diff --git a/stl/inc/random b/stl/inc/random
index ebb66b92c05..79c11840bf9 100644
--- a/stl/inc/random
+++ b/stl/inc/random
@@ -2932,15 +2932,32 @@ private:
             _Ty _Vx1;
             _Ty _Vx2;
             _Ty _Sx;
-            for (;;) { // reject bad values
+            for (;;) { // reject bad values to avoid generating NaN/Inf on the next calculations
                 _Vx1 = 2 * _NRAND(_Eng, _Ty) - 1;
                 _Vx2 = 2 * _NRAND(_Eng, _Ty) - 1;
                 _Sx  = _Vx1 * _Vx1 + _Vx2 * _Vx2;
-                if (_Sx < 1) {
+                if (_Sx < _Ty{1} && _Vx1 != _Ty{0} && _Vx2 != _Ty{0}) {
+                    // good values!
                     break;
                 }
             }
-            const auto _Fx = static_cast<_Ty>(_CSTD sqrt(-2.0 * _CSTD log(_Sx) / _Sx));
+
+            _Ty _LogSx;
+            if (_Sx > _Ty{1e-4}) {
+                _LogSx = _STD log(_Sx);
+            } else {
+                // Bad _Sx value! Very small values will overflow log(_Sx) / _Sx.
+                // Generate a new value based on scaling method.
+                const _Ty _Ln2{_Ty{0.69314718055994530941723212145818}};
+                const _Ty _Maxabs{(_STD max)(_STD abs(_Vx1), _STD abs(_Vx2))};
+                const int _ExpMax{_STD ilogb(_Maxabs)};
+                _Vx1   = _STD scalbn(_Vx1, -_ExpMax);
+                _Vx2   = _STD scalbn(_Vx2, -_ExpMax);
+                _Sx    = _Vx1 * _Vx1 + _Vx2 * _Vx2;
+                _LogSx = _STD log(_Sx) + static_cast<_Ty>(_ExpMax) * (_Ln2 * 2);
+            }
+
+            const auto _Fx = _Ty{_STD sqrt(_Ty{-2} * _LogSx / _Sx)};
             if (_Keep) { // save second value for next call
                 _Xx2   = _Fx * _Vx2;
                 _Valid = true;
@@ -3864,7 +3881,7 @@ public:
                 _Px1 = _CSTD pow(_Px1, _Ty{1} / _Ax);
                 _Px2 = _CSTD pow(_Px2, _Ty{1} / _Bx);
                 _Wx  = _Px1 + _Px2;
-                if (_Wx <= _Ty{1}) {
+                if (_Wx <= _Ty{1} && _Wx != _Ty{0}) {
                     break;
                 }
             }
@@ -3872,11 +3889,21 @@ public:
         } else { // use gamma distributions instead
             _Ty _Px1;
             _Ty _Px2;
+            _Ty _PSum;
             gamma_distribution<_Ty> _Dist1(_Ax, 1);
             gamma_distribution<_Ty> _Dist2(_Bx, 1);
-            _Px1 = _Dist1(_Eng);
-            _Px2 = _Dist2(_Eng);
-            return _Px1 / (_Px1 + _Px2);
+
+            for (;;) { // reject pairs whose sum is zero
+                _Px1  = _Dist1(_Eng);
+                _Px2  = _Dist2(_Eng);
+                _PSum = _Px1 + _Px2;
+
+                if (_PSum != _Ty{0}) {
+                    break;
+                }
+            }
+
+            return _Px1 / _PSum;
         }
     }
 
@@ -4001,12 +4028,18 @@ private:
         _Ty _Px;
         _Ty _Vx1;
         _Ty _Vx2;
+        const _Ty _Vx3{1};
         _Vx1 = static_cast<_Ty>(_Par0._Mx) * static_cast<_Ty>(0.5);
         _Vx2 = static_cast<_Ty>(_Par0._Nx) * static_cast<_Ty>(0.5);
         _Beta_distribution<_Ty> _Dist(_Vx1, _Vx2);
-        _Px = _Dist(_Eng);
+        for (;;) { // reject bad values
+            _Px = _Dist(_Eng);
+            if (_Px != _Vx3) {
+                break;
+            }
+        }
 
-        return (_Vx2 / _Vx1) * (_Px / (_Ty{1} - _Px));
+        return (_Vx2 / _Vx1) * (_Px / (_Vx3 - _Px));
     }
 
     param_type _Par;
@@ -4137,13 +4170,13 @@ private:
             _Vx2 = _Dist(_Eng);
             _Rs  = _Vx1 * _Vx1 + _Vx2 * _Vx2;
 
-            if (_Rs < _Ty{1}) {
+            // very small _Rs will overflow on pow(_Rx0, -_Ty{4} / _Par0._Nx)
+            if (_Rs < _Ty{1} && _Rs > _Ty{1e-12}) {
                 break;
             }
         }
-        _Rx0 = _CSTD sqrt(_Rs);
-
-        return _Vx1 * _CSTD sqrt(_Par0._Nx * (_CSTD pow(_Rx0, -_Ty{4} / _Par0._Nx) - _Ty{1}) / _Rs);
+        _Rx0 = _STD sqrt(_Rs);
+        return _Vx1 * _STD sqrt(_Par0._Nx * (_STD pow(_Rx0, -_Ty{4} / _Par0._Nx) - _Ty{1}) / _Rs);
     }
 
     param_type _Par;
diff --git a/tests/std/tests/GH_001017_discrete_distribution_out_of_range/test.cpp b/tests/std/tests/GH_001017_discrete_distribution_out_of_range/test.cpp
index 5a43af9b4df..d4ded00b997 100644
--- a/tests/std/tests/GH_001017_discrete_distribution_out_of_range/test.cpp
+++ b/tests/std/tests/GH_001017_discrete_distribution_out_of_range/test.cpp
@@ -6,6 +6,23 @@
 
 #include "bad_random_engine.hpp"
 
+template <class Distribution>
+void Test_for_NaN_Inf(Distribution&& distribution) {
+    for (bad_random_generator rng; !rng.has_cycled_through();) {
+        const auto rand_value = distribution(rng);
+        assert(!isnan(rand_value) && !isinf(rand_value));
+    }
+}
+
+template <class T>
+void Test_distributions() {
+    // Additionally test GH-1174 "<random>: Some random number distributions could return NaN"
+    Test_for_NaN_Inf(std::normal_distribution<T>{});
+    Test_for_NaN_Inf(std::lognormal_distribution<T>{});
+    Test_for_NaN_Inf(std::fisher_f_distribution<T>{});
+    Test_for_NaN_Inf(std::student_t_distribution<T>{});
+}
+
 int main() {
     std::discrete_distribution<int> dist{1, 1, 1, 1, 1, 1};
     bad_random_generator rng;
@@ -14,4 +31,8 @@ int main() {
         const auto rand_value = dist(rng);
         assert(0 <= rand_value && rand_value < 6);
     }
+
+    Test_distributions<float>();
+    Test_distributions<double>();
+    Test_distributions<long double>();
 }