### AngleLog.BC - logarithmic function that are semi-linear,
#   changing gradient at each power of the base.

# run with funcs.bc

## Specific functions for base 10

# Generate the x-th number in the sequence:
# 1,2,3,4,5,6,7,8,9,10,20,30,...,90,100,200,300,...,900,1000,2000,...
# e.g. al10(0) = 1 ; al10(11) = 30
define al10(x) {
  return( (rem(x,9)+1) * 10^int(x/9) )
}

# Invert the above
# e.g. ial10(50) = 13 ; ial10(1) = 0
define ial10(x) {
  auto k;
  k = int(log(10,x))
  return( 9*k + x/10^k - 1)
}

## Generalised functions for any base b

# al(10,x) is equivalent to the above al10(x)
define al(b,x) {
  return( (rem(x,b-1)+1) * b^int(x/(b-1)) )
}

# Invert the previous function
define ial(b,x) {
  auto k
  k = int(log(b,x))
  return( (b-1)*k + x/b^k - 1)
}