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blocks in numerical functions. The transcendental functions
include the usual logarithmic and exponential functions, as well
as ln(1+
x) and e
x
-1; financial functions for compound interest
and annuity calculations; trigonometric functions; error and
gamma functions; and a random number generator.
PowerPC Numerics Versus SANE
Although PowerPC Numerics is an implementation of the IEEE
Standard, it is not the Standard Apple Numerics Environment
(SANE). SANE is the numerics environment used on 680x0-based
Macintosh computers, and it is the numerics environment used
when you run a 680x0 application on a PowerPC processor-based
Macintosh computer.
PowerPC Numerics is the environment used when you run an
application built for a PowerPC processor-based Macintosh computer.
There are fundamental differences between PowerPC Numerics and
SANE because of the differences in the microprocessors on which
the two environments are used. The major difference is that SANE
supports an 80-bit extended type and performs all floating-point
computations in extended precision. This protects the user from
roundoff error, overflows, and underflows that might occur in an
intermediate value when determining the result of an expression.
Because the PowerPC processor is double-based, support of an
80-bit data type would be inefficient. It instead supports a 128-
bit type (in software) called double-double (which corresponds to
the long double type in C).
PowerPC Numerics provides this wide type only for cases where
precision greater than that provided by the double format is
necessary; PowerPC Numerics does not perform all computations
in double-double precision. Instead, PowerPC Numerics
recommends a method by which an expression is evaluated in
the widest precision necessary.
Another fundamental difference is that PowerPC Numerics
conforms to the FPCE recommendations as well as to the IEEE
standard. C implementations using SANE do not necessarily
comply with the FPCE recommendations.
About Floating-Point Data Formats
The IEEE standard defines several floating-point data formats,
one required and the others recommended. IEEE requires that
Technical Considerations
iMalc Manual
Technical Considerations
35