Natural logarithm in Unix DC http://enwp.org/dc_(computer_program)

log.dc

# L (x -- y)
# Natural logarithm of `x`.
# By Taylor series expansion of `ln(x)=ln((1+t)/(1-t))`.
# See https://en.wikipedia.org/wiki/Natural_logarithm#Numerical_value
[ 1-d2+/
  d2*Sk              # Initialize multiplier
  d*Sy               # Initialize multiplier factor
  0Ss                # Initialize accumulator
  10K^Sp             # Initialize 10^k power
  [ d1r/lk*ls+lsrdss   # Update accumulator
    -lp*d*1 [s_q]s_>_  # Check precision
    lkly*sk 2+         # Update multiplier and counter
    lfx
  ]Sf
  1lfxLs
LkLyLpLfs_s_s_s_] sL

10k
5lLx 2lLx /p