[Poincare] Proper Integer approximation

poincare/include/poincare/integer.h

@@ -19,6 +19,7 @@ class Integer : public Expression {
     const Integer operator+(const Integer &other) const;
     const Integer operator*(const Integer &other) const;
     bool operator==(const Integer &other) const;
+    virtual float approximate();
   protected:
     virtual void layout();
   private:

poincare/src/integer.cpp

@@ -162,15 +162,15 @@ float Integer::approximate() {
   *
   * We can tell that:
   * - the sign is going to be 0 for now, we only handle positive numbers
-  * - the exponent is the length of our BigInt, in bits + 127
-  * - the mantissa is the beginning of our BigInt
+  * - the exponent is the length of our BigInt, in bits - 1 + 127;
+  * - the mantissa is the beginning of our BigInt, discarding the first bit
   */
   //bool sign = 0;
 
   native_uint_t lastDigit = m_digits[m_numberOfDigits-1];
   uint8_t numberOfBitsInLastDigit = log2(lastDigit);
 
-  uint8_t exponent = 127;
+  uint8_t exponent = 126;
   exponent += (m_numberOfDigits-1)*32;
   exponent += numberOfBitsInLastDigit;
 
@@ -184,7 +184,7 @@ float Integer::approximate() {
   uint_result = 0;
   //uint_result |= (sign << 31);
   uint_result |= (exponent << 23);
-  uint_result |= (mantissa >> (32-23) & 0x7FFFFF);
+  uint_result |= (mantissa >> (32-23-1) & 0x7FFFFF);
 
   return float_result;
 }

poincare/test/integer.cpp

@@ -21,3 +21,7 @@ QUIZ_CASE(poincare_integer_multiply) {
 QUIZ_CASE(poincare_integer_parse_integer) {
   assert(Integer::parseInteger("123") == Integer(123));
 }
+
+QUIZ_CASE(poincare_integer_approximate) {
+  assert(Integer::parseInteger("12345678").approximate() == 12345678.0f);
+}