• Dean Rasheed's avatar
    Improve the performance and accuracy of numeric sqrt() and ln(). · 4083f445
    Dean Rasheed authored
    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
    4083f445
numeric.c 247 KB