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Instead of using Newton's method to compute numeric square roots, use the Karatsuba square root algorithm, which performs better for numbers of all sizes. In practice, this is 3-5 times faster for inputs with just a few digits and up to around 10 times faster for larger inputs. Also, the new algorithm guarantees that the final digit of the result is correctly rounded, since it computes an integer square root with truncation, containing at least 1 extra decimal digit before rounding. The former algorithm would occasionally round the wrong way because it rounded both the intermediate and final results. In addition, arrange for sqrt_var() to explicitly support negative rscale values (rounding before the decimal point). This allows the argument reduction phase of ln_var() to be optimised for large inputs, since it only needs to compute square roots with a few more digits than the final ln() result, rather than computing all the digits before the decimal point. For very large inputs, this can be many thousands of times faster. In passing, optimise div_var_fast() in a couple of places where it was doing unnecessary work. Patch be me, reviewed by Tom Lane and Tels. Discussion: https://postgr.es/m/CAEZATCV1A7+jD3P30Zu31KjaxeSEyOn3v9d6tYegpxcq3cQu-g@mail.gmail.com
PostgreSQL Database Management System ===================================== This directory contains the source code distribution of the PostgreSQL database management system. PostgreSQL is an advanced object-relational database management system that supports an extended subset of the SQL standard, including transactions, foreign keys, subqueries, triggers, user-defined types and functions. This distribution also contains C language bindings. PostgreSQL has many language interfaces, many of which are listed here: https://www.postgresql.org/download/ See the file INSTALL for instructions on how to build and install PostgreSQL. That file also lists supported operating systems and hardware platforms and contains information regarding any other software packages that are required to build or run the PostgreSQL system. Copyright and license information can be found in the file COPYRIGHT. A comprehensive documentation set is included in this distribution; it can be read as described in the installation instructions. The latest version of this software may be obtained at https://www.postgresql.org/download/. For more information look at our web site located at https://www.postgresql.org/.