[poincare] Power: approximation of power of positive real and real is

real. Fix 10^1000 = inf instead of undef

poincare/Makefile

@@ -150,6 +150,7 @@ tests += $(addprefix poincare/test/,\
   function.cpp\
   helper.cpp\
   helpers.cpp\
+  infinity.cpp\
   integer.cpp\
   layouts.cpp\
   logarithm.cpp\

poincare/src/power.cpp

@@ -81,13 +81,21 @@ int PowerNode::getPolynomialCoefficients(Context & context, const char * symbolN
 
 template<typename T>
 Complex<T> PowerNode::compute(const std::complex<T> c, const std::complex<T> d) {
+  std::complex<T> result = std::pow(c, d);
+  if (c.imag() == 0.0 && d.imag() == 0.0 && c.real() >= 0.0) {
+    /* pow: (R+, R) -> R+
+     * However, std::pow(2.0, 1000) = (INFINITY, NAN). Openbsd pow of a
+     * positive real and another real has a undefined imaginary when the real
+     * result is infinity. To avoid this, we force the imaginary part of
+     * pow(R+,R) to 0.0. */
+    result.imag(0.0);
+  }
   /* Openbsd trigonometric functions are numerical implementation and thus are
    * approximative.
    * The error epsilon is ~1E-7 on float and ~1E-15 on double. In order to
    * avoid weird results as e(i*pi) = -1+6E-17*i, we compute the argument of
    * the result of c^d and if arg ~ 0 [Pi], we discard the residual imaginary
    * part and if arg ~ Pi/2 [Pi], we discard the residual real part. */
-  std::complex<T> result = std::pow(c, d);
   return Complex<T>(ApproximationHelper::TruncateRealOrImaginaryPartAccordingToArgument(result));
 }
 

poincare/test/infinity.cpp

@@ -0,0 +1,26 @@
+#include <quiz.h>
+#include <ion.h>
+#include <assert.h>
+#include "helper.h"
+#if POINCARE_TESTS_PRINT_EXPRESSIONS
+#include "../src/expression_debug.h"
+#include <iostream>
+using namespace std;
+#endif
+
+using namespace Poincare;
+
+QUIZ_CASE(poincare_infinity) {
+
+  // 0 and infinity
+  assert_parsed_expression_simplify_to("0/0", Undefined::Name());
+  assert_parsed_expression_simplify_to("0/inf", "0");
+  assert_parsed_expression_simplify_to("inf/0", Undefined::Name());
+  assert_parsed_expression_simplify_to("0*inf", Undefined::Name());
+  assert_parsed_expression_simplify_to("3*inf/inf", "inf/inf"); //TODO undef would be better
+  assert_parsed_expression_simplify_to("1E1000", "inf");
+  assert_parsed_expression_simplify_to("-1E1000", "-inf");
+  assert_parsed_expression_simplify_to("-1E-1000", "0");
+  assert_parsed_expression_simplify_to("1E-1000", "0");
+  assert_parsed_expression_evaluates_to<double>("1*10^1000", "inf");
+}

poincare/test/simplify_mix.cpp

@@ -11,14 +11,6 @@ using namespace std;
 using namespace Poincare;
 
 QUIZ_CASE(poincare_simplify_mix) {
-
-  // 0 and infinity
-  assert_parsed_expression_simplify_to("0/0", Undefined::Name());
-  assert_parsed_expression_simplify_to("0/inf", "0");
-  assert_parsed_expression_simplify_to("inf/0", Undefined::Name());
-  assert_parsed_expression_simplify_to("0*inf", Undefined::Name());
-  assert_parsed_expression_simplify_to("3*inf/inf", "inf/inf"); //TODO undef would be better
-
   // Root at denominator
   assert_parsed_expression_simplify_to("1/(R(2)+R(3))", "(-R(2))+R(3)");
   assert_parsed_expression_simplify_to("1/(5+R(3))", "(5-R(3))/22");