[PATCH] enable basic arithmetic with infinity

[Jeroen Demeyer <jdemeyer@cage.ugent.be>]

Dear pari-dev,

The attached patch enables basic arithmetic with t_INFINITY. It adds 
support for addition, subtraction, multiplication and division of 
infinity by something (division by infinity is still an error). In all 
cases, the other operand must be a t_INT, t_REAL or t_FRAC.

This patch (at least for multiplication) is needed to support Denis 
Simon's 2-descent script which does things like

if (lambda > 2*valuation(x,p),...)

where x can be 0. This gave no problems with PARI-2.7 and earlier 
because valuation(0,p) returned a very large number.


Cheers,
Jeroen.

commit 56a75c6789284da3a1e0cbaca1254ffcb7c43423
Author: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date:   Mon Sep 22 17:20:12 2014 +0200

    Enable basic arithmetic with t_INFINITY

diff --git a/doc/usersch4.tex b/doc/usersch4.tex
index dde26b6..1592650 100644
--- a/doc/usersch4.tex
+++ b/doc/usersch4.tex
@@ -1501,9 +1501,11 @@ variadic, $0$ else.
 This type has a single \typ{INT} component, which is either $1$ or $-1$,
 corresponding to $+\infty$ and $-\infty$ respectively.
 
-\fun{GEN}{mkmoo}{} returns $-\infty$
+\fun{GEN}{mkmoo}{} returns $-\infty$.
 
-\fun{GEN}{mkoo}{} returns $\infty$
+\fun{GEN}{mkoo}{} returns $\infty$.
+
+\fun{GEN}{mksoo}{long s} returns $\infty$ if $s \geq 0$ and $-\infty$ otherwise.
 
 \fun{long}{inf_get_sign}{GEN x} returns $1$ if $x$ is $+\infty$, and $-1$
 if $x$ is $-\infty$.
diff --git a/src/basemath/gen1.c b/src/basemath/gen1.c
index e272eb5..1464e3c 100644
--- a/src/basemath/gen1.c
+++ b/src/basemath/gen1.c
@@ -782,11 +782,16 @@ add_rfrac_scal(GEN y, GEN x)
 static GEN
 add_scal(GEN y, GEN x, long ty)
 {
+  long tx;
   switch(ty)
   {
     case t_POL: return RgX_Rg_add(y, x);
     case t_SER: return add_ser_scal(y, x);
     case t_RFRAC: return add_rfrac_scal(y, x);
+    case t_INFINITY:
+      tx = typ(x);
+      if (tx == t_INT || tx == t_REAL || tx == t_FRAC) return mksoo(inf_get_sign(y));
+      break;
     case t_COL: return RgC_Rg_add(y, x);
     case t_VEC:
       if (isintzero(x)) return gcopy(y);
@@ -1015,6 +1020,9 @@ gadd(GEN x, GEN y)
       if (lx == 1) return cgetg(1, t_MAT);
       if (lgcols(y) != lgcols(x)) pari_err_OP("+",x,y);
       return RgM_add(x,y);
+    case t_INFINITY:
+      if (inf_get_sign(x) == inf_get_sign(y)) return mksoo(inf_get_sign(x));
+      pari_err_OP("+",x,y);
 
     default: pari_err_TYPE2("+",x,y);
   }
@@ -1306,6 +1314,9 @@ gsub(GEN x, GEN y)
       return RgM_sub(x,y);
     }
     case t_RFRAC: case t_SER: break;
+    case t_INFINITY:
+      if (inf_get_sign(x) != inf_get_sign(y)) return mksoo(inf_get_sign(x));
+      pari_err_OP("+",x,y);
 
