append((*polynomial).monomials[i].values[k],&monomial);
+	      // add to post
-	      // sign correction
+	      int_array_append((*polynomial).monomials[i].values[k],&post_monomial);
-	      if(fermion_count % 2 ==1 && is_fermion((*polynomial).monomials[i].values[k], fields)){
+	      // count Fermions to jump
-		sign*=-1;
+	      if(is_fermion((*polynomial).monomials[i].values[k],fields)){
+		fermion_count++;
 	      }
 	    }
 	    else{
-	      // increment fermion_count
+	      // sign correction
-	      if(is_fermion(fields.ids.lhs[j].values[l],fields)){
+	      if(is_fermion(fields.ids.lhs[j].values[l],fields) && fermion_count % 2 == 1){
-		fermion_count++;
+		sign*=-1;
 	      }
 	      // increment "current" field in the id
 	      l++;
@@ -240,30 +264,33 @@ int resolve_ids(Polynomial* polynomial, Fields_Table fields){
 	  // add extra monomials (if there are more than 1)
 	  for(k=1;k<fields.ids.rhs[j].length;k++){
 	    number_prod(num, fields.ids.rhs[j].nums[k], &tmp_num);
-	    polynomial_append(monomial, (*polynomial).factors[i], tmp_num, polynomial);
+	    polynomial_append(pre_monomial, (*polynomial).factors[i], tmp_num, polynomial);
 	    free_Number(tmp_num);
 	    int_array_concat(fields.ids.rhs[j].monomials[k],(*polynomial).monomials+(*polynomial).length-1);
+	    int_array_concat(post_monomial,(*polynomial).monomials+(*polynomial).length-1);
 	    // re-sort monomial
 	    sign=1;
-	    monomial_sort((*polynomial).monomials[(*polynomial).length-1],0,(*polynomial).monomials[(*polynomial).length-1].length-1,fields,&sign);
+	    monomial_sort((*polynomial).monomials[(*polynomial).length-1],fields,&sign);
 	    number_Qprod_chain(quot(sign,1),(*polynomial).nums+(*polynomial).length-1);
 	  } 
 	  // correct i-th monomial
 	  free_Number((*polynomial).nums[i]);
 	  (*polynomial).nums[i]=number_prod_ret(num,fields.ids.rhs[j].nums[0]);
 	  free_Int_Array((*polynomial).monomials[i]);
-	  (*polynomial).monomials[i]=monomial;
+	  (*polynomial).monomials[i]=pre_monomial;
 	  int_array_concat(fields.ids.rhs[j].monomials[0],(*polynomial).monomials+i);
+	  int_array_concat(post_monomial,(*polynomial).monomials+i);
+	  free_Int_Array(post_monomial);
 	  // re-sort monomial
 	  sign=1;
-	  monomial_sort((*polynomial).monomials[i],0,(*polynomial).monomials[i].length-1,fields,&sign);
+	  monomial_sort((*polynomial).monomials[i],fields,&sign);
 	  number_Qprod_chain(quot(sign,1),(*polynomial).nums+i);
 
 	  // free num
 	  free_Number(num);
 
-	  // repeat the step (in order to perform all of the replacements if several are necessary)
+	  // repeat the replacement (in order to perform all of the replacements if several are necessary)
-	  j--;
+	  j=0;
 	  if(at_least_one==0){
 	    at_least_one=1;
 	  }
@@ -275,6 +302,62 @@ int resolve_ids(Polynomial* polynomial, Fields_Table fields){
   return(0);
 }
 
+// check whether an array is a sub-array of another
+// requires noncommuting elements to be next to each other
+// other elements may be separated, but the order must be respected
+// returns the first index of the sub-array
+// IMPORTANT: the noncommuting elements must precede all others in input and in test_array
+int int_array_is_subarray_noncommuting(Int_Array input, Int_Array test_array, Fields_Table fields){
+  int i,j;
+  int matches=0;
+  int post_nc=0;
+  int match_nc;
+  int first=-1;
+
+  // bound noncommuting elements
+  while(is_noncommuting(input.values[post_nc], fields)==1){
+    post_nc++;
+  }
+
+  for(i=0,match_nc=0;i<test_array.length;i++){
+    if(test_array.values[i]==input.values[0]){
+      match_nc=1;
+    }
+    for(j=1;j<post_nc;j++){
+      if(test_array.values[i+j]!=input.values[j]){
+	match_nc=0;
+      }
+    }
+    if(match_nc==1){
+      first=i;
+      break;
+    }
+  }
+
+  if(first<0){
+    return(-1);
+  }
+
+  if(post_nc>0){
+    matches=post_nc;
+  }
+  else{
+    matches=1;
+  }
+
+  for(i=first+1;i<test_array.length && matches<input.length;i++){
+    if(input.values[matches]==test_array.values[i]){
+      matches++;
+    }
+  }
+  if(matches==input.length){
+    return(first);
+  }
+  else{
+    return(-1);
+  }
+}
+
 
 // ------------------ Symbols --------------------
 

src/fields.h

@@ -29,6 +29,8 @@ int free_Fields_Table(Fields_Table fields);
 int field_type(int index, Fields_Table fields);
 // check whether a field anticommutes
 int is_fermion(int index, Fields_Table fields);
+// check whether a field is non-commuting
+int is_noncommuting(int index, Fields_Table fields);
 
 
 // init
@@ -51,6 +53,8 @@ int identities_concat(Identities input, Identities* output);
 
 // resolve the identities
 int resolve_ids(Polynomial* polynomial, Fields_Table fields);
+// check whether an array is a sub-array of another, support for noncommuting elements
+int int_array_is_subarray_noncommuting(Int_Array input, Int_Array test_array, Fields_Table fields);
 
 
 // init

src/flow.c

@@ -24,13 +24,11 @@ limitations under the License.
 #include "number.h"
 #include "array.h"
 #include "coefficient.h"
-
+#include "rcc.h"
 
 
 // compute flow numerically, no exponentials
-//    inputs: flow_equation
+int numerical_flow(Grouped_Polynomial flow_equation, RCC init, Labels labels, int niter, int display_mode){
-//            init, niter, tol (the allowed error at each step), ls (whether to display the results in terms of ls), display_mode (what to print)
-int numerical_flow(Grouped_Polynomial flow_equation, RCC init, Labels labels, int niter, long double tol, int display_mode){
   // running coupling contants
   RCC rccs=init;
   int i,j;
@@ -53,7 +51,7 @@ int numerical_flow(Grouped_Polynomial flow_equation, RCC init, Labels labels, in
 
   for(i=0;i<niter;i++){
     // compute a single step
-    step_flow(&rccs, flow_equation, tol);
+    step_flow(&rccs, flow_equation);
     // convert ls to alphas
     if(display_mode==DISPLAY_NUMERICAL){
       // print the result
@@ -83,14 +81,9 @@ int numerical_flow(Grouped_Polynomial flow_equation, RCC init, Labels labels, in
 }
 
 // single step in the flow no exponentials
-//          inputs: flow_equation, tol
+int step_flow(RCC* rccs, Grouped_Polynomial flow_equation){
-//   input/outputs: rccs
-int step_flow(RCC* rccs, Grouped_Polynomial flow_equation, long double tol){
   int i;
   long double* new_rccs=calloc((*rccs).length,sizeof(long double));
-  Int_Array computed;
-
-  init_Int_Array(&computed, (*rccs).length);
 
   // initialize vectors to 0
   for(i=0;i<(*rccs).length;i++){
@@ -101,10 +94,6 @@ int step_flow(RCC* rccs, Grouped_Polynomial flow_equation, long double tol){
   for(i=0;i<flow_equation.length;i++){
     if(flow_equation.indices[i]<0){
       evalcoef(*rccs, flow_equation.coefs[i], new_rccs+i);
-      // if the new rcc is too small, then ignore it
-      if(fabs(new_rccs[i])<tol){
-	new_rccs[i]=0.;
-      }
       (*rccs).values[i]=new_rccs[i];
     }
   }
@@ -113,10 +102,6 @@ int step_flow(RCC* rccs, Grouped_Polynomial flow_equation, long double tol){
   for(i=0;i<flow_equation.length;i++){
     if(flow_equation.indices[i]>=0){
       evalcoef(*rccs, flow_equation.coefs[i], new_rccs+i);
-      // if the new rcc is too small, then ignore it
-      if(fabs(new_rccs[i])<tol){
-	new_rccs[i]=0.;
-      }
     }
   }
 
@@ -126,7 +111,6 @@ int step_flow(RCC* rccs, Grouped_Polynomial flow_equation, long double tol){
   }
 
   // free memory
-  free_Int_Array(computed);
   free(new_rccs);
   return(0);
 }

src/flow.h

@@ -21,14 +21,12 @@ Compute flow numerically
 #ifndef NUMERICAL_FLOW_H
 #define NUMERICAL_FLOW_H
 
-
+#include "types.h"
-#include "grouped_polynomial.h"
-#include "rcc.h"
 
