extremal rounding test sets for division, RDp and RNp, provide inputs
whose infinitely precise quotients are extremely close to a p-bit number
for RDp or a midpoint between 2 p-bit numbers for RNp. These sets
provide precisely those inputs whose outputs have the maximum number of
like bits after the round bit. Our test set for single
precision directed rounding, RD24 and single
precision round to nearest, RN24 each contain roughly
5.6 million examples. These examples are sorted, in ASCII format, and
may be downloaded in a compressed form.
C++ program for 32-bit native machines RN.cc
and 64-bit native machines RN64.cc
will generate the RNi suites for 3 ≤ i ≤ 28, and is further
described along with the theory in “Generating
a Benchmark Set of Extremal Rounding Boundary Instances for IEEE
Standard Floating Point Division”. The count output
from the program can be checked with the results in Table 3 of the
Unlike division, only one square root example for each precision has the maximum number of like bits after the round bit making it extremely close to a p-bit number or a midpoint between 2 p-bit numbers. Consequently, our single precision extremal square root test suite for directed rounding and our extremal square root test suite for round to nearest contain those inputs whose outputs have at least 12 like bits after the round bit. These suites are in a 2-column ASCII format. The first column is the input for the square root function. The second column indicates the number of like bits after the round bit found in the infinitely precise output.
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