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bc - Basic Calculator

This is a arbitrary-precision infix calculator, that used to compile its
functions into the "dc" stack machine.  The syntax is simular too but not the
same as 'C'.

NOTES:
  * Fixed point precision (scale) is 0, unless -l is used (scale=20)
  * The ';' is optional if followed by a new line
  * A expression that is NOT assigned is printed (or prefix "print")
  * The modulo '%' will fail when scale is not 0
  * Comments are C-like  "/* ... */"
  * POSIX can only use single letters for function and variable names!!!
  * GNU-bc can use '#' for comments, and longer variable names
  * the power-of '^' can only use interger exponents

Examples...
  echo '6.5 / 2.7' | bc
  2

  echo 'scale=3; 6.5 / 2.7' | bc
  2.407

  echo '6.5 / 2.7' | bc -l
  2.40740740740740740740

Variables can be used
The keywork 'auto' can define them local to a function.

  bc <<< '
    scale=3;
    var1 = 6.5 / 2.7;
    var2 = 14 * var1;
    var2
  '
  33.698

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Math Functions (use a -l option - also sets scale to 20)

  s (x)       # The sine of x, x is in radians.
  c (x)       # The cosine of x, x is in radians.
  a (x)       # The arctangent of x, arctangent returns radians.
  l (x)       # The natural logarithm of x.
  e (x)       # The exponential function of raising e to the value x.
  j (n,x)     # The bessel function of integer order n of x.
  sqrt(x)     # Square root of the number x.

  pi=a(1)*4   # set the value of PI


  echo 'pi=a(1)*4; d2r=pi/180; c(30*d2r); s(30*d2r)' | bc -l
  .86602540378443864690
  .49999999999999999976


  /* power-of with non-integers */
  /* Use the fact that x^y == e^(y*log(x)) */
  define p(x,y) {
    return ( e( y * l(x) ) )
  }

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Conditional

  if(condition) {statements} else {statements}

Iterative Statements

  for (assignment; condition; increment) {statements}

  while (condition) {statements}

User defined

  define name(comma separated parameters list) {
    statements
    return statement
  }

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