From 55fdd25a6c7d3fce0cb7c7daa91290eaa17b6197 Mon Sep 17 00:00:00 2001
From: Zeno Rogue <zeno@attnam.com>
Date: Wed, 7 Nov 2018 00:51:41 +0100
Subject: [PATCH] formula parser now understands complex numbers, and some
 extra functions including let(x=2, x*x)

---
 conformal.cpp      | 28 ++++++++++++++--------------
 dialogs.cpp        |  2 +-
 hyper.h            | 13 ++++++++-----
 rogueviz-graph.cpp | 21 ++++++++++++++-------
 util.cpp           | 30 ++++++++++++++++++++++++++----
 5 files changed, 63 insertions(+), 31 deletions(-)

diff --git a/conformal.cpp b/conformal.cpp
index ee2727a4..e6287e40 100644
--- a/conformal.cpp
+++ b/conformal.cpp
@@ -13,7 +13,7 @@ namespace polygonal {
 
   typedef long double xld;
 
-  typedef complex<xld> cld;
+  typedef complex<xld> cxld;
 
   int SI = 4;
   ld  STAR = 0;
@@ -23,13 +23,13 @@ namespace polygonal {
   precise matrix[MSI][MSI];
   precise ans[MSI];
   
-  cld coef[MSI];
+  cxld coef[MSI];
   ld coefr[MSI], coefi[MSI]; 
   int maxcoef, coefid;
   
   void solve() {
     if(pmodel == mdPolynomial) {
-      for(int i=0; i<MSI; i++) coef[i] = cld(coefr[i], coefi[i]);
+      for(int i=0; i<MSI; i++) coef[i] = cxld(coefr[i], coefi[i]);
       return;
       } 
     if(pmodel != mdPolygonal) return;
@@ -74,15 +74,15 @@ namespace polygonal {
       y /= r;
       }
     if(pmodel == mdPolynomial) {
-      cld z(x,y);
-      cld res (0,0);
+      cxld z(x,y);
+      cxld res (0,0);
       for(int i=maxcoef; i>=0; i--) { res += coef[i]; if(i) res *= z; }
       return make_pair(real(res), imag(res));    
       }
       
-    cld z(x, y);
-    cld res (0,0);
-    cld zp = 1; for(int i=0; i<SI; i++) zp *= z;
+    cxld z(x, y);
+    cxld res (0,0);
+    cxld zp = 1; for(int i=0; i<SI; i++) zp *= z;
 
     for(int i=prec; i>0; i--) { 
       res += ans[i]; 
@@ -104,7 +104,7 @@ namespace polygonal {
     else C = cos(ho * M_PI/180), S = sin(ho * M_PI / 180);
 
     for(int r=0; r<=2000; r++) {
-      cld z = exp(cld(0, 2*M_PI * r / 2000.0));
+      cxld z = exp(cxld(0, 2*M_PI * r / 2000.0));
       pair<xld,xld> z2 = compute(real(z), imag(z), deg);
       hyperpoint h;
       h[0] = (z2.first * C - z2.second * S) * vid.radius;
@@ -123,7 +123,7 @@ namespace polygonal {
 namespace spiral {
 
   typedef long double ld;
-  typedef complex<long double> cld;
+  typedef complex<long double> cxld;
 
   int shiftx, shifty, velx, vely;
 
@@ -154,9 +154,9 @@ namespace spiral {
 
     ld k = -2*M_PI*M_PI / log(2.6180339);
 
-//   cld mnoznik = cld(0, M_PI) / cld(k, M_PI);
+//   cxld mnoznik = cxld(0, M_PI) / cxld(k, M_PI);
 
-    cld factor = cld(0, -CY/2/M_PI/M_PI) * cld(k, M_PI);
+    cxld factor = cxld(0, -CY/2/M_PI/M_PI) * cxld(k, M_PI);
     
     Yshift = CY * k / M_PI;
     
@@ -167,8 +167,8 @@ namespace spiral {
     
     for(int y=0; y<SY; y++)
     for(int x=0; x<SX; x++) {
-      cld z(x-xc, y-yc);
-      cld z1 = log(z);
+      cxld z(x-xc, y-yc);
+      cxld z1 = log(z);
 
       z1 = z1 * factor;
 
diff --git a/dialogs.cpp b/dialogs.cpp
index 32258065..502a0411 100644
--- a/dialogs.cpp
+++ b/dialogs.cpp
@@ -605,7 +605,7 @@ namespace dialog {
     if(kind == 's') {
       exp_parser ep;
       ep.s = ne.s;
-      ld x = ep.parse();
+      ld x = real(ep.parse());
       if(!ep.ok()) return;
       if(ne.sc.positive && x <= 0) return;
       *ne.editwhat = x;
diff --git a/hyper.h b/hyper.h
index c1ad2235..6ea5bbfd 100644
--- a/hyper.h
+++ b/hyper.h
@@ -167,6 +167,8 @@ typedef long double ld;
 #define PLDF "Lf"
 #endif
 
+typedef complex<ld> cld;
+
 #define DEBMEM(x) // { x fflush(stdout); }
 
 #define DEBSM(x) 
@@ -4260,7 +4262,7 @@ struct exp_parser {
   int at;
   exp_parser() { at = 0; }
   
