Programming in Anime: Follow-up

Posted in Multiply on Jan 27, ’09 7:18 PM

Hello…

As the title says it, this is a follow-up to this entry I recently posted.

Let’s bring up that picture and code again:


ERRATUM: line 120 should be while s<1 or s>=2 (line now corrected)

100   /* func sample, coast creation */
110   float s
120   while s<1 or s>=2
130        input “ratio 1 to 2”; s
140   endwhile
150   s = (s-1)/10+1
160   screen 1,2,1,1
170   s=sqr(s*s-1)
180   float x0=100, x1=412, y0=0, y1=0
190   fractal(x0,x1,y0,y1,1)
200   line(100, 50, 412, 50, 255, 65535)
210   end
220   func fractal(x0;float,x1;float,y0;float,y1;float,sp;int)
230        float l, r, x2, y2
240        l=sqr[(x1-x0)*(x1-x0)+(y1-y0)*(y1-y0)]
250        if l<2 or sp>=9 then (
260               line(x0,y0/3+50,x1,y1/3+50,255,65535) ; return()
270        )
280        r=rnd()+rnd()+rnd()-2
290        x2=(x0+x1)/2+s*(y1-y0)*r
300        y2=(y0+y1)/2+s(x0+x1)*r
310        sp = sp + 1
320        fractal(x0,x2,y0,y2,sp)
330        fractal(x2,x1,y2,y1,sp)
340   endfunc

Last time, I discussed this, but only superficially. Today, we’ll delve deeper into the code.

Let us dissect the code as we go along.

The comment block at line 100 says that this is a sample coast creation function. I don’t really know what that means, but delving in through the code, we see the line

110   float s
120   while s<1 or s>2
130        input “ratio 1 to 2”; s
140   endwhile

Since the language used was BASIC, I think this is how you say that a person’s input from the keyboard be saved to a variable, in this case s. For those familiar with C, this is its equivalent (if the assumption holds):

float s=0;           /*Initial condition for the program to enter the loop*/
while (s<1 || s>2) {
printf(“ratio 1 to 2”);
scanf(“%f”, &s);
}

In Java,

BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
float s = 0;             /*Initial value of s; in Java, all declared variables should have an initial value (even objects)*/
while (s<1 || s>2) {
System.out.print(“ratio 1 to 2”);
try { s = in.readLine(); } catch (IOException e) {}    /*readline throws IOException, so this is required*/
}

The codes above assume that the program is being run in a command-line environment. If a Graphical User Interface (GUI) is desired, the Java code segment transforms into:

float s=0;
while (s<1 || s>2) {
s = (Double)JOptionPane.showInputDialog(null, “ratio 1 to 2”);
}

This brings up a pop-up window. Of course, you can design your own by making the code inherit JFrame, but then this will take longer segments of code.

In C, GUI is hard to implement, so I will pass writing a code segment.

That aside, another erratum: it is evident that the program only accepts input from the domain [1,2), excluding 2. This implies that input can range from 10000… to 1.99999…, or it will repeat asking you for a valid value until you enter

Then the following line appears:

150   s = (s-1)/10+1

Running this as a C program where s starts with 1 and ends with 1.999999, the output will range from 1.000000 to 1.1000000.

Here is the C code:

#include <stdio.h>

int main (void) {
float s=1;
while (s>=1&&s<2) {
printf (“s=%f,exp=%f\n”, s, (s-1)/10+1);
s=s+0.000001;
}
return 0;
}

Then follows this code segment:
160   screen 1,2,1,1

I really don’t know what this means. (If someone knows, let me know.)

Then,

170   s=sqr(s*s-1)

Which takes the square root of s (range 1.000000 to 1.100000 based on our C program earlier). With this, the value of s will range from 0 to 0.458258. Then follows the declarations

180   float x0=100, x1=412, y0=0, y1=0

and the functions

190   fractal(x0,x1,y0,y1,1)
200   line(100, 50, 412, 50, 255, 65535)

, then the flag indicating the end of the main function

210   end

Then follows the declaration of function fractal:

220   func fractal(x0;float,x1;float,y0;float,y1;float,sp;int)

This says that function fractal takes the following as arguments:
float arguments: x0, x1, y0, y1, sp
integer

Based on the following previous lines

180   float x0=100, x1=412, y0=0, y1=0
190   fractal(x0,x1,y0,y1,1)

The value of s is not used in this function. (It also appears to be not used at all. But then it is utilized at line 290 and 300, as we see later on.)

