updated intro_lab

intro_lab/pi.c

@@ -9,7 +9,7 @@
  */
 int main(int argc, char** argv)
 {
-    unsigned long nsteps = 1<<27; /* around 10^8 steps */
+    unsigned long nsteps = 100000000;
     double dx = 1.0 / nsteps;
 
     double pi = 0.0;
@@ -25,7 +25,7 @@ int main(int argc, char** argv)
 
     double run_time = omp_get_wtime() - start_time;
     double ref_pi = 4.0 * atan(1.0);
-    printf("\npi with %ld steps is %.10f in %.6f seconds (error=%e)\n",
+    printf("pi with %ld steps is %.10f in %.6f seconds (error=%e)\n",
            nsteps, pi, run_time, fabs(ref_pi - pi));
 
     return 0;

intro_lab/pi.f90

-! This program will numerically compute the integral of
-!
-!                   4/(1+x*x) 
-!   
-! from 0 to 1.  The value of this integral is pi -- which 
-! is great since it gives us an easy way to check the answer.
-!
-! The is the original sequential program.  It uses the timer
-! from the OpenMP runtime library
-!
-! History: Written by Tim Mattson, 11/99.
-
-program calc_pi
+! This program computes pi as
+! \pi = 4 arctan(1)
+!     = 4 \int _0 ^1 \frac{1} {1 + x^2} dx
+
+program compute_pi
 
 use omp_lib
 
 implicit none
 
-integer(kind=8) :: num_steps = 100000000
-real(kind=8) step
-
-integer i
-real(kind=8) x, pi, raw_sum
+integer(kind=8) :: nsteps, i
+real(kind=8) :: dx, x, pi, ref_pi
 real(kind=8) start_time, run_time
 
-step = 1.0D0 / num_steps
+nsteps = 100000000
+dx = 1.0D0 / nsteps
+pi = 0.0D0
 
 start_time = OMP_GET_WTIME()
        
-raw_sum = 0.0D0
-       
-do i = 1, num_steps
-    x = (i-0.5D0)*step
-    raw_sum = raw_sum + 4.0D0/(1.0D0+x*x)
+do i = 1, nsteps
+    x = (i - 0.5D0) * dx
+    pi = pi + 1.0D0 / (1.0D0 + x * x)
 enddo
 
-pi = step * raw_sum
+pi = pi * 4.0D0 * dx
+
 run_time = OMP_GET_WTIME() - start_time
-print '(" pi with ", i0, " steps is ", f12.6, " in ", f12.6, " seconds")', num_steps, pi, run_time
+ref_pi = 4.0D0 * atan(1.0D0)
+print '("pi with ", i0, " steps is ", f16.10, " in ", f12.6, " seconds (error=", e12.6, ")")', nsteps, pi, run_time, abs(ref_pi - pi)
 
 end program