Floor and ceil

PRECISION.md

@@ -212,7 +212,8 @@ Ceil is the ceiling function $x \mapsto \lceil x \rceil$, returning the integer
 
 It returns an empty interval on an empty argument.
 
-It outputs integers, so it doesn't need to represent bits after the binary point: $l'=0$.
+Although its result is mathematically an integer, the implementation of the primitive uses `std::ceil`, whose return value is a floating-point number.
+We thus chose to set the output precision to $-1$, which might be under-optimal, but will force the interval library and the code generator to treat the result as floating-point.
 
 ## Checkbox
 
@@ -229,6 +230,15 @@ The smallest gap between two consecutive images is attained at one of the multip
 While it is possible to bound how close to a multiple of $\pi$ a fixed-point number will be, 
 it is too costly to compute for this application, and we will consider that the difference computed at the smallest multiple of $\pi$ (i.e. 0) gives sufficient precision.
 
+## Floor
+
+Floor is the floor function $x \mapsto \lfloor x \rfloor$, returning the integer right above its argument.
+
+It returns an empty interval on an empty argument.
+
+Although its result is mathematically an integer, the implementation of the primitive uses `std::floor`, whose return value is a floating-point number.
+We thus chose to set the output precision to $-1$, which might be under-optimal, but will force the interval library and the code generator to treat the result as floating-point.
+
 # Typology of functions
 
 ## Binary operator

interval/intervalCeil.cpp

@@ -31,7 +31,9 @@ interval interval_algebra::Ceil(const interval& x)
     if (x.isEmpty()) {
         return x;
     }
-    return {ceil(x.lo()), ceil(x.hi()), 0};  // ceil yields integers, thus with LSB 0
+    return {ceil(x.lo()), ceil(x.hi()), -1 };  // even though the output of floor are mathematical integers,
+                                            // they are implemented as floats and thus should not be given precision 0,
+                                            // lest it be cast as an int
 }
 
 void interval_algebra::testCeil()

interval/intervalFloor.cpp

@@ -29,9 +29,11 @@ namespace itv {
 interval interval_algebra::Floor(const interval& x)
 {
     if (x.isEmpty()) {
-        return {};
+        return x;
     }
-    return {floor(x.lo()), floor(x.hi()), 0};  // floor yields integers, thus with LSB 0
+    return {floor(x.lo()), floor(x.hi()), -1};  // even though the output of floor are mathematical integers,
+                                                // they are implemented as floats and thus should not be given precision 0,
+                                                // lest it be cast as an int
 }
 
 void interval_algebra::testFloor()