Then we again find the following declaration:

230        float l, r, x2, y2

Then the following:

240        l=sqr[(x1-x0)*(x1-x0)+(y1-y0)*(y1-y0)]

As we can see, this is the distance formula. Then we find the following if statement block:

250        if l<2 or sp>=9 then (
260               line(x0,y0/3+50,x1,y1/3+50,255,65535) ; return()
270        )

From the following previous lines

180   float x0=100, x1=412, y0=0, y1=0
190   fractal(x0,x1,y0,y1,1)
220   func fractal(x0;float,x1;float,y0;float,y1;float,sp;int)
240        l=sqr[(x1-x0)*(x1-x0)+(y1-y0)*(y1-y0)]

l=312. (line 180 is the initial value when the function is first called)

Then sp=1.

As we can see, line 250 is not satisfied, so control goes to the following:

280        r=rnd()+rnd()+rnd()-2

If I am not mistaken, rnd() returns a random number. Searching the rnd() function via Google, the site http://msdn.microsoft.com/en-us/library/e566zd96(VS.85).aspx states:

The Rnd function returns a value less than 1 but greater than or equal to 0. The value of number determines how Rnd generates a random number:

If number is Rnd generates
Less than zero The same number every time, using number as the seed.
Greater than zero The next random number in the sequence.
Equal to zero The most recently generated number.
Not supplied The next random number in the sequence.

For any given initial seed, the same number sequence is generated because each successive call to the Rnd function uses the previous number as a seed for the next number in the sequence.

Taking the case where rnd() returns 0.999999 (the highest possible number returned at six decimal places), the expression evaluates to:

r = 0.999999+0.999999+0.999999-2
= 0.999997

Then comes the following segment:

290        x2=(x0+x1)/2+s*(y1-y0)*r
300        y2=(y0+y1)/2+s*(x0-x1)*r

ERRATUM: lines 290 and 300 is NOT the midpoint formula, and in line 300, s*(x0-x1), not s(x0+x1). From the previous lines

180   float x0=100, x1=412, y0=0, y1=0
220   func fractal(x0;float,x1;float,y0;float,y1;float,sp;int)

and taking s as 1.100000 and s at 0.999997 (the highest possible value at 6 places we have established later on),

x2=256.000000
y2=-343.198970

Then it increments sp by 1, as evident in the following line:

310        sp = sp + 1

Then

320        fractal(x0,x2,y0,y2,sp)

This line calls recursively function fractal, which then executes the function again until the if statement block becomes true, which then calls

260               line(x0,y0/3+50,x1,y1/3+50,255,65535) ; return()

After the function returns, it then executes the following line:

330        fractal(x2,x1,y2,y1,sp)

which does again what is stated above, albeit different values in its arguments. Then the following ends the function:

340   endfunc

The program is then assumed to be terminated, since there are no other instructions that follow.

I have converted the code above into a C program:

#include <stdio.h>
#include <math.h>
#include <time.h>

void fractal (float x0, float x1, float y0, float y1, float sp, double s);
void line (float x0, float x1, float y0, float y1, int char_largest_value, int int_largest_value);

int main (void) {
double s=0;
float x0=100, x1=412, y0=0, y1=0;

while (s<1 || s>2){
printf (“\nRatio 1 to 2: “);
scanf (“%lf”, &s);
}
s=(s-1)/10+1;
s=sqrt(s*s-1);
fractal(x0,x1,y0,y1,1,s);
line(100,50,412,50,255,65535);
return 0;
}

void fractal (float x0, float x1, float y0, float y1, float sp, double s) {
float l, r, x2, y2;
l=sqrt((x1-x0)*(x1-x0)+(y1-y0)*(y1-y0));
if (l<2 || sp>=9) {
line(x0,y0/3+50,x1,y1/3+50,255,65535);
return;
}
srand(time(NULL));
r=rand()+rand()+rand()-2;
x2=(x0+x1)/2+s*(y1-y0)*r;
y2=(y0+y1)/2+s*(x0+x1)*r;
sp = sp + 1;
fractal(x0,x2,y0,y2,sp,s);
fractal(x2,x1,y2,y1,sp,s);
}

void line (float x0, float x1, float y0, float y1, int char_largest_value, int int_largest_value) {
printf (“\nx0=%f, x1=%f, y0=%f, y1=%f, char_largest_value=%d, int_largest_value=%d”, x0,x1,y0,y1,char_largest_value,int_largest_value);
}

