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<H1><A NAME="SEC34" HREF="maxima_toc.html#TOC34">Floating Point</A></H1>
<H2><A NAME="SEC35" HREF="maxima_toc.html#TOC35">Definitions for Floating Point</A></H2>
<P>
<DL>
<DT><U>Function:</U> <B>BFFAC</B> <I>(exp,n)</I>
<DD><A NAME="IDX275"></A>
BFLOAT version of the Factorial (shifted Gamma)
function. The 2nd argument is how many digits to retain and return,
it's a good idea to request a couple of extra. This function is
available by doing LOAD(BFFAC); .
</DL>
</P>
<P>
<DL>
<DT><U>Variable:</U> <B>ALGEPSILON</B>
<DD><A NAME="IDX276"></A>
The default value is 10^-8. The value of ALGEPSILON is used by ALGSYS.
</DL>
</P>
<P>
<DL>
<DT><U>Function:</U> <B>BFLOAT</B> <I>(X)</I>
<DD><A NAME="IDX277"></A>
converts all numbers and functions of numbers to bigfloat
numbers. Setting FPPREC[16] to N, sets the bigfloat precision to N
digits. If FLOAT2BF[FALSE] is FALSE a warning message is printed when
a floating point number is converted into a bigfloat number (since
this may lead to loss of precision).
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>BFLOATP</B> <I>(exp)</I>
<DD><A NAME="IDX278"></A>
is TRUE if exp is a bigfloat number else FALSE.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>BFPSI</B> <I>(n,z,fpprec)</I>
<DD><A NAME="IDX279"></A>
gives polygammas of real arg and integer order.
For digamma, BFPSI0(z,fpprec) is more direct. Note -BFPSI0(1,fpprec)
provides BFLOATed %GAMMA. To use this do LOAD(BFFAC);
</P>
</DL>
<P>
<DL>
<DT><U>Variable:</U> <B>BFTORAT</B>
<DD><A NAME="IDX280"></A>
default: [FALSE] controls the conversion of bfloats to
rational numbers. If
<PRE>
BFTORAT:FALSE
</PRE>
<P>
RATEPSILON will be used to
control the conversion (this results in relatively small rational
numbers). If
<PRE>
BFTORAT:TRUE
</PRE>
<P>
, the rational number generated will
accurately represent the bfloat.
</P>
</DL>
<P>
<DL>
<DT><U>Variable:</U> <B>BFTRUNC</B>
<DD><A NAME="IDX281"></A>
default: [TRUE] causes trailing zeroes in non-zero bigfloat
numbers not to be displayed. Thus, if BFTRUNC:FALSE, BFLOAT(1);
displays as 1.000000000000000B0. Otherwise, this is displayed as
1.0B0.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>CBFAC</B> <I>(z,fpprec)</I>
<DD><A NAME="IDX282"></A>
a factorial for complex bfloats. It may be used by
doing LOAD(BFAC); For more details see share2/bfac.usg.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>FLOAT</B> <I>(exp)</I>
<DD><A NAME="IDX283"></A>
converts integers, rational numbers and bigfloats in exp
to floating point numbers. It is also an EVFLAG, FLOAT causes
non-integral rational numbers and bigfloat numbers to be converted to
floating point.
</P>
</DL>
<P>
<DL>
<DT><U>Variable:</U> <B>FLOAT2BF</B>
<DD><A NAME="IDX284"></A>
default: [FALSE] if FALSE, a warning message is printed when
a floating point number is converted into a bigfloat number (since
this may lead to loss of precision).
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>FLOATDEFUNK</B>
<DD><A NAME="IDX285"></A>
- is a utility for making floating point functions from
mathematical expression. It will take the input expression and FLOAT it,
then OPTIMIZE it, and then insert MODE_DECLAREations for all the variables.
This is THE way to use ROMBERG, PLOT2, INTERPOLATE, etc. e.g.
EXP:some-hairy-macsyma-expression;
</P>
<PRE>
FLOATDEFUNK('F,['X],EXP);
</PRE>
<P>
will define the function F(X) for you.
(Do PRINTFILE(MCOMPI,DOC,MAXDOC); for more details.)
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>FLOATNUMP</B> <I>(exp)</I>
<DD><A NAME="IDX286"></A>
is TRUE if exp is a floating point number else FALSE.
</P>
</DL>
<P>
<DL>
<DT><U>Variable:</U> <B>FPPREC</B>
<DD><A NAME="IDX287"></A>
default: [16] - Floating Point PRECision. Can be set to an
integer representing the desired precision.
</P>
</DL>
<P>
<DL>
<DT><U>Variable:</U> <B>FPPRINTPREC</B>
<DD><A NAME="IDX288"></A>
default: [0] - The number of digits to print when
printing a bigfloat number, making it possible to compute with a large
number of digits of precision, but have the answer printed out with a
smaller number of digits. If FPPRINTPREC is 0 (the default), or >=
FPPREC, then the value of FPPREC controls the number of digits used
for printing. However, if FPPRINTPREC has a value between 2 and
FPPREC-1, then it controls the number of digits used. (The minimal
number of digits used is 2, one to the left of the point and one to
the right. The value 1 for FPPRINTPREC is illegal.)
</DL>
</P>
<P>
<DL>
<DT><U>Function:</U> <B>?ROUND</B> <I>(x,&optional-divisor)</I>
<DD><A NAME="IDX289"></A>
round the floating point X to the nearest integer. The argument
must be a regular system float, not a bigfloat. The ? beginning the name
indicates this is normal common lisp function.
</P>
<PRE>
(C3) ?round(-2.8);
(D3) - 3
</PRE>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>?TRUNCATE</B> <I>(x,&optional-divisor)</I>
<DD><A NAME="IDX290"></A>
truncate the floating point X towards 0, to become an integer. The argument
must be a regular system float, not a bigfloat. The ? beginning the name
indicates this is normal common lisp function.
</DL>
<PRE>
(C4) ?truncate(-2.8);
(D4) - 2
(C5) ?truncate(2.4);
(D5) 2
(C6) ?truncate(2.8);
(D6) 2
</PRE>
<P>
<DL>
<DT><U>Variable:</U> <B>ZUNDERFLOW</B>
<DD><A NAME="IDX291"></A>
default: [TRUE] - if FALSE, an error will be signaled if
floating point underflow occurs.
Currently in NIL Macsyma, all floating-point underflow, floating-point
overflow, and division-by-zero errors signal errors, and this switch
is ignored.
</P>
</DL>
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