Engineer's Toolbox

Floating Point in Mathematica

Volume 2, Issue 3
Summer 1992

Mathematica provides both traditional machine-level floating point numbers and software-implemented variable-precision floating-point numbers. There are two different notions of precision: an estimate of the maximum possible relative error, which is propagated through arithmetic operations based on the precision of the operands; and the number of digits used to represent the significand (mantissa). Mathematica links the first notion to the second, throwing away digits that it cannot prove are significant. In iterative calculations the precision can ratchet down a little each iteration, until there is nothing left.