From d3cbc671099cb2da802ee4ad6097cd1bbf7064fe Mon Sep 17 00:00:00 2001
From: kamischi <karl-michael.schindler@web.de>
Date: Wed, 6 Mar 2024 13:55:20 +0100
Subject: [PATCH] New tests and summary
---
.gitignore | 1 +
tests/phint optimization/README & RESULTS | 53 ++++++++++++++++++
tests/phint optimization/dooptimization.sh | 10 ----
tests/phint optimization/phint10.f90 | 49 +++++++++++++++++
tests/phint optimization/phint8.f90 | 8 +--
tests/phint optimization/phint9.f90 | 61 +++++++++++++++++++++
tests/phint optimization/phintdriver | Bin 34616 -> 51288 bytes
tests/phint optimization/phintdriver.f90 | 25 ++++++++-
8 files changed, 192 insertions(+), 15 deletions(-)
create mode 100644 tests/phint optimization/README & RESULTS
delete mode 100755 tests/phint optimization/dooptimization.sh
create mode 100644 tests/phint optimization/phint10.f90
create mode 100644 tests/phint optimization/phint9.f90
diff --git a/.gitignore b/.gitignore
index ee9ddc1..7319c4b 100644
--- a/.gitignore
+++ b/.gitignore
@@ -18,3 +18,4 @@ tests/oxlog/bosou
tests/oxlog/bosonf90
tests/oxlog/eelsou
tests/phintlog/eelsf90
+tests/phint optimization/phintdriver
diff --git a/tests/phint optimization/README & RESULTS b/tests/phint optimization/README & RESULTS
new file mode 100644
index 0000000..21ec55a
--- /dev/null
+++ b/tests/phint optimization/README & RESULTS
@@ -0,0 +1,53 @@
+These programs compare different versions of phint.
+
+Phint is calculated for
+ 0 <= phi <= π
+ 0.2 <= u <= 2.4
+ a = 1.73205
+
+Phint: original from Lambin
+Phint1: new formula
+Phint2: new formula, use conjugate complex
+Phint3: new formula, partial formula ?
+Phint4: new formula, partial formula ?
+Phint5: new formula,
+Phint6: new formula, consider conjugate complex property
+Phint7: new formula, consider conjugate complex property, extract common sub-expressions
+Phint8: new formula, consider conjugate complex property, extract common sub-expressions, treat phi = π
+Phint9: new formula, consider conjugate complex property, extract common sub-expressions, treat phi = π, use rational approximation of original Lambin code
+Phint10: new formula, consider conjugate complex property, no common sub-expression, treat phi = π, leave everything to the compiler.
+
+Log:
+
+>% gfortran -O0 phintdriver.f90 phint.f90 phint1.f90 phint2.f90 phint3.f90 phint4.f90 phint5.f90 phint6.f90 phint7.f90 phint8.f90 phint9.f90 phint10.f90 -o phintdriver
+>% phintdriver
+Time for phint: 9.277 s
+Time for phint1: 17.785 s
+Time for phint2: 14.707 s
+Time for phint3: 8.899 s
+Time for phint4: 17.914 s
+Time for phint5: 25.697 s
+Time for phint6: 12.598 s
+Time for phint7: 6.052 s
+Time for phint8: 6.455 s
+Time for phint9: 6.594 s
+Time for phint10: 7.036 s
+
+>% gfortran -O7 phintdriver.f90 phint.f90 phint1.f90 phint2.f90 phint3.f90 phint4.f90 phint5.f90 phint6.f90 phint7.f90 phint8.f90 phint9.f90 phint10.f90 -o phintdriver
+>% phintdriver
+Time for phint: 8.648 s
+Time for phint1: 13.632 s
+Time for phint2: 13.302 s
+Time for phint3: 8.099 s
+Time for phint4: 11.682 s
+Time for phint5: 14.071 s
+Time for phint6: 8.823 s
+Time for phint7: 5.859 s
+Time for phint8: 5.008 s
+Time for phint9: 5.023 s
+Time for phint10: 4.963 s
+
+Summary:
+Considering the conjugate complex property is a major plus. As expected.
+Manually extracting common sub-expression is a plus with -O0, but no advantage, maybe even a small disadvantage with -O7. Not really expected.
