===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/Q.c,v
retrieving revision 1.9
retrieving revision 1.10
diff -u -p -r1.9 -r1.10
--- OpenXM_contrib2/asir2000/engine/Q.c	2002/08/14 04:49:52	1.9
+++ OpenXM_contrib2/asir2000/engine/Q.c	2018/03/29 01:32:51	1.10
@@ -45,7 +45,7 @@
  * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
  * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
  *
- * $OpenXM: OpenXM_contrib2/asir2000/engine/Q.c,v 1.8 2002/08/08 10:57:01 noro Exp $ 
+ * $OpenXM: OpenXM_contrib2/asir2000/engine/Q.c,v 1.9 2002/08/14 04:49:52 noro Exp $ 
 */
 #include "ca.h"
 #include "base.h"
@@ -53,326 +53,326 @@
 
 void addq(Q n1,Q n2,Q *nr)
 {
-	N nm,dn,nm1,nm2,nm3,dn0,dn1,dn2,g,g1,g0,m;
-	int sgn;
-	unsigned t,t1;
+  N nm,dn,nm1,nm2,nm3,dn0,dn1,dn2,g,g1,g0,m;
+  int sgn;
+  unsigned t,t1;
 
-	if ( !n1 ) 
-		*nr = n2;
-	else if ( !n2 ) 
-		*nr = n1;
-	else if ( INT(n1) ) 
-		if ( INT(n2) ) {
-			nm1 = NM(n1); nm2 = NM(n2);
-			if ( SGN(n1) == SGN(n2) ) {
-				if ( PL(nm1) == 1 && PL(nm2) == 1 ) {
-					t1 = BD(nm1)[0]; t = t1+BD(nm2)[0];
-					if ( t < t1 ) {
-						m = NALLOC(2); PL(m) = 2; BD(m)[0] = t; BD(m)[1] = 1;
-					} else
-						UTON(t,m);
-				} else
-					addn(NM(n1),NM(n2),&m);
-				NTOQ(m,SGN(n1),*nr);
-			} else {
-				if ( PL(nm1) == 1 && PL(nm2) == 1 ) {
-					t1 = BD(nm1)[0]; t = t1-BD(nm2)[0];
-					if ( !t )
-						sgn = 0;
-					else if ( t > t1 ) {
-						sgn = -1; t = -((int)t); UTON(t,m);
-					} else {
-						sgn = 1; UTON(t,m);
-					}
-				} else
-					sgn = subn(NM(n1),NM(n2),&m);
-				if ( sgn ) {
-					if ( SGN(n1) == sgn )
-						NTOQ(m,1,*nr);
-					else
-						NTOQ(m,-1,*nr);
-				} else 
-					*nr = 0;
-			}
-		} else {
-			kmuln(NM(n1),DN(n2),&m);
-			if ( SGN(n1) == SGN(n2) ) {
-				sgn = SGN(n1); addn(m,NM(n2),&nm);
-			} else
-				sgn = SGN(n1)*subn(m,NM(n2),&nm);
-			if ( sgn ) {
-				dn = DN(n2); NDTOQ(nm,dn,sgn,*nr);
-			} else 
-				*nr = 0;
-		}
-	else if ( INT(n2) ) {
-		kmuln(NM(n2),DN(n1),&m);
-		if ( SGN(n1) == SGN(n2) ) {
-			sgn = SGN(n1); addn(m,NM(n1),&nm);
-		} else 
-			sgn = SGN(n1)*subn(NM(n1),m,&nm);
-		if ( sgn ) {
-			dn = DN(n1); NDTOQ(nm,dn,sgn,*nr);
-		} else 
-			*nr = 0;
-	} else {
-		gcdn(DN(n1),DN(n2),&g); divsn(DN(n1),g,&dn1); divsn(DN(n2),g,&dn2);
-		kmuln(NM(n1),dn2,&nm1); kmuln(NM(n2),dn1,&nm2);
-		if ( SGN(n1) == SGN(n2) ) {
-			sgn = SGN(n1); addn(nm1,nm2,&nm3);
-		} else 
-			sgn = SGN(n1)*subn(nm1,nm2,&nm3);
-		if ( sgn ) {
-			gcdn(nm3,g,&g1); divsn(nm3,g1,&nm); divsn(g,g1,&g0);
-			kmuln(dn1,dn2,&dn0); kmuln(g0,dn0,&dn);
-			if ( UNIN(dn) )
-				NTOQ(nm,sgn,*nr);
-			else 
-				NDTOQ(nm,dn,sgn,*nr);
-		} else 
-			*nr = 0;
-	}
+  if ( !n1 ) 
+    *nr = n2;
+  else if ( !n2 ) 
+    *nr = n1;
+  else if ( INT(n1) ) 
+    if ( INT(n2) ) {
+      nm1 = NM(n1); nm2 = NM(n2);
+      if ( SGN(n1) == SGN(n2) ) {
+        if ( PL(nm1) == 1 && PL(nm2) == 1 ) {
+          t1 = BD(nm1)[0]; t = t1+BD(nm2)[0];
+          if ( t < t1 ) {
+            m = NALLOC(2); PL(m) = 2; BD(m)[0] = t; BD(m)[1] = 1;
+          } else
+            UTON(t,m);
+        } else
+          addn(NM(n1),NM(n2),&m);
+        NTOQ(m,SGN(n1),*nr);
+      } else {
+        if ( PL(nm1) == 1 && PL(nm2) == 1 ) {
+          t1 = BD(nm1)[0]; t = t1-BD(nm2)[0];
+          if ( !t )
+            sgn = 0;
+          else if ( t > t1 ) {
+            sgn = -1; t = -((int)t); UTON(t,m);
+          } else {
+            sgn = 1; UTON(t,m);
+          }
+        } else
+          sgn = subn(NM(n1),NM(n2),&m);
+        if ( sgn ) {
+          if ( SGN(n1) == sgn )
+            NTOQ(m,1,*nr);
+          else
+            NTOQ(m,-1,*nr);
+        } else 
+          *nr = 0;
+      }
+    } else {
+      kmuln(NM(n1),DN(n2),&m);
+      if ( SGN(n1) == SGN(n2) ) {
+        sgn = SGN(n1); addn(m,NM(n2),&nm);
+      } else
+        sgn = SGN(n1)*subn(m,NM(n2),&nm);
+      if ( sgn ) {
+        dn = DN(n2); NDTOQ(nm,dn,sgn,*nr);
+      } else 
+        *nr = 0;
+    }
+  else if ( INT(n2) ) {
+    kmuln(NM(n2),DN(n1),&m);
+    if ( SGN(n1) == SGN(n2) ) {
+      sgn = SGN(n1); addn(m,NM(n1),&nm);
+    } else 
+      sgn = SGN(n1)*subn(NM(n1),m,&nm);
+    if ( sgn ) {
+      dn = DN(n1); NDTOQ(nm,dn,sgn,*nr);
+    } else 
+      *nr = 0;
+  } else {
+    gcdn(DN(n1),DN(n2),&g); divsn(DN(n1),g,&dn1); divsn(DN(n2),g,&dn2);
+    kmuln(NM(n1),dn2,&nm1); kmuln(NM(n2),dn1,&nm2);
+    if ( SGN(n1) == SGN(n2) ) {
+      sgn = SGN(n1); addn(nm1,nm2,&nm3);
+    } else 
+      sgn = SGN(n1)*subn(nm1,nm2,&nm3);
+    if ( sgn ) {
+      gcdn(nm3,g,&g1); divsn(nm3,g1,&nm); divsn(g,g1,&g0);
+      kmuln(dn1,dn2,&dn0); kmuln(g0,dn0,&dn);
+      if ( UNIN(dn) )
+        NTOQ(nm,sgn,*nr);
+      else 
+        NDTOQ(nm,dn,sgn,*nr);
+    } else 
+      *nr = 0;
+  }
 }
 
