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<title>GMTMATH</title>
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<body bgcolor="#ffffff">
<h1 align=center>GMTMATH</h1>
<a href="#NAME">NAME</a><br>
<a href="#SYNOPSIS">SYNOPSIS</a><br>
<a href="#DESCRIPTION">DESCRIPTION</a><br>
<a href="#OPTIONS">OPTIONS</a><br>
<a href="#ASCII FORMAT PRECISION">ASCII FORMAT PRECISION</a><br>
<a href="#NOTES ON OPERATORS">NOTES ON OPERATORS</a><br>
<a href="#EXAMPLES">EXAMPLES</a><br>
<a href="#REFERENCES">REFERENCES</a><br>
<a href="#SEE ALSO">SEE ALSO</a><br>
<hr>
<a name="NAME"></a>
<h2>NAME</h2>
<p style="margin-left:11%; margin-top: 1em">gmtmath −
Reverse Polish Notation calculator for data tables</p>
<a name="SYNOPSIS"></a>
<h2>SYNOPSIS</h2>
<p style="margin-left:11%; margin-top: 1em"><b>gmtmath</b>
[ <b>−A</b><i>t_f(t).d</i> ] [
<b>−C</b><i>cols</i> ] [ <b>−F</b><i>cols</i> ]
[ <b>−H</b>[<b>i</b>][<i>nrec</i>] ] [ <b>−I</b>
] [ <b>−N</b><i>n_col</i>/<i>t_col</i> ] [
<b>−Q</b> ] [ <b>−S</b>[<b>f</b>|<b>l</b>] ] [
<b>−T</b><i>t_min</i>/<i>t_max</i>/<i>t_inc</i>[<b>+</b>]|<i>tfile</i>
] [ <b>−V</b> ] [
<b>−b</b>[<b>i</b>|<b>o</b>][<b>s</b>|<b>S</b>|<b>d</b>|<b>D</b>[<i>ncol</i>]|<b>c</b>[<i>var1</i><b>/</b><i>...</i>]]
] [ <b>−f</b>[<b>i</b>|<b>o</b>]<i>colinfo</i> ] [
<b>−m</b>[<b>i</b>|<b>o</b>][<i>flag</i>] ]
<i>operand</i> [ <i>operand</i> ] <b>OPERATOR</b> [
<i>operand</i> ] <b>OPERATOR</b> ... <b>=</b> [
<i>outfile</i> ]</p>
<a name="DESCRIPTION"></a>
<h2>DESCRIPTION</h2>
<p style="margin-left:11%; margin-top: 1em"><b>gmtmath</b>
will perform operations like add, subtract, multiply, and
divide on one or more table data files or constants using
Reverse Polish Notation (RPN) syntax (e.g., Hewlett-Packard
calculator-style). Arbitrarily complicated expressions may
therefore be evaluated; the final result is written to an
output file [or standard output]. When two data tables are
on the stack, each element in file A is modified by the
corresponding element in file B. However, some operators
only require one operand (see below). If no data tables are
used in the expression then options <b>−T</b>,
<b>−N</b> can be set (and optionally <b>−b</b>
to indicate the data domain). If STDIN is given,
<stdin> will be read and placed on the stack as if a
file with that content had been given on the command line.
