* algebra/integer.spad.pamphlet (Integer): Use builtin functions

	%irem and %iquo.
	* algebra/si.spad.pamphlet (SingleInteger): Likewise.

4 files changed, 30 insertions, 27 deletions

diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet
index 9685c43d..1b67fd0e 100644
--- a/src/algebra/integer.spad.pamphlet
+++ b/src/algebra/integer.spad.pamphlet
@@ -91,6 +91,8 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with
       import %iadd: (%,%) -> %         from Foreign Builtin
       import %isub: (%,%) -> %         from Foreign Builtin
       import %imul: (%,%) -> %         from Foreign Builtin
+      import %irem: (%,%) -> %         from Foreign Builtin
+      import %iquo: (%,%) -> %         from Foreign Builtin
       import %imax: (%,%) -> %         from Foreign Builtin
       import %imin: (%,%) -> %         from Foreign Builtin
       import %igcd: (%,%) -> %         from Foreign Builtin
@@ -210,8 +212,8 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with
       max(x,y) == %imax(x,y)
       min(x,y) == %imin(x,y)
       divide(x,y) == DIVIDE2(x,y)$Lisp
-      x quo y == QUOTIENT2(x,y)$Lisp
-      x rem y == REMAINDER2(x,y)$Lisp
+      x quo y == %iquo(x,y)
+      x rem y == %irem(x,y)
       shift(x, y) == ASH(x,y)$Lisp
       recip(x) == if one? x or x=-1 then x else "failed"
       gcd(x,y) == %igcd(x,y)
diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet
index 98fe1168..6a7ef5a3 100644
--- a/src/algebra/si.spad.pamphlet
+++ b/src/algebra/si.spad.pamphlet
@@ -181,9 +181,9 @@ IntegerNumberSystem(): Category ==
 
 
 -- Lisp dependencies
--- EQ, ABSVAL, TIMES, INTEGER-LENGTH, HASHEQ, REMAINDER
+-- EQ, ABSVAL, TIMES, INTEGER-LENGTH, HASHEQ, 
 -- QSLESSP, QSGREATERP, QSADD1, QSSUB1, QSMINUS, QSPLUS, QSDIFFERENCE
--- QSTIMES, QSREMAINDER, QSODDP, QSZEROP, QSMAX, QSMIN, QSNOT, QSAND
+-- QSTIMES,, QSODDP, QSZEROP, QSMAX, QSMIN, QSNOT, QSAND
 -- QSOR, QSXOR, QSLEFTSHIFT, QSADDMOD, QSDIFMOD, QSMULTMOD
 
 
@@ -215,6 +215,8 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM
    import %iadd: (%,%) -> %         from Foreign Builtin
    import %isub: (%,%) -> %         from Foreign Builtin
    import %imul: (%,%) -> %         from Foreign Builtin
+   import %irem: (%,%) -> %         from Foreign Builtin
+   import %iquo: (%,%) -> %         from Foreign Builtin
    import %ineg: % -> %             from Foreign Builtin
    import %iabs: % -> %             from Foreign Builtin
    import %imax: (%,%) -> %         from Foreign Builtin
@@ -312,8 +314,8 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM
    x:% * y:% == %imul(x,y)
    x:% ** n:NonNegativeInteger == 
       (%ipow(x, n)$Foreign(Builtin) pretend Integer)::%
-   x quo y   == QSQUOTIENT(x,y)$Lisp
-   x rem y   == QSREMAINDER(x,y)$Lisp
+   x quo y   == %iquo(x,y)
+   x rem y   == %irem(x,y)
    divide(x, y)   == CONS(QSQUOTIENT(x,y)$Lisp,QSREMAINDER(x,y)$Lisp)$Lisp
    gcd(x,y)  == %igcd(x,y)
    abs(x)    == %iabs x
@@ -339,7 +341,7 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM
         [m pretend Matrix(Integer), v pretend Vector(Integer)]
 
    positiveRemainder(x,n) ==
-      r := QSREMAINDER(x,n)$Lisp
+      r := %irem(x,n)
       negative? r =>
         negative? n => x - n 
         r + n
@@ -348,8 +350,8 @@ SingleInteger(): Join(IntegerNumberSystem,OrderedFinite,BooleanLogic,Logic,OpenM
    coerce(x:Integer):% == per x
 
    random() ==
-      seed := REMAINDER(TIMES(MULTIPLIER,seed)$Lisp,MODULUS)$Lisp
-      REMAINDER(seed,BASE)$Lisp
+      seed := TIMES(MULTIPLIER,seed)$Lisp rem MODULUS
+      seed rem BASE
 
    random(n) == RANDOM(n)$Lisp
 
diff --git a/src/algebra/strap/INT.lsp b/src/algebra/strap/INT.lsp
index 2f9194a2..5ef3c73c 100644
--- a/src/algebra/strap/INT.lsp
+++ b/src/algebra/strap/INT.lsp
@@ -212,12 +212,12 @@
 (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|)
                 |INT;quo;3$;49|)) 
 
-(PUT '|INT;quo;3$;49| '|SPADreplace| 'QUOTIENT2) 
+(PUT '|INT;quo;3$;49| '|SPADreplace| '|%iquo|) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|)
                 |INT;rem;3$;50|)) 
 
