6.30.3 Arithmetics

Function: fxadd1 fx

Function: fxsub1 fx

Add or subtract ‘1’ to fx.

Function: fxabs fx

Return the absolute value of the fixnum fx as a fixnum; if fx is (least-fixnum): its absolute value is a bignum, in which case this function raises an implementation restriction violation.

To compute the general absolute value without overflow we must use abs or $abs-fixnum.

Function: fxsign fx

Return one of the fixnums +1, -1, 0 representing the sign of the fixnum fx.

Procedure: fxquotient fx1 fx2

Procedure: fxremainder fx1 fx2

Procedure: fxmodulo fx1 fx2

These procedures implement number–theoretic (integer) division on fixnum arguments. fx2 must be non–zero. All three procedures return fixnum objects. If fx1/fx2 is an integer object:

(fxquotient  fx1 fx2)  ⇒ fx1/fx2
(fxremainder fx1 fx2)  ⇒ 0
(fxmodulo    fx1 fx2)  ⇒ 0

If fx1/fx2 is not an integer object:

(fxquotient  fx1 fx2)  ⇒ n_q
(fxremainder fx1 fx2)  ⇒ n_r
(fxmodulo    fx1 fx2)  ⇒ n_m

where n_q is fx1/fx2 rounded towards zero,

0 < |n_r| < |fx2|
0 < |n_m| < |fx2|

n_r and n_m differ from fx1 by a multiple of fx2, n_r has the same sign as fx1, and n_m has the same sign as fx2.

Consequently, for integer objects fx1 and fx2 with fx2 not equal to 0,

(= fx1 (+ (* fx2 (fxquotient  fx1 fx2))
                 (fxremainder fx1 fx2)))
⇒ #t

provided all number object involved in that computation are exact.

(fxmodulo 13 4)           ⇒  1
(fxremainder 13 4)        ⇒  1

(fxmodulo -13 4)          ⇒  3
(fxremainder -13 4)       ⇒  -1

(fxmodulo 13 -4)          ⇒  -3
(fxremainder 13 -4)       ⇒  1

(fxmodulo -13 -4)         ⇒  -1
(fxremainder -13 -4)      ⇒  -1