This lecture’s transcript was included in the edited volume from the conference, viz. Backus, J., “Programming in America in the 1950s – Some Personal Impressions,” in Metropolis, N., and Howlett, J., Rota, Gian-Carlo, A History of Computing in the Twentieth Century, New York: Academic Press, 1980, pp. 125 – 135.
program arcsine
implicitnone real :: x
complex :: c, ci = (0.0, 1.0)
integer :: i
do i =1, 10callrandom_number(x)
print*, x, ':', asin(x), -ci *log(ci*x+sqrt(1.0-x*x))
end doprint*do i =1, 10
c =cmplx(i*i*i, i*i) *1.0e-2print*, c, ':', asin(c), -ci *log(ci*c+sqrt(1.0-c*c))
end doend program arcsine
program euler_gamma
implicitnoneinteger, parameter :: kd =kind(0.0d0)
real(kd) :: s
integer :: i, n =10**7
s =0.0_kddo i = n, 1, -1
s = s +1.0_kd/ i
end doprint*, s -log(real(n)), s -log(n +0.5_kd), 1.0_kd/real(n)**2/24end program euler_gamma
block real(kd) :: s, t, u, v
integer :: i, n =10**7
s =0.0_kd
v =0.0_kddo i =1, n
u =1.0_kd/ i - v
t = s + u
v = (t - s) - u
s = t
end doprint*, s -log(real(n)), s -log(n +0.5_kd), 1.0_kd/real(n)**2/24end block
program euler_gamma
implicitnoneinteger, parameter :: kd =kind(0.0d0)
integer :: i, j, n, m, m0, m1, nmax
real(kd) :: s, t, x2
nmax =27
s =0.5_kd
m1 =1do n =1, nmax
t =0.0_kd
m0 = m1
m1 =2**n
do m = m0, m1 -1
x2 =2* m
t = t + n / (x2 * (x2 +1) * (x2 +2))
end do
s = s + t
print*, n, m1, s, t
if (t <1.0e-16_kd) exitend doprint*, 'gamma =', s
end program euler_gamma