By default, all columns except the "time" column
are operated on, but this can be changed (see
<b>−C</b>). <i><br>
operand</i></p>
<p style="margin-left:22%;">If <i>operand</i> can be opened
as a file it will be read as an ASCII (or binary, see
<b>−bi</b>) table data file. If not a file, it is
interpreted as a numerical constant or a special symbol (see
below). The special argument STDIN means that <i>stdin</i>
will be read and placed on the stack; STDIN can appear more
than once if necessary.</p>
<p style="margin-left:11%;"><i>outfile</i></p>
<p style="margin-left:22%;">The name of a table data file
that will hold the final result. If not given then the
output is sent to stdout.</p>
<p style="margin-left:11%;"><b>OPERATORS</b></p>
<p style="margin-left:22%;">Choose among the following 131
operators. "args" are the number of input and
output arguments.</p>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top">Operator</p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">args</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Returns</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ABS</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">abs (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ACOS</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">acos (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ACOSH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">acosh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ACOT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">acot (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ACSC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">acsc (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ADD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A + B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>AND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">NaN if A and B == NaN, B if A == NaN, else
A.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ASEC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">asec (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ASIN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">asin (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ASINH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">asinh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ATAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">atan (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ATAN2</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">atan2 (A, B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ATANH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">atanh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>BEI</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">bei (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>BER</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">ber (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CEIL</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">ceil (A) (smallest integer >= A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CHICRIT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Critical value for
chi-squared-distribution, with alpha = A and n = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CHIDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">chi-squared-distribution P(chi2,n), with
chi2 = A and n = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COL</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Places column A on the stack.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CORRCOEFF</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Correlation coefficient r(A, B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COS</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cos (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COSD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cos (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COSH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cosh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cot (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COTD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cot (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CPOISS</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Cumulative Poisson distribution
F(x,lambda), with x = A and lambda = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CSC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">csc (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CSCD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">csc (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>D2DT2</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">d^2(A)/dt^2 2nd derivative.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>D2R</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Converts Degrees to Radians.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>DDT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">d(A)/dt Central 1st derivative.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>DILOG</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">dilog (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>DIV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A / B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>DUP</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 2</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Places duplicate of A on the stack.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>EQ</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A == B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ERF</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Error function erf (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ERFC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Complementary Error function erfc (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ERFINV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Inverse error function of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>EXCH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 2</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Exchanges A and B on the stack.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>EXP</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">exp (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FACT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A! (A factorial).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FCRIT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Critical value for F-distribution, with
alpha = A, n1 = B, and n2 = C.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">F-distribution Q(F,n1,n2), with F = A, n1 =
B, and n2 = C.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FLIPUD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Reverse order of each column.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FLOOR</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">floor (A) (greatest integer <= A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FMOD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A % B (remainder after truncated
division).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>GE</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A >= B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>GT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A > B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>HYPOT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">hypot (A, B) = sqrt (A*A + B*B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>I0</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (1st kind,
order 0).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>I1</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (1st kind,
order 1).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>IN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (1st kind,
order B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>INRANGE</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if B <= A <= C, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>INT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Numerically integrate A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>INV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 / A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ISNAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A == NaN, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>J0</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (1st kind, order
0).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>J1</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (1st kind, order
1).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>JN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (1st kind, order
B).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>K0</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Kelvin function of A (2nd kind,
order 0).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>K1</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (2nd kind,
order 1).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>KEI</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">kei (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>KER</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">ker (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>KN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (2nd kind,
order B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>KURT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Kurtosis of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LE</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A <= B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LMSSCL</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">LMS scale estimate (LMS STD) of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOG</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">log (A) (natural log).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOG10</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">log10 (A) (base 10).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOG1P</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">log (1+A) (accurate for small A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOG2</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">log2 (A) (base 2).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOWER</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">The lowest (minimum) value of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LRAND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Laplace random noise with mean A and std.
deviation B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LSQFIT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 0</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Let current table be [A | b]; return least
squares solution x = A \ b.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A < B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MAD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Median Absolute Deviation (L1 STD) of
A.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MAX</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Maximum of A and B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MEAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Mean value of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MED</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Median value of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MIN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Minimum of A and B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MOD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A mod B (remainder after floored
division).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MODE</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Mode value (Least Median of Squares) of
A.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MUL</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A * B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">NaN if A == B, else A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NEG</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">-A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NEQ</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A != B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NOT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">NaN if A == NaN, 1 if A == 0, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NRAND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Normal, random values with mean A and std.
