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Data Types and Sizes
Motorola
About g56k
4-7
One major difference is the use of affine arithmetic in the IEEE standard versus the use of
saturation arithmetic in the DSP56KCC format. Affine arithmetic gives separate identity
to plus infinity, minus infinity, plus zero and minus zero. In operations involving these
values, finite quantities remain finite and infinite quantities remain infinite. In contrast,
DSP56KCC format gives special identity only to unsigned zero. This format performs
saturation arithmetic such that any result out of the representable floating-point range is
replaced with the closest floating-point representation. Since the dynamic range of this
format is quite large, it is adequate for most applications.
The IEEE floating-point standard provides extensive error handling required by affine
arithmetic, denormalized numbers, signaling Not-a-Numbers (NaNs) and quiet NaNs. It
postpones the introduction of computational errors by using internal signaling and user
traps to process each exception condition. Computational errors will be introduced by the
application program if the calculation is completed instead of aborting the program. The
DSP56KCC format introduces computation errors when an exception occurs in order to
maintain real-time execution. An error flag (L bit in CCR) is set to inform the application
program that an exception has occurred. This bit will remain set until reset by the
application program. The user can then eliminate the exception by algorithm
modifications.
4.4.3 Pointer Types
With DSP56KCC, all pointers are 16-bits (see Table 4-7). When computing addresses
with integer arithmetic, only the least significant 16-bits are relevant.
Rounding
Round to Nearest
Round to Nearest
Round to +/- Infinity
Round to Zero
Infinity Arithmetic
Saturation Limiting
Affine Operations
Denormalized Numbers
No (Forced to Zero)
Yes (with Min Exp)
Exceptions
Divide by Zero
Overflow
Negative Square
Root
Invalid Operation
Divide by Zero
Overflow
Underflow
Inexact Arithmetic
Table 4-6. Comparison of DSP56KCC and IEEE 754-1985
CHARACTERISTIC
DSP56KCC
FORMAT
IEEE FORMAT
F
Freescale Semiconductor, Inc.
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