#N canvas 0 0 916 640 10;
#X obj 0 0 doc_demo;
#X obj 0 30 cnv 15 906 22 empty empty empty 20 12 0 14 20 -66577 0;
#X text 10 30 op name;
#X text 96 30 description;
#X text 446 30 effect on pixels;
#X text 676 30 effect on coords;
#X obj 0 70 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 70 op ignore;
#X text 96 70  A ;
#X text 446 70 no effect;
#X text 676 70 no effect;
#X obj 0 89 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 89 op put;
#X text 96 89  B ;
#X text 446 89 replace by;
#X text 676 89 replace by;
#X obj 0 108 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 108 op +;
#X text 96 108  A + B ;
#X text 446 108 brightness \,  crossfade;
#X text 676 108 move \,  morph;
#X obj 0 127 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 127 op -;
#X text 96 127  A - B ;
#X text 446 127 brightness \,  motion detection;
#X text 676 127 move \,  motion detection;
#X obj 0 146 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 146 op inv+;
#X text 96 146  B - A ;
#X text 446 146 negate then contrast;
#X text 676 146 180 degree rotate then move;
#X obj 0 165 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 165 op *;
#X text 96 165  A * B ;
#X text 446 165 contrast;
#X text 676 165 zoom out;
#X obj 0 184 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 184 op *>>8;
#X text 96 184  (A * B) >> 8 ;
#X text 446 184 contrast;
#X text 676 184 zoom out;
#X obj 0 203 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 203 op /;
#X text 96 203  A / B \,  rounded towards zero ;
#X text 446 203 contrast;
#X text 676 203 zoom in;
#X obj 0 222 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 222 op div;
#X text 96 222  A / B \,  rounded downwards ;
#X text 446 222 contrast;
#X text 676 222 zoom in;
#X obj 0 241 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 241 op inv*;
#X text 96 241  B / A \,  rounded towards zero ;
#X obj 0 260 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 260 op swapdiv;
#X text 96 260  B / A \,  rounded downwards ;
#X obj 0 279 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 279 op %;
#X text 96 279  A % B \,  modulo (goes with div) ;
#X text 446 279 --;
#X text 676 279 tile;
#X obj 0 298 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 298 op swap%;
#X text 96 298  B % A \,  modulo (goes with div) ;
#X obj 0 317 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 317 op rem;
#X text 96 317  A % B \,  remainder (goes with /) ;
#X obj 0 336 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 336 op swaprem;
#X text 96 336  B % A \,  remainder (goes with /) ;
#X obj 0 355 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 355 op gcd;
#X text 96 355 greatest common divisor;
#X obj 0 374 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 374 op lcm;
#X text 96 374 least common multiple;
#X obj 0 393 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 393 op |;
#X text 96 393  A or B \,  bitwise ;
#X text 446 393 bright munchies;
#X text 676 393 bottomright munchies;
#X obj 0 412 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 412 op ^;
#X text 96 412  A xor B \,  bitwise ;
#X text 446 412 symmetric munchies (fractal checkers);
#X text 676 412 symmetric munchies (fractal checkers);
#X obj 0 431 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 431 op &;
#X text 96 431  A and B \,  bitwise ;
#X text 446 431 dark munchies;
#X text 676 431 topleft munchies;
#X obj 0 450 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 450 op <<;
#X text 96 450  A * pow(2 \, mod(B \, 32)) \,  which is left-shifting ;
#X text 446 450 like *;
#X text 676 450 like *;
#X obj 0 469 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 469 op >>;
#X text 96 469  A / pow(2 \, mod(B \, 32)) \,  which is right-shifting ;
#X text 446 469 like / \, div;
#X text 676 469 like / \, div;
#X obj 0 488 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 488 op ||;
#X text 96 488  if A is zero then B else A ;
#X obj 0 507 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 507 op &&;
#X text 96 507  if A is zero then zero else B;
#X obj 0 526 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 526 op min;
#X text 96 526  the lowest value in A \, B ;
#X text 446 526 clipping;
#X text 676 526 clipping (of individual points);
#X obj 0 545 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 545 op max;
#X text 96 545  the highest value in A \, B ;
#X text 446 545 clipping;
#X text 676 545 clipping (of individual points);