deviation B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>OR</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">NaN if A or B == NaN, else A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PLM</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Associated Legendre polynomial P(A) degree
B order C.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PLMg</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Normalized associated Legendre polynomial
P(A) degree B order C (geophysical convention).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>POP</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 0</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Delete top element from the stack.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>POW</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A ^ B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PQUANT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">The B’th Quantile (0-100%) of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PSI</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Psi (or Digamma) of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Legendre function Pv(A) of degree v =
real(B) + imag(C).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>QV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Legendre function Qv(A) of degree v =
real(B) + imag(C).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>R2</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">R2 = A^2 + B^2.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>R2D</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Convert Radians to Degrees.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>RAND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Uniform random values between A and B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>RINT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">rint (A) (nearest integer).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ROOTS</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Treats col A as f(t) = 0 and returns its
roots.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ROTT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Rotate A by the (constant) shift B in the
t-direction.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SEC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sec (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SECD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sec (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SIGN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sign (+1 or -1) of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SIN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sin (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SINC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sinc (A) (sin (pi*A)/(pi*A)).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SIND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sin (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SINH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sinh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SKEW</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Skewness of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SQR</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A^2.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SQRT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sqrt (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>STD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Standard deviation of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>STEP</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Heaviside step function H(A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>STEPT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Heaviside step function H(t-A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SUB</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A - B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SUM</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Cumulative sum of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">tan (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TAND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">tan (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TANH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">tanh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TCRIT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Critical value for Student’s
t-distribution, with alpha = A and n = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Student’s t-distribution A(t,n), with
t = A, and n = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Chebyshev polynomial Tn(-1<A<+1) of
degree B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>UPPER</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">The highest (maximum) value of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>XOR</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">B if A == NaN, else A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>Y0</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (2nd kind, order
0).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>Y1</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (2nd kind, order
1).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>YN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (2nd kind, order
B).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ZCRIT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Critical value for the normal-distribution,
with alpha = A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ZDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Cumulative normal-distribution C(x), with x
= A.</p></td>
</table>
<p style="margin-left:11%;"><b>SYMBOLS</b></p>
<p style="margin-left:22%;">The following symbols have
special meaning:</p>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PI</b></p></td>
<td width="77%">
<p valign="top">3.1415926...</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>E</b></p></td>
<td width="77%">
<p valign="top">2.7182818...</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>EULER</b></p></td>
<td width="77%">
<p valign="top">0.5772156...</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TMIN</b></p></td>
<td width="77%">
<p valign="top">Minimum t value</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TMAX</b></p></td>
<td width="77%">
<p valign="top">Maximum t value</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TINC</b></p></td>
<td width="77%">
<p valign="top">t increment</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>N</b></p></td>
<td width="77%">
<p valign="top">The number of records</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>T</b></p></td>
<td width="77%">
<p valign="top">Table with t-coordinates</p></td>
</table>
<a name="OPTIONS"></a>
<h2>OPTIONS</h2>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−A</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Requires
<b>−N</b> and will partially initialize a table with
values from the given file containing <i>t</i> and
<i>f(t)</i> only. The <i>t</i> is placed in column
<i>t_col</i> while <i>f(t)</i> goes into column <i>n_col</i>
- 1 (see <b>−N</b>).</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−C</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Select the columns
that will be operated on until next occurrence of
<b>−C</b>. List columns separated by commas; ranges
like 1,3-5,7 are allowed. <b>−C</b> (no arguments)
resets the default action of using all columns except time
column (see <b>−N</b>). <b>−Ca</b> selects all
columns, including time column, while <b>−Cr</b>
reverses (toggles) the current choices.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−F</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Give a
comma-separated list of desired columns or ranges that
should be part of the output (0 is first column) [Default
outputs all columns].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−H</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Input file(s) has
header record(s). If used, the default number of header
records is <b><A HREF="gmtdefaults.html#N_HEADER_RECS">N_HEADER_RECS</A></b>. Use <b>−Hi</b> if
only input data should have header records [Default will
write out header records if the input data have them]. Blank
lines and lines starting with # are always skipped.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−I</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Reverses the output
row sequence from ascending time to descending
[ascending].</p> </td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−N</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Select the number
of columns and the column number that contains the
"time" variable. Columns are numbered starting at
0 [2/0].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−Q</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Quick mode for
scalar calculation. Shorthand for <b>−Ca
−N</b>1/0 <b>−T</b>0/0/1.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−S</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Only report the
first or last row of the results [Default is all rows]. This
is useful if you have computed a statistic (say the
<b>MODE</b>) and only want to report a single number instead
of numerous records with identical values. Append <b>l</b>
to get the last row and <b>f</b> to get the first row only
[Default].</p> </td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−T</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Required when no
input files are given. Sets the t-coordinates of the first
and last point and the equidistant sampling interval for the
"time" column (see <b>−N</b>). Append
<b>+</b> if you are specifying the number of equidistant
points instead. If there is no time column (only data
columns), give <b>−T</b> with no arguments; this also
implies <b>−Ca</b>. Alternatively, give the name of a
file whose first column contains the desired t-coordinates
which may be irregular.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−V</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects verbose
mode, which will send progress reports to stderr [Default
runs "silently"].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−bi</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects binary
input. Append <b>s</b> for single precision [Default is
<b>d</b> (double)]. Uppercase <b>S</b> or <b>D</b> will
force byte-swapping. Optionally, append <i>ncol</i>, the
number of columns in your binary input file if it exceeds
the columns needed by the program. Or append <b>c</b> if the
input file is netCDF. Optionally, append
<i>var1</i><b>/</b><i>var2</i><b>/</b><i>...</i> to specify
the variables to be read.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−bo</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects binary
output. Append <b>s</b> for single precision [Default is
<b>d</b> (double)]. Uppercase <b>S</b> or <b>D</b> will
force byte-swapping. Optionally, append <i>ncol</i>, the
number of desired columns in your binary output file.