 void subq(Q n1,Q n2,Q *nr)
 {
-	Q m;
+  Q m;
 
-	if ( !n1 ) 
-		if ( !n2 ) 
-			*nr = 0;
-		else {
-			DUPQ(n2,*nr); SGN(*nr) = -SGN(n2);
-		}
-	else if ( !n2 ) 
-		*nr = n1;
-	else if ( n1 == n2 ) 
-		*nr = 0;
-	else {
-		DUPQ(n2,m); SGN(m) = -SGN(n2); addq(n1,m,nr);
-	}
+  if ( !n1 ) 
+    if ( !n2 ) 
+      *nr = 0;
+    else {
+      DUPQ(n2,*nr); SGN(*nr) = -SGN(n2);
+    }
+  else if ( !n2 ) 
+    *nr = n1;
+  else if ( n1 == n2 ) 
+    *nr = 0;
+  else {
+    DUPQ(n2,m); SGN(m) = -SGN(n2); addq(n1,m,nr);
+  }
 }
 
 void mulq(Q n1,Q n2,Q *nr)
 {
-	N nm,nm1,nm2,dn,dn1,dn2,g;
-	int sgn;
-	unsigned u,l;
+  N nm,nm1,nm2,dn,dn1,dn2,g;
+  int sgn;
+  unsigned u,l;
 