#X obj 0 564 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 564 op cmp;
#X text 96 564  -1 when A<B \,  0 when A=B \,  1 when A>B ;
#X obj 0 583 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 583 op ==;
#X text 96 583  is A equal to B ? 1=true \,  0=false ;
#X obj 0 602 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 602 op !=;
#X text 96 602  is A not equal to B ? ;
#X obj 0 621 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 621 op >;
#X text 96 621  is A greater than B ? ;
#X obj 0 640 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 640 op <=;
#X text 96 640  is A not greater than B ? ;
#X obj 0 659 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 659 op <;
#X text 96 659  is A less than B ? ;
#X obj 0 678 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 678 op >=;
#X text 96 678 is A not less than B ? ;
#X obj 0 697 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 697 op sin*;
#X text 96 697  B * sin(A) in centidegrees ;
#X text 446 697 --;
#X text 676 697 waves \,  rotations;
#X obj 0 716 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 716 op cos*;
#X text 96 716  B * cos(A) in centidegrees ;
#X text 446 716 --;
#X text 676 716 waves \,  rotations;
#X obj 0 735 cnv 15 906 26 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 735 op atan;
#X text 96 735  arctan(A/B) in centidegrees ;
#X text 446 735 --;
#X text 676 735 find angle to origin \;  (part of polar transform);
#X obj 0 763 cnv 15 906 26 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 763 op tanh*;
#X text 96 763  B * tanh(A) in centidegrees ;
#X text 446 763 smooth clipping;
#X text 676 763 smooth clipping (of individual points) \;  neural sigmoid \,  fuzzy logic;
#X obj 0 791 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 791 op log*;
#X text 96 791  B * log(A) in base e ;
#X obj 0 810 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 810 op /exp;
#X text 96 810  exp(A / B) in base e ;
#X obj 0 829 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 829 op gamma;
#X text 96 829  floor(pow(a/256.0 \, 256.0/b)*256.0) ;
#X text 446 829 gamma correction;
#X obj 0 848 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 848 op **;
#X text 96 848  A**B \,  that is \,  A raised to power B ;
#X text 446 848 gamma correction;
#X obj 0 867 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 867 op abs-;
#X text 96 867  absolute value of (A-B) ;
#X obj 0 886 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 886 op rand;
#X text 96 886  randomly produces a non-negative number below A ;
#X obj 0 905 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 905 op sqrt;
#X text 96 905  square root of A \,  rounded downwards ;
#X obj 0 924 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 924 op sq-;
#X text 96 924  (A-B) times (A-B) ;
#X obj 0 943 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 943 op avg;
#X text 96 943  (A+B)/2 ;
#X obj 0 962 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 962 op hypot;
#X text 96 962  distance function: square root of (A*A+B*B) ;
#X obj 0 981 cnv 15 906 26 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 981 op clip+;
#X text 96 981  like A+B but overflow causes clipping instead of wrapping around ;
#X obj 0 1009 cnv 15 906 26 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1009 op clip-;
#X text 96 1009  like A-B but overflow causes clipping instead of wrapping around ;
#X obj 0 1037 cnv 15 906 26 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1037 op erf*;
#X text 96 1037  integral of e^(-x*x) dx ... (coming soon \;  what ought to be the scaling factor?) ;
#X obj 0 1065 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1065 op weight;
#X text 96 1065  number of "1" bits in an integer;
#X obj 0 1084 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1084 op sin;
#X text 96 1084 sin(A-B) in radians \,  float only;
#X obj 0 1103 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1103 op cos;
#X text 96 1103 cos(A-B) in radians \,  float only;
#X obj 0 1122 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1122 op atan2;
#X text 96 1122 atan2(A \, B) in radians \,  float only;
#X obj 0 1141 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1141 op tanh;
#X text 96 1141 tanh(A-B) in radians \,  float only;
#X obj 0 1160 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1160 op exp;
#X text 96 1160 exp(A-B) in radians \,  float only;
#X obj 0 1179 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1179 op log;
#X text 96 1179 log(A-B) in radians \,  float only;
