

single precision directed rounding single precision round to nearest extremal square root test suite for directed rounding extremal square root test suite for round to nearest

The
extremal rounding test sets for division, RD_{p} and RN_{p}, provide inputs
whose infinitely precise quotients are extremely close to a pbit number
for RD_{p} or a midpoint between 2 pbit numbers for RN_{p}. 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, RD_{24} and single
precision round to nearest, RN_{24} each contain roughly
5.6 million examples. These examples are sorted, in ASCII format, and
may be downloaded in a compressed form. The
C++ program for 32bit native machines RN.cc
and 64bit native machines RN64.cc
will generate the RN_{i} 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
paper. 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 pbit number or a midpoint between 2 pbit 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 2column 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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