EDIT Apparently I was timing IO which (a) made the timing longer than necessary and (b) is contrary to bullet #6. I've updated the code to reflect this. I've also discovered that using a kind=8 integer with the intrinsic subroutine system_clock gives microsecond accuracy.
With this updated code, I am now computing each set of values of the trigonometric functions in about 0.3 microseconds (the significant digits in the end vary run-to-run, but it's consistently hovering near 0.31 us), a significant reduction from the previous iteration that timed IO.
program SinCosTan
!use iso_fortran_env, only: real64
implicit none
integer, parameter :: real64 = selected_real_kind(15,307)
real(real64), parameter :: PI = 3.1415926535897932384626433832795028842
real(real64), parameter :: TAU = 6.2831853071795864769252867665590057684
real(real64), parameter :: half = 0.500000000000000000000_real64
real(real64), allocatable :: trigs(3:,:), angles(:)
real(real64) :: time(2), times, angb
character(len=12) :: tout
integer :: i,j,ierr,amax
integer(kind=8) :: cnt(2)
open(unit=10,file='trig.out',status='replace')
open(unit=12,file='trigfile='CodeGolf/trig.in',status='old')
! compute trig functions & time it
check timesto =see 0.0_real64
how many angles callthere cpu_time(time(1))are
i=0
do
read(12,*,iostat=ierr) angb
if(ierr/=0) exit
i=i+1
enddo !-
print '(a,i0,a)',"There are ",i," angles"
amax = i
! allocate array
allocate(trigs(3,amax),angles(amax))
! rewind the file then read the angles into the array
rewind(12)
do i=1,amax
read(12,*) angles(i)
enddo !- i
! compute trig functions & time it
times = 0.0_real64
call findemsystem_clock(angcnt(1)) ! <-- system_clock with an 8-bit INT can time to us
do i=1,amax
call CORDIC(angles(i), trigs(:,i), 40)
enddo !- i
call system_clock(cnt(2))
times = times + (cnt(2) - cnt(1))
! write the angles to the file
do i=1,amax
do j=1,3
if(trigs(j,i) > 1d100) then
write(tout,'(a1)') 'n'
elseif(abs(trigs(j,i)) > 1.0) then
write(tout,'(f10.6)') trigs(j,i)
elseif(abs(trigs(j,i)) < 0.1) then
write(tout,'(f10.8)') trigs(j,i)
else
write(tout,'(f9.7)') trigs(j,i)
endif
write(10,'(a)',advance='no') tout
enddo !- ij
write(10,*)" "
enddo !- j
call cpu_time(time(2))
times = times + time(2) - time(1)i
print *,"computation took",times/real(i,real64)*1e6,"us""us per angle"
close(10); close(12)
contains
!> @brief compute sine/cosine/tangent
subroutine findemCORDIC(a,t,n)
real(real64), intent(in) :: a
real(real64), intent(inout) :: t(3)
integer, intent(in) :: n
! local variables
real(real64), parameter :: deg2rad = 1.745329252e-2
real(real64), parameter :: angles(60) = &
[ 7.8539816339744830962e-01_real64, 4.6364760900080611621e-01_real64, &
2.4497866312686415417e-01_real64, 1.2435499454676143503e-01_real64, &
6.2418809995957348474e-02_real64, 3.1239833430268276254e-02_real64, &
1.5623728620476830803e-02_real64, 7.8123410601011112965e-03_real64, &
3.9062301319669718276e-03_real64, 1.9531225164788186851e-03_real64, &
9.7656218955931943040e-04_real64, 4.8828121119489827547e-04_real64, &
2.4414062014936176402e-04_real64, 1.2207031189367020424e-04_real64, &
6.1035156174208775022e-05_real64, 3.0517578115526096862e-05_real64, &
1.5258789061315762107e-05_real64, 7.6293945311019702634e-06_real64, &
3.8146972656064962829e-06_real64, 1.9073486328101870354e-06_real64, &
9.5367431640596087942e-07_real64, 4.7683715820308885993e-07_real64, &
2.3841857910155798249e-07_real64, 1.1920928955078068531e-07_real64, &
5.9604644775390554414e-08_real64, 2.9802322387695303677e-08_real64, &
1.4901161193847655147e-08_real64, 7.4505805969238279871e-09_real64, &
3.7252902984619140453e-09_real64, 1.8626451492309570291e-09_real64, &