#X obj 0 1214 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1214 op C.*    ;
#X text 96 1214 A*B;
#X obj 0 1233 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1233 op C.*conj;
#X text 96 1233 A*conj(B);
#X obj 0 1252 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1252 op C./    ;
#X text 96 1252 A/B;
#X obj 0 1271 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1271 op C./conj;
#X text 96 1271 A/conj(B);
#X obj 0 1290 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1290 op C.sq-  ;
#X text 96 1290 (A-B)*(A-B);
#X obj 0 1309 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1309 op C.abs- ;
#X text 96 1309 abs(A-B);
#X obj 0 1328 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1328 op C.sin  ;
#X text 96 1328 sin(A-B);
#X obj 0 1347 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1347 op C.cos  ;
#X text 96 1347 cos(A-B);
#X obj 0 1366 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1366 op C.tanh ;
#X text 96 1366 tanh(A-B);
#X obj 0 1385 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1385 op C.exp  ;
#X text 96 1385 exp(A-B);
#X obj 0 1404 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1404 op C.log  ;
#X text 96 1404 log(A-B);
#X obj 0 1439 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
#X msg 10 1439 op c2p;
#X text 96 1439 hypot \, atan two-in-one;
#X obj 0 1458 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
#X msg 10 1458 op p2c;
#X text 96 1458 cos* \, sin* two-in-one;
#X obj 10 1487 outlet;
#X connect 7 0 260 0;
#X connect 12 0 260 0;
#X connect 17 0 260 0;
#X connect 22 0 260 0;
#X connect 27 0 260 0;
#X connect 32 0 260 0;
#X connect 37 0 260 0;
#X connect 42 0 260 0;
#X connect 47 0 260 0;
#X connect 52 0 260 0;
#X connect 55 0 260 0;
#X connect 58 0 260 0;
#X connect 63 0 260 0;
#X connect 66 0 260 0;
#X connect 69 0 260 0;
#X connect 72 0 260 0;
#X connect 75 0 260 0;
#X connect 78 0 260 0;
#X connect 83 0 260 0;
#X connect 88 0 260 0;
#X connect 93 0 260 0;
#X connect 98 0 260 0;
#X connect 103 0 260 0;
#X connect 106 0 260 0;
#X connect 109 0 260 0;
#X connect 114 0 260 0;
#X connect 119 0 260 0;
#X connect 122 0 260 0;
#X connect 125 0 260 0;
#X connect 128 0 260 0;
#X connect 131 0 260 0;
#X connect 134 0 260 0;
#X connect 137 0 260 0;
#X connect 140 0 260 0;
#X connect 145 0 260 0;
#X connect 150 0 260 0;
#X connect 155 0 260 0;
#X connect 160 0 260 0;
#X connect 163 0 260 0;
#X connect 166 0 260 0;
#X connect 170 0 260 0;
#X connect 174 0 260 0;
#X connect 177 0 260 0;
#X connect 180 0 260 0;
#X connect 183 0 260 0;
#X connect 186 0 260 0;
#X connect 189 0 260 0;
#X connect 192 0 260 0;
#X connect 195 0 260 0;
#X connect 198 0 260 0;
#X connect 201 0 260 0;
#X connect 204 0 260 0;
#X connect 207 0 260 0;
#X connect 210 0 260 0;
#X connect 213 0 260 0;
#X connect 216 0 260 0;
#X connect 219 0 260 0;
#X connect 222 0 260 0;
#X connect 225 0 260 0;
#X connect 228 0 260 0;
#X connect 231 0 260 0;
#X connect 234 0 260 0;
#X connect 237 0 260 0;
#X connect 240 0 260 0;
#X connect 243 0 260 0;
#X connect 246 0 260 0;
#X connect 249 0 260 0;
#X connect 252 0 260 0;
#X connect 255 0 260 0;
#X connect 258 0 260 0;
#X obj 95 30 cnv 0 0 1507 empty empty empty -1 12 0 14 0 -66577 0;
#X obj 445 30 cnv 0 0 1507 empty empty empty -1 12 0 14 0 -66577 0;
#X obj 675 30 cnv 0 0 1507 empty empty empty -1 12 0 14 0 -66577 0;
#X obj 0 54 cnv 15 906 14 empty empty empty 20 12 0 14 -248881 -66577 0;
#X text 10 52 numops;
#X obj 0 1198 cnv 15 906 14 empty empty empty 20 12 0 14 -248881 -66577 0;
#X text 10 1196 vecops for complex numbers;
#X obj 0 1423 cnv 15 906 14 empty empty empty 20 12 0 14 -248881 -66577 0;
#X text 10 1421 vecops for other things;
#X text 10 1507 
	note: a centidegree is 0.01 degree. There are 36000 centidegrees in a circle.
        Some angle operators use centidegrees \,  while some others use radians. To
        convert degrees into centidegrees \,  multiply by 100 .
        To convert degrees into radians \,  divide by 57.2957 .
        Thus \,  to convert centidegrees into radians \,  divide by 5729.57 .
        All the complex number operators are only for floats.
	VecOps are called VecOps because each operation happens between more than just two numbers.
	Complex VecOps are those that arise when a pair of numbers (A0 A1) is considered as a single number A0+A1*sqrt(-1).
	If you need complex numbers but don't know yet how they work \, 
	learn them using a math tutorial and then those VecOps will begin to look familiar.
;