+The rational approximation of the original Lambin code does not give any advantage.
diff --git a/tests/phint optimization/dooptimization.sh b/tests/phint optimization/dooptimization.sh
deleted file mode 100755
index 65b4fb9..0000000
--- a/tests/phint optimization/dooptimization.sh
+++ /dev/null
@@ -1,10 +0,0 @@
-#!/bin/sh -v
-for number in 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 ; do
- echo '*** File number' $number '***'
-
- cp ../inputFiles/'eelsin'$number eelsin
- ./eelsf90 >/dev/null
- cp phint.log logFiles/'phint'$number'.log'
-
- rm -f eelsin eelsou
-done
diff --git a/tests/phint optimization/phint10.f90 b/tests/phint optimization/phint10.f90
new file mode 100644
index 0000000..93965b9
--- /dev/null
+++ b/tests/phint optimization/phint10.f90
@@ -0,0 +1,49 @@
+double precision function phint10(phi, a, u)
+
+! ******************************************************************
+! * *
+! * evaluate the integral from zero to phi of *
+! * *
+! * u 2 *
+! * ( ----------------------------- ) dphi *
+! * 2 2 *
+! * (1 - a * u * cos(phi)) + u *
+! * *
+! * for 0 <= phi <= pi , u >= 0 and a >= 0 *
+! * *
+! ******************************************************************
+
+ implicit none
+
+ double precision, intent(in) :: phi
+ double precision, intent(in) :: a
+ double precision, intent(in) :: u
+
+ double precision :: e, pi, tanPhi2, sinPhi, cosPhi, Term1
+
+ double complex :: preFactor
+
+ if (phi == 0) then
+ phint10 = 0
+ else
+ e = a*u
+ pi = 4 * atan (1.0d0)
+ preFactor = cmplx((e**2 - 1)/u + 2*u, 3) / sqrt(cmplx(e**2 - 1 + u**2, 2*u))**3
+ if (pi - phi < 1e-6) then
+ phint10 = pi / 2 * real(preFactor)
+ else
+ tanPhi2 = tan(phi/2)
+ sinPhi = sin(phi)
+ cosPhi = cos(phi)
+ Term1 = real(preFactor * atan(cmplx(u, 1 + e) / sqrt(cmplx(e**2 - 1 + u**2, 2*u)) * tanPhi2))
+
+ phint10 = &
+ Term1 + &
+ 0.5 * e * (e**2 - 1 + 3*u**2 - e*(e**2 - 1 + u**2)*cosPhi) * sinPhi / &
+ (((e**2 - 1)**2 + 2*(1 + e**2)*u**2 + u**4) * (1 + u**2 + e*cosPhi*(-2 + e*cosPhi)))
+ endif
+
+ endif
+
+ return
+end function phint10
diff --git a/tests/phint optimization/phint8.f90 b/tests/phint optimization/phint8.f90
index 7b2d140..647090c 100644
--- a/tests/phint optimization/phint8.f90
+++ b/tests/phint optimization/phint8.f90
@@ -40,11 +40,11 @@ double precision function phint8(phi, a, u)
tanPhi2 = tan(phi/2)
sinPhi = sin(phi)
cosPhi = cos(phi)
- Term1 = real(preFactor * atan(cmplx(u,1+e) / denominator * tanPhi2))
+ Term1 = real(preFactor * atan(cmplx(u,1+e) / denominator * tanPhi2))
- phint8 = &
- Term1 + &
- 0.5 * e * (e21 + 3*u2 - e*(e21 + u2)*cosPhi) * sinPhi / &
+ phint8 = &
+ Term1 + &
+ 0.5 * e * (e21 + 3*u2 - e*(e21 + u2)*cosPhi) * sinPhi / &
((e21**2 + 2*(1 + e2)*u2 + u2**2) * (1 + u2 + e*cosPhi*(-2 + e*cosPhi)))
endif
diff --git a/tests/phint optimization/phint9.f90 b/tests/phint optimization/phint9.f90
new file mode 100644
index 0000000..8e12f40
--- /dev/null
+++ b/tests/phint optimization/phint9.f90
@@ -0,0 +1,61 @@
+double precision function phint9(phi, a, u)
+
