However, 19.95 can't be precisely represented as a
binary floating point number,...,
Why not? Surely there is a bit pattern in the IEEE float
format that precisely represents 19.95 (1.995E1). If a
float is stored in,say, 32 bits on a particulat platfrom,
some bits are for the mantissa and some are for the exponent...
That's not how it works.
What you are describing would be a base10 representation --
ie: you store a number and a base 10 exponent. What is
typicaly used is a number and a base 2 exponent.
| what you want: |
mantissa * (10 ** exp) |
| what you get: |
mantissa * (2 ** exp) |
IEEE 854 specifies support for base10 representations,
but no one uses it -- what gets used is
IEEE 754. When you
get a sizable chunk of free time, read through
What Every Computer Scientist Should Know About Floating-Point Arithmetic --
in the mean time, John Darcy (Sun's floating point guru) has
a great set of
slides
about Floats in java -- but the information is equally useful for perl programmers.
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