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Math functions

add(summand, addend, sum) : Add cell #0 with #1, save the result in #2

/**
 *  INPUT:  summand & addend
 *  CODES:
 *          int sum  = 0;   // #2
 *          int temp = 0;   // #3
 *          
 *          // 1st: copy #0 to #2
 *          while (summand) {
 *              decrease(summand);
 *              increase(sum);
 *              increase(temp);
 *          }
 *          while (temp) {
 *              decrease(temp);
 *              increase(summand);
 *          }
 *          
 *          // 2nd: add #1 to #2
 *          while (addend) {
 *              decrease(addend);
 *              increase(sum);
 *              increase(temp);
 *          }
 *          while (temp) {
 *              decrease(temp);
 *              increase(addend);
 *          }
 */

>>[-]>[-]<<<        // clear cell #2 and #3
[->>+>+<<<]         // copy cell #0 to #2 and #3
>
    >>[-<<<+>>>]<<  // move cell #3 back to #0
    [->+>+<<]       // add cell #1 to #2
    >>[-<<+>>]<<    // move cell #3 back to #1
<

minus(minuend, subtrahend, difference) : Minus cell #0 with #1, save the result in #2

/**
 *  INPUT:  minuend & subtrahend
 *  CODES:
 *          int difference = 0; // #2
 *          int temp       = 0; // #3
 *          
 *          // 1st: copy #0 to #2
 *          while (minuend) {
 *              decrease(minuend);
 *              increase(difference);
 *              increase(temp);
 *          }
 *          while (temp) {
 *              decrease(temp);
 *              increase(minuend);
 *          }
 *          
 *          // 2nd: minus #2 with #1
 *          while (subtrahend) {
 *              decrease(subtrahend);
 *              decrease(difference);
 *              increase(temp);
 *          }
 *          while (temp) {
 *              decrease(temp);
 *              increase(subtrahend);
 *          }
 */

>>[-]>[-]<<<        // clear cell #2 and #3
[->>+>+<<<]         // copy cell #0 to #2 and #3
>
    >>[-<<<+>>>]<<  // move cell #3 back to #0
    [->->+<<]       // minus cell #2 by #1
    >>[-<<+>>]<<    // move cell #3 back to #1
<

multiply(multiplicand, multiplier, product) : Multiply cell #0 with #1, save the result in #2

/**
 *  INPUT:  multiplicand & multiplier
 *  CODES:
 *          int product = 0;    // #2
 *          int t       = 0;    // #3
 *          int m       = 0;    // #4
 *          
 *          while (multiplicand) {
 *              decrease(multiplicand);
 *              ADD multiplier(#1) TO product(#2) WITH t(#3) ONCE;
 *              increase(m);
 *          }
 *          while (m) {
 *              decrease(m);
 *              increase(multiplicand);
 *          }
 */

>>[-]>[-]>[-]<<<<       // clear cell #2 and #3 and #4
[
    ->
    [->+>+<<]           // add cell #1 to #2
    >>
        [-<<+>>]        // move cell #3 back to #1
        >+<             // copy cell #0 to #4
    <<
    <
]
>>>>[-<<<<+>>>>]<<<<    // move cell #4 back to #0

divide(numerator, denominator, quotient, remainder) : Divide cell #0 with #1, save quotient in #2 and remainder in #3

/**
 *  INPUT:  numerator & denominator
 *  CODES:
 *          int quotient  = 0;          // #2
 *          int remainder = numerator;  // #3
 *          int t4        = 0;          // #4
 *          int divisor   = 0;          // #5
 *          int t6        = 0;          // #6
 *          int t7        = 0;          // #7
 *          
 *          while (remainder) {
 *              divisor = denominator;          // copy #1 to #5 with #4
 *              while (divisor) {
 *                  decrease(divisor);
 *                  if (remainder) {
 *                      decrease(remainder);    // decrease #3 when not 0 with #4
 *                      t7 = divisor;           // copy #5 to #7 with #6
 *                  }
 *              }
 *              increase(quotient);
 *          }
 *          
 *          if (t7) {
 *              remainder = denominator MINUS t7;
 *              decrease(quotient);             // quotient NOT touched ceil when remainder NOT 0
 *          }
 */

