Re: cotan() bug

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

This patch corrects the following bugs:
The CVS version has been updated.


? .5*O(3)
  ***   bus error: bug in GP (please report).
? I*O(5)
%1 = O(5)*I  
? cos(%)
%2 = 0.E-2495630 + 0.E-2495659*I
? cotan(I)
  ***   division by zero in gdiv, gdivgs or ginv
? tan(I)
  ***   division by zero in gdiv, gdivgs or ginv
?\ps2
   seriesprecision = 2 significant terms
? cos(x+I)
%3 = (0.E-28 + 0.E-28*I) + (0.E-28 + 0.E-28*I)*x + O(x^2) 
? tan(1+I)
%4 = -0.1797295366441293115045978048 + 1.381927396681501465499460288*I

Now we get:

? .5*O(3)
  ***   forbidden multiplication t_REAL * t_PADIC.
? I*O(5)
%1 = O(5)*I  
? cos(%)
  ***   forbidden multiplication t_REAL * t_PADIC.
? cotan(I)
%2 = 0.E-28 - 1.313035285499331303636161246*I
? tan(I)
%3 = 0.E-29 + 0.7615941559557648881194582826*I
? \ps2
   seriesprecision = 2 significant terms
? cos(x+I)
%4 = (1.543080634815243778477905620 + 0.E-28*I) + (0.E-28 - 1.175201193643801456882381850*I)*x + O(x^2)
? tan(1+I)
%5 = 0.2717525853195117165288437224 + 1.083923327338694543475752061*I

The number of untested features of PARI is unbelievable.

Index: src/basemath/gen1.c
===================================================================
RCS file: /home/megrez/cvsroot/pari/src/basemath/gen1.c,v
retrieving revision 1.4
diff -u -r1.4 gen1.c
--- src/basemath/gen1.c	1999/10/21 09:51:07	1.4
+++ src/basemath/gen1.c	1999/10/30 18:08:02
@@ -964,7 +964,7 @@
 	    l=avma; p1=co8(y,lg(x)); tetpil=avma;
 	    return gerepile(l,tetpil,gmul(p1,x));
 	
-	  case t_INTMOD: err(gmulerf,tx,ty);
+	  case t_PADIC: case t_INTMOD: err(gmulerf,tx,ty);
 	}
 	
       case t_INTMOD:
Index: src/basemath/trans1.c
===================================================================
RCS file: /home/megrez/cvsroot/pari/src/basemath/trans1.c,v
retrieving revision 1.5
diff -u -r1.5 trans1.c
--- src/basemath/trans1.c	1999/10/29 09:04:52	1.5
+++ src/basemath/trans1.c	1999/10/30 18:08:03
@@ -1340,8 +1340,8 @@
     case t_COMPLEX:
       y=cgetg(3,t_COMPLEX); av=avma;
       r=gexp((GEN)x[2],prec); p1=ginv(r);
-      p2=gmul2n(mpadd(p1,r),-1);
-      p1=mpsub(p2,r);
+      p2=gmul2n(gadd(p1,r),-1);
+      p1=gsub(p2,r);
       gsincos((GEN)x[1],&u,&v,prec);
       tetpil=avma;
       y[1]=lmul(p2,v); y[2]=lmul(p1,u);
@@ -1419,8 +1419,8 @@
     case t_COMPLEX:
       y=cgetg(3,t_COMPLEX); av=avma;
       r=gexp((GEN)x[2],prec); p1=ginv(r);
-      p2=gmul2n(mpadd(p1,r),-1);
-      p1=mpsub(p2,p1);
+      p2=gmul2n(gadd(p1,r),-1);
+      p1=gsub(p2,p1);
       gsincos((GEN)x[1],&u,&v,prec);
       tetpil=avma;
       y[1]=lmul(p2,u); y[2]=lmul(p1,v);
@@ -1506,12 +1506,12 @@
       ps=cgetg(3,t_COMPLEX); pc=cgetg(3,t_COMPLEX);
       *s=ps; *c=pc; av=avma;
       r=gexp((GEN)x[2],prec); p1=ginv(r);
-      p2=gmul2n(mpadd(p1,r),-1);
-      p1=mpsub(p2,p1); r=mpsub(p2,r);
+      v1=gmul2n(gadd(p1,r),-1);
+      u1=gsub(v1,p1); r=gsub(v1,r);/*u1=I*sin(I*Im(x));v1=cos(I*Im(x));r=-u1*/
       gsincos((GEN)x[1],&u,&v,prec);
       tetpil=avma;
-      p1=gmul(p2,u); p2=gmul(p1,v);
-      p3=gmul(p2,v); p4=gmul(r,u);
+      p1=gmul(v1,u); p2=gmul(u1,v);
+      p3=gmul(v1,v); p4=gmul(r,u);
       gptr[0]=&p1; gptr[1]=&p2; gptr[2]=&p3; gptr[3]=&p4;
       gerepilemanysp(av,tetpil,gptr,4);
       ps[1]=(long)p1; ps[2]=(long)p2; pc[1]=(long)p3; pc[2]=(long)p4;