FFTの係数の準備をするときに、必ずしもsin(π/2)=1, cos(π/2)=0, sin(π/4)=cos(π/4)とかではないので、0<=θ<=π/４のsinθ, cosθを使うべき

sincos.F

! sincos.F
! You cannot say "sin(pi/2)=1, cos(pi/2)=0, sin(pi/4)=cos(pi/4)".
! Time-stamp: <2015-12-14 08:12:49 takeshi>
! Author: Takeshi NISHIMATSU
! Ref1: http://notabs.org/fpuaccuracy/index.htm
! Ref2: http://tomeapp.jp/archives/1282
! Ref3: https://sourceware.org/ml/libc-alpha/2015-12/msg00205.html
! Ref4: https://twitter.com/takehiro_t/status/676006684259540992
!!
#if defined(__PGI) || defined(__sparc)
#  define command_argument_count iargc
#  define get_command_argument getarg
#endif
program sincos
  implicit none
  integer i, N, command_argument_count
  real*8 :: inv_N
  complex*16 :: e(0:1023)
  complex*16,parameter :: itwopi = (0.0d0,1.0d0)*6.28318530717958647693d0
  character(len=100) :: str
  if (command_argument_count().eq.1) then
     call get_command_argument(1,str)
     read(str,*) N
  else
     N=32
  end if
  inv_N = 1.0d0/N
  do i=0,N/4
     e(i) = exp(itwopi*inv_N*i)
  end do
  do i=0,N/4
     write(6,'(i7,2f22.18)') i,e(i)
  end do
end program sincos
!
! Results:
!      0  1.000000000000000000  0.000000000000000000
!      1  0.980785280403230431  0.195090322016128248
!      2  0.923879532511286738  0.382683432365089782
!      3  0.831469612302545236  0.555570233019602178
!      4  0.707106781186547573  0.707106781186547462
!      5  0.555570233019602289  0.831469612302545236
!      6  0.382683432365089782  0.923879532511286738
!      7  0.195090322016128304  0.980785280403230431
!      8  0.000000000000000061  1.000000000000000000
!
!Local variables:
!  compile-command: "gfortran -Wall -ffree-form -o sincos sincos.F && ./sincos"
!End: