A precise measurement of the cross section of the process e+ e- to pi+ pi- (gamma) from threshold to an energy of 3 GeV is obtained with the initial state radiation (ISR) method using 232 fb^-1 of data collected with the BABAR detector at e+ e- center-of-mass energies near 10.6 GeV. The ISR luminosity is determined from a study of the leptonic process e+ e- to mu+ mu- gamma (gamma). The leading-order hadronic contribution to the muon magnetic anomaly calculated using the pi pi cross section measured from threshold to 1.8 GeV is (514.1 +-2.2(stat} +-3.1(syst}) x 10^{-10}.
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