Ticket #9620: pari-2.3.5.patch

pari-2.3.5.p1

@@ -182 +182 @@
       gel(y,1) = Pi2n(-1, lg(x));
       gel(y,2) = mpach(x);
       if (sx < 0)
-      {
         setsigne(y[1],-signe(y[1]));
+      else
         setsigne(y[2],-signe(y[2]));
-      }
       return y;
 
     case t_COMPLEX:
@@ -254 +253 @@
       if (expo(x) < 0) return mpacos(x);
 
       y = cgetg(3,t_COMPLEX); p1 = mpach(x);
-      if (sx < 0) gel(y,1) = mppi(lg(x));
-      else {
-        gel(y,1) = gen_0;
+      if (sx < 0) {
+        gel(y,1) = mppi(lg(x));
         setsigne(p1,-signe(p1));
-      }
+      } else gel(y,1) = gen_0;
       gel(y,2) = p1; return y;
 
-    case t_COMPLEX: av = avma;
-      return gerepilecopy(av, mulcxmI(gach(x,prec)));
+    case t_COMPLEX:
+      av = avma;
+      p1 = gadd(x, gsqrt(gaddsg(-1,gsqr(x)), prec)); /* x + sqrt(x^2-1) */
+      y = glog(p1,prec);
+      if (typ(y) == t_COMPLEX && signe(y[2]) > 0) y = gneg(y);
+      return gerepilecopy(av, mulcxI(y));
 
     case t_INTMOD: case t_PADIC: pari_err(typeer,"gacos");
     case t_SER:
@@ -502 +504 @@
 }
 /********************************************************************/
 /**                                                                **/
-/**                     ARG-HYPERBOLIC SINE                        **/
+/**                     AREA HYPERBOLIC SINE                       **/
 /**                                                                **/
 /********************************************************************/
 
@@ -545 +547 @@
         sx = gsigne(p1);
         sy = 0;
       }
-      if (sx > 0 || (!sx && sy*sz<=0)) return gerepileupto(av, y);
-
-      p1 = mppi(prec); if (sy<0) setsigne(p1,-1);
-      return gerepileupto(av, gadd(gneg_i(y), pureimag(p1)));
+      return gerepileupto(av, y);
     case t_INTMOD: case t_PADIC: pari_err(typeer,"gash");
     default:
       av = avma; if (!(y = toser_i(x))) break;
@@ -570 +569 @@
 }
 /********************************************************************/
 /**                                                                **/
-/**                     ARG-HYPERBOLIC COSINE                      **/
+/**                     AREA HYPERBOLIC COSINE                     **/
 /**                                                                **/
 /********************************************************************/
 
@@ -601 +600 @@
       if (absrnz_egal1(x)) { y = cgetimag(); gel(y,2) = mppi(lg(x)); return y; }
       y = cgetg(3,t_COMPLEX);
       av = avma; p1 = mpach(x);
-      setsigne(p1, -signe(p1));
       gel(y,1) = p1;
       gel(y,2) = mppi(lg(x)); return y;
 
@@ -609 +607 @@
       av = avma; 
       p1 = gadd(x, gsqrt(gaddsg(-1,gsqr(x)), prec)); /* x + sqrt(x^2-1) */
       y = glog(p1,prec);
-      if (typ(y) == t_COMPLEX && signe(y[2]) < 0) y = gneg(y);
+      if (signe(y[1]) < 0) y = gneg(y);
       return gerepileupto(av, y);
 
     case t_INTMOD: case t_PADIC: pari_err(typeer,"gach");
@@ -640 +638 @@
 }
 /********************************************************************/
 /**                                                                **/
-/**                     ARG-HYPERBOLIC TANGENT                     **/
+/**                     AREA HYPERBOLIC TANGENT                    **/
 /**                                                                **/
 /********************************************************************/
 
@@ -659 +657 @@
 GEN
 gath(GEN x, long prec)
 {
+  long sx;
   pari_sp av;
   GEN a, y, p1;
 
   switch(typ(x))
   {
     case t_REAL:
-      if (!signe(x)) return real_0_bit(expo(x));
+      sx = signe(x);
+      if (!sx) return real_0_bit(expo(x));
       if (expo(x) < 0) return mpath(x);
 
       y = cgetg(3,t_COMPLEX);
@@ -675 +675 @@
       p1 = logr_abs(p1);
       setexpo(p1, expo(p1)-1);
       gel(y,1) = gerepileuptoleaf(av, p1);
-      gel(y,2) = Pi2n(-1, lg(x)); return y;
+      gel(y,2) = Pi2n(-1, lg(x));
+      if (sx > 0)
+        setsigne(y[2],-signe(y[2]));
+      return y;
 
     case t_COMPLEX:
       av = avma; p1 = glog( gaddgs(gdivsg(2,gsubsg(1,x)),-1), prec );