[Default is same as input, but see <b>−F</b>]</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−m</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Multiple segment
file(s). Segments are separated by a special record. For
ASCII files the first character must be <i>flag</i> [Default
is ’>’]. For binary files all fields must be
NaN and <b>−b</b> must set the number of output
columns explicitly. By default the <b>−m</b> setting
applies to both input and output. Use <b>−mi</b> and
<b>−mo</b> to give separate settings to input and
output.</p> </td>
</table>
<a name="ASCII FORMAT PRECISION"></a>
<h2>ASCII FORMAT PRECISION</h2>
<p style="margin-left:11%; margin-top: 1em">The ASCII
output formats of numerical data are controlled by
parameters in your .gmtdefaults4 file. Longitude and
latitude are formatted according to
<b><A HREF="gmtdefaults.html#OUTPUT_DEGREE_FORMAT">OUTPUT_DEGREE_FORMAT</A></b>, whereas other values are
formatted according to <b><A HREF="gmtdefaults.html#D_FORMAT">D_FORMAT</A></b>. Be aware that the
format in effect can lead to loss of precision in the
output, which can lead to various problems downstream. If
you find the output is not written with enough precision,
consider switching to binary output (<b>−bo</b> if
available) or specify more decimals using the
<b><A HREF="gmtdefaults.html#D_FORMAT">D_FORMAT</A></b> setting.</p>
<a name="NOTES ON OPERATORS"></a>
<h2>NOTES ON OPERATORS</h2>
<p style="margin-left:11%; margin-top: 1em">(1) The
operators <b>PLM</b> and <b>PLMg</b> calculate the
associated Legendre polynomial of degree L and order M in x
which must satisfy -1 <= x <= +1 and 0 <= M <=
L. x, L, and M are the three arguments preceding the
operator. <b>PLM</b> is not normalized and includes the
Condon-Shortley phase (-1)^M. <b>PLMg</b> is normalized in
the way that is most commonly used in geophysics. The C-S
phase can be added by using -M as argument. <b>PLM</b> will
overflow at higher degrees, whereas <b>PLMg</b> is stable
until ultra high degrees (at least 3000).</p>
<p style="margin-left:11%; margin-top: 1em">(2) Files that
have the same names as some operators, e.g., <b>ADD</b>,
<b>SIGN</b>, <b>=</b>, etc. should be identified by
prepending the current directory (i.e., ./LOG).</p>
<p style="margin-left:11%; margin-top: 1em">(3) The stack
depth limit is hard-wired to 100.</p>
<p style="margin-left:11%; margin-top: 1em">(4) All
functions expecting a positive radius (e.g., <b>LOG</b>,
<b>KEI</b>, etc.) are passed the absolute value of their
argument.</p>
<p style="margin-left:11%; margin-top: 1em">(5) The
<b>DDT</b> and <b>D2DT2</b> functions only work on regularly
spaced data.</p>
<p style="margin-left:11%; margin-top: 1em">(6) All
derivatives are based on central finite differences, with
natural boundary conditions.</p>
<p style="margin-left:11%; margin-top: 1em">(7)
<b>ROOTS</b> must be the last operator on the stack, only
followed by <b>=</b>.</p>
<a name="EXAMPLES"></a>
<h2>EXAMPLES</h2>
<p style="margin-left:11%; margin-top: 1em">To take the
square root of the content of the second data column being
piped through <b>gmtmath</b> by process1 and pipe it through
a 3rd process, use</p>
<p style="margin-left:11%; margin-top: 1em">process1 |
<b>gmtmath</b> STDIN <b>SQRT =</b> | process3</p>
<p style="margin-left:11%; margin-top: 1em">To take log10
of the average of 2 data files, use</p>
<p style="margin-left:11%; margin-top: 1em"><b>gmtmath</b>
file1.d file2.d <b>ADD</b> 0.5 <b>MUL LOG10 =</b>
file3.d</p>
<p style="margin-left:11%; margin-top: 1em">Given the file
samples.d, which holds seafloor ages in m.y. and seafloor
depth in m, use the relation depth(in m) = 2500 + 350 * sqrt
(age) to print the depth anomalies:</p>
