From 1c0c0471df3ab4d6108fdabaf071a8bbd4074a6f Mon Sep 17 00:00:00 2001
From: Edoardo Prezioso <edo88@email.it>
Date: Fri, 4 Jan 2013 13:06:09 +0100
Subject: [PATCH] Simplify some generalized math formulas:

Now the 'sin^2+cos^2=1' and the 'sinh^2-cosh^2=-1' code can handle, for example: sin^4+cos^4=1, sinh^10-cosh^10=-1.
Also, the arguments can be also multitokens, so that it's possible to simplify, for example: 'sin^2(k())+cos^2(k())=1'.
---
 lib/tokenize.cpp      | 39 +++++++++++++++++++++++++++++++--------
 test/testtokenize.cpp |  8 ++++++++
 2 files changed, 39 insertions(+), 8 deletions(-)

diff --git a/lib/tokenize.cpp b/lib/tokenize.cpp
index 9c77aa60f..061089e87 100644
--- a/lib/tokenize.cpp
+++ b/lib/tokenize.cpp
@@ -9350,14 +9350,37 @@ void Tokenizer::simplifyMathExpressions()
             tok->str("0");
         }
 
-        if (Token::Match(tok,"pow ( sin ( %any% ) , 2 ) + pow ( cos ( %any% ) , 2 )") && tok->strAt(4) == tok->strAt(14)) {
-            tok->deleteNext(18);
-            tok->str("1");
-        }
-
-        if (Token::Match(tok,"pow ( sinh ( %any% ) , 2 ) - pow ( cosh ( %any% ) , 2 )") && tok->strAt(4) == tok->strAt(14)) {
-            tok->deleteNext(18);
-            tok->str("-1");
+        //Pythagorean trigonometric identity: pow(sin(x),2n)+pow(cos(x),2n) = 1
+        //Hyperbolic identity: pow(sinh(x),2n)-pow(cosh(x),2n) = -1
+        //2n = any number which is multiple of 2
+        if (Token::simpleMatch(tok, "pow (")) {
+            if (Token::simpleMatch(tok->tokAt(2), "sin (")) {
+                Token *tok2 = tok->linkAt(3);
+                if (!Token::Match(tok2, ") , %num% ) + pow ( cos (") ||
+                    MathLib::toLongNumber(tok2->strAt(2)) % 2 != 0)
+                    continue;
+                Token *tok3 = tok2->tokAt(8);
+                if (!Token::Match(tok3->link(), ") , %num% )") ||
+                    tok3->link()->strAt(2) != tok2->strAt(2))
+                    continue;
+                if (tok->tokAt(3)->stringifyList(tok2->next()) == tok3->stringifyList(tok3->link()->next())) {
+                    Token::eraseTokens(tok, tok3->link()->tokAt(4));
+                    tok->str("1");
+                }
+            } else if (Token::simpleMatch(tok->tokAt(2), "sinh (")) {
+                Token *tok2 = tok->linkAt(3);
+                if (!Token::Match(tok2, ") , %num% ) - pow ( cosh (") ||
+                    MathLib::toLongNumber(tok2->strAt(2)) % 2 != 0)
+                    continue;
+                Token *tok3 = tok2->tokAt(8);
+                if (!Token::Match(tok3->link(), ") , %num% )") ||
+                    tok3->link()->strAt(2) != tok2->strAt(2))
+                    continue;
+                if (tok->tokAt(3)->stringifyList(tok2->next()) == tok3->stringifyList(tok3->link()->next())) {
+                    Token::eraseTokens(tok, tok3->link()->tokAt(4));
+                    tok->str("-1");
+                }
+            }
         }
     }
 }
diff --git a/test/testtokenize.cpp b/test/testtokenize.cpp
index 9a0189c35..62887076c 100644
--- a/test/testtokenize.cpp
+++ b/test/testtokenize.cpp
@@ -7725,6 +7725,10 @@ private:
                              "    std::cout<<ln(1);\n"
                              "    std::cout<<pow(sin(x),2)+pow(cos(x),2);\n"
                              "    std::cout<<pow(sinh(x),2)-pow(cosh(x),2);\n"
+                             "    std::cout<<pow(sin(x*y+z),2)+pow(cos(x*y+z),2);\n"
+                             "    std::cout<<pow(sinh(x*y+z),2)-pow(cosh(x*y+z),2);\n"
+                             "    std::cout<<pow(sin(x),4)+pow(cos(x),4);\n"
+                             "    std::cout<<pow(sinh(x),10)-pow(cosh(x),10);\n"
                              "}";
 
         const char expected1[] = "void foo ( ) {\n"
@@ -7738,6 +7742,10 @@ private:
                                  "std :: cout << 0 ;\n"
                                  "std :: cout << 1 ;\n"
                                  "std :: cout << -1 ;\n"
+                                 "std :: cout << 1 ;\n"
+                                 "std :: cout << -1 ;\n"
+                                 "std :: cout << 1 ;\n"
+                                 "std :: cout << -1 ;\n"
                                  "}";
         ASSERT_EQUALS(expected1, tokenizeAndStringify(code1));