-(PUT '|INT;rem;3$;50| '|SPADreplace| 'REMAINDER2) 
+(PUT '|INT;rem;3$;50| '|SPADreplace| '|%irem|) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Integer| |%Shell|) |%Integer|)
                 |INT;shift;3$;51|)) 
@@ -264,6 +264,9 @@
 (PUT '|INT;negative?;$B;15| '|SPADreplace|
      '(XLAM (|x|) (|%ilt| |x| 0))) 
 
+(PUT '|INT;mulmod;4$;22| '|SPADreplace|
+     '(XLAM (|a| |b| |p|) (|%irem| (|%imul| |a| |b|) |p|))) 
+
 (PUT '|INT;unitCanonical;2$;55| '|SPADreplace| '|%iabs|) 
 
 (DEFUN |INT;writeOMInt| (|dev| |x| $)
@@ -348,7 +351,8 @@
   (LET ((|c| (- |a| |b|))) (COND ((MINUSP |c|) (+ |c| |p|)) (T |c|)))) 
 
 (DEFUN |INT;mulmod;4$;22| (|a| |b| |p| $)
-  (REMAINDER2 (* |a| |b|) |p|)) 
+  (DECLARE (IGNORE $))
+  (REM (* |a| |b|) |p|)) 
 
 (DEFUN |INT;convert;$F;23| (|x| $)
   (SPADCALL |x| (|getShellEntry| $ 53))) 
@@ -374,9 +378,7 @@
     (RETURN
       (COND
         ((|INT;negative?;$B;15|
-             (LETT |r| (REMAINDER2 |a| |b|)
-                   |INT;positiveRemainder;3$;28|)
-             $)
+             (LETT |r| (REM |a| |b|) |INT;positiveRemainder;3$;28|) $)
          (COND ((MINUSP |b|) (- |r| |b|)) (T (+ |r| |b|))))
         (T |r|))))) 
 
@@ -432,11 +434,9 @@
 
 (DEFUN |INT;quo;3$;49| (|x| |y| $)
   (DECLARE (IGNORE $))
-  (QUOTIENT2 |x| |y|)) 
+  (TRUNCATE |x| |y|)) 
 
-(DEFUN |INT;rem;3$;50| (|x| |y| $)
-  (DECLARE (IGNORE $))
-  (REMAINDER2 |x| |y|)) 
+(DEFUN |INT;rem;3$;50| (|x| |y| $) (DECLARE (IGNORE $)) (REM |x| |y|)) 
 
 (DEFUN |INT;shift;3$;51| (|x| |y| $)
   (DECLARE (IGNORE $))
diff --git a/src/algebra/strap/SINT.lsp b/src/algebra/strap/SINT.lsp
index 071264f8..b891bed3 100644
--- a/src/algebra/strap/SINT.lsp
+++ b/src/algebra/strap/SINT.lsp
@@ -164,12 +164,12 @@
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
                 |SINT;quo;3$;37|)) 
 
-(PUT '|SINT;quo;3$;37| '|SPADreplace| 'QSQUOTIENT) 
+(PUT '|SINT;quo;3$;37| '|SPADreplace| '|%iquo|) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
                 |SINT;rem;3$;38|)) 
 
-(PUT '|SINT;rem;3$;38| '|SPADreplace| 'QSREMAINDER) 
+(PUT '|SINT;rem;3$;38| '|SPADreplace| '|%irem|) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Pair|)
                 |SINT;divide;2$R;39|)) 
@@ -413,11 +413,11 @@
 
 (DEFUN |SINT;quo;3$;37| (|x| |y| $)
   (DECLARE (IGNORE $))
-  (QSQUOTIENT |x| |y|)) 
+  (TRUNCATE |x| |y|)) 
 
 (DEFUN |SINT;rem;3$;38| (|x| |y| $)
   (DECLARE (IGNORE $))
-  (QSREMAINDER |x| |y|)) 
+  (REM |x| |y|)) 
 
 (DEFUN |SINT;divide;2$R;39| (|x| |y| $)
   (CONS (QSQUOTIENT |x| |y|) (QSREMAINDER |x| |y|))) 
@@ -485,7 +485,7 @@
   (CONS |m| |v|)) 
 
 (DEFUN |SINT;positiveRemainder;3$;58| (|x| |n| $)
-  (LET ((|r| (QSREMAINDER |x| |n|)))
+  (LET ((|r| (REM |x| |n|)))
     (COND
       ((QSMINUSP |r|)
        (COND ((QSMINUSP |n|) (- |x| |n|)) (T (+ |r| |n|))))
@@ -496,9 +496,8 @@
 
 (DEFUN |SINT;random;$;60| ($)
   (SEQ (|setShellEntry| $ 6
-           (REMAINDER (TIMES 314159269 (|getShellEntry| $ 6))
-               2147483647))
-       (EXIT (REMAINDER (|getShellEntry| $ 6) 67108864)))) 
+           (REM (TIMES 314159269 (|getShellEntry| $ 6)) 2147483647))
+       (EXIT (REM (|getShellEntry| $ 6) 67108864)))) 
 
 (DEFUN |SINT;random;2$;61| (|n| $) (DECLARE (IGNORE $)) (RANDOM |n|))