This file documents @sc{cln}, a Class Library for Numbers.
Published by Bruno Haible, @code{<haible@@clisp.cons.org>} and
-Richard Kreckel, @code{<kreckel@@ginac.de>}.
+Richard B. Kreckel, @code{<kreckel@@ginac.de>}.
-Copyright (C) Bruno Haible 1995, 1996, 1997, 1998, 1999, 2000, 2001.
-Copyright (C) Richard Kreckel 2000, 2001, 2002.
+Copyright (C) Bruno Haible 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004.
+Copyright (C) Richard B. Kreckel 2000, 2001, 2002, 2003, 2004.
Permission is granted to make and distribute verbatim copies of
this manual provided the copyright notice and this permission notice
@author by Bruno Haible
@page
@vskip 0pt plus 1filll
-Copyright @copyright{} Bruno Haible 1995, 1996, 1997, 1998, 1999, 2000, 2001.
+Copyright @copyright{} Bruno Haible 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004.
@sp 0
-Copyright @copyright{} Richard Kreckel 2000, 2001.
+Copyright @copyright{} Richard Kreckel 2000, 2001, 2002, 2003, 2004.
@sp 2
Published by Bruno Haible, @code{<haible@@clisp.cons.org>} and
@page
+@c Table of contents
+@contents
+
+
@node Top, Introduction, (dir), (dir)
@c @menu
@cindex Sch{@"o}nhage-Strassen multiplication
@end iftex
@ifinfo
-Schönhage-Strassen
-@cindex Schönhage-Strassen multiplication
+Schnhage-Strassen
+@cindex Schnhage-Strassen multiplication
@end ifinfo
multiplication, which is an asymptotically optimal multiplication
algorithm, for multiplication, division and radix conversion.
If you use @code{g++} 3.0.x or 3.1, I recommend adding
@samp{-finline-limit=1000} to the CXXFLAGS. This is essential for good code.
-If you use @code{g++} gcc-2.95.x or gcc-3.0.x , I recommend adding
+If you use @code{g++} gcc-2.95.x or gcc-3.x , I recommend adding
@samp{-fno-exceptions} to the CXXFLAGS. This will likely generate better code.
-If you use @code{g++} from gcc-2.95.x on Sparc, add either @samp{-O},
-@samp{-O1} or @samp{-O2 -fno-schedule-insns} to the CXXFLAGS. With full
-@samp{-O2}, @code{g++} miscompiles the division routines. If you use
-@code{g++} older than 2.95.3 on Sparc you should also specify
-@samp{--disable-shared} because of bad code produced in the shared
-library.
+If you use @code{g++} from gcc-3.0.4 or older on Sparc, add either
+@samp{-O}, @samp{-O1} or @samp{-O2 -fno-schedule-insns} to the
+CXXFLAGS. With full @samp{-O2}, @code{g++} miscompiles the division
+routines. If you use @code{g++} older than 2.95.3 on Sparc you should
+also specify @samp{--disable-shared} because of bad code produced in the
+shared library. Also, do not use gcc-3.0 on Sparc for compiling CLN, it
+won't work at all.
If you use @code{g++} on OSF/1 or Tru64 using gcc-2.95.x, you should
specify @samp{--disable-shared} because of linker problems with
duplicate symbols in shared libraries. If you use @code{g++} from
gcc-3.0.n, with n larger than 1, you should @emph{not} add
@samp{-fno-exceptions} to the CXXFLAGS, since that will generate wrong
-code (gcc-3.1.0 is okay again, as is gcc-3.0.0).
+code (gcc-3.1 is okay again, as is gcc-3.0).
+
+Also, please do not compile CLN with @code{g++} using the @code{-O3}
+optimization level. This leads to inferior code quality.
If you use @code{g++} from gcc-3.1, it will need 235 MB of virtual memory.
You might need some swap space if your machine doesn't have 512 MB of RAM.
C++ terminology) are not provided. Instead, you can assert and check
that a value belongs to a certain subclass, and return it as element of that
class, using the @samp{As} and @samp{The} macros.
+@cindex cast
@cindex @code{As()()}
@code{As(@var{type})(@var{value})} checks that @var{value} belongs to
@var{type} and returns it as such.
@code{a} must be > 0. @code{b} must be >0 and != 1. If log(a,b) is
rational number, this function returns true and sets *l = log(a,b), else
it returns false.
+
+@item int jacobi (sint32 a, sint32 b)
+@cindex @code{jacobi()}
+@itemx int jacobi (const cl_I& a, const cl_I& b)
+Returns the Jacobi symbol
+@tex
+$\left({a\over b}\right)$,
+@end tex
+@ifnottex
+(a/b),
+@end ifnottex
+@code{a,b} must be integers, @code{b>0} and odd. The result is 0
+iff gcd(a,b)>1.
+
+@item cl_boolean isprobprime (const cl_I& n)
+@cindex prime
+@cindex @code{isprobprime()}
+Returns true if @code{n} is a small prime or passes the Miller-Rabin
+primality test. The probability of a false positive is 1:10^30.
+
+@item cl_I nextprobprime (const cl_R& x)
+@cindex @code{nextprobprime()}
+Returns the smallest probable prime >=@code{x}.
@end table
@item cl_UP R->one()
@cindex @code{one ()}
-This returns @code{1 in R}, a polynomial of degree <= 0.
+This returns @code{1 in R}, a polynomial of degree == 0.
@item cl_UP R->canonhom (const cl_I& x)
@cindex @code{canonhom ()}
@cindex @code{degree ()}
Returns the degree of the polynomial. The zero polynomial has degree @code{-1}.
+@item sintL ldegree (const cl_UP& x)
+@cindex @code{degree ()}
+Returns the low degree of the polynomial. This is the degree of the first
+non-vanishing polynomial coefficient. The zero polynomial has ldegree @code{-1}.
+
@item cl_ring_element coeff (const cl_UP& x, uintL index)
@cindex @code{coeff ()}
Returns the coefficient of @code{X^index} in the polynomial @code{x}.
@cindex Sch{@"o}nhage-Strassen multiplication
@end iftex
@ifinfo
-Schönhage-Strassen
-@cindex Schönhage-Strassen multiplication
+Schnhage-Strassen
+@cindex Schnhage-Strassen multiplication
@end ifinfo
multiplication, which is an asymptotically optimal multiplication
algorithm.
@printindex my
-@c Table of contents
-@contents
-
-
@bye
git://www.ginac.de / cln.git / blobdiff