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the standard arithmetic operations (add, subtract, multiply, divide) as well as
a few others such as square root. When the computer performs such a oating
point operation, the operands must be available in the processor registers or
in memory. The operands are therefore, by de nition, oating point numbers,
even if they are only approximations to the original program data. However,
the result of a standard operation on two oating point numbers may well not
be a oating point number. For example, 1 and 10 are both oating point
numbers but we have already seen that 1=10 is not. In fact, multiplication
of two arbitrary 24-bit signi cands generally gives a 48-bit signi cand which
cannot be represented exactly in single precision.
When the result of a oating point operation is not a oating point number, the IEEE standard requires that the computed result must be the correctly rounded value of the exact result, using the rounding mode and precision
currently in e ect. It is worth stating this requirement carefully. Let x and
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This note was uploaded on 02/12/2014 for the course MATH 4800 taught by Professor Lie during the Spring '09 term at Rensselaer Polytechnic Institute.
- Spring '09