, compiled and ran it. The code has the following characteristics:

160   screen 1,2,1,1

was omitted since it is not known what this does. Function line is assumed to just print the values of its parameters. s was added as a sixth parameter to

190   fractal(x0,x1,y0,y1,1)

since s should be passed to function fractal.

srand(time(NULL));

was added in order to make the rand() function generate more numbers more randomly.

Running the compiled code with 1 as an argument, the resulting input is:

x0=100.000000, x1=50.000000, y0=101.218750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=101.218750, x1=50.000000, y0=102.437500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=102.437500, x1=50.000000, y0=103.656250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=103.656250, x1=50.000000, y0=104.875000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=104.875000, x1=50.000000, y0=106.093750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=106.093750, x1=50.000000, y0=107.312500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=107.312500, x1=50.000000, y0=108.531250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=108.531250, x1=50.000000, y0=109.750000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=109.750000, x1=50.000000, y0=110.968750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=110.968750, x1=50.000000, y0=112.187500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=112.187500, x1=50.000000, y0=113.406250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=113.406250, x1=50.000000, y0=114.625000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=114.625000, x1=50.000000, y0=115.843750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=115.843750, x1=50.000000, y0=117.062500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=117.062500, x1=50.000000, y0=118.281250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=118.281250, x1=50.000000, y0=119.500000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=119.500000, x1=50.000000, y0=120.718750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=120.718750, x1=50.000000, y0=121.937500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=121.937500, x1=50.000000, y0=123.156250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=123.156250, x1=50.000000, y0=124.375000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=124.375000, x1=50.000000, y0=125.593750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=125.593750, x1=50.000000, y0=126.812500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=126.812500, x1=50.000000, y0=128.031250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=128.031250, x1=50.000000, y0=129.250000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=129.250000, x1=50.000000, y0=130.468750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=130.468750, x1=50.000000, y0=131.687500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=131.687500, x1=50.000000, y0=132.906250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=132.906250, x1=50.000000, y0=134.125000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=134.125000, x1=50.000000, y0=135.343750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=135.343750, x1=50.000000, y0=136.562500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=136.562500, x1=50.000000, y0=137.781250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=137.781250, x1=50.000000, y0=139.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=139.000000, x1=50.000000, y0=140.218750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=140.218750, x1=50.000000, y0=141.437500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=141.437500, x1=50.000000, y0=142.656250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=142.656250, x1=50.000000, y0=143.875000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=143.875000, x1=50.000000, y0=145.093750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=145.093750, x1=50.000000, y0=146.312500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=146.312500, x1=50.000000, y0=147.531250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=147.531250, x1=50.000000, y0=148.750000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=148.750000, x1=50.000000, y0=149.968750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=149.968750, x1=50.000000, y0=151.187500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=151.187500, x1=50.000000, y0=152.406250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=152.406250, x1=50.000000, y0=153.625000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=153.625000, x1=50.000000, y0=154.843750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=154.843750, x1=50.000000, y0=156.062500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=156.062500, x1=50.000000, y0=157.281250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=157.281250, x1=50.000000, y0=158.500000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=158.500000, x1=50.000000, y0=159.718750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=159.718750, x1=50.000000, y0=160.937500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=160.937500, x1=50.000000, y0=162.156250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=162.156250, x1=50.000000, y0=163.375000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=163.375000, x1=50.000000, y0=164.593750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=164.593750, x1=50.000000, y0=165.812500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=165.812500, x1=50.000000, y0=167.031250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=167.031250, x1=50.000000, y0=168.250000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=168.250000, x1=50.000000, y0=169.468750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=169.468750, x1=50.000000, y0=170.687500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=170.687500, x1=50.000000, y0=171.906250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=171.906250, x1=50.000000, y0=173.125000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=173.125000, x1=50.000000, y0=174.343750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=174.343750, x1=50.000000, y0=175.562500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=175.562500, x1=50.000000, y0=176.781250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=176.781250, x1=50.000000, y0=178.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=178.000000, x1=50.000000, y0=179.218750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=179.218750, x1=50.000000, y0=180.437500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=180.437500, x1=50.000000, y0=181.656250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=181.656250, x1=50.000000, y0=182.875000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=182.875000, x1=50.000000, y0=184.093750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=184.093750, x1=50.000000, y0=185.312500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=185.312500, x1=50.000000, y0=186.531250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=186.531250, x1=50.000000, y0=187.750000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=187.750000, x1=50.000000, y0=188.968750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=188.968750, x1=50.000000, y0=190.187500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=190.187500, x1=50.000000, y0=191.406250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=191.406250, x1=50.000000, y0=192.625000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=192.625000, x1=50.000000, y0=193.843750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=193.843750, x1=50.000000, y0=195.062500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=195.062500, x1=50.000000, y0=196.281250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=196.281250, x1=50.000000, y0=197.500000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=197.500000, x1=50.000000, y0=198.718750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=198.718750, x1=50.000000, y0=199.937500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=199