The Multithreaded version of FORM

Abstract

We present TFORM, the version of the symbolic manipulation system FORM that can make simultaneous use of several processors in a shared memory architecture. The implementation uses Posix threads, also called pthreads, and is therefore easily portable between various operating systems. Most existing FORM programs will be able to take advantage of the increased processing power, without the need for modifications. In some cases some minor additions may be needed. For a computer with two processors a typical improvement factor in the running time is 1.7 when compared to the traditional version of FORM. In the case of computers with 4 processors a typical improvement factor in the execution time is slightly above 3.

18 pages

References in corpus (14)

• Hadronic Z- and tau-Decays in Order alpha_s^4
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• QCD Decoupling at Four Loops
• Four-Loop Decoupling Relations for the Strong Coupling
• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles
• Strange Quark Mass from Tau Lepton Decays with O(alpha_s^3) Accuracy
• Two-Loop Formfactors in Theories with Mass Gap and Z-Boson Production
• The 16th Moment of the Non--Singlet Structure Functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$ to $O({\alpha }_s^3)$
• Automated Calculation Scheme for alpha^n Contributions of QED to Lepton g-2: Generating Renormalized Amplitudes for Diagrams without Lepton Loops
• Two-Loop Bhabha Scattering in QED
• Extension of the functionality of the symbolic program FORM by external software
• ParFORM: recent development
• Counting Complex Disordered States by Efficient Pattern Matching: Chromatic Polynomials and Potts Partition Functions

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