     default: pari_err_TYPE2("+",x,y);
   }
@@ -1370,6 +1381,7 @@ mul_rfrac_scal(GEN n, GEN d, GEN x)
 static GEN
 mul_scal(GEN y, GEN x, long ty)
 {
+  int s;
   switch(ty)
   {
     case t_POL:
@@ -1377,6 +1389,10 @@ mul_scal(GEN y, GEN x, long ty)
       return RgX_Rg_mul(y, x);
     case t_SER: return mul_ser_scal(y, x);
     case t_RFRAC: return mul_rfrac_scal(gel(y,1),gel(y,2), x);
+    case t_INFINITY:
+      s = gsigne(x) * inf_get_sign(y);
+      if (!s) pari_err_OP("*",x,y);
+      return mksoo(s);
     case t_QFI: case t_QFR:
       if (typ(x) == t_INT && gequal1(x)) return gcopy(y); /* fall through */
   }
@@ -1914,6 +1930,7 @@ gmul(GEN x, GEN y)
       }
       return z;
 
+    case t_INFINITY: return mksoo(inf_get_sign(x) * inf_get_sign(y));
 
     default:
       pari_err_TYPE2("*",x,y);
@@ -2503,6 +2520,7 @@ GEN
 gdiv(GEN x, GEN y)
 {
   long tx = typ(x), ty = typ(y), lx, ly, vx, vy, i;
+  int s;
   pari_sp av, tetpil;
   GEN z, p1, p2;
 
@@ -2836,6 +2854,10 @@ gdiv(GEN x, GEN y)
       return z;
     case t_LIST: case t_STR: case t_VECSMALL: case t_CLOSURE:
       pari_err_TYPE2("/",x,y);
+    case t_INFINITY:
+      s = inf_get_sign(x) * gsigne(y);
+      if (!s) pari_err_INV("/", y);
+      return mksoo(s);
   }
 
   vy = gvar(y);
diff --git a/src/basemath/gen2.c b/src/basemath/gen2.c
index 0a94fc4..d85cfda 100644
--- a/src/basemath/gen2.c
+++ b/src/basemath/gen2.c
@@ -1731,7 +1731,7 @@ gneg(GEN x)
     case t_VEC: return RgV_neg(x);
     case t_COL: return RgC_neg(x);
     case t_MAT: return RgM_neg(x);
-    case t_INFINITY: return inf_get_sign(x) == 1? mkmoo(): mkoo();
+    case t_INFINITY: return mksoo(-inf_get_sign(x));
     default:
       pari_err_TYPE("gneg",x);
       return NULL; /* not reached */
@@ -1799,6 +1799,8 @@ gneg_i(GEN x)
       gel(y,1) = gneg_i(gel(x,1));
       gel(y,2) = gel(x,2); break;
 
+    case t_INFINITY: return mksoo(-inf_get_sign(x));
+
     default:
       pari_err_TYPE("gneg_i",x);
       return NULL; /* not reached */
diff --git a/src/headers/paridecl.h b/src/headers/paridecl.h
index 7e02467..b4ac1c2 100644
--- a/src/headers/paridecl.h
+++ b/src/headers/paridecl.h
@@ -4163,6 +4163,7 @@ INLINE GEN    mkcomplex(GEN x, GEN y);
 INLINE GEN    mkerr(long n);
 INLINE GEN    mkmoo();
 INLINE GEN    mkoo();
+INLINE GEN    mksoo(long s);
 INLINE GEN    mkfrac(GEN x, GEN y);
 INLINE GEN    mkfraccopy(GEN x, GEN y);
 INLINE GEN    mkintmod(GEN x, GEN y);
diff --git a/src/headers/pariinl.h b/src/headers/pariinl.h
index 9a67a02..6912ae1 100644
--- a/src/headers/pariinl.h
+++ b/src/headers/pariinl.h
@@ -235,6 +235,8 @@ INLINE GEN
 mkoo() { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
 INLINE GEN
 mkmoo() { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
+INLINE GEN
+mksoo(long s) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = (s >= 0) ? gen_1 : gen_m1; return v; }
 INLINE long
 inf_get_sign(GEN x) { return signe(gel(x,1)); }
 /* pol */