.937500, x1=50.000000, y0=201.156250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=201.156250, x1=50.000000, y0=202.375000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=202.375000, x1=50.000000, y0=203.593750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=203.593750, x1=50.000000, y0=204.812500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=204.812500, x1=50.000000, y0=206.031250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=206.031250, x1=50.000000, y0=207.250000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=207.250000, x1=50.000000, y0=208.468750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=208.468750, x1=50.000000, y0=209.687500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=209.687500, x1=50.000000, y0=210.906250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=210.906250, x1=50.000000, y0=212.125000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=212.125000, x1=50.000000, y0=213.343750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=213.343750, x1=50.000000, y0=214.562500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=214.562500, x1=50.000000, y0=215.781250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=215.781250, x1=50.000000, y0=217.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=217.000000, x1=50.000000, y0=218.218750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=218.218750, x1=50.000000, y0=219.437500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=219.437500, x1=50.000000, y0=220.656250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=220.656250, x1=50.000000, y0=221.875000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=221.875000, x1=50.000000, y0=223.093750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=223.093750, x1=50.000000, y0=224.312500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=224.312500, x1=50.000000, y0=225.531250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=225.531250, x1=50.000000, y0=226.750000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=226.750000, x1=50.000000, y0=227.968750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=227.968750, x1=50.000000, y0=229.187500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=229.187500, x1=50.000000, y0=230.406250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=230.406250, x1=50.000000, y0=231.625000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=231.625000, x1=50.000000, y0=232.843750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=232.843750, x1=50.000000, y0=234.062500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=234.062500, x1=50.000000, y0=235.281250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=235.281250, x1=50.000000, y0=236.500000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=236.500000, x1=50.000000, y0=237.718750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=237.718750, x1=50.000000, y0=238.937500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=238.937500, x1=50.000000, y0=240.156250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=240.156250, x1=50.000000, y0=241.375000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=241.375000, x1=50.000000, y0=242.593750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=242.593750, x1=50.000000, y0=243.812500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=243.812500, x1=50.000000, y0=245.031250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=245.031250, x1=50.000000, y0=246.250000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=246.250000, x1=50.000000, y0=247.468750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=247.468750, x1=50.000000, y0=248.687500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=248.687500, x1=50.000000, y0=249.906250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=249.906250, x1=50.000000, y0=251.125000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=251.125000, x1=50.000000, y0=252.343750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=252.343750, x1=50.000000, y0=253.562500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=253.562500, x1=50.000000, y0=254.781250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=254.781250, x1=50.000000, y0=256.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=256.000000, x1=50.000000, y0=257.218750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=257.218750, x1=50.000000, y0=258.437500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=258.437500, x1=50.000000, y0=259.656250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=259.656250, x1=50.000000, y0=260.875000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=260.875000, x1=50.000000, y0=262.093750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=262.093750, x1=50.000000, y0=263.312500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=263.312500, x1=50.000000, y0=264.531250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=264.531250, x1=50.000000, y0=265.750000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=265.750000, x1=50.000000, y0=266.968750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=266.968750, x1=50.000000, y0=268.187500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=268.187500, x1=50.000000, y0=269.406250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=269.406250, x1=50.000000, y0=270.625000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=270.625000, x1=50.000000, y0=271.843750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=271.843750, x1=50.000000, y0=273.062500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=273.062500, x1=50.000000, y0=274.281250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=274.281250, x1=50.000000, y0=275.500000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=275.500000, x1=50.000000, y0=276.718750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=276.718750, x1=50.000000, y0=277.937500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=277.937500, x1=50.000000, y0=279.156250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=279.156250, x1=50.000000, y0=280.375000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=280.375000, x1=50.000000, y0=281.593750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=281.593750, x1=50.000000, y0=282.812500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=282.812500, x1=50.000000, y0=284.031250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=284.031250, x1=50.000000, y0=285.250000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=285.250000, x1=50.000000, y0=286.468750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=286.468750, x1=50.000000, y0=287.687500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=287.687500, x1=50.000000, y0=288.906250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=288.906250, x1=50.000000, y0=290.125000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=290.125000, x1=50.000000, y0=291.343750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=291.343750, x1=50.000000, y0=292.562500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=292.562500, x1=50.000000, y0=293.781250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=293.781250, x1=50.000000, y0=295.