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From: Keith McKay <mckaymeister@gmail.com>
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Subject: Arithmetic Overflow error in MetaFun
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Colleagues

I'm having problems with an Arithmetic Overflow error when calculating 
the x and y values for functions of the form:

y = ax^4 + bx^3 + cx^2 + dx + e

to which I then add a bit of randomness and other embellishments. I have 
had a look in the Metafun and Metafont manuals but nothing jumps out at 
me. In the minimum working example below, this Arithmetic Overflow 
occurs when xord =13.5 but I can get the calculation to work if I 
separate out the equation and then add together, since it seems to be 
failing on the pow(xord,4) instruction. Is there a switch in MetaFont 
that should be set or a better way of getting round this Arithmetic 
Overflow error?

Thanks

Best Wishes

Keith McKay

%%%%%%%%%%%%%MWE%%%%%%%%%%%

\setuppapersize [A4,landscape]

\starttext

\startMPpage

StartPage;

width := PaperWidth ; height := PaperHeight ; unit := cm ;

path p;

p := unitsquare scaled .1cm ;

path pat;

pat := (0.0*cm,19.935*cm);

for xord = 0 step 0.1 until 25:

show xord;

%%%%%%%%fails at xord = 13.5%%%%%%%%%

yord := ((-0.000268117) * pow(xord,4)) +(0.0136949 * pow(xord, 3)) + 
((-0.16608) * sqr(xord)) + ((-0.771743) * xord) + 19.935;

%%%%%comment out above and uncomment below and it works%%%%

% yord1 := (-0.000268117) * sqr(xord);

% yord1a := yord1 * sqr(xord);

% yord2 := (0.0136949 * pow(xord, 3));

% yord3 := ((-0.16608) * sqr(xord));

% yord4 := ((-0.771743) * xord);

% yord := yord1 + yord1a + yord2 + yord3 + yord4 + 19.935;

xrand := (uniformdeviate(1) - 0.5)*2;

yrand := uniformdeviate(1) - 0.5;

xcoord := xord + xrand;

ycoord := yord + yrand;

if odd xord:

pat := pat ... (xcoord*cm, ycoord*cm);

else:

pat := pat --- (xcoord*cm, ycoord*cm);

fill p shifted (xcoord*cm, ycoord*cm) withcolor 
(uniformdeviate(1),uniformdeviate(1),uniformdeviate(1)) ;

fi;

draw pat withpen pencircle scaled (uniformdeviate(0.75)*mm) withcolor 
(uniformdeviate(1),uniformdeviate(1),uniformdeviate(1)); 
%withtransparency (1, .5);

drawdot (xcoord*cm, ycoord*cm) withpen pencircle scaled 
(uniformdeviate(2.5)*mm) withcolor 
(uniformdeviate(1),uniformdeviate(1),uniformdeviate(1));

endfor;

StopPage;

\stopMPpage

\stoptext


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<html>
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    <meta http-equiv="content-type" content="text/html; charset=UTF-8">
  </head>
  <body>
    <p>Colleagues</p>
    <p>I'm having problems with an Arithmetic Overflow error when calculating the x and y values for functions of the form:</p>
    <p>y = ax^4 + bx^3 + cx^2 + dx + e</p>
    <p>to which I then add a bit of randomness and other embellishments. I have had a look in the Metafun and Metafont manuals but nothing jumps out at me. In the minimum working example below, this Arithmetic Overflow occurs when xord =13.5 but I can get the calculation to work if I separate out the equation and then add together, since it seems to be failing on the pow(xord,4) instruction. Is there a switch in MetaFont that should be set or a better way of getting round this Arithmetic Overflow error?</p>
    <p>Thanks</p>
    <p>Best Wishes</p>
    <p>Keith McKay</p>
    <p>%%%%%%%%%%%%%MWE%%%%%%%%%%%
</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">\setuppapersize [A4,landscape]</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">\starttext</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">\startMPpage</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">StartPage;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">width := PaperWidth ; height := PaperHeight ; unit := cm ;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">path p;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">p := unitsquare scaled .1cm ;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">path pat;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">pat := (0.0*cm,19.935*cm);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">for xord = 0 step 0.1 until 25:</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	show xord;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">%%%%%%%%fails at xord = 13.5%%%%%%%%%
</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	yord := ((-0.000268117) * pow(xord,4)) +(0.0136949 * pow(xord, 3)) + ((-0.16608) * sqr(xord)) + ((-0.771743) * xord) + 19.935;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">%%%%%comment out above and uncomment below and it works%%%%
</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">%	yord1 := (-0.000268117) * sqr(xord);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">%	yord1a := yord1 * sqr(xord);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">%	yord2 := (0.0136949 * pow(xord, 3));</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">%	yord3 := ((-0.16608) * sqr(xord));</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">%	yord4 := ((-0.771743) * xord);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">%	yord := yord1 + yord1a + yord2 + yord3 + yord4 + 19.935;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	xrand := (uniformdeviate(1) - 0.5)*2;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	yrand := uniformdeviate(1) - 0.5;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	xcoord := xord + xrand;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	ycoord := yord + yrand;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	if odd xord:</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">		pat := pat ... (xcoord*cm, ycoord*cm);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	else:</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">		pat := pat --- (xcoord*cm, ycoord*cm);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">		fill p shifted (xcoord*cm, ycoord*cm) withcolor (uniformdeviate(1),uniformdeviate(1),uniformdeviate(1)) ;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	fi;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	draw pat withpen pencircle scaled (uniformdeviate(0.75)*mm) withcolor (uniformdeviate(1),uniformdeviate(1),uniformdeviate(1)); %withtransparency (1, .5);</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">	drawdot (xcoord*cm, ycoord*cm) withpen pencircle scaled (uniformdeviate(2.5)*mm) withcolor (uniformdeviate(1),uniformdeviate(1),uniformdeviate(1));</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">endfor;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">StopPage;</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">\stopMPpage</p>
    <p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">\stoptext</p>
    <p><style type="text/css">
p, li { white-space: pre-wrap; }</style></p>
  </body>
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