From 469bdc80712dbf9c12562059dc4594620b59a076 Mon Sep 17 00:00:00 2001 From: Ian Jauslin Date: Wed, 7 Oct 2015 12:51:41 +0000 Subject: Support MPFR floats in numkondo Remove '-D' option (error tolerance) in numkondo --- doc/meankondo-doc.html | 16 ++++++++++++---- 1 file changed, 12 insertions(+), 4 deletions(-) (limited to 'doc/meankondo-doc.html') diff --git a/doc/meankondo-doc.html b/doc/meankondo-doc.html index c4a7e2a..7074b56 100644 --- a/doc/meankondo-doc.html +++ b/doc/meankondo-doc.html @@ -69,10 +69,10 @@ -

meankondo v1.3

+

meankondo v1.4

- This is the official documentation for meankondo, version 1.3. The aim of this document is not to give a technical description of how to use the various programs bundled with meankondo, nor is it to explain where hierarchical models come from and what their meaning is, but rather a conceptual overview of how meankondo 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 meankondo 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 meankondo, version 1.4. The aim of this document is not to give a technical description of how to use the various programs bundled with meankondo, nor is it to explain where hierarchical models come from and what their meaning is, but rather a conceptual overview of how meankondo 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 meankondo source code. For a more theoretical discussion of Fermionic hierarchical models, see [G.Benfatto, G.Gallavotti, I.Jauslin, 2015].

Table of contents

@@ -150,7 +150,7 @@
  • external: which are organized in pairs, and are denoted by \((\Psi_i^+,\Psi_i^-)\) for \(i\in\{1,\cdots,E\}\).
  • super-external: 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 Definition below)). - 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 polynomials over the fields is well defined). Some of the fields (Fermions) anti-commute with each other (two fields \(a\) and \(b\) are said to anti-commute if \(ab\equiv-ba\)), and the rest (Bosons) commute. Which fields are Fermions and which are Bosons is specified in the #!fields entry in the configuration file. (Warning: As of version 1.3, all internal fields must be Fermions.) + 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 polynomials over the fields is well defined). Some of the fields (Fermions) anti-commute with each other (two fields \(a\) and \(b\) are said to anti-commute if \(ab\equiv-ba\)), and the rest (Bosons) commute. Which fields are Fermions and which are Bosons is specified in the #!fields entry in the configuration file. (Warning: As of version 1.4, all internal fields must be Fermions.)

    In the configuration file of the meankondo program, the fields are specified in the #!fields entry. @@ -286,7 +286,15 @@ Numerical evaluations are not exact. The numbers manipulated meankondo 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 \(2^{-1022}\).

    -->

    - Numerical evaluations are not exact. The numbers manipulated meankondo 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 meankondo are either "long doubles" or "MPFR floats", depending on the options passed to numkondo (see man numkondo). +

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