>>[-]>[-]>[-]>[-]>[-]<<<<<< // clear cells #2~6
[->>+>+<<<]                 // copy cell #0 to #2 and #3
>>[-<<+>>]<<                // move cell #2 back to #0
>
    >>[                     // check #3: remainder
        <<[->>>+>+<<<<]>>   // copy cell #1 to #4 #5
        >[-<<<+>>>]<        // move cell #4 back to #1
        >>[-                // decrease #5: divisor
            <<
            [-              // decrease #3: remainder
                [->+<]      // move cell #3 to #4
                >>
                >>[-]<<     // clear cell #7
                [->+>+<<]   // move cell #5 to #6 and #7
                <<
            ]
            >
            [-<+>]          // move cell #4 back to #3
            >>
            [-<+>]          // move cell #6 back to #5
            <
        ]<<
        <+>                 // increase #2: quotient
    ]<<
    >>>>>>[<<<<<<           // check #7
        [->>+>+<<<]         // copy cell #1 to #3 and #4
        >>>
        [-<<<+>>>]          // move cell #4 back to #1
        >>>[-<<<<->>>>]<<<  // minus cell #3 with #7
        <<-<
    >>>>>>]<<<<<<
<

pow(x, n) : Multiply x(#0) for n(#1) times, save the result in #2

/**
 *  INPUT:  x & n
 *  CODES:
 *          int result = 0; // #2
 *          int m1     = 1; // #3
 *          int m2     = x; // #4
 *          int p      = 0; // #5
 *          
 *          while (n) {
 *              decrease(n);
 *              increase(result);
 *              m1 = m1 * m2;
 *          }
 *          
 *          n = result;
 *          result = m1;
 */

>>[-]>[-]>[-]<<<<    // clear cells #2~5
[->>+>>+<<<<]        // copy cell #0 to #2 #4
>>[-<<+>>]<<         // move cell #2 back to #0
>
    >>+<<            // set cell #3 to 1
    [                // use loop to do the math
        ->+>         // move cell #1 to #2
            multiply(#3, #4, #5);   // do the multiply from cell #3 and #4
            [-]                     // clear cell #3
            >>[-<<+>>]<<            // move cell #5(the result) back to #3
        <<
    ]                // calculate done! the result is saved in cell #3
    >
        backward(#2);    // move cell #2 backward
        >
        backward(#3);    // move cell #3 backward
        >[-]<            // clear cell #4
        <
    <
<

Extends

mod(dividend, divisor, remainder) : Divide cell #0 with #1, save remainder(mod) in #2

divide(dividend, divisor, *quotient, *remainder);
>>>
backward(*remainder);
<<<

ceil(dividend, divisor, quotient) : Divide cell #0 with #1, save the ceil in #2

>>[-]>[-]>[-]>[-]>[-]<<<<<< // clear cells #2~6
[->>+>+<<<]                 // copy cell #0 to #2 and #3
>>[-<<+>>]<<                // move cell #2 back to #0
>
    >>[                     // check #3: remainder
        <<[->>>+>+<<<<]>>   // copy cell #1 to #4 #5
        >[-<<<+>>>]<        // move cell #4 back to #1
        >>[-                // decrease #5: divisor
            <<
            [-              // decrease #3: remainder
                [->+<]      // move cell #3 to #4
                >>[->+<]<<  // move cell #5 to #6
            ]
            >
            [-<+>]          // move cell #4 back to #3
            >>
            [-<+>]          // move cell #6 back to #5
            <
        ]<<
        <+>                 // increase #2: quotient
    ]<<
<

square(x) : Calculate x*x

>[-]++<
pow(x, n);
>>
    backward(#2);
<<

cube(x) : Calculate x^3

>[-]+++<
pow(x, n);
>>
    backward(#2);
<<