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=295.000000, x1=50.000000, y0=296.218750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=296.218750, x1=50.000000, y0=297.437500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=297.437500, x1=50.000000, y0=298.656250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=298.656250, x1=50.000000, y0=299.875000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=299.875000, x1=50.000000, y0=301.093750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=301.093750, x1=50.000000, y0=302.312500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=302.312500, x1=50.000000, y0=303.531250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=303.531250, x1=50.000000, y0=304.750000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=304.750000, x1=50.000000, y0=305.968750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=305.968750, x1=50.000000, y0=307.187500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=307.187500, x1=50.000000, y0=308.406250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=308.406250, x1=50.000000, y0=309.625000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=309.625000, x1=50.000000, y0=310.843750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=310.843750, x1=50.000000, y0=312.062500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=312.062500, x1=50.000000, y0=313.281250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=313.281250, x1=50.000000, y0=314.500000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=314.500000, x1=50.000000, y0=315.718750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=315.718750, x1=50.000000, y0=316.937500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=316.937500, x1=50.000000, y0=318.156250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=318.156250, x1=50.000000, y0=319.375000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=319.375000, x1=50.000000, y0=320.593750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=320.593750, x1=50.000000, y0=321.812500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=321.812500, x1=50.000000, y0=323.031250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=323.031250, x1=50.000000, y0=324.250000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=324.250000, x1=50.000000, y0=325.468750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=325.468750, x1=50.000000, y0=326.687500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=326.687500, x1=50.000000, y0=327.906250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=327.906250, x1=50.000000, y0=329.125000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=329.125000, x1=50.000000, y0=330.343750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=330.343750, x1=50.000000, y0=331.562500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=331.562500, x1=50.000000, y0=332.781250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=332.781250, x1=50.000000, y0=334.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=334.000000, x1=50.000000, y0=335.218750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=335.218750, x1=50.000000, y0=336.437500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=336.437500, x1=50.000000, y0=337.656250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=337.656250, x1=50.000000, y0=338.875000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=338.875000, x1=50.000000, y0=340.093750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=340.093750, x1=50.000000, y0=341.312500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=341.312500, x1=50.000000, y0=342.531250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=342.531250, x1=50.000000, y0=343.750000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=343.750000, x1=50.000000, y0=344.968750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=344.968750, x1=50.000000, y0=346.187500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=346.187500, x1=50.000000, y0=347.406250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=347.406250, x1=50.000000, y0=348.625000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=348.625000, x1=50.000000, y0=349.843750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=349.843750, x1=50.000000, y0=351.062500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=351.062500, x1=50.000000, y0=352.281250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=352.281250, x1=50.000000, y0=353.500000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=353.500000, x1=50.000000, y0=354.718750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=354.718750, x1=50.000000, y0=355.937500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=355.937500, x1=50.000000, y0=357.156250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=357.156250, x1=50.000000, y0=358.375000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=358.375000, x1=50.000000, y0=359.593750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=359.593750, x1=50.000000, y0=360.812500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=360.812500, x1=50.000000, y0=362.031250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=362.031250, x1=50.000000, y0=363.250000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=363.250000, x1=50.000000, y0=364.468750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=364.468750, x1=50.000000, y0=365.687500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=365.687500, x1=50.000000, y0=366.906250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=366.906250, x1=50.000000, y0=368.125000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=368.125000, x1=50.000000, y0=369.343750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=369.343750, x1=50.000000, y0=370.562500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=370.562500, x1=50.000000, y0=371.781250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=371.781250, x1=50.000000, y0=373.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=373.000000, x1=50.000000, y0=374.218750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=374.218750, x1=50.000000, y0=375.437500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=375.437500, x1=50.000000, y0=376.656250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=376.656250, x1=50.000000, y0=377.875000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=377.875000, x1=50.000000, y0=379.093750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=379.093750, x1=50.000000, y0=380.312500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=380.312500, x1=50.000000, y0=381.531250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=381.531250, x1=50.000000, y0=382.750000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=382.750000, x1=50.000000, y0=383.968750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=383.968750, x1=50.000000, y0=385.187500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=385.187500, x1=50.000000, y0=386.406250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=386.406250, x1=50.000000, y0=387.625000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=387.625000, x1=50.000000, y0=388.843750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=388.843750, x1=50.000000, y0=390.062500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=390.062500, x1=50.000000, y0=391.281250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=391.281250, x1=50.000000, y0=392.500000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=392.500000, x1=50.000000, y0=393.718750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=393.718750, x1=50.000000, y0=394.937500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=394.937500, x1=50.000000, y0=396.156250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=396.156250, x1=50.000000, y0=397.375000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=397.375000, x1=50.000000, y0=398.593750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=398.593750, x1=50.000000, y0=399.812500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=399.812500, x1=50.000000, y0=401.031250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=401.031250, x1=50.000000, y0=402.250000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=402.250000, x1=50.000000, y0=403.468750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=403.468750, x1=50.000000, y0=404.687500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=404.687500, x1=50.000000, y0=405.906250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=405.906250, x1=50.000000, y0=407.125000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=407.125000, x1=50.000000, y0=408.343750, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=408.343750, x1=50.000000, y0=409.562500, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=409.562500, x1=50.000000, y0=410.781250, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=410.781250, x1=50.000000, y0=412.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=100.000000, x1=50.000000, y0=412.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535