 // compute flow
-int numerical_flow(Grouped_Polynomial flow_equation, RCC init, Labels labels, int niter, long double tol, int display_mode);
+int numerical_flow(Grouped_Polynomial flow_equation, RCC init, Labels labels, int niter, int display_mode);
 // single step
-int step_flow(RCC* rccs, Grouped_Polynomial flow_equation, long double tol);
+int step_flow(RCC* rccs, Grouped_Polynomial flow_equation);
 
 // print the label of an rcc (takes constants and derivatives into account)
 int print_label(int index, Labels labels);

src/flow_mpfr.c

@@ -0,0 +1,128 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "flow_mpfr.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdarg.h>
+// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
+#define MPFR_USE_VA_LIST
+// define MPFR_USE_FILE to enable the use of mpfr_printf
+#define MPFR_USE_FILE
+#include <mpfr.h>
+#include "tools.h"
+#include "math.h"
+#include "definitions.cpp"
+#include "number.h"
+#include "array.h"
+#include "coefficient.h"
+#include "flow.h"
+#include "rcc_mpfr.h"
+
+
+
+// compute flow numerically
+int numerical_flow_mpfr(Grouped_Polynomial flow_equation, RCC_mpfr init, Labels labels, int niter, int display_mode){
+  // running coupling contants
+  RCC_mpfr rccs=init;
+  int i,j;
+
+  if(display_mode==DISPLAY_NUMERICAL){
+    // print labels
+    printf("%5s  ","n");
+    for(j=0;j<rccs.length;j++){
+      print_label(rccs.indices[j], labels);
+    }
+    printf("\n\n");
+
+    // print initial values
+    printf("%5d  ",0);
+    for(j=0;j<rccs.length;j++){
+      mpfr_printf("% 14.7Re  ",rccs.values[j]);
+    }
+    printf("\n");
+  }
+
+  for(i=0;i<niter;i++){
+    // compute a single step
+    step_flow_mpfr(&rccs, flow_equation);
+    // convert ls to alphas
+    if(display_mode==DISPLAY_NUMERICAL){
+      // print the result
+      printf("%5d  ",i+1);
+      for(j=0;j<rccs.length;j++){
+	mpfr_printf("% 14.7Re  ",rccs.values[j]);
+      }
+      printf("\n");
+    }
+  }
+
+  if(display_mode==DISPLAY_NUMERICAL){
+    // print labels
+    printf("\n");
+    printf("%5s  ","n");
+    for(j=0;j<rccs.length;j++){
+      print_label(rccs.indices[j], labels);
+    }
+    printf("\n\n");
+  }
+
+  if(display_mode==DISPLAY_FINAL){
+    RCC_mpfr_print(rccs);
+  }
+
+  return(0);
+}
+
+// single step in the flow
+int step_flow_mpfr(RCC_mpfr* rccs, Grouped_Polynomial flow_equation){
+  int i;
+  mpfr_t* res;
+
+  // security: this function assumes that the length of the rcc and the flow_equation are the same
+  if((*rccs).length!=flow_equation.length){
+    fprintf(stderr,"error: mismatch in the size of the flow equation and the rccs");
+    exit(-1);
+  }
+  
+  res=calloc((*rccs).length,sizeof(mpfr_t));
+
+  // compute the constants first
+  for(i=0;i<flow_equation.length;i++){
+    if(flow_equation.indices[i]<0){
+      evalcoef_mpfr(*rccs, flow_equation.coefs[i], res[i]);
+      mpfr_set((*rccs).values[i], res[i], MPFR_RNDN);
+    }
+  }
+
+  // for each equation
+  for(i=0;i<flow_equation.length;i++){
+    if(flow_equation.indices[i]>=0){
+      evalcoef_mpfr(*rccs, flow_equation.coefs[i], res[i]);
+    }
+  }
+
+  // set new rccs
+  for(i=0;i<flow_equation.length;i++){
+    mpfr_set((*rccs).values[i], res[i], MPFR_RNDN);
+    mpfr_clear(res[i]);
+  }
+
+  // free memory
+  free(res);
+  return(0);
+}

src/flow_mpfr.h

@@ -0,0 +1,32 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+Compute flow numerically
+*/
+
+#ifndef NUMERICAL_FLOW_MPFR_H
+#define NUMERICAL_FLOW_MPFR_H
+
+
+#include "types.h"
+
+// compute flow
+int numerical_flow_mpfr(Grouped_Polynomial flow_equation, RCC_mpfr init, Labels labels, int niter, int display_mode);
+// single step
+int step_flow_mpfr(RCC_mpfr* rccs, Grouped_Polynomial flow_equation);
+
+#endif

src/grouped_polynomial.c

@@ -732,7 +732,7 @@ int char_array_to_Grouped_Polynomial(Char_Array str, Grouped_Polynomial* output)
 }
 
 
-// evaluate an equation on a vector
+// eValuate an equation on a vector
 int evaleq(RCC* rccs, Grouped_Polynomial poly){
   int i;
   long double* res=calloc((*rccs).length,sizeof(long double));
@@ -762,4 +762,32 @@ int evaleq(RCC* rccs, Grouped_Polynomial poly){
   return(0);
 
 }
+// evaluate an equation on a vector (using mpfr floats)
+int evaleq_mpfr(RCC_mpfr* rccs, Grouped_Polynomial poly){
+  int i;
+  mpfr_t* res;
+
+  if((*rccs).length!=poly.length){
+    fprintf(stderr, "error: trying to evaluate an flow equation with %d components on an rcc with %d\n",poly.length,(*rccs).length);
+    exit(-1);
+  }
+
+  res=calloc((*rccs).length,sizeof(mpfr_t));
+
+  // for each equation
+  for(i=0;i<poly.length;i++){
+    evalcoef_mpfr(*rccs, poly.coefs[i], res[i]);
+  }
+
+  // copy res to rccs
+  for(i=0;i<(*rccs).length;i++){
+    mpfr_set((*rccs).values[i], res[i], MPFR_RNDN);
+    mpfr_clear(res[i]);
+  }
+
+  // free memory
+  free(res);
+  return(0);
+}
+
 

src/grouped_polynomial.h

@@ -70,5 +70,7 @@ int char_array_to_Grouped_Polynomial(Char_Array str, Grouped_Polynomial* output)
 
 // evaluate an equation on an RCC
 int evaleq(RCC* rccs, Grouped_Polynomial poly);
+// evaluate an equation on a vector (using mpfr floats)
+int evaleq_mpfr(RCC_mpfr* rccs, Grouped_Polynomial poly);
 
 #endif

src/kondo.c

@@ -29,16 +29,17 @@ limitations under the License.
 #include "definitions.cpp"
 #include "rational.h"
 
-// dimension of A, B and h (must be <10)
+// dimension of A, B, h and t (must be <10)
 #define KONDO_DIM 3
 // number of spin components
 #define KONDO_SPIN 2
 
-// offsets for indices of A, B and h
+// offsets for indices of A, B, h and t
 // order matters for symbols table
 #define KONDO_A_OFFSET 1
 #define KONDO_B_OFFSET 2
 #define KONDO_H_OFFSET 3
+#define KONDO_T_OFFSET 4
 
 // parsing modes (from parse_file.c)
 #define PP_NULL_MODE 0
@@ -193,13 +194,19 @@ int kondo_fields_table(int box_count, Char_Array* str_fields, Fields_Table* fiel
 
   //  parameters
   char_array_append_str("h:",str_fields);
+  // h
   for(i=0;i<KONDO_DIM;i++){
-    char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_H_OFFSET));
+    char_array_snprintf(str_fields, "%d,", 10*(i+10*KONDO_H_OFFSET));
+  }
+  // t
+  for(i=0;i<KONDO_DIM;i++){
+    char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_T_OFFSET));
     if(i<KONDO_DIM-1){
-      char_array_append(',',str_fields);
+      char_array_append(',', str_fields);
     }
   }
-  char_array_append('\n',str_fields);
+  char_array_append('\n', str_fields);
+
 
   // declare Fermions
   char_array_append_str("f:",str_fields);
@@ -226,6 +233,16 @@ int kondo_fields_table(int box_count, Char_Array* str_fields, Fields_Table* fiel
   }
   char_array_append('\n',str_fields);
 
+  // declare noncommuting
+  char_array_append_str("a:",str_fields);
+  for(i=0;i<KONDO_DIM;i++){
+    char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_T_OFFSET));
+    if(i<KONDO_DIM-1){
+      char_array_append(',',str_fields);
+    }
+  }
+  char_array_append('\n', str_fields);
+
   // parse fields table
   parse_input_fields(*str_fields, fields);
 
@@ -245,7 +262,7 @@ int kondo_symbols(Char_Array* str_symbols, int box_count, Fields_Table* fields){
 
