[flang] Fix SPACING() of very small values

SPACING() must return TINY() for zero arguments (which we do)
and also for subnormal values smaller than TINY() in absolute value,
which we get wrong.  Fix folding and the runtime.

Differential Revision: https://reviews.llvm.org/D151272

Author: klausler

flang/lib/Evaluate/real.cpp

@@ -745,12 +745,12 @@ template <typename W, int P> Real<W, P> Real<W, P>::SPACING() const {
     return *this;
   } else if (IsInfinite()) {
     return NotANumber();
-  } else if (IsZero()) {
-    return TINY();
+  } else if (IsZero() || IsSubnormal()) {
+    return TINY(); // mandated by standard
   } else {
     Real result;
     result.Normalize(false, Exponent(), Fraction::MASKR(1));
-    return result;
+    return result.IsZero() ? TINY() : result;
   }
 }
 

flang/runtime/numeric.cpp

@@ -239,8 +239,9 @@ template <int PREC, typename T> inline T Spacing(T x) {
     // subnormal.
     return std::numeric_limits<T>::min(); // 0 -> TINY(x)
   } else {
-    return std::ldexp(
-        static_cast<T>(1.0), std::ilogb(x) + 1 - PREC); // 2**(e-p)
+    T result{
+        std::ldexp(static_cast<T>(1.0), std::ilogb(x) + 1 - PREC)}; // 2**(e-p)
+    return result == 0 ? /*TINY(x)*/ std::numeric_limits<T>::min() : result;
   }
 }
 

flang/test/Evaluate/fold-spacing.f90

@@ -7,6 +7,7 @@ module m
   logical, parameter :: test_4 = spacing(0.) == tiny(0.)
   logical, parameter :: test_5 = spacing(tiny(0.)) == 1.e-45
   logical, parameter :: test_6 = spacing(8388608.) == 1.
+  logical, parameter :: test_7 = spacing(spacing(tiny(.0))) == tiny(0.)
   logical, parameter :: test_11 = rrspacing(3.0) == scale(0.75, 24)
   logical, parameter :: test_12 = rrspacing(-3.0) == scale(0.75, 24)
   logical, parameter :: test_13 = rrspacing(3.0d0) == scale(0.75, 53)