-	if ( !n1 || !n2 ) *nr = 0;
-	else if ( INT(n1) ) 
-		if ( INT(n2) ) {
-			nm1 = NM(n1); nm2 = NM(n2);
-			if ( PL(nm1) == 1 && PL(nm2) == 1 ) {
-				DM(BD(NM(n1))[0],BD(NM(n2))[0],u,l)
-				if ( u ) {
-					nm = NALLOC(2); PL(nm) = 2; BD(nm)[0] = l; BD(nm)[1] = u;
-				} else {
-					nm = NALLOC(1); PL(nm) = 1; BD(nm)[0] = l;
-				}
-			} else
-				kmuln(nm1,nm2,&nm);
-			sgn = (SGN(n1)==SGN(n2)?1:-1); NTOQ(nm,sgn,*nr);
-		} else {
-			gcdn(NM(n1),DN(n2),&g); divsn(NM(n1),g,&nm1); divsn(DN(n2),g,&dn);
-			kmuln(nm1,NM(n2),&nm); sgn = SGN(n1)*SGN(n2);
-			if ( UNIN(dn) )
-				NTOQ(nm,sgn,*nr);
-			else 
-				NDTOQ(nm,dn,sgn,*nr);
-		}
-	else if ( INT(n2) ) {
-		gcdn(NM(n2),DN(n1),&g); divsn(NM(n2),g,&nm2); divsn(DN(n1),g,&dn);
-		kmuln(nm2,NM(n1),&nm); sgn = SGN(n1)*SGN(n2);
-		if ( UNIN(dn) )
-			NTOQ(nm,sgn,*nr);
-		else 
-			NDTOQ(nm,dn,sgn,*nr);
-	} else {
-		gcdn(NM(n1),DN(n2),&g); divsn(NM(n1),g,&nm1); divsn(DN(n2),g,&dn2);
-		gcdn(DN(n1),NM(n2),&g); divsn(DN(n1),g,&dn1); divsn(NM(n2),g,&nm2);
-		kmuln(nm1,nm2,&nm); kmuln(dn1,dn2,&dn); sgn = SGN(n1) * SGN(n2);
-		if ( UNIN(dn) )
-			NTOQ(nm,sgn,*nr);
-		else 
-			NDTOQ(nm,dn,sgn,*nr);
-	}
+  if ( !n1 || !n2 ) *nr = 0;
+  else if ( INT(n1) ) 
+    if ( INT(n2) ) {
+      nm1 = NM(n1); nm2 = NM(n2);
+      if ( PL(nm1) == 1 && PL(nm2) == 1 ) {
+        DM(BD(NM(n1))[0],BD(NM(n2))[0],u,l)
+        if ( u ) {
+          nm = NALLOC(2); PL(nm) = 2; BD(nm)[0] = l; BD(nm)[1] = u;
+        } else {
+          nm = NALLOC(1); PL(nm) = 1; BD(nm)[0] = l;
+        }
+      } else
+        kmuln(nm1,nm2,&nm);
+      sgn = (SGN(n1)==SGN(n2)?1:-1); NTOQ(nm,sgn,*nr);
+    } else {
+      gcdn(NM(n1),DN(n2),&g); divsn(NM(n1),g,&nm1); divsn(DN(n2),g,&dn);
+      kmuln(nm1,NM(n2),&nm); sgn = SGN(n1)*SGN(n2);
+      if ( UNIN(dn) )
+        NTOQ(nm,sgn,*nr);
+      else 
+        NDTOQ(nm,dn,sgn,*nr);
+    }
+  else if ( INT(n2) ) {
+    gcdn(NM(n2),DN(n1),&g); divsn(NM(n2),g,&nm2); divsn(DN(n1),g,&dn);
+    kmuln(nm2,NM(n1),&nm); sgn = SGN(n1)*SGN(n2);
+    if ( UNIN(dn) )
+      NTOQ(nm,sgn,*nr);
+    else 
+      NDTOQ(nm,dn,sgn,*nr);
+  } else {
+    gcdn(NM(n1),DN(n2),&g); divsn(NM(n1),g,&nm1); divsn(DN(n2),g,&dn2);
+    gcdn(DN(n1),NM(n2),&g); divsn(DN(n1),g,&dn1); divsn(NM(n2),g,&nm2);
+    kmuln(nm1,nm2,&nm); kmuln(dn1,dn2,&dn); sgn = SGN(n1) * SGN(n2);
+    if ( UNIN(dn) )
+      NTOQ(nm,sgn,*nr);
+    else 
+      NDTOQ(nm,dn,sgn,*nr);
+  }
 }
 
 void divq(Q n1,Q n2,Q *nq)
 {
-	Q m;
+  Q m;
 
-	if ( !n2 ) {
-		error("division by 0");
-		*nq = 0;
-		return;
-	} else if ( !n1 ) 
-		*nq = 0;
-	else if ( n1 == n2 ) 
-		*nq = ONE;
-	else {
-		invq(n2,&m); mulq(n1,m,nq);
-	}
+  if ( !n2 ) {
+    error("division by 0");
+    *nq = 0;
+    return;
+  } else if ( !n1 ) 
+    *nq = 0;
+  else if ( n1 == n2 ) 
+    *nq = ONE;
+  else {
+    invq(n2,&m); mulq(n1,m,nq);
+  }
 }
 
 void divsq(Q n1,Q n2,Q *nq)
 {
-	int sgn;
-	N tn;
+  int sgn;
+  N tn;
 
-	if ( !n2 ) {
-		error("division by 0");
-		*nq = 0;
-		return;
-	} else if ( !n1 ) 
-		*nq = 0;
-	else if ( n1 == n2 ) 
-		*nq = ONE;
-	else {
-		divsn(NM(n1),NM(n2),&tn);
-		sgn = SGN(n1)*SGN(n2);
-		NTOQ(tn,sgn,*nq);
-	}
+  if ( !n2 ) {
+    error("division by 0");
+    *nq = 0;
+    return;
+  } else if ( !n1 ) 
+    *nq = 0;
+  else if ( n1 == n2 ) 
+    *nq = ONE;
+  else {
+    divsn(NM(n1),NM(n2),&tn);
+    sgn = SGN(n1)*SGN(n2);
+    NTOQ(tn,sgn,*nq);
+  }
 }
 
 void invq(Q n,Q *nr)
 {
-	N nm,dn;
+  N nm,dn;
 