<p style="margin-left:11%; margin-top: 1em"><b>gmtmath</b>
samples.d <b>T SQRT</b> 350 <b>MUL</b> 2500 <b>ADD SUB =</b>
| lpr</p>
<p style="margin-left:11%; margin-top: 1em">To take the
average of columns 1 and 4-6 in the three data sets sizes.1,
sizes.2, and sizes.3, use</p>
<p style="margin-left:11%; margin-top: 1em"><b>gmtmath
−C</b>1,4-6 sizes.1 sizes.2 <b>ADD</b> sizes.3 <b>ADD
3 DIV =</b> ave.d</p>
<p style="margin-left:11%; margin-top: 1em">To take the
1-column data set ages.d and calculate the modal value and
assign it to a variable, try</p>
<p style="margin-left:11%; margin-top: 1em">set mode_age =
‘<b>gmtmath −S −T</b> ages.d <b>MODE
=</b>‘</p>
<p style="margin-left:11%; margin-top: 1em">To evaluate the
dilog(x) function for coordinates given in the file t.d:</p>
<p style="margin-left:11%; margin-top: 1em"><b>gmtmath
−T</b>t.d <b>T DILOG =</b> dilog.d</p>
<p style="margin-left:11%; margin-top: 1em">To use gmtmath
as a RPN Hewlett-Packard calculator on scalars (i.e., no
input files) and calculate arbitrary expressions, use the
<b>−Q</b> option. As an example, we will calculate the
value of Kei (((1 + 1.75)/2.2) + cos (60)) and store the
result in the shell variable z:</p>
<p style="margin-left:11%; margin-top: 1em">set z =
‘<b>gmtmath −Q</b> 1 1.75 <b>ADD</b> 2.2
<b>DIV</b> 60 <b>COSD ADD KEI =</b>‘</p>
<p style="margin-left:11%; margin-top: 1em">To use
<b>gmtmath</b> as a general least squares equation solver,
imagine that the current table is the augmented matrix [ A |
b ] and you want the least squares solution x to the matrix
equation A * x = b. The operator <b>LSQFIT</b> does this; it
is your job to populate the matrix correctly first. The
<b>−A</b> option will facilitate this. Suppose you
have a 2-column file ty.d with <i>t</i> and <i>b(t)</i> and
you would like to fit a the model y(t) = a + b*t +
c*H(t-t0), where H is the Heaviside step function for a
given t0 = 1.55. Then, you need a 4-column augmented table
loaded with t in column 0 and your observed y(t) in column
3. The calculation becomes</p>
<p style="margin-left:11%; margin-top: 1em"><b>gmtmath
−N</b>4/1 <b>−A</b>ty.d <b>-C</b>0 1 <b>ADD
−C</b>2 1.55 <b>STEPT ADD −Ca LSQFIT =</b>
solution.d</p>
<p style="margin-left:11%; margin-top: 1em">Note we use the
<b>−C</b> option to select which columns we are
working on, then make active all the columns we need (here
all of them, with <b>−Ca</b>) before calling
<b>LSQFIT</b>. The second and fourth columns (col numbers 1
and 3) are preloaded with t and y(t), respectively, the
other columns are zero. If you already have a precalculated
table with the augmented matrix [ A | b ] in a file (say
lsqsys.d), the least squares solution is simply</p>
<p style="margin-left:11%; margin-top: 1em"><b>gmtmath
−T</b> lsqsys.d <b>LSQFIT =</b> solution.d</p>
<a name="REFERENCES"></a>
<h2>REFERENCES</h2>
<p style="margin-left:11%; margin-top: 1em">Abramowitz, M.,
and I. A. Stegun, 1964, <i>Handbook of Mathematical
Functions</i>, Applied Mathematics Series, vol. 55, Dover,
New York. <br>
Holmes, S. A., and W. E. Featherstone, 2002, A unified
approach to the Clenshaw summation and the recursive
computation of very high degree and order normalised
associated Legendre functions. <i>Journal of Geodesy</i>,
76, 279-299. <br>
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P.
Flannery, 1992, <i>Numerical Recipes</i>, 2nd edition,
Cambridge Univ., New York. <br>
Spanier, J., and K. B. Oldman, 1987, <i>An Atlas of
Functions</i>, Hemisphere Publishing Corp.</p>
<a name="SEE ALSO"></a>
<h2>SEE ALSO</h2>
<p style="margin-left:11%; margin-top: 1em"><i><A HREF="GMT.html">GMT</A></i>(1),
<i><A HREF="grdmath.html">grdmath</A></i>(1)</p>
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