   // loop over box index
   for(i=1;i<=box_count;i++){
-    // loop over letters
+    // loop over letters (A and B)
     for(j=0;j<2;j++){
       // loop over space dimension
       for(k=0;k<KONDO_DIM;k++){
@@ -255,7 +272,7 @@ int kondo_symbols(Char_Array* str_symbols, int box_count, Fields_Table* fields){
 	init_Char_Array(&tmp_str, 6);
 	char_array_snprintf(&tmp_str, "%c%d%d", letters[j], k, i);
 	// compute corresponding polynomial
-	kondo_resolve_ABh(tmp_str.str, &poly, *fields);
+	kondo_resolve_ABht(tmp_str.str, &poly, *fields);
 	free_Char_Array(tmp_str);
 	// write to output
 	polynomial_sprint(poly, str_symbols);
@@ -320,45 +337,6 @@ int kondo_symbols(Char_Array* str_symbols, int box_count, Fields_Table* fields){
   return(0);
 }
 
-// generate Kondo symbols (older method: one symbol for each scalar product)
-int kondo_symbols_scalarprod(Char_Array* str_symbols, int box_count, Fields_Table* fields){
-  int i,j,k;
-  Char_Array tmp_str;
-  Polynomial poly;
-  char letters[3]={'A','B','h'};
-
-  init_Char_Array(str_symbols, STR_SIZE);
-  char_array_snprintf(str_symbols, "#!symbols\n");
-
-  // loop over box index
-  for(i=1;i<=box_count;i++){
-    // loop over letters
-    for(j=0;j<3;j++){
-      for(k=0;k<3;k++){
-	// write index
-	char_array_snprintf(str_symbols, "%d=", 100*(10*(KONDO_A_OFFSET+j)+KONDO_A_OFFSET+k)+i);
-	// write the name of the scalar product
-	init_Char_Array(&tmp_str, 6);
-	char_array_snprintf(&tmp_str, "%c%d.%c%d", letters[j], i, letters[k], i);
-	// compute corresponding polynomial
-	kondo_resolve_scalar_prod(tmp_str.str, &poly, *fields);
-	free_Char_Array(tmp_str);
-	// write to output
-	polynomial_sprint(poly, str_symbols);
-	free_Polynomial(poly);
-	// add ,
-	if(i<box_count || j<2 || k<2){
-	  char_array_snprintf(str_symbols,",\n");
-	}
-      }
-    }
-  }
-
-  parse_input_symbols(*str_symbols, fields);
-
-  return(0);
-}
-
 
 // generate Kondo groups (groups of independent variables)
 int kondo_groups(Char_Array* str_groups, int box_count){
@@ -395,12 +373,21 @@ int kondo_groups(Char_Array* str_groups, int box_count){
 
 // generate Kondo identities
 // h_3^2=1-h_1^2-h_2^2
+// and Pauli matrices
 int kondo_identities(Char_Array* str_identities){
   int i;
 
   init_Char_Array(str_identities,STR_SIZE);
   char_array_snprintf(str_identities, "#!identities\n");
 
+  // Pauli matrices
+  for(i=0;i<KONDO_DIM;i++){
+    char_array_snprintf(str_identities,"[f%d][f%d]=(1),\n",10*(10*KONDO_T_OFFSET+i),10*(10*KONDO_T_OFFSET+i));
+    char_array_snprintf(str_identities,"[f%d][f%d]=(s{-1})[f%d],\n",10*(10*KONDO_T_OFFSET+i),10*(10*KONDO_T_OFFSET+(i+1)%3),10*(10*KONDO_T_OFFSET+(i+2)%3));
+    char_array_snprintf(str_identities,"[f%d][f%d]=((-1)s{-1})[f%d],\n",10*(10*KONDO_T_OFFSET+(i+2)%3),10*(10*KONDO_T_OFFSET+(i+1)%3),10*(10*KONDO_T_OFFSET+i));
+  }
+
+  // h
   char_array_snprintf(str_identities, "[f%d][f%d]=(1)",10*(KONDO_DIM-1+10*KONDO_H_OFFSET),10*(KONDO_DIM-1+10*KONDO_H_OFFSET));
   for(i=0;i<KONDO_DIM-1;i++){
     char_array_snprintf(str_identities, "+(-1)[f%d][f%d]",10*(i+10*KONDO_H_OFFSET),10*(i+10*KONDO_H_OFFSET));
@@ -809,11 +796,10 @@ int parse_kondo_polynomial_str(char* str_polynomial, Polynomial* output, Fields_
 	  if(tmp_poly.length>0){
 	    for(i=0;i<tmp_poly.length;i++){
 	      if(mode==PP_FIELD_SCALAR_MODE){
-		if(offset1!=KONDO_H_OFFSET || offset2!=KONDO_H_OFFSET){
+		int_array_append(1000*(10*offset1+offset2)+index, tmp_poly.monomials+i);
-		  int_array_append(1000*(10*offset1+offset2)+index, tmp_poly.monomials+i);
-		}
 	      }
 	      else{
+		// vector product
 		int_array_append(100*(100*KONDO_A_OFFSET+10*KONDO_B_OFFSET+KONDO_H_OFFSET)+index, tmp_poly.monomials+i);
 	      }
 	    }
@@ -822,28 +808,15 @@ int parse_kondo_polynomial_str(char* str_polynomial, Polynomial* output, Fields_
 	  else{
 	    init_Int_Array(&tmp_monomial, MONOMIAL_SIZE);
 	    if(mode==PP_FIELD_SCALAR_MODE){
-	      if(offset1!=KONDO_H_OFFSET || offset2!=KONDO_H_OFFSET){
+	      int_array_append(1000*(10*offset1+offset2)+index, &tmp_monomial);
-		int_array_append(1000*(10*offset1+offset2)+index, &tmp_monomial);
-	      }
 	    }
 	    else{
+	      // vector product
 	      int_array_append(100*(100*KONDO_A_OFFSET+10*KONDO_B_OFFSET+KONDO_H_OFFSET)+index, &tmp_monomial);
 	    }
 	    init_Int_Array(&dummy_factor, 1);
 	    polynomial_append_noinit(tmp_monomial, dummy_factor, number_one(), &tmp_poly);
 	  }
-	  /* // older method in which a scalar product was expanded in A, B and h
-	  // resolve scalar product
-	  kondo_resolve_scalar_prod_symbols(buffer, &scalar_prod_poly);
-	  // add to tmp_poly
-	  if(tmp_poly.length==0){
-	    polynomial_concat(scalar_prod_poly,&tmp_poly);
-	  }
-	  else{
-	    polynomial_prod_chain(scalar_prod_poly,&tmp_poly,fields);
-	  }
-	  free_Polynomial(scalar_prod_poly);
-	  */
 	}
 	// switch back to null mode
 	mode=PP_NULL_MODE;
@@ -941,10 +914,10 @@ int parse_kondo_polynomial(Char_Array kondo_polynomial_str, Polynomial* polynomi
 }
 
 
-// read Aij, Bij, hi where i is a space dimension and j is a box index
+// read Aij, Bij, hi, ti where i is a space dimension and j is a box index
-int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
+int kondo_resolve_ABht(char* str, Polynomial* output, Fields_Table fields){
   char* ptr;
-  // offset (A,B or H)
+  // offset (A,B, H or T)
   int offset=-1;
   // dimension
   int dim=-1;
@@ -978,6 +951,9 @@ int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
     case 'h':
       offset=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset=KONDO_T_OFFSET;
+      break;
     default:
       // set index if dim was already set
       if(dim>=0){
@@ -1001,8 +977,8 @@ int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
     }
   }
 
-  // h's
+  // h's and t's
-  if(offset==KONDO_H_OFFSET){
+  if(offset==KONDO_H_OFFSET || offset==KONDO_T_OFFSET){
     // external field
     init_Int_Array(&monomial,1);
     init_Int_Array(&factor,1);
@@ -1039,6 +1015,8 @@ int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
 	polynomial_conjugate(poly_conjugate);
 	polynomial_multiply_scalar(poly_conjugate, pauli_mat.matrix[a][b]);
 	polynomial_prod_chain(psi[a],&poly_conjugate,fields);
+	// correct sign: psi[a]^+ should be on the left of psi[b]^-
+	polynomial_multiply_Qscalar(poly_conjugate,quot(-1,1));
 	// add to poly
 	polynomial_concat_noinit(poly_conjugate, output);
       }
@@ -1060,7 +1038,7 @@ int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
 // read a Kondo scalar product (generalized to vector products as well)
 int kondo_resolve_scalar_prod(char* str, Polynomial* output, Fields_Table fields){
   char* ptr;
-  // offset of each term (A,B or H)
+  // offset of each term (A,B,H or T)
   int offset=-1;
   // index of each term (0,...,box_count)
   int index=0;
@@ -1089,6 +1067,9 @@ int kondo_resolve_scalar_prod(char* str, Polynomial* output, Fields_Table fields
     case 'h':
       offset=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset=KONDO_T_OFFSET;
+      break;
 
     // scalar product
     case '.':
@@ -1193,8 +1174,8 @@ int kondo_polynomial_vector(int offset, int index, Polynomial (*polys)[3], Field
     init_Polynomial((*polys)+i,POLY_SIZE);
   }
 