-	if ( INT(n) )
-		if ( UNIN(NM(n)) )
-			if ( SGN(n) > 0 )
-				*nr = ONE;
-			else {
-				nm = ONEN; NTOQ(nm,SGN(n),*nr);
-			}
-		else {
-			nm = ONEN; dn = NM(n); NDTOQ(nm,dn,SGN(n),*nr);
-		}
-	else if ( UNIN(NM(n)) ) {
-		nm = DN(n); NTOQ(nm,SGN(n),*nr);
-	} else {
-		nm = DN(n); dn = NM(n); NDTOQ(nm,dn,SGN(n),*nr);
-	}
+  if ( INT(n) )
+    if ( UNIN(NM(n)) )
+      if ( SGN(n) > 0 )
+        *nr = ONE;
+      else {
+        nm = ONEN; NTOQ(nm,SGN(n),*nr);
+      }
+    else {
+      nm = ONEN; dn = NM(n); NDTOQ(nm,dn,SGN(n),*nr);
+    }
+  else if ( UNIN(NM(n)) ) {
+    nm = DN(n); NTOQ(nm,SGN(n),*nr);
+  } else {
+    nm = DN(n); dn = NM(n); NDTOQ(nm,dn,SGN(n),*nr);
+  }
 }
 
 void chsgnq(Q n,Q *nr)
 {
-	Q t;
+  Q t;
 
-	if ( !n )
-		*nr = 0;
-	else {
-		DUPQ(n,t); SGN(t) = -SGN(t); *nr = t;
-	}
+  if ( !n )
+    *nr = 0;
+  else {
+    DUPQ(n,t); SGN(t) = -SGN(t); *nr = t;
+  }
 }
 
 void pwrq(Q n1,Q n,Q *nr)
 {
-	N nm,dn;
-	int sgn;
+  N nm,dn;
+  int sgn;
 
-	if ( !n || UNIQ(n1) ) 
-		*nr = ONE;
-	else if ( !n1 ) 
-		*nr = 0;
-	else if ( !INT(n) ) {
-		error("can't calculate fractional power."); *nr = 0;
-	} else if ( MUNIQ(n1) )
-		*nr = BD(NM(n))[0]%2 ? n1 : ONE;
-	else if ( PL(NM(n)) > 1 ) {
-		error("exponent too big."); *nr = 0;
-	} else {
-		sgn = ((SGN(n1)>0)||EVENN(NM(n))?1:-1);
-		pwrn(NM(n1),BD(NM(n))[0],&nm);
-		if ( INT(n1) ) {
-			if ( UNIN(nm) )
-				if ( sgn == 1 )
-					*nr = ONE;
-				else
-					NTOQ(ONEN,sgn,*nr);
-			else if ( SGN(n) > 0 )
-				NTOQ(nm,sgn,*nr);
-			else
-				NDTOQ(ONEN,nm,sgn,*nr);
-		} else {
-			pwrn(DN(n1),BD(NM(n))[0],&dn);
-			if ( SGN(n) > 0 )
-				NDTOQ(nm,dn,sgn,*nr);
-			else if ( UNIN(nm) )
-				NTOQ(dn,sgn,*nr);
-			else
-				NDTOQ(dn,nm,sgn,*nr);
-		}
-	}
+  if ( !n || UNIQ(n1) ) 
+    *nr = ONE;
+  else if ( !n1 ) 
+    *nr = 0;
+  else if ( !INT(n) ) {
+    error("can't calculate fractional power."); *nr = 0;
+  } else if ( MUNIQ(n1) )
+    *nr = BD(NM(n))[0]%2 ? n1 : ONE;
+  else if ( PL(NM(n)) > 1 ) {
+    error("exponent too big."); *nr = 0;
+  } else {
+    sgn = ((SGN(n1)>0)||EVENN(NM(n))?1:-1);
+    pwrn(NM(n1),BD(NM(n))[0],&nm);
+    if ( INT(n1) ) {
+      if ( UNIN(nm) )
+        if ( sgn == 1 )
+          *nr = ONE;
+        else
+          NTOQ(ONEN,sgn,*nr);
+      else if ( SGN(n) > 0 )
+        NTOQ(nm,sgn,*nr);
+      else
+        NDTOQ(ONEN,nm,sgn,*nr);
+    } else {
+      pwrn(DN(n1),BD(NM(n))[0],&dn);
+      if ( SGN(n) > 0 )
+        NDTOQ(nm,dn,sgn,*nr);
+      else if ( UNIN(nm) )
+        NTOQ(dn,sgn,*nr);
+      else
+        NDTOQ(dn,nm,sgn,*nr);
+    }
+  }
 }
 
 int cmpq(Q q1,Q q2)
 {
-	int sgn;
-	N t,s;
+  int sgn;
+  N t,s;
 
