On page 202 of the Absoft Language Reference Manual, there is an example shoing that for large angles, sine losses almost all its precision and becomes useless. This is a known 'feature' of floating point computations. However, the limitation in Absoft's compiler seems to be relatively low.
The example in the LRM uses single precision floating point.
Here is a program using double precision numbers, showing the value of cos(2**n) and sin(2**n), together with some quick checks (sum of square should be 1, and double-hangle formulas should hold).
program trig
implicit none
double precision :: t, x, y, s, xp, yp, sx, sy
integer :: n
xp = cos(1d0)
yp = sin(1d0)
do n = 1, 99
t = 2d0**n
x = cos(t)
y = sin(t)
sx = abs(xp**2 - yp**2 - x)
sy = abs(2d0 * xp * yp - y)
s = hypot(x, y) - 1d0
print "(I2,2F12.8,3E12.4)", n, x, y, sx, sy, s
xp = x
yp = y
end do
end program
What happens is this: starting from 2**28, both sine and cosine are zero.
A closer look shows that the maximum argument giving relevant (nonzero) values is roughly pi*2**26. [1]
It's not very large, though, since it's close to 2.1d8, far below the precision limit of double precision numbers (which affords 17 digits).
That is, pi*2**26 should give 8 or 9 digits of precision after the decimal separator, and trigonometric functions would still be usable,
though not with extra high precision.
I am not sure this limit is documented in the manual, but it's worth knowing.
Tests were made with Absoft 2017 on Windows, both 64 bits.
[1] Roughly, but not exactly. For cosine, the factor is not pi but 3.141592628198916999, and for sine it's 3.141592651605606399,
while pi=3.141592653589793238.
