HP-UX Floating-Point Guide

182 Chapter 7
Performance Tuning
Denormalized Operands
Denormalized Operands
Denormalized values usually occur as the result of an operation that
underflows. On HP 9000 systems, the occurrence of a denormalized
operand or result, either at an intermediate stage of a computation or at
the end, can reduce the speed of an operation significantly. There are
several solutions to this problem:
• Change single-precision data to double-precision.
• Assign the value zero to data that would normally be denormalized.
• On systems that support it, enable flush-to-zero mode.
• Scale the entire data set upwards in magnitude so that the smallest
values that occur are guaranteed to be normalized.
The first solution applies primarily to code that uses single-precision
data. Because of the range of the two formats, a value that is
denormalized in single-precision will be normalized in double-precision.
On HP 9000 systems, denormalized numbers are so costly that it is
worth converting to double-precision even if this means converting
several operands from single-precision to double-precision, performing
several operations, and then converting the result back to
single-precision. The code will still run much faster than it would if it
had to process a single denormalized operand.
The second solution is useful only if you can determine that your
algorithm will work equally well when a denormalized value is treated
as zero. In this case, you can explicitly assign it the value 0 before
entering a loop where it is repeatedly accessed. For example, if A is a
denormalized operand in the following example, this code will run very
slowly on a HP 9000 system:
SUBROUTINE VECTOR_SCALE(A, V)
REAL A, V(1000)
PRINT *, 'A IS', A
DO 10 I = 1,1000
10 V(I) = V(I) * A
RETURN
END
If A is likely to be denormalized once in a while, it may be a good idea to
add the following line before the loop:
IF (ABS(A) .LT. 1.1754944E-38)A=0.0