-	if ( !q1 ) 
-		if ( !q2 ) 
-			return ( 0 );
-		else 
-			return ( -SGN(q2) );
-	else if ( !q2 ) 
-		return ( SGN(q1) );
-	else if ( SGN(q1) != SGN(q2) ) 
-			return ( SGN(q1) );
-	else if ( INT(q1) )
-			if ( INT(q2) ) {
-				sgn = cmpn(NM(q1),NM(q2));
-				if ( !sgn )
-					return ( 0 );
-				else
-					return ( SGN(q1)==sgn?1:-1 );
-			} else {
-				kmuln(NM(q1),DN(q2),&t); sgn = cmpn(t,NM(q2));
-				return ( SGN(q1) * sgn );
-			}
-	else if ( INT(q2) ) {
-		kmuln(NM(q2),DN(q1),&t); sgn = cmpn(NM(q1),t);
-		return ( SGN(q1) * sgn );
-	} else {
-		kmuln(NM(q1),DN(q2),&t); kmuln(NM(q2),DN(q1),&s); sgn = cmpn(t,s);
-		return ( SGN(q1) * sgn );
-	}
+  if ( !q1 ) 
+    if ( !q2 ) 
+      return ( 0 );
+    else 
+      return ( -SGN(q2) );
+  else if ( !q2 ) 
+    return ( SGN(q1) );
+  else if ( SGN(q1) != SGN(q2) ) 
+      return ( SGN(q1) );
+  else if ( INT(q1) )
+      if ( INT(q2) ) {
+        sgn = cmpn(NM(q1),NM(q2));
+        if ( !sgn )
+          return ( 0 );
+        else
+          return ( SGN(q1)==sgn?1:-1 );
+      } else {
+        kmuln(NM(q1),DN(q2),&t); sgn = cmpn(t,NM(q2));
+        return ( SGN(q1) * sgn );
+      }
+  else if ( INT(q2) ) {
+    kmuln(NM(q2),DN(q1),&t); sgn = cmpn(NM(q1),t);
+    return ( SGN(q1) * sgn );
+  } else {
+    kmuln(NM(q1),DN(q2),&t); kmuln(NM(q2),DN(q1),&s); sgn = cmpn(t,s);
+    return ( SGN(q1) * sgn );
+  }
 }
 
 void remq(Q n,Q m,Q *nr)
 {
-	N q,r,s;
+  N q,r,s;
 
-	if ( !n ) {
-		*nr = 0;
-		return;
-	}
-	divn(NM(n),NM(m),&q,&r); 
-	if ( !r )
-		*nr = 0;
-	else if ( SGN(n) > 0 )
-		NTOQ(r,1,*nr);
-	else {
-		subn(NM(m),r,&s); NTOQ(s,1,*nr);
-	}
+  if ( !n ) {
+    *nr = 0;
+    return;
+  }
+  divn(NM(n),NM(m),&q,&r); 
+  if ( !r )
+    *nr = 0;
+  else if ( SGN(n) > 0 )
+    NTOQ(r,1,*nr);
+  else {
+    subn(NM(m),r,&s); NTOQ(s,1,*nr);
+  }
 }
 
 /* t = [nC0 nC1 ... nCn] */
 
 void mkbc(int n,Q *t)
 {
-	int i;
-	N c,d;
+  int i;
+  N c,d;
 
-	for ( t[0] = ONE, i = 1; i <= n/2; i++ ) {
-		c = NALLOC(1); PL(c) = 1; BD(c)[0] = n-i+1;
-		kmuln(NM(t[i-1]),c,&d); divin(d,i,&c); NTOQ(c,1,t[i]);
-	}
-	for ( ; i <= n; i++ )
-		t[i] = t[n-i];
+  for ( t[0] = ONE, i = 1; i <= n/2; i++ ) {
+    c = NALLOC(1); PL(c) = 1; BD(c)[0] = n-i+1;
+    kmuln(NM(t[i-1]),c,&d); divin(d,i,&c); NTOQ(c,1,t[i]);
+  }
+  for ( ; i <= n; i++ )
+    t[i] = t[n-i];
 }
 
 /*
@@ -384,19 +384,19 @@ void mkbc(int n,Q *t)
 
 void mkwc(int k,int l,Q *t)
 {
-	int i,n,up,low;
-	N nm,d,c;
+  int i,n,up,low;
+  N nm,d,c;
 
-	n = MIN(k,l);
-	for ( t[0] = ONE, i = 1; i <= n; i++ ) {
-		DM(k-i+1,l-i+1,up,low);
-		if ( up ) {
-			nm = NALLOC(2); PL(nm) = 2; BD(nm)[0] = low; BD(nm)[1] = up;
-		} else {
-			nm = NALLOC(1); PL(nm) = 1; BD(nm)[0] = low;
-		}
-		kmuln(NM(t[i-1]),nm,&d); divin(d,i,&c); NTOQ(c,1,t[i]);
-	}
+  n = MIN(k,l);
+  for ( t[0] = ONE, i = 1; i <= n; i++ ) {
+    DM(k-i+1,l-i+1,up,low);
+    if ( up ) {
+      nm = NALLOC(2); PL(nm) = 2; BD(nm)[0] = low; BD(nm)[1] = up;
+    } else {
+      nm = NALLOC(1); PL(nm) = 1; BD(nm)[0] = low;
+    }
+    kmuln(NM(t[i-1]),nm,&d); divin(d,i,&c); NTOQ(c,1,t[i]);
+  }
 }
 
 /* mod m table */
@@ -404,40 +404,40 @@ void mkwc(int k,int l,Q *t)
 
 void mkwcm(int k,int l,int m,int *t)
 {
-	int i,n;
-	Q *s;
+  int i,n;
+  Q *s;
 
