From 069501e66c5936cc951495d9270dfcedcd2f8e4d Mon Sep 17 00:00:00 2001
From: "supritsj@Arch" <supritsj05@gmail.com>
Date: Thu, 6 Mar 2025 11:47:24 +0530
Subject: [PATCH 1/3] fix: special gamma functions

---
 src/stdlib_specialfunctions_gamma.fypp | 12 +++++++-----
 1 file changed, 7 insertions(+), 5 deletions(-)

diff --git a/src/stdlib_specialfunctions_gamma.fypp b/src/stdlib_specialfunctions_gamma.fypp
index 88a73063b..4d0c34409 100644
--- a/src/stdlib_specialfunctions_gamma.fypp
+++ b/src/stdlib_specialfunctions_gamma.fypp
@@ -575,9 +575,9 @@ contains
     ! Fortran 90 program by Jim-215-Fisher
     !
         ${t1}$, intent(in) :: p, x
-        integer :: n, m
+        integer :: n
 
-        ${t2}$ :: res, p_lim, a, b, g, c, d, y, ss
+        ${t2}$ :: res, p_lim, a, b, g, c, d, y
         ${t2}$, parameter :: zero = 0.0_${k2}$, one = 1.0_${k2}$
         ${t2}$, parameter :: dm = tiny(1.0_${k2}$) * 10 ** 6
         ${t1}$, parameter :: zero_k1 = 0.0_${k1}$
@@ -603,6 +603,9 @@ contains
             call error_stop("Error(gpx): Incomplete gamma function with "      &
             //"negative x must come with a whole number p not too small")
 
+        if(x < zero_k1) call error_stop("Error(gpx): Incomplete gamma"         &
+            // " function with negative x must have an integer parameter p")
+
         if(p >= p_lim) then     !use modified Lentz method of continued fraction
                                 !for eq. (15) in the above reference.
             a = one
@@ -670,7 +673,6 @@ contains
 
         else                            !Algorithm 2 in the reference
 
-            m = nint(ss)
             a = - x
             c = one / a
             d = p - one
@@ -689,9 +691,9 @@ contains
 
             end do
 
-            if(y >= b * tol_${k2}$ .and. mod(m , 2) /= 0) b = b + d * c / a
+            if(y >= b * tol_${k2}$ .and. mod(int(p), 2) /= 0) b = b + d * c / a
 
-            g = ((-1) ** m * exp(-a + log_gamma(p) - (p - 1) * log(a)) + b) / a
+            g = ((-1) ** p * exp(-a + log_gamma(p) - (p - 1) * log(a)) + b) / a
         end if
 
         res = g

From c0ce8dc6e59b9de77b2e5fd89ee1d744a1359ad1 Mon Sep 17 00:00:00 2001
From: "supritsj@Arch" <supritsj05@gmail.com>
Date: Thu, 6 Mar 2025 12:15:49 +0530
Subject: [PATCH 2/3] remove unreachable code

---
 src/stdlib_specialfunctions_gamma.fypp | 23 -----------------------
 1 file changed, 23 deletions(-)

diff --git a/src/stdlib_specialfunctions_gamma.fypp b/src/stdlib_specialfunctions_gamma.fypp
index 4d0c34409..6a28c2116 100644
--- a/src/stdlib_specialfunctions_gamma.fypp
+++ b/src/stdlib_specialfunctions_gamma.fypp
@@ -671,29 +671,6 @@ contains
 
             end do
 
-        else                            !Algorithm 2 in the reference
-
-            a = - x
-            c = one / a
-            d = p - one
-            b = c * (a - d)
-            n = 1
-
-            do
-
-                c = d * (d - one) / (a * a)
-                d = d - 2
-                y = c * (a - d)
-                b = b + y
-                n = n + 1
-
-                if(n > int((p - 2) / 2) .or. y < b * tol_${k2}$) exit
-
-            end do
-
-            if(y >= b * tol_${k2}$ .and. mod(int(p), 2) /= 0) b = b + d * c / a
-
-            g = ((-1) ** p * exp(-a + log_gamma(p) - (p - 1) * log(a)) + b) / a
         end if
 
         res = g

From 499052f2edf0c6b98ab7f0076f16d857a95ebbe1 Mon Sep 17 00:00:00 2001
From: "supritsj@Arch" <supritsj05@gmail.com>
Date: Thu, 6 Mar 2025 22:17:09 +0530
Subject: [PATCH 3/3] add else clause to cover all branches

---
 src/stdlib_specialfunctions_gamma.fypp | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/src/stdlib_specialfunctions_gamma.fypp b/src/stdlib_specialfunctions_gamma.fypp
index 6a28c2116..d051c94df 100644
--- a/src/stdlib_specialfunctions_gamma.fypp
+++ b/src/stdlib_specialfunctions_gamma.fypp
@@ -4,6 +4,7 @@
 #:set CI_KINDS_TYPES = INT_KINDS_TYPES + C_KINDS_TYPES
 module stdlib_specialfunctions_gamma
     use iso_fortran_env, only : qp => real128
+    use ieee_arithmetic, only: ieee_value, ieee_quiet_nan
     use stdlib_kinds, only :  sp, dp, int8, int16, int32, int64
     use stdlib_error, only : error_stop
 
@@ -671,6 +672,9 @@ contains
 
             end do
 
+        else
+            g = ieee_value(1._${k1}$, ieee_quiet_nan)
+
         end if
 
         res = g