[poincare] IEEE754: add methods to find the next and the previous

IEEE754 exactly representable float/double

poincare/Makefile

@@ -165,6 +165,7 @@ tests_src += $(addprefix poincare/test/,\
   function_solver.cpp\
   helper.cpp\
   helpers.cpp\
+  ieee754.cpp\
   integer.cpp\
   layout.cpp\
   layout_cursor.cpp\

poincare/include/poincare/ieee754.h

@@ -28,7 +28,6 @@ public:
     assert(k_totalNumberOfBits == 8*sizeof(T));
     return k_totalNumberOfBits;
   }
-
   static T buildFloat(bool sign, uint16_t exponent, uint64_t mantissa) {
     static uint64_t oneOnMantissaBits = ((uint64_t)1 << k_mantissaNbBits)-1;
     uint_float u;
@@ -74,11 +73,41 @@ public:
     }
     return exponentBase10;
   }
+  static T next(T f) {
+    return nextOrPrevious(f, true);
+  }
+
+  static T previous(T f) {
+    return nextOrPrevious(f, false);
+  }
+
 private:
   union uint_float {
     uint64_t ui;
     T f;
   };
+  static T nextOrPrevious(T f, bool isNext) {
+    if (std::isinf(f) || std::isnan(f)) {
+      return f;
+    }
+    uint_float u;
+    u.ui = 0;
+    u.f = f;
+    uint64_t oneBitOnSignBit = (uint64_t)1 << (k_exponentNbBits + k_mantissaNbBits);
+    if ((isNext && (u.ui & oneBitOnSignBit) > 0) // next: Negative float
+     || (!isNext && (u.ui & oneBitOnSignBit) == 0)) { // previous: Positive float
+      if ((isNext && u.ui == oneBitOnSignBit) // next: -0.0
+       || (!isNext && u.ui == 0.0)) { // previous: 0.0
+        u.ui = isNext ? 0 : oneBitOnSignBit;
+      } else {
+        u.ui -= 1;
+      }
+    } else { // next: Positive float, previous: Negative float
+      u.ui += 1;
+    }
+    return u.f;
+  }
+
   constexpr static size_t k_signNbBits = 1;
   constexpr static size_t k_exponentNbBits = sizeof(T) == sizeof(float) ? 8 : 11;
   constexpr static size_t k_mantissaNbBits = sizeof(T) == sizeof(float) ? 23 : 52;

poincare/test/ieee754.cpp

@@ -0,0 +1,43 @@
+#include <quiz.h>
+#include <poincare/ieee754.h>
+#include <string.h>
+#include <ion.h>
+#include <stdlib.h>
+#include <assert.h>
+#include <cmath>
+#include "helper.h"
+
+using namespace Poincare;
+
+template<typename T>
+void assert_next_and_previous_IEEE754_is(T a, T b) {
+  T next = IEEE754<T>::next(a);
+  T previous = IEEE754<T>::previous(b);
+  assert((std::isnan(next) && std::isnan(b)) || next == b);
+  assert((std::isnan(previous) && std::isnan(a)) || previous == a);
+}
+
+QUIZ_CASE(ieee754_next_and_previous) {
+  assert_next_and_previous_IEEE754_is<float>(0.0f, 1.4E-45f);
+  assert_next_and_previous_IEEE754_is<float>(INFINITY, INFINITY);
+  assert_next_and_previous_IEEE754_is<float>(NAN, NAN);
+  assert_next_and_previous_IEEE754_is<float>(2.2566837E-10f, 2.2566839E-10f);
+  assert_next_and_previous_IEEE754_is<float>(-INFINITY, -INFINITY);
+  assert_next_and_previous_IEEE754_is<float>(-0.0f, 0.0f);
+  assert_next_and_previous_IEEE754_is<float>(-1.4E-45f, -0.0f);
+  assert_next_and_previous_IEEE754_is<float>(-3.4359738E10f, -3.43597363E10f);
+  assert(IEEE754<float>::next(3.4028235E38f) == INFINITY);
+  assert(IEEE754<float>::previous(-3.4028235E38f) == -INFINITY);
+
+  assert_next_and_previous_IEEE754_is<double>(0.0f, 4.94065645841246544176568792868E-324);
+  assert_next_and_previous_IEEE754_is<double>(INFINITY, INFINITY);
+  assert_next_and_previous_IEEE754_is<double>(NAN, NAN);
+  assert_next_and_previous_IEEE754_is<double>(1.936766735060658315512927142E-282, 1.93676673506065869777770528092E-282);
+  assert_next_and_previous_IEEE754_is<double>(-INFINITY, -INFINITY);
+  assert_next_and_previous_IEEE754_is<double>(-0.0, 0.0);
+  assert_next_and_previous_IEEE754_is<double>(-4.94065645841246544176568792868E-324, -0.0);
+  assert_next_and_previous_IEEE754_is<double>(-1.38737906372912431085182213247E201, -1.38737906372912403890916981028E201);
+  assert(IEEE754<double>::next(1.79769313486231570814527423732E308) == INFINITY);
+  assert(IEEE754<double>::previous(-1.79769313486231570814527423732E308) == -INFINITY);
+
+}