-	n = MIN(k,l);
-	s = (Q *)ALLOCA((n+1)*sizeof(Q));
-	mkwc(k,l,s);
-	for ( i = 0; i <= n; i++ ) {
-		t[i] = rem(NM(s[i]),m);
-	}
+  n = MIN(k,l);
+  s = (Q *)ALLOCA((n+1)*sizeof(Q));
+  mkwc(k,l,s);
+  for ( i = 0; i <= n; i++ ) {
+    t[i] = rem(NM(s[i]),m);
+  }
 }
 
 #if 0
 void factorial(int n,Q *r)
 {
-	Q t,iq,s;
-	unsigned int i,m,m0;
-	unsigned int c;
+  Q t,iq,s;
+  unsigned int i,m,m0;
+  unsigned int c;
 
-	if ( !n )
-		*r = ONE;
-	else if ( n < 0 ) 
-		*r = 0;
-	else {
-		for ( i = 1, t = ONE; (int)i <= n; ) {
-			for ( m0 = m = 1, c = 0; ((int)i <= n) && !c; i++ ) {
-				m0 = m; DM(m0,i,c,m)
-			}
-			if ( c ) {
-				m = m0; i--;
-			}
-			UTOQ(m,iq); mulq(t,iq,&s); t = s;
-		}
-		*r = t;
-	}
+  if ( !n )
+    *r = ONE;
+  else if ( n < 0 ) 
+    *r = 0;
+  else {
+    for ( i = 1, t = ONE; (int)i <= n; ) {
+      for ( m0 = m = 1, c = 0; ((int)i <= n) && !c; i++ ) {
+        m0 = m; DM(m0,i,c,m)
+      }
+      if ( c ) {
+        m = m0; i--;
+      }
+      UTOQ(m,iq); mulq(t,iq,&s); t = s;
+    }
+    *r = t;
+  }
 }
 #endif
 
@@ -445,204 +445,204 @@ void partial_factorial(int s,int e,N *r);
 
 void factorial(int n,Q *r)
 {
-	N nm;
+  N nm;
 
-	if ( !n )
-		*r = ONE;
-	else if ( n < 0 ) 
-		*r = 0;
-	else {
-		partial_factorial(1,n,&nm);
-		NTOQ(nm,1,*r);
-	}
+  if ( !n )
+    *r = ONE;
+  else if ( n < 0 ) 
+    *r = 0;
+  else {
+    partial_factorial(1,n,&nm);
+    NTOQ(nm,1,*r);
+  }
 }
 
 /* s*(s+1)*...*e */
 void partial_factorial(int s,int e,N *r)
 {
-	unsigned int len,i,m,m0,c;
-	unsigned int *p,*p1,*p2;
-	N nm,r1,r2;
+  unsigned int len,i,m,m0,c;
+  unsigned int *p,*p1,*p2;
+  N nm,r1,r2;
 
-	/* XXX */
-	if ( e-s > 2000 ) {
-		m = (e+s)/2;
-		partial_factorial(s,m,&r1);
-		partial_factorial(m+1,e,&r2);
-		kmuln(r1,r2,r);	
-		return;
-	}
-	/* find i s.t. 2^(i-1) < m <= 2^i */
-	for ( i = 0, m = 1; m < e; m <<=1, i++ );
-	 /* XXX estimate of word length of the result */
-	len = (i*(e-s+1)+1+31)/32;
-	p = ALLOCA((len+1)*sizeof(int));
-	p1 = ALLOCA((len+1)*sizeof(int));
-	p[0] = s;
-	len = 1;
-	for ( i = s+1; (int)i <= e; ) {
-		for ( m0 = m = 1, c = 0; ((int)i <= e) && !c; i++ ) {
-			m0 = m; DM(m0,i,c,m)
-		}
-		if ( c ) {
-			m = m0; i--;
-		}
-		bzero(p1,(len+1)*sizeof(int));
-		muln_1(p,len,m,p1);
-		if ( p1[len] )
-			len++;
-		p2 = p; p = p1; p1 = p2;
-	}
-	*r = nm = NALLOC(len);
-	bcopy(p,BD(nm),sizeof(int)*len);
-	PL(nm) = len;
+  /* XXX */
+  if ( e-s > 2000 ) {
+    m = (e+s)/2;
+    partial_factorial(s,m,&r1);
+    partial_factorial(m+1,e,&r2);
+    kmuln(r1,r2,r);  
+    return;
+  }
+  /* find i s.t. 2^(i-1) < m <= 2^i */
+  for ( i = 0, m = 1; m < e; m <<=1, i++ );
+   /* XXX estimate of word length of the result */
+  len = (i*(e-s+1)+1+31)/32;
+  p = ALLOCA((len+1)*sizeof(int));
+  p1 = ALLOCA((len+1)*sizeof(int));
+  p[0] = s;
+  len = 1;
+  for ( i = s+1; (int)i <= e; ) {
+    for ( m0 = m = 1, c = 0; ((int)i <= e) && !c; i++ ) {
+      m0 = m; DM(m0,i,c,m)
+    }
+    if ( c ) {
+      m = m0; i--;
+    }
+    bzero(p1,(len+1)*sizeof(int));
+    muln_1(p,len,m,p1);
+    if ( p1[len] )
+      len++;
+    p2 = p; p = p1; p1 = p2;
+  }
+  *r = nm = NALLOC(len);
+  bcopy(p,BD(nm),sizeof(int)*len);
+  PL(nm) = len;
 }
 
 void invl(Q a,Q mod,Q *ar)
 {
-	Q f1,f2,a1,a2,q,m,s;
-	N qn,rn;
+  Q f1,f2,a1,a2,q,m,s;
+  N qn,rn;
 
