4.6.3.1 Integer division

Scheme’s operations for performing integer division rely on mathematical operations div, mod, div_0, and mod_0, that are defined as follows:

• div, mod, div_0, and mod_0 each accept two real numbers x_1 and x_2 as operands, where x_2 must be nonzero.
• div returns an integer, and mod returns a real. Their results are specified by:

  x_1 div x_2 = n_d
  x_1 mod x_2 = x_m
  

  where:

  x_1 = n_d * x_2 + x_m
  0  <= x_m < |x_2|
  

  Examples:

   123 div  10 =  12
   123 mod  10 =   3
   123 div -10 = -12
   123 mod -10 =   3
  -123 div  10 = -13
  -123 mod  10 =   7
  -123 div -10 =  13
  -123 mod -10 =   7
  

• div_0 and mod_0 are like div and mod, except the result of mod_0 lies within a half–open interval centered on zero. The results are specified by:

  x_1 div_0 x_2 = n_d
  x_1 mod_0 x_2 = x_m
  

  where:

  x_1 = n_d * x_2 + x_m
  -|x_2/2| <= x_m < |x_2/2|
  

  Examples:

   123 div_0  10 =  12
   123 mod_0  10 =   3
   123 div_0 -10 = -12
   123 mod_0 -10 =   3
  -123 div_0  10 = -12
  -123 mod_0  10 =  -3
  -123 div_0 -10 =  12
  -123 mod_0 -10 =  -3