-  // h's
+  // h's and t's
-  if(offset==KONDO_H_OFFSET){
+  if(offset==KONDO_H_OFFSET || offset==KONDO_T_OFFSET){
     // construct every component field
     for(i=0;i<KONDO_DIM;i++){
       // external field
@@ -1235,6 +1216,8 @@ int kondo_polynomial_vector(int offset, int index, Polynomial (*polys)[3], Field
 	  polynomial_conjugate(poly_conjugate);
 	  polynomial_multiply_scalar(poly_conjugate, pauli_mat.matrix[a][b]);
 	  polynomial_prod_chain(psi[a],&poly_conjugate,fields);
+	  // correct sign: psi[a]^+ should be on the left of psi[b]^-
+	  polynomial_multiply_Qscalar(poly_conjugate,quot(-1,1));
 	  // add to polys[j]
 	  polynomial_concat_noinit(poly_conjugate, (*polys)+i);
 	}
@@ -1257,7 +1240,7 @@ int kondo_resolve_scalar_prod_symbols(char* str, Polynomial* output){
   char* ptr;
   // first or second term
   int term=0;
-  // offset of each term (A,B or H)
+  // offset of each term (A,B,H or T)
   int offset[2];
   // index of each term (0,...,box_count)
   int index[2]={0,0};
@@ -1285,6 +1268,9 @@ int kondo_resolve_scalar_prod_symbols(char* str, Polynomial* output){
     case 'h':
       offset[term]=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset[term]=KONDO_T_OFFSET;
+      break;
     // switch term
     case '.':
       term=1-term;
@@ -1300,13 +1286,13 @@ int kondo_resolve_scalar_prod_symbols(char* str, Polynomial* output){
     init_Int_Array(&monomial,2);
     init_Int_Array(&factor, 1);
 
-    if(offset[0]==KONDO_H_OFFSET){
+    if(offset[0]==KONDO_H_OFFSET || offset[0]==KONDO_T_OFFSET){
       int_array_append(10*(10*offset[0]+i)+index[0], &monomial);
     }
     else{
       int_array_append(100*(10*offset[0]+i)+index[0], &monomial);
     }
-    if(offset[1]==KONDO_H_OFFSET){
+    if(offset[1]==KONDO_H_OFFSET || offset[1]==KONDO_T_OFFSET){
       int_array_append(10*(10*offset[1]+i)+index[1], &monomial);
     }
     else{
@@ -1340,6 +1326,9 @@ int get_offset_index(char* str, int* offset, int* index){
     case 'h':
       *offset=KONDO_H_OFFSET;
       break;
+    case 't':
+      *offset=KONDO_T_OFFSET;
+      break;
     default:
       // char to int
       *index=*ptr-'0';
@@ -1374,6 +1363,9 @@ int get_offsets_index(char* str, int* offset1, int* offset2, int* index){
     case 'h':
       offset[term]=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset[term]=KONDO_T_OFFSET;
+      break;
     // switch term
     case '.':
       term=1-term;
@@ -1387,6 +1379,11 @@ int get_offsets_index(char* str, int* offset1, int* offset2, int* index){
   *offset1=offset[0];
   *offset2=offset[1];
 
+  // if no A's or B's, then index=0
+  if((offset[0]==KONDO_H_OFFSET || offset[0]==KONDO_T_OFFSET) && (offset[1]==KONDO_H_OFFSET || offset[1]==KONDO_T_OFFSET)){
+    *index=0;
+  }
+
   return(0);
 }
 
@@ -1425,6 +1422,9 @@ int get_symbol_index(char* str){
     case 'h':
       offset=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset=KONDO_T_OFFSET;
+      break;
     default:
       // set index if dim was already set
       if(dim>=0){
@@ -1439,8 +1439,8 @@ int get_symbol_index(char* str){
   if(offset==-1){
     return(-1);
   }
-  // no symbol for h
+  // no symbol for h or t
-  if(offset==KONDO_H_OFFSET){
+  if(offset==KONDO_H_OFFSET || offset==KONDO_T_OFFSET){
     return(10*(10*offset+dim));
   }
   else{

src/kondo.h

@@ -55,7 +55,7 @@ int parse_kondo_polynomial_str(char* str_polynomial, Polynomial* output, Fields_
 int parse_kondo_polynomial(Char_Array kondo_polynomial_str, Polynomial* polynomial, Fields_Table fields);
 
 // read Aij, Bij, hi where i is a space dimension and j is a box index
-int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields);
+int kondo_resolve_ABht(char* str, Polynomial* output, Fields_Table fields);
 // read a Kondo scalar product
 int kondo_resolve_scalar_prod(char* str, Polynomial* output, Fields_Table fields);
 // compute a scalar product of polynomial vectors

src/mean.c

@@ -42,7 +42,7 @@ int mean(Int_Array monomial, Polynomial* out, Fields_Table fields, Polynomial_Ma
   *out=polynomial_one();
 
   // sort first
-  monomial_sort(monomial, 0, monomial.length-1, fields, &sign);
+  monomial_sort(monomial, fields, &sign);
   polynomial_multiply_Qscalar(*out, quot(sign,1));
   // get internals
   // (*out).monomials is the first element of out but it only has 1 element
@@ -417,7 +417,7 @@ int mean_symbols(Int_Array monomial, Polynomial* output, Fields_Table fields, Po
     if(check_monomial_match(tmp_monomial, fields)==1){
       // sort monomial
       sign=1;
-      monomial_sort(tmp_monomial, 0, tmp_monomial.length-1, fields, &sign);
+      monomial_sort(tmp_monomial, fields, &sign);
       number_Qprod_chain(quot(sign,1), &tmp_num);
 
       // mean
@@ -628,7 +628,7 @@ int mean_groups(Int_Array monomial, Polynomial* output, Fields_Table fields, Pol
   init_Polynomial(output, MONOMIAL_SIZE);
 
   // check whether there are symbols
-  // requires the symbols to be at the end of the monomial
+  // IMPORTANT: the symbols must be at the end of the monomial
   if(monomial.length==0 || field_type(monomial.values[monomial.length-1], fields)!=FIELD_SYMBOL){
     // mean
     mean(monomial, &num_mean, fields, propagator);
@@ -639,7 +639,7 @@ int mean_groups(Int_Array monomial, Polynomial* output, Fields_Table fields, Pol
     // sort into groups
     if(groups.length>0){
       sign=1;
-      monomial_sort_groups(monomial, 0, monomial.length-1, fields, groups, &sign);
+      monomial_sort_groups(monomial, fields, groups, &sign);
     }
     // construct groups and take mean
     init_Int_Array(&tmp_monomial, MONOMIAL_SIZE);

src/meantools.c

@@ -108,7 +108,7 @@ int read_args_meantools(int argc,const char* argv[], Str_Array* str_args, Meanto
 
 // print usage message
 int print_usage_meantools(){
-  printf("\nusage:\n   meantools exp <filename>\n   meantools derive [-d derivatives] -V <variables> <filename>\n   meantools eval -R <rccs> <filename>\n\n");
+  printf("\nusage:\n   meantools exp [config_file]\n   meantools derive [-d derivatives] [-V variables] [-C] [config_file]\n   meantools eval [-R values] [-P precision] [-E max_exponent] [config_file]\n\n");
   return(0);
 }
 

src/meantools_deriv.c

@@ -46,6 +46,8 @@ int tool_deriv_read_args(int argc, const char* argv[], Str_Array* str_args, Mean
   (*opts).deriv_derivs=1;
   // derive with respect to all variables
   (*opts).deriv_vars.length=-1;
+  // do not chain
+  (*opts).chain=0;
 
 
   // loop over arguments
@@ -61,6 +63,10 @@ int tool_deriv_read_args(int argc, const char* argv[], Str_Array* str_args, Mean
 	case 'V':
 	  flag=CP_FLAG_VARS;
 	  break;
+	// chain
+	case 'C':
+	  (*opts).chain=1;
+	  break;
 	}
       }
     }
@@ -104,6 +110,8 @@ int tool_deriv(Str_Array str_args, Meantools_Options opts){
   // flow equation for the derivatives
   Grouped_Polynomial flow_equation_deriv;
   int i;
+  // header of the entry
+  Char_Array arg_header;
 
 
   // parse flow equation
@@ -142,6 +150,29 @@ int tool_deriv(Str_Array str_args, Meantools_Options opts){
   // compute derivatives
   flow_equation_derivative(opts.deriv_derivs, opts.deriv_vars, flow_equation, &flow_equation_deriv);
 
+  // print
+  // if chain then print config file
+  if(opts.chain==1){
+    for(i=0;i<str_args.length;i++){
+      // check whether to print the str_arg
+      get_str_arg_title(str_args.strs[i], &arg_header);
+      if (\
+	str_cmp(arg_header.str, "flow_equation")==0 &&\
+	str_cmp(arg_header.str, "symbols")==0 &&\
+	str_cmp(arg_header.str, "groups")==0 &&\
+	str_cmp(arg_header.str, "fields")==0 &&\
+	str_cmp(arg_header.str, "identities")==0 &&\
+	str_cmp(arg_header.str, "propagator")==0 &&\
+	str_cmp(arg_header.str, "input_polynomial")==0 &&\
+	str_cmp(arg_header.str, "id_table")==0 ){
+
+	  printf("%s\n&\n",str_args.strs[i].str);
+      }
+      free_Char_Array(arg_header);
+    }
+    // print flow equation
+    printf("#!flow_equation\n");
+  }
   grouped_polynomial_print(flow_equation_deriv,'%','%');
 
   // free memory
@@ -164,12 +195,17 @@ int flow_equation_derivative(int n, Int_Array variables, Grouped_Polynomial flow
   // output polynomial
   grouped_polynomial_cpy(flow_equation, flow_equation_derivs);
 
-  for(j=0,dflow=flow_equation;j<n;j++){
+  // init dflow to flow_equation
+  grouped_polynomial_cpy(flow_equation, &dflow);
+
+  for(j=0;j<n;j++){
     // tmp flow contains the result of the previous derivative
     grouped_polynomial_cpy(dflow, &tmpflow);
-    // derive
+    // free dflow
+    free_Grouped_Polynomial(dflow);
+    // next derivative
     flow_equation_derivx(tmpflow, indices, &dflow);
-    // free
+    // free tmpflow
     free_Grouped_Polynomial(tmpflow);
 
     // add the derived indices as variables for the next derivative

src/meantools_eval.c

@@ -18,16 +18,22 @@ limitations under the License.
 
