Polyhedral end games for polynomial homotopies in PHCv2.4.86

This directory was isolated in version 2.3.75 for clarity.
New in release 2.3 is Newton's method with deflation for singularities
and improved endgame routines based on extrapolation methods.

Run "gprbuild end_games.gpr" to make all test programs.
On windows, type "gprbuild end_games.gpr -Xos=windows"
at the PowerShell prompt.
The "gprclean end_games.gpr" removes all files created by gprbuild.

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file name                        : short description
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standard_vlprs_tables            : extrapolation tables with standard numbers
dobldobl_vlprs_tables            : extrapolation tables with double doubles
quaddobl_vlprs_tables            : extrapolation tables with quad doubles
multprec_vlprs_tables            : extrapolation tables with multprec numbers
standard_vlprs_algorithm         : extrapolation in standard arithmetic
dobldobl_vlprs_algorithm         : extrapolation in double double arithmetic
quaddobl_vlprs_algorithm         : extrapolation in quad double arithmetic
multprec_vlprs_algorithm         : extrapolation in multiprecision arithmetic
standard_winding_numbers         : standard extrapolate for winding numbers
dobldobl_winding_numbers         : winding numbers with double doubles
quaddobl_winding_numbers         : winding numbers with quad doubles
multprec_winding_numbers         : multprec extrapolate for winding numbers
ts_vlprs                         : test extrapolation on generated series
directions_of_standard_paths     : routines for polyhedral end game
directions_of_dobldobl_paths     : polyhedral end game with double doubles
directions_of_quaddobl_paths     : polyhedral end game with quad doubles
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driver_for_winding_numbers       : driver for winding number calculations
valipoco                         : validation of computed path directions
postpoco                         : stand-alone routine for polyhedral end game
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double_theta_algorithm           : theta algorithm on real doubles
double_double_theta_algorithm    : theta algorithm on real double doubles
quad_double_theta_algorithm      : theta algorithm on real quad doubles
octo_double_theta_algorithm      : theta algorithm on real octo doubles
test_theta_algorithm             : tests the theta algorithm
ts_theta                         : calls the main test on the theta algorithm
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double_rho_algorithm             : rho algorithm on real doubles
double_complex_rho_algorithm     : rho algorithm on complex doubles
dobldobl_complex_rho_algorithm   : rho algorithm on complex double doubles
test_rho_algorithm               : tests the rho algorithm
ts_rho                           : calls the main test on the rho algorithm
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