9.3132257461547851536e-10_real64, 4.6566128730773925778e-10_real64, &
2.3283064365386962890e-10_real64, 1.1641532182693481445e-10_real64, &
5.8207660913467407226e-11_real64, 2.9103830456733703613e-11_real64, &
1.4551915228366851807e-11_real64, 7.2759576141834259033e-12_real64, &
3.6379788070917129517e-12_real64, 1.8189894035458564758e-12_real64, &
9.0949470177292823792e-13_real64, 4.5474735088646411896e-13_real64, &
2.2737367544323205948e-13_real64, 1.1368683772161602974e-13_real64, &
5.6843418860808014870e-14_real64, 2.8421709430404007435e-14_real64, &
1.4210854715202003717e-14_real64, 7.1054273576010018587e-15_real64, &
3.5527136788005009294e-15_real64, 1.7763568394002504647e-15_real64, &
8.8817841970012523234e-16_real64, 4.4408920985006261617e-16_real64, &
2.2204460492503130808e-16_real64, 1.1102230246251565404e-16_real64, &
5.5511151231257827021e-17_real64, 2.7755575615628913511e-17_real64, &
1.3877787807814456755e-17_real64, 6.9388939039072283776e-18_real64, &
3.4694469519536141888e-18_real64, 1.7347234759768070944e-18_real64]
real(real64), parameter :: kvalues(33) = &
[ 0.70710678118654752440e+00_real64, 0.63245553203367586640e+00_real64, &
0.61357199107789634961e+00_real64, 0.60883391251775242102e+00_real64, &
0.60764825625616820093e+00_real64, 0.60735177014129595905e+00_real64, &
0.60727764409352599905e+00_real64, 0.60725911229889273006e+00_real64, &
0.60725447933256232972e+00_real64, 0.60725332108987516334e+00_real64, &
0.60725303152913433540e+00_real64, 0.60725295913894481363e+00_real64, &
0.60725294104139716351e+00_real64, 0.60725293651701023413e+00_real64, &
0.60725293538591350073e+00_real64, 0.60725293510313931731e+00_real64, &
0.60725293503244577146e+00_real64, 0.60725293501477238499e+00_real64, &
0.60725293501035403837e+00_real64, 0.60725293500924945172e+00_real64, &
0.60725293500897330506e+00_real64, 0.60725293500890426839e+00_real64, &
0.60725293500888700922e+00_real64, 0.60725293500888269443e+00_real64, &
0.60725293500888161574e+00_real64, 0.60725293500888134606e+00_real64, &
0.60725293500888127864e+00_real64, 0.60725293500888126179e+00_real64, &
0.60725293500888125757e+00_real64, 0.60725293500888125652e+00_real64, &
0.60725293500888125626e+00_real64, 0.60725293500888125619e+00_real64, &
0.60725293500888125617e+00_real64 ]
real(real64) :: beta, c, c2, factor, poweroftwo, s,
real(real64) :: s2, sigma, sign_factor, theta, angle
integer :: j
! scale to radians
beta = a*deg2rad
! ensure angle is shifted to appropriate range
call angleShift(beta, -PI, theta)
! check for signs
if( theta < -half*PI) then
theta = theta + PI
sign_factor = -1.0_real64
else if( half*PI < theta) then
theta = theta - PI
sign_factor = -1.0_real64
else
sign_factor = +1.0_real64
endif
! set up some initializations...
c = 1.0_real64
s = 0.0_real64
poweroftwo = 1.0_real64
angle = angles(1)
! run for 30 iterations (should be good enough, need testing)
do j=1,n
sigma = merge(-1.0_real64, +1.0_real64, theta < 0.0_real64)
factor = sigma*poweroftwo
c2 = c - factor*s
s2 = factor*c + s
c = c2
s = s2
! update remaining angle
theta = theta - sigma*angle
poweroftwo = poweroftwo*0.5_real64
if(j+1 > 60) then
angle = angle * 0.5_real64
else
angle = angles(j+1)
endif
enddo !- j
if(n > 0) then
c = c*Kvalues(min(n,33))
s = s*Kvalues(min(n,33))
endif
c = c*sign_factor
s = s*sign_factor
t = [s, c, s/c]
end subroutine findemCORDIC
subroutine angleShift(alpha, beta, gamma)
real(real64), intent(in) :: alpha, beta
real(real64), intent(out) :: gamma
if(alpha < beta) then
gamma = beta - mod(beta - alpha, TAU) + TAU
else
gamma = beta + mod(alpha - beta, TAU)
endif
end subroutine angleShift
end program SinCosTan