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    Re: Sun semidiameter
    From: Paul Hirose
    Date: 2007 Apr 15, 19:48 -0700

    Alexandre E Eremenko wrote:
    > The reason of these errors is probably the rounding
    > subroutine. To get the last digit really true,
    > yoiu have to do all computations with one more digit,
    > and then apply an exact rounding algorithm, while
    > in most cases they just cut off the last digit
    > instead. Because nobody really cares about the exactness
    > of the
    > decimal minute digit.
    Generally, programming languages don't provide any way to carry one
    more digit in computations. You can control precision in a coarse
    manner by the choice of data type, e.g., single precision or double
    precision floating point. But the machine stores and computes that type
    to full accuracy, whether you need it or not.
    On output you can specify precision. In all the C family languages
    I've used, floating point output is rounded. For example, if you print
    pi to three decimal places, the result is 3.142, not 3.141. This control
    over precision only affects the output formatting, though.
    To reduce the precision of the variable itself, the Microsoft .NET
    Framework (accessible with Visual Basic, Visual C#, et al) has routines
    to round a value to a specified number of decimal places:
    But since that's extra work for the machine, normally you'd round only
    the human-readable output, and maintain variables to full precision.
    Astronomical computing has changed a lot since the days when "computers"
    were human beings running desk calculators. Nowadays even a cheap
    machine has a floating point processor in the CPU. Many of the old labor
    saving methods disappeared because on today's hardware there's no
    penalty for carrying extra significant digits.
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