Oct is a portable Lisp implementation of quad-double arithmetic. This gives about 65 digits of precision. Quad-double arithmetic uses four double-float numbers to represent an extended precision number.
The implementation is modeled on the quad-double package by Yozo Hida. This package is in C++, but we have translated parts of it and extended it to use Lisp. The intent is to provide all of the CL arithmetic functions with a quad-double implementation.
Further information will be provided at a later date. This is currently a work in progress, but the current code has the basic functionality implemented and includes all of the special functions specified by CL. There are, undoubtedly, many bugs.
This package has been tested with CMUCL, SBCL, Clisp, and Allegro. All tests pass. Note that development is primarily done using CMUCL.
%quad-doublenumbers, many functions now support an optional third arg which is where the result should be written. This is like how
bit-andworks. This should work correctly with both an array or
(complex double-double-float)implementation, but perhaps some care is needed to make sure it works for both.
(complex double-double-float)to store a
%quad-double. However, simple timing measurements indicate that arrays are slightly slower to much slower than using
OCTpackage has been renamed. The package is now
NET.COMMON-LISP.OCT, with a nickname of
QDis no longer a nickname for
QUAD-DOUBLE-INTERNALhas been renamed to
OCT-INTERNAL, with a nickname of
OCTI. The old nickname
QDIhas been removed
MK:DEFSYSfrom clocc, if you don't already have a copy. Or you can also use
ASDF. Note that this might be out-of-date compared to the
(mk:oos "oct" :compile)will compile up everything. Or use
(asdf:oos 'asdf:load-op :oct)
(mk:oos "oct-test" :compile)will compile up some simple tests.
(qdi::all-tests)will run a series of tests. The accuracy of the results should be on the order of about 200 bits or more. There are a few cases where accuracy is much less than this, but that is due to the algorithm. If you have a copy of RT, you should run
(rt:do-tests)to run the tests. All tests should pass.
Everything in Oct resides in the
with a nickname of
The basic arithmetic operations
CL are shadowed in this package so you can use
natural Lisp expressions to operate on quad-doubles. Special
functions are included.
There are two types added:
- A quad-double type. This has about 65 digits of precision, or about 212 bits.
- A complex type consisting of two
The reader is also modified to make it easier to enter quad-double
#q is used to enter both
QD-COMPLEX types. For example
QD-REAL with the value 125000. The exponent
q. To enter a
#q(r i) where
the real and imaginary parts. The parts will be coerced to
QD-REAL type if necessary.
Here are a few examples:
QD> (/ (sqrt #q3) 2) #q0.866025403784438646763723170752936183471402626905190314027903489696q0 QD> (sin (/ +pi+ 3)) #q0.86602540378443864676372317075293618347140262690519031402790348972q0 QD> (sqrt #q-1) #q(#q0.0q0 #q1.0q0) QD> (coerce 7 'qd-complex) #q(#q7.0q0 #q0.0q0) QD> (integer-decode-float +pi+) 165424160919322423196824703508232170249081435635340508251270944637 -215 1 QD> +pi+ #q3.1415926535897932384626433832795028841971693993751058209749445923q0 QD> (* 4 (atan #q1)) #q3.1415926535897932384626433832795028841971693993751058209749445923q0
+pi+ is the
QD-REAL value for pi.
Here are some simple benchmarks on the performance of this
quad-double implementation. These benchmarks were run using CMUCL on
a 1.42 GHz PPC. The columns are times relative to a
the time using the internal implementaiton, without the overhead of
QD-REAL column shows the effect
|Square root||125||133||There is no FP sqrt instruction on a PPC|
Here are some timing results using CMUCL on a 1.5 GHz UltraSparc IIIi
|Square root||13400||13600||UltraSparc has a FP sqrt instruction|
Here are some timing results using CMUCL with SSE2 support on a 3.06 GHz Core i3
Hida's QD package has a few timing tests. The lisp equivalent was written and here are the timing results. Note that the Lisp equivalent tried to be exactly the same as the QD reference, but no guarantees on that.
|Test||QD||Oct||Relative speed Oct/QD|
The second and third columns are microsec per operation. The last column is the relative time of Oct vs QD. All of these were run on a 1.5 GHz Ultrasparc III. Sun Studio 11 was used to compile the C code. CMUCL 2007-10 was used for the Lisp code.
It's surprising that Oct does as well as it does. To be fair, the times for Oct include the cost of CLOS dispatch since QD uses templates and classes in the tests. Except for add and mul, QD and Oct are within a few percent. The sin test is a bit slower in Oct. I don't know why, but the test did include the accurate argument reduction. The log test is quite a bit faster for Oct. This is probably due to using a different algorithm. QD uses a Newton iteration to compute the log. Oct uses Halley's iteration.
Currently, there are no official releases. However, you may find occasional snapshots of the sources here.
It is known that CMUCL and SBCL have the desired rounding by default. Allegro works fine on ppc and x86 now.
#qreader macro. This may interfere with other systems that want to use
You can browse our CVS repository or download the development tree via anonymous cvs, as described here. Note that CVS is no longer up-to-date
You can browse our git repository or clone it if desired.