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Precision and Range of Numbers
The largest value that can be represented is just over 7.0779863,
often written as 7.077e9863, and the smallest non-zero positive number is just
under 3.533-9865 or 3.533e-9865. Negative numbers have the same
limits on their magnitudes. If the result of any addition, subtraction,
multiplication, or division gives a result outside this range, an "Overflow" or
"Underflow" error is signalled. (The "Underflow" error guards against losing
all precision by silently rounding a value down to zero. Such practice is all
too common elsewhere.)
(The precise limiting values can be calculated as 10^(32767*log10(2)-9863) and
10^(-32769*log10(2)+9865) to avoid overflow and underflow, and then including
the power of 10.)
The range of numbers that can actually be entered is rather less than the maximum that can be represented. The smallest magnitude that can be entered is about 1.4e-9844, and the largest is about 1.2e9844.
Expressions are calculated with a nominal precision of 128 bits, which corresponds to 38 decimal digits. Results can be displayed to a precision of 8, 12 or 16 digits, or displayed with automatic precision, in which case as many digits as possible are shown, depending on the width of the window.