 #include <stdio.h>
 #include <stdlib.h>
+#include <mpfr.h>
 #include "parse_file.h"
 #include "cli_parser.h"
 #include "grouped_polynomial.h"
 #include "array.h"
 #include "rcc.h"
+#include "rcc_mpfr.h"
 
 
 #define CP_FLAG_RCCS 1
+#define CP_FLAG_MPFR_PREC 2
+#define CP_FLAG_MPFR_EXP 3
 // read command line arguments
 int tool_eval_read_args(int argc, const char* argv[], Str_Array* str_args, Meantools_Options* opts){
+  // temporary long int
+  long int tmp_lint;
   // file to read the polynomial from in flow mode
   const char* file="";
   // whether a file was specified on the command-line
@@ -40,6 +46,9 @@ int tool_eval_read_args(int argc, const char* argv[], Str_Array* str_args, Meant
   // defaults
   // mark rccstring so that it can be recognized whether it has been set or not
   (*opts).eval_rccstring.length=-1;
+  // no mpfr
+  (*opts).mpfr_prec=0;
+  (*opts).mpfr_emax=0;
 
   // loop over arguments
   for(i=2;i<argc;i++){
@@ -51,6 +60,14 @@ int tool_eval_read_args(int argc, const char* argv[], Str_Array* str_args, Meant
 	case 'R':
 	  flag=CP_FLAG_RCCS;
 	  break;
+	// mpfr precision
+	case 'P':
+	  flag=CP_FLAG_MPFR_PREC;
+	  break;
+	// mpfr emax
+	case 'E':
+	  flag=CP_FLAG_MPFR_EXP;
+	  break;
 	}
       }
     }
@@ -59,6 +76,18 @@ int tool_eval_read_args(int argc, const char* argv[], Str_Array* str_args, Meant
       str_to_char_array((char*)argv[i], &((*opts).eval_rccstring));
       flag=0;
     }
+    // mpfr precision
+    else if(flag==CP_FLAG_MPFR_PREC){
+      sscanf(argv[i],"%ld",&tmp_lint);
+      (*opts).mpfr_prec=(mpfr_prec_t)tmp_lint;
+      flag=0;
+    }
+    // mpfr emax
+    else if(flag==CP_FLAG_MPFR_EXP){
+      sscanf(argv[i],"%ld",&tmp_lint);
+      (*opts).mpfr_emax=(mpfr_exp_t)tmp_lint;
+      flag=0;
+    }
     // read file name from command-line
     else{
       file=argv[i];
@@ -78,9 +107,21 @@ int tool_eval(Str_Array str_args, Meantools_Options opts){
   int arg_index;
   // rccs
   RCC rccs;
+  RCC_mpfr rccs_mpfr;
   // flow equation
   Grouped_Polynomial flow_equation;
+  // whether or not to use mpfr floats
+  int mpfr_flag=0;
 
+  // set mpfr defaults
+  if(opts.mpfr_prec!=0){
+    mpfr_set_default_prec(opts.mpfr_prec);
+    mpfr_flag=1;
+  }
+  if(opts.mpfr_emax!=0){
+    mpfr_set_emax(opts.mpfr_emax);
+    mpfr_flag=1;
+  }
 
   // parse flow equation
   // if there is a unique argument, assume it is the flow equation
@@ -108,22 +149,33 @@ int tool_eval(Str_Array str_args, Meantools_Options opts){
   }
 
   // initialize the rccs
-  prepare_init(flow_equation.indices,flow_equation.length,&rccs);
+  if(mpfr_flag==0){
+    prepare_init(flow_equation.indices,flow_equation.length,&rccs);
+  }
+  else{
+    prepare_init_mpfr(flow_equation.indices,flow_equation.length,&rccs_mpfr);
+  }
   // read rccs from string
   if(opts.eval_rccstring.length!=-1){
-    parse_init_cd(opts.eval_rccstring, &rccs);
+    parse_init_cd(opts.eval_rccstring, &rccs, &rccs_mpfr, mpfr_flag);
     free_Char_Array(opts.eval_rccstring);
   }
 
   // evaluate
-  evaleq(&rccs, flow_equation);
+  if(mpfr_flag==0){
+    evaleq(&rccs, flow_equation);
+    RCC_print(rccs);
+    free_RCC(rccs);
+  }
+  else{
+    evaleq_mpfr(&rccs_mpfr, flow_equation);
+    RCC_mpfr_print(rccs_mpfr);
+    free_RCC_mpfr(rccs_mpfr);
+  }
 
-  // print
-  RCC_print(rccs);
 
   // free memory
   free_Grouped_Polynomial(flow_equation);
-  free_RCC(rccs);
   return(0);
 }
 

src/number.c

@@ -18,6 +18,10 @@ limitations under the License.
 #include <stdlib.h>
 #include <stdio.h>
 #include <math.h>
+#include <stdarg.h>
+// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
+#define MPFR_USE_VA_LIST
+#include <mpfr.h>
 #include "istring.h"
 #include "definitions.cpp"
 #include "tools.h"
@@ -358,6 +362,30 @@ long double number_double_val(Number x){
   }
   return(ret);
 }
+// approximate numerical expression (as mpfr float)
+int number_mpfr_val(mpfr_t out, Number x){
+  int i;
+  // auxiliary variables (do not initialize A)
+  mpfr_t A,b,c;
+  mpfr_inits(b,c, (mpfr_ptr)NULL);
+
+  mpfr_init(out);
+  mpfr_set_zero(out,1);
+
+  for(i=0;i<x.length;i++){
+    if(x.scalars[i].numerator!=0){
+      mpfr_sqrt_ui(b, x.base[i], MPFR_RNDN);
+      Q_mpfr_value(A, x.scalars[i]);
+      mpfr_mul(c, A, b, MPFR_RNDN);
+      mpfr_add(b, out, c, MPFR_RNDN);
+      mpfr_set(out, b, MPFR_RNDN);
+    }
+  }
+
+  mpfr_clears(A,b,c, (mpfr_ptr)NULL);
+
+  return(0);
+}
 
 
 // print to string

src/number.h

@@ -98,6 +98,8 @@ int number_is_zero(Number x);
 
 // approximate numerical expression
 long double number_double_val(Number x);
+// approximate numerical expression (as mpfr float)
+int number_mpfr_val(mpfr_t out, Number x);
 
 // print to string
 int number_sprint(Number number, Char_Array* out);

src/numkondo.c

@@ -30,6 +30,7 @@ Compute the flow of a flow equation numerically
 
 // rccs
 #include "rcc.h"
+#include "rcc_mpfr.h"
 // grouped representation of polynomials
 #include "grouped_polynomial.h"
 // command line parser
@@ -38,6 +39,7 @@ Compute the flow of a flow equation numerically
 #include "parse_file.h"
 // numerical flow
 #include "flow.h"
+#include "flow_mpfr.h"
 // arrays
 #include "array.h"
 
@@ -68,10 +70,13 @@ int main (int argc, const char* argv[]){
 
 // parse command-line arguments
 #define CP_FLAG_NITER 1
-#define CP_FLAG_TOL 2
+#define CP_FLAG_RCCS 2
-#define CP_FLAG_RCCS 3
+#define CP_FLAG_MPFR_PREC 3
+#define CP_FLAG_MPFR_EXP 4
 int read_args_numkondo(int argc,const char* argv[], Str_Array* str_args, Numkondo_Options* opts){
   int i;
+  // temporary long int
+  long int tmp_lint;
   // pointers
   char* ptr;
   // file to read the polynomial from in flow mode
@@ -92,10 +97,11 @@ int read_args_numkondo(int argc,const char* argv[], Str_Array* str_args, Numkond
   (*opts).display_mode=DISPLAY_NUMERICAL;
   // default niter
   (*opts).niter=100;
-  // default to 0 tolerance
-  (*opts).tol=0;
   // mark rccstring so that it can be recognized whether it has been set or not
   (*opts).eval_rccstring.length=-1;
+  // no mpfr
+  (*opts).mpfr_prec=0;
+  (*opts).mpfr_emax=0;
 
