mirror of https://github.com/macssh/macssh.git
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7.0 KiB
HTML
195 lines
7.0 KiB
HTML
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
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<html>
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<head>
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<title>
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GMP Development Projects
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</title>
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</head>
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<body bgcolor=pink>
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<center>
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<h1>
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GMP Development Projects
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</h1>
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</center>
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<comment>
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An up-to-date version of this file is available at
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<a href="http://www.swox.com/gmp/projects.html">http://www.swox.com/gmp/projects.html</a>.
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</comment>
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<p> This file lists projects suitable for volunteers. Please see the
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<a href="tasks.html">tasks file</a> for smaller tasks.
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<p> If you want to work on any of the projects below, please let tege@swox.com
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know. If you want to help with a project that already somebody else is
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working on, please talk to that person too, tege@swox.com can put you in
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touch. (There are no email addresses of volunteers below, due to spamming
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problems.)
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<ul>
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<li> <strong>C++ wrapper</strong>
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<p> A C++ wrapper for GMP is highly desirable. Several people have started
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writing one, but nobody has so far finished it. For a wrapper to be useful,
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one needs to pay attention to efficiency.
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<ol>
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<li> Write arithmetic functions for direct applications of most
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elementary C++ types. This might be necessary to avoid
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ambiguities, but it is also desirable from an efficiency
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standpoint.
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<li> Avoid running constructors/destructors when not necessary.
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For example, implement <code>a += b</code> by directly applying mpz_add.
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</ol>
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<p> <li> <strong>Faster multiplication</strong>
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<p> The current multiplication code uses Karatsuba, 3-way Toom-Cook,
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or Fermat FFT. Several new developments are desirable:
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<ol>
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<li> Handle multiplication of operands with different digit count
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better than today. We now split the operands in a very
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inefficient way, see mpn/generic/mul.c.
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<li> Consider N-way Toom-Cook. See Knuth's Seminumerical
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Algorithms for details on the method. Code implementing it
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exists. This is asymptotically inferior to FFTs, but is finer
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grained. A toom-4 might fit in between toom-3 and the FFTs
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(or it might not).
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<li> It's possible CPU dependent effects like cache locality will
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have a greater impact on speed than algorithmic improvements.
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</ol>
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<p> <li> <strong>Assembly routines</strong>
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<p> Write new and tune existing assembly routines. The programs in mpn/tests
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and the tune/speed.c program are useful for testing and timing the routines
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you write. See the README files in those directories for more information.
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<p> Please make sure your new routines are fast for these three situations:
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<ol>
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<li> Operands that fit into the cache.
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<li> Small operands of less than, say, 10 limbs.
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<li> Huge operands that does not fit into the cache.
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</ol>
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<p> The most important routines are mpn_addmul_1, mpn_mul_basecase and
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mpn_sqr_basecase. The latter two don't exist for all machines, while
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mpn_addmul_1 exists for almost all machines.
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<p> Standard techniques for these routines are unrolling, software
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pipelining, and specialization for common operand values. For machines with
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poor integer multiplication, it is often possible to improve the performance
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using floating-point operations, or SIMD operations such as MMX or Sun's VIS.
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<p> Using floating-point operations is interesting but somewhat tricky.
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Since IEEE double has 53 bit of mantissa, one has to split the operands in
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small prices, so that no result is greater than 2^53. For 32-bit computers,
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splitting one operand into 16-bit pieces works. For 64-bit machines, one
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operand can be split into 21-bit pieces and the other into 32-bit pieces. (A
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64-bit operand can be split into just three 21-bit pieces if one allows the
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split operands to be negative!)
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<p> <li> <strong>Faster extended GCD</strong>
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<p> We currently have extended GCD based on Lehmer's method.
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But the binary method can quite easily be improved for bignums
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in a similar way Lehmer improved Euclid's algorithm. The result should
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beat Lehmer's method by about a factor of 2. Furthermore, the multiprecision
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step of Lehmer's method and the binary method will be identical, so the
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current code can mostly be reused. It should be possible to share code
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between GCD and GCDEXT, and probably with Jacobi symbols too.
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<p> <li> <strong>Math functions for the mpf layer</strong>
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<p> Implement the functions of math.h for the GMP mpf layer! Check the book
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"Pi and the AGM" by Borwein and Borwein for ideas how to do this. These
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functions are desirable: acos, acosh, asin, asinh, atan, atanh, atan2, cos,
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cosh, exp, log, log10, pow, sin, sinh, tan, tanh.
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<p> <li> <strong>Faster sqrt</strong>
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<p> The current code for computing square roots use a Newton iteration that
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rely on division. It is possible to avoid using division by computing
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1/sqrt(A) using this formula:
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<pre>
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2
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x = x (3 - A x )/2.
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i+1 i i </pre>
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The final result is then computed without division using,
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<pre>
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sqrt(A) = A x .
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n </pre>
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The resulting code should be substantially faster than the current code.
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<p> <li> <strong>Nth root</strong>
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<p> Implement, at the mpn level, a routine for computing the nth root of a
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number. The routine should use Newton's method, preferably without using
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division.
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<p> If the routine becomes fast enough, perhaps square roots could be computed
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using this function.
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<p> <li> <strong>More random number generators</strong>
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<p> Implement some more pseudo random number generator algorithms.
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Today there's only Linear Congruential.
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<p> <li> <strong>Test Suite</strong>
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<p> Add a test suite for old bugs. These tests wouldn't loop or use
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random numbers, but just test for specific bugs found in the
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past.
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<p> More importantly, improve the random number controls for test
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collections:
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<ol>
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<li> Use the new random number framework.
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<li> Have every test accept a seed parameter.
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<li> Allow `make check' to set the seed parameter.
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<li> Add more tests for important, now untested functions.
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</ol>
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<p> With this in place, it should be possible to rid GMP of
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practically all bugs by having some dedicated GMP test machines
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running "make check" with ever increasing seeds (and
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periodically updating to the latest GMP).
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<p> If a few more ASSERTs were sprinkled through the code, running
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some tests with --enable-assert might be useful, though not a
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substitute for tests on the normal build.
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<p> An important feature of any random tests will be to record the
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seeds used, and perhaps to snapshot operands before performing
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each test, so any problem exposed can be reproduced.
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</ul>
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<hr>
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<table width="100%">
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<tr>
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<td>
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<font size=2>
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Please send comments about this page to
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<a href="mailto:tege@swox.com">tege@swox.com</a>.<br>
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Copyright (C) 1999, 2000 Torbj<62>rn Granlund.
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</font>
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</td>
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<td align=right>
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</td>
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</tr>
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</table>
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</body>
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</html>
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