-	a1 = ONE; a2 = 0;
-	DUPQ(a,f1); SGN(f1) = 1; f2 = mod;
+  a1 = ONE; a2 = 0;
+  DUPQ(a,f1); SGN(f1) = 1; f2 = mod;
 
-	while ( 1 ) {
-		divn(NM(f1),NM(f2),&qn,&rn); 
-		if ( !qn )
-			q = 0;
-		else 
-			NTOQ(qn,1,q);
+  while ( 1 ) {
+    divn(NM(f1),NM(f2),&qn,&rn); 
+    if ( !qn )
+      q = 0;
+    else 
+      NTOQ(qn,1,q);
 
-		f1 = f2; 
-		if ( !rn ) 
-			break;
-		else 
-			NTOQ(rn,1,f2);
+    f1 = f2; 
+    if ( !rn ) 
+      break;
+    else 
+      NTOQ(rn,1,f2);
 
-		mulq(a2,q,&m); subq(a1,m,&s); a1 = a2;
-		if ( !s ) 
-			a2 = 0;
-		else
-			remq(s,mod,&a2);
-	}
-	if ( SGN(a) < 0 ) 
-		chsgnq(a2,&m); 
-	else
-		m = a2;
+    mulq(a2,q,&m); subq(a1,m,&s); a1 = a2;
+    if ( !s ) 
+      a2 = 0;
+    else
+      remq(s,mod,&a2);
+  }
+  if ( SGN(a) < 0 ) 
+    chsgnq(a2,&m); 
+  else
+    m = a2;
 
-	if ( SGN(m) >= 0 ) 
-		*ar = m;
-	else 
-		addq(m,mod,ar); 
+  if ( SGN(m) >= 0 ) 
+    *ar = m;
+  else 
+    addq(m,mod,ar); 
 }
 
 int kara_mag=100;
 
 void kmuln(N n1,N n2,N *nr)
 {
-	N n,t,s,m,carry;
-	int d,d1,d2,len,i,l;
-	int *r,*r0;
+  N n,t,s,m,carry;
+  int d,d1,d2,len,i,l;
+  int *r,*r0;
 
-	if ( !n1 || !n2 ) {
-		*nr = 0; return;
-	}
-	d1 = PL(n1); d2 = PL(n2);
-	if ( (d1 < kara_mag) || (d2 < kara_mag) ) {
-		muln(n1,n2,nr); return;
-	}
-	if ( d1 < d2 ) {
-		n = n1; n1 = n2; n2 = n;
-		d = d1; d1 = d2; d2 = d;
-	}
-	if ( d2 > (d1+1)/2 ) {
-		kmulnmain(n1,n2,nr); return;
-	}
-	d = (d1/d2)+((d1%d2)!=0);
-	len = (d+1)*d2;
-	r0 = (int *)ALLOCA(len*sizeof(int));
-	bzero((char *)r0,len*sizeof(int));
-	for ( carry = 0, i = 0, r = r0; i < d; i++, r += d2 ) {
-		extractn(n1,i*d2,d2,&m);
-		if ( m ) {
-			kmuln(m,n2,&t);
-			addn(t,carry,&s);
-			copyn(s,d2,r);
-			extractn(s,d2,d2,&carry);
-		} else {
-			copyn(carry,d2,r);
-			carry = 0;
-		}
-	}
-	copyn(carry,d2,r);
-	for ( l = len - 1; !r0[l]; l-- );
-	l++;
-	*nr = t = NALLOC(l); PL(t) = l;
-	bcopy((char *)r0,(char *)BD(t),l*sizeof(int));
+  if ( !n1 || !n2 ) {
+    *nr = 0; return;
+  }
+  d1 = PL(n1); d2 = PL(n2);
+  if ( (d1 < kara_mag) || (d2 < kara_mag) ) {
+    muln(n1,n2,nr); return;
+  }
+  if ( d1 < d2 ) {
+    n = n1; n1 = n2; n2 = n;
+    d = d1; d1 = d2; d2 = d;
+  }
+  if ( d2 > (d1+1)/2 ) {
+    kmulnmain(n1,n2,nr); return;
+  }
+  d = (d1/d2)+((d1%d2)!=0);
+  len = (d+1)*d2;
+  r0 = (int *)ALLOCA(len*sizeof(int));
+  bzero((char *)r0,len*sizeof(int));
+  for ( carry = 0, i = 0, r = r0; i < d; i++, r += d2 ) {
+    extractn(n1,i*d2,d2,&m);
+    if ( m ) {
+      kmuln(m,n2,&t);
+      addn(t,carry,&s);
+      copyn(s,d2,r);
+      extractn(s,d2,d2,&carry);
+    } else {
+      copyn(carry,d2,r);
+      carry = 0;
+    }
+  }
+  copyn(carry,d2,r);
+  for ( l = len - 1; !r0[l]; l-- );
+  l++;
+  *nr = t = NALLOC(l); PL(t) = l;
+  bcopy((char *)r0,(char *)BD(t),l*sizeof(int));
 }
 
 void extractn(N n,int index,int len,N *nr)
 {
-	unsigned int *m;
-	int l;
-	N t;
+  unsigned int *m;
+  int l;
+  N t;
 