 // loop over arguments
 for(i=1;i<argc;i++){
@@ -111,14 +117,18 @@ for(i=1;i<argc;i++){
 	case 'N':
 	  flag=CP_FLAG_NITER;
 	  break;
-	// tolerance
-	case 'D':
-	  flag=CP_FLAG_TOL;
-	  break;
 	// initial condition
 	case 'I':
 	  flag=CP_FLAG_RCCS;
 	  break;
+	// mpfr precision
+	case 'P':
+	  flag=CP_FLAG_MPFR_PREC;
+	  break;
+	// mpfr emax
+	case 'E':
+	  flag=CP_FLAG_MPFR_EXP;
+	  break;
 	// print version
 	case 'v':
 	  printf("numkondo " VERSION "\n");
@@ -134,16 +144,23 @@ for(i=1;i<argc;i++){
       // reset flag
       flag=0;
     }
-    // tolerance
-    else if (flag==CP_FLAG_TOL){
-      sscanf(argv[i],"%Lf",&((*opts).tol));
-      flag=0;
-    }
     // init condition
     else if(flag==CP_FLAG_RCCS){
       str_to_char_array((char*)argv[i], &((*opts).eval_rccstring));
       flag=0;
     }
+    // mpfr precision
+    else if(flag==CP_FLAG_MPFR_PREC){
+      sscanf(argv[i],"%ld",&tmp_lint);
+      (*opts).mpfr_prec=(mpfr_prec_t)tmp_lint;
+      flag=0;
+    }
+    // mpfr emax
+    else if(flag==CP_FLAG_MPFR_EXP){
+      sscanf(argv[i],"%ld",&tmp_lint);
+      (*opts).mpfr_emax=(mpfr_exp_t)tmp_lint;
+      flag=0;
+    }
     // read file name from command-line
     else{
       file=argv[i];
@@ -158,7 +175,7 @@ for(i=1;i<argc;i++){
 
 // print usage message
 int print_usage_numkondo(){
-  printf("\nusage:\n   numkondo [-F] [-N niter] [-D tolerance] [-I initial_condition] <filename>\n\n");
+  printf("\nusage:\n   numkondo [-F] [-N niter] [-I initial_condition] [-P precision] [-E exponent_range] <filename>\n\n");
   return(0);
 }
 
@@ -171,8 +188,22 @@ int numflow(Str_Array str_args, Numkondo_Options opts){
   Labels labels;
   // initial condition
   RCC init_cd;
+  RCC_mpfr init_cd_mpfr;
   // flow equation
   Grouped_Polynomial flow_equation;
+  // whether or not to use mpfr floats
+  int mpfr_flag=0;
+
+  // set mpfr defaults
+  if(opts.mpfr_prec!=0){
+    mpfr_set_default_prec(opts.mpfr_prec);
+    mpfr_flag=1;
+  }
+  if(opts.mpfr_emax!=0){
+    mpfr_set_emax(opts.mpfr_emax);
+    mpfr_flag=1;
+  }
+
 
   // parse id table
   arg_index=find_str_arg("labels", str_args);
@@ -207,20 +238,31 @@ int numflow(Str_Array str_args, Numkondo_Options opts){
     }
   }
   // initialize the rccs
-  prepare_init(flow_equation.indices,flow_equation.length,&init_cd);
+  if(mpfr_flag==0){
+    prepare_init(flow_equation.indices,flow_equation.length,&init_cd);
+  }
+  else{
+    prepare_init_mpfr(flow_equation.indices,flow_equation.length,&init_cd_mpfr);
+  }
+
   // read rccs from string
   if(opts.eval_rccstring.length!=-1){
-    parse_init_cd(opts.eval_rccstring, &init_cd);
+    parse_init_cd(opts.eval_rccstring, &init_cd, &init_cd_mpfr, mpfr_flag);
     free_Char_Array(opts.eval_rccstring);
   }
 
-  numerical_flow(flow_equation, init_cd, labels, opts.niter, opts.tol, opts.display_mode);
+  if(mpfr_flag==0){
+    numerical_flow(flow_equation, init_cd, labels, opts.niter, opts.display_mode);
+    free_RCC(init_cd);
+  }
+  else{
+    numerical_flow_mpfr(flow_equation, init_cd_mpfr, labels, opts.niter, opts.display_mode);
+    free_RCC_mpfr(init_cd_mpfr);
+  }
 
-  free_RCC(init_cd);
 
   // free memory
   free_Labels(labels);
   free_Grouped_Polynomial(flow_equation);
   return(0);
 }
-

src/parse_file.c

@@ -18,12 +18,14 @@ limitations under the License.
 
 #include <stdio.h>
 #include <stdlib.h>
+#include <mpfr.h>
 #include "array.h"
 #include "fields.h"
 #include "rational.h"
 #include "number.h"
 #include "polynomial.h"
 #include "rcc.h"
+#include "rcc_mpfr.h"
 #include "definitions.cpp"
 #include "istring.h"
 #include "tools.h"
@@ -44,16 +46,17 @@ limitations under the License.
 #define PP_EXTERNAL_MODE 8
 #define PP_INTERNAL_MODE 9
 #define PP_FERMIONS_MODE 10
+#define PP_NONCOMMUTING_MODE 11
 // indices
-#define PP_INDEX_MODE 11
+#define PP_INDEX_MODE 12
 // factors or monomials
-#define PP_BRACKET_MODE 12
+#define PP_BRACKET_MODE 13
 // labels
-#define PP_LABEL_MODE 13
+#define PP_LABEL_MODE 14
 // polynomial
-#define PP_POLYNOMIAL_MODE 14
+#define PP_POLYNOMIAL_MODE 15
 // group
-#define PP_GROUP_MODE 15
+#define PP_GROUP_MODE 16
 
 
 // parse fields list
@@ -101,6 +104,11 @@ int parse_input_fields(Char_Array str_fields, Fields_Table* fields){
 	  mode=PP_FERMIONS_MODE;
 	}
 	break;
+      case 'a':
+	if(mode==PP_NULL_MODE){
+	  mode=PP_NONCOMMUTING_MODE;
+	}
+	break;
 
       // reset buffer
       case ':':
@@ -123,6 +131,9 @@ int parse_input_fields(Char_Array str_fields, Fields_Table* fields){
 	else if(mode==PP_FERMIONS_MODE){
 	  int_array_append(i,&((*fields).fermions));
 	}
+	else if(mode==PP_NONCOMMUTING_MODE){
+	  int_array_append(i,&((*fields).noncommuting));
+	}
 	buffer_ptr=buffer;
 	*buffer_ptr='\0';
 	break;
@@ -142,6 +153,9 @@ int parse_input_fields(Char_Array str_fields, Fields_Table* fields){
 	else if(mode==PP_FERMIONS_MODE){
 	  int_array_append(i,&((*fields).fermions));
 	}
+	else if(mode==PP_NONCOMMUTING_MODE){
+	  int_array_append(i,&((*fields).noncommuting));
+	}
 	mode=PP_NULL_MODE;
 	break;
 
@@ -417,7 +431,7 @@ int parse_input_identities(Char_Array str_identities, Fields_Table* fields){
   (*fields).ids.length=0;
   for(i=0;i<tmp;i++){
     sign=1;
-    monomial_sort((*fields).ids.lhs[i], 0, (*fields).ids.lhs[i].length-1, *fields, &sign);
+    monomial_sort((*fields).ids.lhs[i], *fields, &sign);
     polynomial_simplify((*fields).ids.rhs+i, *fields);
     polynomial_multiply_Qscalar((*fields).ids.rhs[i],quot(sign,1));
   }
@@ -704,8 +718,8 @@ int parse_labels(Char_Array str_labels, Labels* labels){
 }
 
 
-// read initial condition for numerical computation
+// read initial condition for numerical computation (using either RCC or RCC_mpfr, as specified by mpfr_flag)
-int parse_init_cd(Char_Array init_cd, RCC* init){
+int parse_init_cd(Char_Array init_cd, RCC* init, RCC_mpfr* init_mpfr, int mpfr_flag){
   char* buffer=calloc(init_cd.length+1,sizeof(char));
   char* buffer_ptr=buffer;
   int index=0;
@@ -726,7 +740,12 @@ int parse_init_cd(Char_Array init_cd, RCC* init){
       // new term
       case ',':
 	// write init
-	sscanf(buffer,"%Lf",(*init).values+intlist_find_err((*init).indices,(*init).length,index));
+	if(mpfr_flag==0){
+	  sscanf(buffer,"%Lf",(*init).values+intlist_find_err((*init).indices,(*init).length,index));
+	}
+	else{
+	  mpfr_strtofr((*init_mpfr).values[intlist_find_err((*init_mpfr).indices,(*init_mpfr).length,index)], buffer, &buffer_ptr, 10, MPFR_RNDN);
+	}
 	// reset buffer
 	buffer_ptr=buffer;
 	*buffer_ptr='\0';
@@ -770,7 +789,12 @@ int parse_init_cd(Char_Array init_cd, RCC* init){
   }
 
