This implements fmadd, fmsub, fnmadd, fnmsub and their
single-precision counterparts. The single-precision versions operate
the same as the double-precision versions until the final rounding and
overflow/underflow steps.
This adds an S register to store the low bits of the product. S
shifts into R on left shifts, and can be negated, but doesn't do any
other arithmetic.
This adds a test for the double-precision versions of these
instructions.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
This implements the floating square-root calculation using a table
lookup of the inverse square root approximation, followed by three
iterations of Goldschmidt's algorithm, which gives estimates of both
sqrt(FRB) and 1/sqrt(FRB). Then the residual is calculated as
FRB - R * R and that is multiplied by the 1/sqrt(FRB) estimate to get
an adjustment to R. The residual and the adjustment can be negative,
and since we have an unsigned multiplier, the upper bits can be wrong.
In practice the adjustment fits into an 8-bit signed value, and the
bottom 8 bits of the adjustment product are correct, so we sign-extend
them, divide by 4 (because R is in 10.54 format) and add them to R.
Finally the residual is calculated again and compared to 2*R+1 to see
if a final increment is needed. Then the result is rounded and
written back.
This implements fsqrts as fsqrt, but with rounding to single precision
and underflow/overflow calculation using the single-precision exponent
range. This could be optimized later.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
This implements frsqrte by table lookup. We first normalize the input
if necessary and adjust so that the exponent is even, giving us a
mantissa value in the range [1.0, 4.0), which is then used to look up
an entry in a 768-entry table. The 768 entries are appended to the
table for reciprocal estimates, giving a table of 1024 entries in
total. frsqrtes is implemented identically to frsqrte.
The estimate supplied is accurate to 1 part in 1024 or better.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
This just returns the value from the inverse lookup table. The result
is accurate to better than one part in 512 (the architecture requires
1/256).
This also adds a simple test, which relies on the particular values in
the inverse lookup table, so it is not a general test.
Signed-off-by: Paul Mackerras <paulus@ozlabs.org>
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 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