Paste: pi calc

Author: rex
Mode: fortran
Date: Thu, 30 Apr 2009 19:38:51
Plain Text | 
module simpsons_rule
	contains
	
	real (kind = 8) function f(x)
		implicit none
		real (kind=8),intent(in)::x
		
		f=sqrt(16.-x**2)
		
		if(isnan(f)) then
			f=0.0
		end if
		return
	end function f
	
	real (kind=8) function simple(a,b)
		implicit none
		real (kind=8),intent(in)::a,b
		simple=((b-a)/6.)*(f(a)+4*f((a+b)/2.)+f(b))
		return
	end function simple
	
	
	real (kind=8) function composite(a,b,accuracy)
		implicit none
		real , intent(in)::a,b
		integer, intent(in)::accuracy
		integer::n,i
		real (kind=8)::h,integral

		integral=0.0
		n=accuracy		
		if(mod(n,2)==0) then
			n=n+1
		end if
		h=(b-a)/n
		do i=0,n-1
			integral=integral+simple(a+i*h,a+(i+1)*h)
		end do
		composite=integral
		return
	end function composite


end module simpsons_rule

program pi
	use simpsons_rule
	implicit none
	integer::i
	
	write(*,*)"Approximations of pi:"
	do i=50000,10000000,1000000
		write(*,*)"n=",i+1,composite(-4.0,4.0,i+1)/8.
	end do
	write(*,*)"n=",20000000,composite(-4.,4.,20000000)/8;
end program pi

Annotation: almost generalized circle size

Author: rex
Mode: fortran
Date: Fri, 1 May 2009 01:02:47
Plain Text | 
module simpsons_rule
	
	integer::r2
	
	contains
	
	real (kind = 8) function f(x)
		implicit none
		real (kind=8),intent(in)::x
		
		f=sqrt(r2-x**2)
		
		if(isnan(f)) then
			f=0.0
		end if
		return
	end function f
	
	real (kind=8) function simple(a,b)
		implicit none
		real (kind=8),intent(in)::a,b
		simple=((b-a)/6.)*(f(a)+4*f((a+b)/2.)+f(b))
		return
	end function simple
	
	
	real (kind=8) function composite(a,b,accuracy)
		implicit none
		real , intent(in)::a,b
		integer, intent(in)::accuracy
		integer::n,i
		real (kind=8)::h,integral

		integral=0.0
		n=accuracy		
		if(mod(n,2)==0) then
			n=n+1
		end if
		h=(b-a)/n
		do i=0,n-1
			integral=integral+simple(a+i*h,a+(i+1)*h)
		end do
		composite=integral
		return
	end function composite


end module simpsons_rule

program pi
	use simpsons_rule
	implicit none
	integer::max_t=17
	integer::ln_n,current_n
	real::r
	r2=1
	r=floor(sqrt(real(r2)))
	write(*,*)"Approximations of pi:"
	do n=1,max_t,1
		
		write(*,*)"n=",floor(exp(t)),composite((-1)*r,r,n)*(2./r2)
	end do
end program pi

Annotation: finished

Author: rex
Mode: fortran
Date: Fri, 1 May 2009 03:01:59
Plain Text | 
module simpsons_rule
	
	integer::r2=2**30
	
	contains
	
	real (kind = 8) function f(x)
		implicit none
		real (kind=8),intent(in)::x
		
		f=sqrt(r2-x**2.)
		
		if(isnan(f)) then
			f=0.0
		end if
		return
	end function f
	
	real (kind=8) function simple(a,b)
		implicit none
		real (kind=8),intent(in)::a,b
		simple=((b-a)/6.)*(f(a)+4*f((a+b)/2.)+f(b))
		return
	end function simple
	
	
	real (kind=8) function composite(a,b,accuracy)
		implicit none
		real , intent(in)::a,b
		integer, intent(in)::accuracy
		integer::n,i
		real (kind=8)::h,integral

		integral=0.0
		n=accuracy		
		if(mod(n,2)==0) then
			n=n+1
		end if
		h=(b-a)/n
		do i=0,n-1
			integral=integral+simple(a+i*h,a+(i+1)*h)
		end do
		composite=integral
		return
	end function composite


end module simpsons_rule



program pi
	use simpsons_rule
	implicit none
	integer::max_t=18
	integer::t,f_e_r_t,c=3
	real::r
	r=floor(sqrt(real(r2)))
	write(*,*)"Approximations of pi:"
	do t=1,max_t,2
		f_e_r_t=3**t
		write(*,*)"n=",f_e_r_t,":",composite((-1)*r,r,f_e_r_t)*(2./r2)
	end do
	write(*,*)"n=",2**30,":",composite((-1)*r,r,2**23)*(2./r2)
end program pi

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