For nearly all applications, the built-in floating-point types,
double if this offers higher precision
double) offer enough precision,
typically a dozen decimal digits.
Some reasons why one would want to use a higher precision:
Many functions and distributions have differences from exact values that are only a few least significant bits - computation noise. Others, often those for which analytical solutions are not available, require approximations and iteration: these may lose several decimal digits of precision.
If you require a value which is as accurate as can be represented in the
floating-point type, and is thus the closest representable value and has
an error less than 1/2 a least
significant bit or ulp
it may be useful to use a higher-precision type, for example,
cpp_dec_float_50, to generate this value.
Conversion of this value to a built-in floating-point type ('float',
double) will not cause any further
loss of precision. A decimal digit string will also be 'read' precisely by
the compiler into a built-in floating-point type to the nearest representable
In contrast, reading a value from an
William Kahan coined the term Table-Maker's Dilemma for the problem of correctly rounding functions. Using a much higher precision (50 or 100 decimal digits) is a practical way of generating (almost always) correctly rounded values.