-	if ( !n ) {
-		*nr = 0; return;
-	}
-	m = BD(n)+index;
-	if ( (l = PL(n)-index) >= len ) {
-		for ( l = len - 1; (l >= 0) && !m[l]; l-- );
-		l++;
-	}
-	if ( l <= 0 ) {
-		*nr = 0; return;
-	} else {
-		*nr = t = NALLOC(l); PL(t) = l;
-		bcopy((char *)m,(char *)BD(t),l*sizeof(int));
-	}
+  if ( !n ) {
+    *nr = 0; return;
+  }
+  m = BD(n)+index;
+  if ( (l = PL(n)-index) >= len ) {
+    for ( l = len - 1; (l >= 0) && !m[l]; l-- );
+    l++;
+  }
+  if ( l <= 0 ) {
+    *nr = 0; return;
+  } else {
+    *nr = t = NALLOC(l); PL(t) = l;
+    bcopy((char *)m,(char *)BD(t),l*sizeof(int));
+  }
 }
 
 void copyn(N n,int len,int *p)
 {
-	if ( n )
-		bcopy((char *)BD(n),(char *)p,MIN(PL(n),len)*sizeof(int));
+  if ( n )
+    bcopy((char *)BD(n),(char *)p,MIN(PL(n),len)*sizeof(int));
 }
 
 void dupn(N n,N p)
 {
-	if ( n )
-		bcopy((char *)n,(char *)p,(1+PL(n))*sizeof(int));
+  if ( n )
+    bcopy((char *)n,(char *)p,(1+PL(n))*sizeof(int));
 }
 
 void kmulnmain(N n1,N n2,N *nr)
 {
-	int d1,d2,h,sgn,sgn1,sgn2,len;
-	N n1lo,n1hi,n2lo,n2hi,hi,lo,mid1,mid2,mid,s1,s2,t1,t2;
+  int d1,d2,h,sgn,sgn1,sgn2,len;
+  N n1lo,n1hi,n2lo,n2hi,hi,lo,mid1,mid2,mid,s1,s2,t1,t2;
 
-	d1 = PL(n1); d2 = PL(n2); h = (d1+1)/2;
-	extractn(n1,0,h,&n1lo); extractn(n1,h,d1-h,&n1hi);
-	extractn(n2,0,h,&n2lo); extractn(n2,h,d2-h,&n2hi);
-	kmuln(n1hi,n2hi,&hi); kmuln(n1lo,n2lo,&lo);
-	len = PL(hi)+2*h; t1 = NALLOC(len); PL(t1) = len;
-	bzero((char *)BD(t1),len*sizeof(int));
-	if ( lo )
-		bcopy((char *)BD(lo),(char *)BD(t1),PL(lo)*sizeof(int));
-	if ( hi )
-		bcopy((char *)BD(hi),(char *)(BD(t1)+2*h),PL(hi)*sizeof(int));
+  d1 = PL(n1); d2 = PL(n2); h = (d1+1)/2;
+  extractn(n1,0,h,&n1lo); extractn(n1,h,d1-h,&n1hi);
+  extractn(n2,0,h,&n2lo); extractn(n2,h,d2-h,&n2hi);
+  kmuln(n1hi,n2hi,&hi); kmuln(n1lo,n2lo,&lo);
+  len = PL(hi)+2*h; t1 = NALLOC(len); PL(t1) = len;
+  bzero((char *)BD(t1),len*sizeof(int));
+  if ( lo )
+    bcopy((char *)BD(lo),(char *)BD(t1),PL(lo)*sizeof(int));
+  if ( hi )
+    bcopy((char *)BD(hi),(char *)(BD(t1)+2*h),PL(hi)*sizeof(int));
 
-	addn(hi,lo,&mid1);
-	sgn1 = subn(n1hi,n1lo,&s1); sgn2 = subn(n2lo,n2hi,&s2);
-	kmuln(s1,s2,&mid2); sgn = sgn1*sgn2;
-	if ( sgn > 0 )
-		addn(mid1,mid2,&mid);
-	else
-		subn(mid1,mid2,&mid);
-	if ( mid ) {
-		len = PL(mid)+h; t2 = NALLOC(len); PL(t2) = len;
-		bzero((char *)BD(t2),len*sizeof(int));
-		bcopy((char *)BD(mid),(char *)(BD(t2)+h),PL(mid)*sizeof(int));
-		addn(t1,t2,nr);
-	} else
-		*nr = t1;
+  addn(hi,lo,&mid1);
+  sgn1 = subn(n1hi,n1lo,&s1); sgn2 = subn(n2lo,n2hi,&s2);
+  kmuln(s1,s2,&mid2); sgn = sgn1*sgn2;
+  if ( sgn > 0 )
+    addn(mid1,mid2,&mid);
+  else
+    subn(mid1,mid2,&mid);
+  if ( mid ) {
+    len = PL(mid)+h; t2 = NALLOC(len); PL(t2) = len;
+    bzero((char *)BD(t2),len*sizeof(int));
+    bcopy((char *)BD(mid),(char *)(BD(t2)+h),PL(mid)*sizeof(int));
+    addn(t1,t2,nr);
+  } else
+    *nr = t1;
 }