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fix: gamma functions #943

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merged 3 commits into from
Mar 7, 2025
Merged

fix: gamma functions #943

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069501e
fix: special gamma functions
wassup05 Mar 6, 2025
c0ce8dc
remove unreachable code
wassup05 Mar 6, 2025
499052f
add else clause to cover all branches
wassup05 Mar 6, 2025
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33 changes: 8 additions & 25 deletions src/stdlib_specialfunctions_gamma.fypp
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Original file line number Diff line number Diff line change
Expand Up @@ -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

Expand Down Expand Up @@ -575,9 +576,9 @@ 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_${k1}$
Expand All @@ -603,6 +604,9 @@ 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
Expand Down Expand Up @@ -668,30 +672,9 @@ contains

end do

else !Algorithm 2 in the reference

m = nint(ss)
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(m , 2) /= 0) b = b + d * c / a
else
g = ieee_value(1._${k1}$, ieee_quiet_nan)

g = ((-1) ** m * exp(-a + log_gamma(p) - (p - 1) * log(a)) + b) / a
end if

res = g
Expand Down
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