-  map<string, ld> extra_params;
+  map<string, cld> extra_params;
 
   bool ok() { return at == isize(s); }
   char next() { if(at == isize(s) || at == -1) return 0; else return s[at]; }
@@ -4273,14 +4275,15 @@ struct exp_parser {
     return false;
     }
 
-  ld parse(int prio = 0);
+  cld parse(int prio = 0);
 
-  ld parsepar() {
-    ld res = parse();
+  cld parsepar() {
+    cld res = parse();
     if(next() != ')') { at = -1; return res; }
     at++;
     return res;
-    }  
+    }
+
   };
 
 #ifdef CAP_COMPLEX2
diff --git a/rogueviz-graph.cpp b/rogueviz-graph.cpp
index 4f49ca86..702ea6de 100644
--- a/rogueviz-graph.cpp
+++ b/rogueviz-graph.cpp
@@ -285,6 +285,12 @@ hyperpoint err = hpxyz(500,0,0);
 
 bool iserror(hyperpoint h) { return sqhypot2(h) > 10000 || std::isnan(h[0]) || std::isnan(h[1]) || std::isnan(h[2]) || std::isinf(h[0]) || std::isinf(h[1]) || std::isinf(h[2]); }
 
+hyperpoint xy_to_point(ld x, ld y) {
+  if(sphere && hypot(x, y) > 1)
+    return err;
+  return hpxy(x, y);
+  }
+  
 hyperpoint find_point(ld t) {
   exp_parser ep;
   auto &dict = ep.extra_params;
@@ -298,17 +304,18 @@ hyperpoint find_point(ld t) {
     ep.at = 0;
     while(!among(ep.next(), '=', -1)) varname += ep.next(), ep.at++;
     ep.at++;
-    ld x = ep.parse();
+    cld x = ep.parse();
     if(!ep.ok()) return err;
     dict[varname] = x;
     }
   if(!dict.count("y") && dict.count("r"))
-    return xspinpush0(dict["phi"], dict["r"]);
-  if(dict.count("z"))
-    return hpxyz(dict["x"], dict["y"], dict["z"]);
-  if(sphere && hypot(dict["x"], dict["y"]) > 1)
-    return err;
-  return hpxy(dict["x"], dict["y"]);   
+    return xspinpush0(real(dict["phi"]), real(dict["r"]));
+  if(dict.count("z") && dict.count("x"))
+    return hpxyz(real(dict["x"]), real(dict["y"]), real(dict["z"]));
+  if(dict.count("z")) {
+   return xy_to_point(real(dict["z"]), imag(dict["z"]));
+   }
+  return xy_to_point(real(dict["x"]), real(dict["y"]));
   }
 
 hyperpoint gcurvestart = err;
diff --git a/util.cpp b/util.cpp
index 027ab916..16f840dc 100644
--- a/util.cpp
+++ b/util.cpp
@@ -151,8 +151,9 @@ struct indenter {
 
 void doindent() { for(int i=0; i<current_indentation; i++) printf(" "); }
 
-ld exp_parser::parse(int prio) {
-  ld res;
+cld exp_parser::parse(int prio) {
+  cld res;
+  while(next() == ' ') at++;
   if(eat("sin(")) res = sin(parsepar());
   else if(eat("cos(")) res = cos(parsepar());
   else if(eat("sinh(")) res = sinh(parsepar());
@@ -167,7 +168,27 @@ ld exp_parser::parse(int prio) {
   else if(eat("tanh(")) res = tanh(parsepar());
   else if(eat("atan(")) res = atan(parsepar());
   else if(eat("atanh(")) res = atanh(parsepar());
-  else if(next() == '(') at++, res = parsepar();
+  else if(eat("abs(")) res = abs(parsepar());
+  else if(eat("re(")) res = real(parsepar());
+  else if(eat("im(")) res = imag(parsepar());
+  else if(eat("conj(")) res = std::conj(parsepar());
+  else if(eat("let(")) {
+    string name;
+    while(true) {
+      char c = next();
+      if((c >= '0' && c <= '9') || c == '.' || (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z') || c == '_')
+        name += c, at++;
+      else break;
+      }
+    if(next() != '=') { at = -1; return 0; }
+    at++;
+    cld val = parse(0);
+    if(next() != ',') { at = -1; return 0; }
+    at++;
+    dynamicval<cld> d(extra_params[name], val);
+    return parsepar();
+    }
+  else if(next() == '(') at++, res = parsepar(); 
   else {
     string number;
     while(true) {
@@ -177,6 +198,7 @@ ld exp_parser::parse(int prio) {
       else break;
       }
     if(number == "e") res = exp(1);
+    else if(number == "i") res = cld(0, 1);
     else if(number == "p" || number == "pi") res = M_PI;
     else if(number == "" && next() == '-') res = 0, prio = 0;
     else if(number == "") at = -1;
@@ -198,7 +220,7 @@ ld exp_parser::parse(int prio) {
 ld parseld(const string& s) {
   exp_parser ep;
   ep.s = s;
-  return ep.parse();
+  return real(ep.parse());
   }
 
 }