This implements floating-point division A/B by a process that starts
with normalizing both inputs if necessary. Then an estimate of 1/B
from a lookup table is refined by 3 Newton-Raphson iterations and then
multiplied by A to get a quotient. The remainder is calculated as
A - R * B (where R is the result, i.e. the quotient) and the remainder
is compared to 0 and to B to see whether the quotient needs to be
incremented by 1. The calculations of 1 / B are done with 56 fraction
bits and intermediate results are truncated rather than rounded,
meaning that the final estimate of 1 / B is always correct or a little
bit low, never too high, and thus the calculated quotient is correct
or 1 unit too low. Doing the estimate of 1 / B with sufficient
precision that the quotient is always correct to the last bit without
needing any adjustment would require many more bits of precision.
This implements fdivs by computing a double-precision quotient and
then rounding it to single precision. It would be possible to
optimize this by e.g. doing only 2 iterations of Newton-Raphson and
then doing the remainder calculation and adjustment at single
precision rather than double precision.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
This implements the fmul and fmuls instructions.
For fmul[s] with denormalized operands we normalize the inputs
before doing the multiplication, to eliminate the need for doing
count-leading-zeroes on P. This adds 3 or 5 cycles to the
execution time when one or both operands are denormalized.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
This implements fctiw, fctiwz, fctiwu, fctiwuz, fctid, fctidz, fctidu
and fctiduz, and adds tests for them.
There are some subtleties around the setting of the inexact (XX) and
invalid conversion (VXCVI) flags in the FPSCR. If the rounded value
ends up being out of range, we need to set VXCVI and not XX. For a
conversion to unsigned word or doubleword of a negative value that
rounds to zero, we need to set XX and not VXCVI.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
This implements fcfid, fcfidu, fcfids and fcfidus, which convert
64-bit integer values in an FPR into a floating-point value.
This brings in a lot of the datapath that will be needed in
future, including the shifter, adder, mask generator and
count-leading-zeroes logic, along with the machinery for rounding
to single-precision or double-precision, detecting inexact results,
signalling inexact-result exceptions, and updating result flags
in the FPSCR.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
This implements fmr, fneg, fabs, fnabs and fcpsgn and adds tests
for them.
This adds logic to unpack and repack floating-point data from the
64-bit packed form (as stored in memory and the register file) into
the unpacked form in the fpr_reg_type record. This is not strictly
necessary for fmr et al., but will be useful for when we do actual
arithmetic.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
This tests mffs, mtfsf and the generation of floating-point type
program interrupts that occur as a result of mtfsf.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
This tests that floating-point unavailable exceptions occur as expected
on FP loads and stores, and that the simple FP loads and stores appear
to give reasonable results.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
Paul Mackerras