   // write init
-  sscanf(buffer,"%Lf",(*init).values+unlist_find((*init).indices,(*init).length,index));
+  if(mpfr_flag==0){
+    sscanf(buffer,"%Lf",(*init).values+intlist_find_err((*init).indices,(*init).length,index));
+  }
+  else{
+    mpfr_strtofr((*init_mpfr).values[intlist_find_err((*init_mpfr).indices,(*init_mpfr).length,index)], buffer, &buffer_ptr, 10, MPFR_RNDN);
+  }
 
   free(buffer);
   return(0);
@@ -794,3 +818,20 @@ int prepare_init(int* indices, int length, RCC* init){
   }
   return(0);
 }
+// set indices and length of init for RCC_mpfr
+int prepare_init_mpfr(int* indices, int length, RCC_mpfr* init){
+  int i;
+  init_RCC_mpfr(init, length);
+  for(i=0;i<length;i++){
+    (*init).indices[i]=indices[i];
+    // set constants to 1
+    if(indices[i]<0 && indices[i]>-DOFFSET){
+      mpfr_set_ui((*init).values[i],1,MPFR_RNDN);
+    }
+    else{
+      mpfr_set_zero((*init).values[i],1);
+    }
+
+  }
+  return(0);
+}

src/parse_file.h

@@ -47,10 +47,12 @@ int parse_input_id_table(Char_Array str_idtable, Id_Table* idtable, Fields_Table
 // parse a list of labels
 int parse_labels(Char_Array str_labels, Labels* labels);
 
-// parse the initial condition
+// read initial condition for numerical computation (using either RCC or RCC_mpfr, as specified by mpfr_flag)
-int parse_init_cd(Char_Array init_cd, RCC* init);
+int parse_init_cd(Char_Array init_cd, RCC* init, RCC_mpfr* init_mpfr, int mpfr_flag);
 
 // set indices and length of init
 int prepare_init(int* indices, int length, RCC* init);
+// set indices and length of init for RCC_mpfr
+int prepare_init_mpfr(int* indices, int length, RCC_mpfr* init);
 
 #endif

src/polynomial.c

@@ -688,7 +688,7 @@ int polynomial_simplify(Polynomial* polynomial, Fields_Table fields){
   // sort monomials and factors
   for(i=0;i<(*polynomial).length;i++){
     sign=1;
-    monomial_sort((*polynomial).monomials[i],0,(*polynomial).monomials[i].length-1,fields,&sign);
+    monomial_sort((*polynomial).monomials[i],fields,&sign);
     number_Qprod_chain(quot(sign,1),(*polynomial).nums+i);
     int_array_sort((*polynomial).factors[i],0,(*polynomial).factors[i].length-1);
   }
@@ -787,7 +787,30 @@ int exchange_polynomial_terms(int i, int j, Polynomial* polynomial){
 }
 
 // sort a monomial (with sign coming from exchanging two Fermions)
-int monomial_sort(Int_Array monomial, int begin, int end, Fields_Table fields, int* sign){
+// if the monomial contains noncommuting elements, put them at the beginning of the monomial
+int monomial_sort(Int_Array monomial, Fields_Table fields, int* sign){
+  int i,j;
+  int tmp;
+  // first index after noncommuting indices
+  int post_nc=0;
+
+  for(i=0;i<monomial.length;i++){
+    if(is_noncommuting(monomial.values[i], fields)){
+      tmp=monomial.values[i];
+      for(j=i;j>post_nc;j--){
+	monomial.values[j]=monomial.values[j-1];
+      }
+      monomial.values[post_nc]=tmp;
+      post_nc++;
+    }
+  }
+
+  monomial_sort_nonc(monomial, post_nc, monomial.length-1, fields, sign);
+
+  return(0);
+}
+// without noncommuting terms
+int monomial_sort_nonc(Int_Array monomial, int begin, int end, Fields_Table fields, int* sign){
   int i;
   int index;
   // the pivot: middle of the monomial
@@ -812,8 +835,8 @@ int monomial_sort(Int_Array monomial, int begin, int end, Fields_Table fields, i
     exchange_monomial_terms(monomial, index, end, fields, sign);
 
     // recurse
-    monomial_sort(monomial, begin, index-1, fields, sign);
+    monomial_sort_nonc(monomial, begin, index-1, fields, sign);
-    monomial_sort(monomial, index+1, end, fields, sign);
+    monomial_sort_nonc(monomial, index+1, end, fields, sign);
   }
   return(0);
 }
@@ -872,7 +895,30 @@ int exchange_monomial_terms(Int_Array monomial, int pos1, int pos2, Fields_Table
 
 
 // sort a monomial by putting each group together
-int monomial_sort_groups(Int_Array monomial, int begin, int end, Fields_Table fields, Groups groups, int* sign){
+// if the monomial contains noncommuting elements, put them at the beginning of the monomial
+int monomial_sort_groups(Int_Array monomial, Fields_Table fields, Groups groups, int* sign){
+  int i,j;
+  int tmp;
+  // first index after noncommuting indices
+  int post_nc=0;
+
+  for(i=0;i<monomial.length;i++){
+    if(is_noncommuting(monomial.values[i], fields)){
+      tmp=monomial.values[i];
+      for(j=post_nc;j<i;j++){
+	monomial.values[j+1]=monomial.values[j];
+      }
+      monomial.values[post_nc]=tmp;
+      post_nc++;
+    }
+  }
+
+  monomial_sort_groups_nonc(monomial, post_nc, monomial.length-1, fields, groups, sign);
+
+  return(0);
+}
+// without noncommuting terms
+int monomial_sort_groups_nonc(Int_Array monomial, int begin, int end, Fields_Table fields, Groups groups, int* sign){
   int i;
   int index;
   // the pivot: middle of the monomial
@@ -897,8 +943,8 @@ int monomial_sort_groups(Int_Array monomial, int begin, int end, Fields_Table fi
     exchange_monomial_terms(monomial, index, end, fields, sign);
 
     // recurse
-    monomial_sort(monomial, begin, index-1, fields, sign);
+    monomial_sort_groups_nonc(monomial, begin, index-1, fields, groups, sign);
-    monomial_sort(monomial, index+1, end, fields, sign);
+    monomial_sort_groups_nonc(monomial, index+1, end, fields, groups, sign);
   }
   return(0);
 }

src/polynomial.h

@@ -99,14 +99,18 @@ int polynomial_sort(Polynomial* polynomial, int begin, int end);
 int exchange_polynomial_terms(int i, int j, Polynomial* polynomial);
 
 // sort a monomial (with sign coming from exchanging two Fermions)
-int monomial_sort(Int_Array monomial, int begin, int end, Fields_Table fields, int* sign);
+int monomial_sort(Int_Array monomial, Fields_Table fields, int* sign);
+// without noncommuting terms
+int monomial_sort_nonc(Int_Array monomial, int begin, int end, Fields_Table fields, int* sign);
 // order fields: parameter, external, internal
 int compare_monomial_terms(Int_Array monomial, int pos1, int pos2, Fields_Table fields);
 // exchange two fields (with sign)
 int exchange_monomial_terms(Int_Array monomial, int pos1, int pos2, Fields_Table fields, int* sign);
 
 // sort a monomial by putting each group together
-int monomial_sort_groups(Int_Array monomial, int begin, int end, Fields_Table fields, Groups groups, int* sign);
+int monomial_sort_groups(Int_Array monomial, Fields_Table fields, Groups groups, int* sign);
+// without noncommuting terms
+int monomial_sort_groups_nonc(Int_Array monomial, int begin, int end, Fields_Table fields, Groups groups, int* sign);
 // order fields: group, then parameter, external, internal
 int compare_monomial_terms_groups(Int_Array monomial, int pos1, int pos2, Fields_Table fields, Groups groups);
 

src/rational_float.c

@@ -19,21 +19,14 @@ limitations under the License.
 #include "rational_float.h"
 #include <stdio.h>
 #include <stdlib.h>
+#include <stdarg.h>
+// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
+#define MPFR_USE_VA_LIST
+#include <mpfr.h>
 #include "istring.h"
 #include "array.h"
 #include "math.h"
 
-Q quot(long double p, long double q){
-  Q ret;
-  if(q==0){
-    fprintf(stderr,"error: %Lf/%Lf is ill defined\n",p,q);
-    exit(-1);
-  }
-  ret.numerator=p;
-  ret.denominator=q;
-  return(ret);
-}
-
 // add
 Q Q_add(Q x1,Q x2){
   Q ret;
@@ -141,6 +134,16 @@ long double lcm(long double x,long double y){
 double Q_double_value(Q q){
   return(1.0*q.numerator/q.denominator);
 }
+// approximate value as mpfr float
+int Q_mpfr_value(mpfr_t out, Q q){
+  mpfr_t x;
+  mpfr_init(out);
+  mpfr_init(x);
+  mpfr_set_ld(x, q.denominator, MPFR_RNDN);
+  mpfr_ld_div(out, q.numerator, x, MPFR_RNDN);
+  mpfr_clear(x);
+  return(0);
+}
 
 
 // print to string

src/rational_float.h

@@ -54,6 +54,8 @@ long double lcm(long double x,long double y);
 