With 1.999999 as an argument (the largest value at six decimal places), the following were the output:

x0=100.000000, x1=50.000000, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=nan, y1=inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=inf, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
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x0=nan, x1=-inf, y0=-inf, y1=-inf, char_largest_value=255, int_largest_value=65535
x0=-inf, x1=-inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=-inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=-inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=-inf, y1=-inf, char_largest_value=255, int_largest_value=65535
x0=-inf, x1=-inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=-inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=-inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=-1109745987560455274496.000000, y1=-155654289986452039720960524288.000000, char_largest_value=255, int_largest_value=65535
x0=-1109745987560455274496.000000, x1=-155654289986452039720960524288.000000, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=nan, y1=inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=inf, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=inf, y1=-436561587360523581038476132352.000000, char_largest_value=255, int_largest_value=65535
x0=inf, x1=-436561587360523581038476132352.000000, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=nan, y1=inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=inf, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=inf, y1=inf, char_largest_value=255, int_largest_value=65535
x0=inf, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=inf, char_largest_value=255, int_largest_value=65535
x0=nan, x1=inf, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=nan, y1=nan, char_largest_value=255, int_largest_value=65535
x0=nan, x1=nan, y0=412.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535
x0=100.000000, x1=50.000000, y0=412.000000, y1=50.000000, char_largest_value=255, int_largest_value=65535

Legend:

nan – not a number. This means the output was not a valid number, something like the square root of -1.

inf – infinity. Meaning the number is too large.

-inf – negative infinity. The number is very small.

What does these numbers really mean?

I’ll post again later. 🙂

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