note 68654 deleted from language.operators.arithmetic by hholzgra

Note Submitter: Ulf Wostner ---- # There are several natural ways to define the mod operator for integers. # Requirement: If mod(k, m) = r, then k and r differ by a multiple of m. # For m=7, think days-of-the-week. Both mod(13, 7) = 6 and mod(13, 7) = -1 # satisfy the requirement. Six days from today, or one day ago, are the same DOW. # There are several natural ways to define the mod operator for integers. # Requirement: If mod(k, m) = r, then k and r differ by a multiple of m. # For m=7, think days-of-the-week. Both mod(13, 7) = 6 and mod(13, 7) = -1 # satisfy the requirement. Six days from today, or one day ago, are the same DOW. # Here are four mod operators: # 1. mod_php. # Same as the built-in PHP function, so mod_php($k,$m) == ($k % $m). # A negative value might jolt a programmer using it for array index. function mod_php($k, $m) {return $k % $m; } # 2. Standard math definition. # Nice. But, if for some reason m is negative, be prepared for negative values. function mod_math($k, $m) { return ($k - $m * floor($k/$m)); } # 3. Smallest absolute value. # Sometimes convenient for large integers, making good use of the sign-bit. # Also, for mere humans, "-2 months from May", might be easier than "10 months from May". function mod_min($k, $m) { $r = mod_pos($k, $m); if($r > abs($m)/2) $r -= abs($m); return $r; } # 4. Smallest non-negative value. # Maybe closest to the concept that mod is the remainder when dividing $k by $m. function mod_pos($k, $m) { return ($k - abs($m) * floor($k/abs($m))); } # This table compares the four functions. k m mod_php mod_math mod_min mod_pos 18 7 4 4 -3 4 17 7 3 3 3 3 16 7 2 2 2 2 -16 7 -2 5 -2 5 -17 7 -3 4 -3 4 -18 7 -4 3 3 3 18 -7 4 -3 -3 4 17 -7 3 -4 3 3 16 -7 2 -5 2 2 -16 -7 -2 -2 -2 5 -17 -7 -3 -3 -3 4 -18 -7 -4 -4 3 3