 // approximate value as double
 double Q_double_value(Q q);
+// approximate value as mpfr float
+int Q_mpfr_value(mpfr_t out, Q q);
 
 // print to string
 int Q_sprint(Q num, Char_Array* out);

src/rational_int.c

@@ -19,6 +19,10 @@ limitations under the License.
 #include "rational_int.h"
 #include <stdio.h>
 #include <stdlib.h>
+#include <stdarg.h>
+// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
+#define MPFR_USE_VA_LIST
+#include <mpfr.h>
 #include "istring.h"
 #include "array.h"
 
@@ -135,6 +139,16 @@ long int lcm(long int x,long int y){
 double Q_double_value(Q q){
   return(1.0*q.numerator/q.denominator);
 }
+// approximate value as mpfr float
+int Q_mpfr_value(mpfr_t out, Q q){
+  mpfr_t x;
+  mpfr_init(out);
+  mpfr_init(x);
+  mpfr_set_si(x, q.denominator, MPFR_RNDN);
+  mpfr_si_div(out, q.numerator, x, MPFR_RNDN);
+  mpfr_clear(x);
+  return(0);
+}
 
 
 // print to string

src/rational_int.h

@@ -49,6 +49,8 @@ long int lcm(long int x,long int y);
 
 // approximate value as double
 double Q_double_value(Q q);
+// approximate value as mpfr float
+int Q_mpfr_value(mpfr_t out, Q q);
 
 // print to string
 int Q_sprint(Q num, Char_Array* out);

src/rcc_mpfr.c

@@ -0,0 +1,124 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "rcc_mpfr.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdarg.h>
+// define MPFR_USE_VA_LIST to enable the use of mpfr_inits and mpfr_clears
+#define MPFR_USE_VA_LIST
+// define MPFR_USE_FILE to enable the use of mpfr_printf
+#define MPFR_USE_FILE
+#include <mpfr.h>
+#include <math.h>
+#include "array.h"
+
+// init
+int init_RCC_mpfr(RCC_mpfr* rcc_mpfr, int size){
+  int i;
+  (*rcc_mpfr).values=calloc(size,sizeof(mpfr_t));
+  (*rcc_mpfr).indices=calloc(size,sizeof(int));
+  (*rcc_mpfr).length=size;
+  for(i=0;i<size;i++){
+    mpfr_init((*rcc_mpfr).values[i]);
+  }
+
+  return(0);
+}
+
+int free_RCC_mpfr(RCC_mpfr rcc_mpfr){
+  int i;
+  for(i=0;i<rcc_mpfr.length;i++){
+    mpfr_clear(rcc_mpfr.values[i]);
+  }
+  free(rcc_mpfr.values);
+  free(rcc_mpfr.indices);
+  return(0);
+}
+
+// set a given element of an rcc_mpfr
+int RCC_mpfr_set_elem(mpfr_t value, int index, RCC_mpfr* rcc_mpfr, int pos){
+  mpfr_set((*rcc_mpfr).values[pos], value, MPFR_RNDN);
+  (*rcc_mpfr).indices[pos]=index;
+  return(0);
+}
+
+int RCC_mpfr_cpy(RCC_mpfr input,RCC_mpfr* output){
+  int i;
+
+  init_RCC_mpfr(output,input.length);
+  for(i=0;i<input.length;i++){
+    RCC_mpfr_set_elem(input.values[i], input.indices[i], output, i);
+  }
+  return(0);
+}
+
+// concatenate rcc_mpfr
+int RCC_mpfr_concat(RCC_mpfr rcc_mpfr1, RCC_mpfr rcc_mpfr2, RCC_mpfr* output){
+  int i;
+
+  init_RCC_mpfr(output,rcc_mpfr1.length+rcc_mpfr2.length);
+
+  for(i=0;i<rcc_mpfr1.length;i++){
+    RCC_mpfr_set_elem(rcc_mpfr1.values[i], rcc_mpfr1.indices[i], output, i);
+  }
+
+  for(i=0;i<rcc_mpfr2.length;i++){
+    RCC_mpfr_set_elem(rcc_mpfr2.values[i], rcc_mpfr2.indices[i], output, i+rcc_mpfr1.length);
+  }
+  
+  return(0);
+}
+
+// append an rcc_mpfr at the end of another
+int RCC_mpfr_append(RCC_mpfr input, RCC_mpfr* output){
+  int i;
+  for(i=0;i<input.length;i++){
+    RCC_mpfr_set_elem(input.values[i], input.indices[i], output, i+(*output).length);
+  }
+  (*output).length+=input.length;
+  return(0);
+}
+
+// print an rcc_mpfr vector with maximal precision
+int RCC_mpfr_print(RCC_mpfr rcc_mpfr){
+  int j;
+  // the printf format
+  Char_Array printf_format;
+  // number of digits in output
+  int size;
+
+  // compute size
+  // WARNING: assumes mpfr_default_prec is an int
+  size=mpfr_get_default_prec()*log10(2)-1;
+
+  init_Char_Array(&printf_format,12);
+  char_array_snprintf(&printf_format,"%%d:%%.%dRe",size);
+
+  for(j=0;j<rcc_mpfr.length;j++){
+    mpfr_printf(printf_format.str,rcc_mpfr.indices[j],rcc_mpfr.values[j]);
+    if(j<rcc_mpfr.length-1){
+      printf(",\n");
+    }
+    else{
+      printf("\n");
+    }
+  }
+
+  free_Char_Array(printf_format);
+
+  return(0);
+}

src/rcc_mpfr.h

@@ -0,0 +1,43 @@
+/*
+Copyright 2015 Ian Jauslin
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+/*
+ RCC_mpfr struct
+ 
+ This data type is similar to RCC but the values of the rcc's are specified as mpfr floats
+*/
+
+#ifndef RCC_MPFR_H
+#define RCC_MPFR_H
+
+#include "types.h"
+
+// init
+int init_RCC_mpfr(RCC_mpfr* rcc_mpfr, int size);
+int free_RCC_mpfr(RCC_mpfr rcc_mpfr);
+// set an element of an rcc_mpfr
+int RCC_mpfr_set_elem(mpfr_t value, int index, RCC_mpfr* rcc_mpfr, int pos);
+// copy
+int RCC_mpfr_cpy(RCC_mpfr input,RCC_mpfr* output);
+// concatenate 2 rcc_mpfr_mpfr
+int RCC_mpfr_concat(RCC_mpfr rcc_mpfr_mpfr1, RCC_mpfr rcc_mpfr_mpfr2, RCC_mpfr* output);
+// append an rcc_mpfr to another
+int RCC_mpfr_append(RCC_mpfr input, RCC_mpfr* output);
+
+// print an rcc_mpfr vector with maximal precision
+int RCC_mpfr_print(RCC_mpfr rcc_mpfr_mpfr);
+
+#endif

src/types.h

@@ -21,6 +21,8 @@ limitations under the License.
 #ifndef TYPES_H
 #define TYPES_H
 
+#include <mpfr.h>
+
 
 // rational number
 typedef struct Q{
@@ -114,6 +116,12 @@ typedef struct RCC{
   int* indices;
   int length;
 } RCC;
+// rcc using mpfr floats
+typedef struct RCC_mpfr{
+  mpfr_t* values;
+  int* indices;
+  int length;
+} RCC_mpfr;
 
 // identities between fields
 typedef struct Identities{
@@ -154,6 +162,8 @@ typedef struct Fields_Table{
   Symbols symbols;
   // list of anti-commuting variables (fields or symbols)
   Int_Array fermions;
+  // list of non-commuting variables (fields or symbols)
+  Int_Array noncommuting;
 } Fields_Table;
 
 // index labels
@@ -172,25 +182,6 @@ typedef struct Id_Table{
   int memory;
 } Id_Table;
 
-/*
-// polynomial scalar and vectors
-typedef struct Polynomial_Scalar{
-  Coefficient coef;
-  int* indices;
-  int length;
-} Polynomial_Scalar;
-typedef struct Polynomial_Vector{
-  Coefficient* coefv;
-  int* indices;
-  int length;
-} Polynomial_Vector;
-typedef struct Polynomial_Matrix{
-  Coefficient** coefm;
-  int* indices;
-  int length;
-} Polynomial_Matrix;
-*/
-
 
 // command line options
 typedef struct Meankondo_Options{
@@ -201,8 +192,9 @@ typedef struct Meankondo_Options{
 typedef struct Numkondo_Options{
   int display_mode;
   int niter;
-  long double tol;
   Char_Array eval_rccstring;
+  mpfr_prec_t mpfr_prec;
+  mpfr_exp_t mpfr_emax;
 } Numkondo_Options;
 
 typedef struct Meantools_Options{
@@ -210,6 +202,9 @@ typedef struct Meantools_Options{
   int deriv_derivs;
   Int_Array deriv_vars;
   Char_Array eval_rccstring;
+  int chain;
+  mpfr_prec_t mpfr_prec;
+  mpfr_exp_t mpfr_emax;
 } Meantools_Options;
 
 typedef struct Kondopp_Options{