+! ******************************************************************
+! * *
+! * evaluate the integral from zero to phi of *
+! * *
+! * u 2 *
+! * ( ----------------------------- ) dphi *
+! * 2 2 *
+! * (1 - a * u * cos(phi)) + u *
+! * *
+! * for 0 <= phi <= pi , u >= 0 and a >= 0 *
+! * *
+! ******************************************************************
+
+ implicit none
+
+ double precision, intent(in) :: phi
+ double precision, intent(in) :: a
+ double precision, intent(in) :: u
+
+ double precision :: e, e2, e21, pi, u2, zr, esr, tanPhi2, sinPhi, cosPhi, Term1
+
+ double complex :: nominator, denominator, preFactor
+
+ if (phi == 0) then
+ phint9 = 0
+ else
+ e = a*u
+ e2 = e*e
+ u2 = u*u
+ e21 = e2 - 1
+ pi = 4 * atan (1.0d0)
+ nominator = cmplx(e21/u + 2*u ,3)
+ denominator = sqrt(cmplx(e21 + u2,2*u))
+ preFactor = nominator / denominator**3
+ if (pi - phi < 1e-6) then
+ phint9 = pi / 2 * real(preFactor)
+ else
+ tanPhi2 = tan(phi/2)
+ sinPhi = sin(phi)
+ cosPhi = cos(phi)
+ if (u < 1.0d0 .and. e < 1.0d-02 * (1.0d0 + u2)) then
+ zr = 1.0d0 + u2
+ esr = e / zr
+ phint9 = u2 / zr**2 * ((( (4.0d0 / 3.0d0) * (2.0d0 + cosPhi**2) * sinPhi * (5.0d0 - 3 * u2) * &
+ esr + (phi + cosPhi * sinPhi) * (5.0d0 - u2)) * esr + 4 * sinPhi) * esr + phi)
+ else
+ Term1 = real(preFactor * atan(cmplx(u,1+e) / denominator * tanPhi2))
+
+ phint9 = &
+ Term1 + &
+ 0.5 * e * (e21 + 3*u2 - e*(e21 + u2)*cosPhi) * sinPhi / &
+ ((e21**2 + 2*(1 + e2)*u2 + u2**2) * (1 + u2 + e*cosPhi*(-2 + e*cosPhi)))
+ endif
+ endif
+
+ endif
+
+ return
+end function phint9
diff --git a/tests/phint optimization/phintdriver b/tests/phint optimization/phintdriver
index 5d6deeb066e287ef7622eaa0cfe8fb5f4694a901..bc3454f117149dc1a0762e451cb747f18e07d273 100755
GIT binary patch
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diff --git a/tests/phint optimization/phintdriver.f90 b/tests/phint optimization/phintdriver.f90
index e5caf4d..686307d 100644
--- a/tests/phint optimization/phintdriver.f90
+++ b/tests/phint optimization/phintdriver.f90
@@ -3,7 +3,8 @@ program phintdriver
implicit none
double precision :: phi, a, u, result
- double precision :: phint, phint1, phint2, phint3, phint4, phint5, phint6, phint7, phint8
+ double precision :: phint, phint1, phint2, phint3, phint4, phint5
+ double precision :: phint6, phint7, phint8, phint9, phint10
double precision :: step_phi, step_u
integer :: i, j, number
@@ -114,4 +115,26 @@ program phintdriver
call cpu_time(finish)
print '("Time for phint8: ", f6.3, " s")',finish-start
+ call cpu_time(start)
+ do i = 0, number
+ phi = i * step_phi
+ do j = 0, number
+ u = 0.2 + j * step_u
+ result = phint9(phi, a, u)
+ enddo
+ enddo
+ call cpu_time(finish)
+ print '("Time for phint9: ", f6.3, " s")',finish-start
+
+ call cpu_time(start)
+ do i = 0, number
+ phi = i * step_phi
+ do j = 0, number
+ u = 0.2 + j * step_u
+ result = phint10(phi, a, u)
+ enddo
+ enddo
+ call cpu_time(finish)
+ print '("Time for phint10: ", f6.3, " s")',finish-start
+
end program phintdriver
--
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