Random floating point double in Inclusive Range

Question

We can easily get random floating point numbers within a desired range [X,Y) (note that X is inclusive and Y is exclusive) with the function listed below since

Answer 1

Generating a random floating-point number in a range is non-trivial. For example, the common practice of multiplying or dividing a random integer by a constant, or by scaling a uniform floating-point number to the desired range, have the disadvantage that not all numbers a floating-point format can represent in the range can be covered this way, and may have subtle bias problems. These problems are discussed in detail in "Generating Random Floating-Point Numbers by Dividing Integers: a Case Study" by F. Goualard.

Just to show how non-trivial the problem is, the following pseudocode generates a random floating-point number in the closed interval [lo, hi], where the number is of the form FPSign * FPSignificand * FPRADIX^FPExponent. The pseudocode below was reproduced from my section on floating-point number generation. Note that it works for any precision and any base (including binary and decimal) of floating-point numbers.

METHOD RNDRANGE(lo, hi)
  losgn = FPSign(lo)
  hisgn = FPSign(hi)
  loexp = FPExponent(lo)
  hiexp = FPExponent(hi)
  losig = FPSignificand(lo)
  hisig = FPSignificand(hi)
  if lo > hi: return error
  if losgn == 1 and hisgn == -1: return error
  if losgn == -1 and hisgn == 1
    // Straddles negative and positive ranges
    // NOTE: Changes negative zero to positive
    mabs = max(abs(lo),abs(hi))
    while true
       ret=RNDRANGE(0, mabs)
       neg=RNDINT(1)
       if neg==0: ret=-ret
       if ret>=lo and ret<=hi: return ret
    end
  end
  if lo == hi: return lo
  if losgn == -1
    // Negative range
    return -RNDRANGE(abs(lo), abs(hi))
  end
  // Positive range
  expdiff=hiexp-loexp
  if loexp==hiexp
    // Exponents are the same
    // NOTE: Automatically handles
    // subnormals
    s=RNDINTRANGE(losig, hisig)
    return s*1.0*pow(FPRADIX, loexp)
  end
  while true
    ex=hiexp
    while ex>MINEXP
      v=RNDINTEXC(FPRADIX)
      if v==0: ex=ex-1
      else: break
    end
    s=0
    if ex==MINEXP
      // Has FPPRECISION or fewer digits
      // and so can be normal or subnormal
      s=RNDINTEXC(pow(FPRADIX,FPPRECISION))
    else if FPRADIX != 2
      // Has FPPRECISION digits
      s=RNDINTEXCRANGE(
        pow(FPRADIX,FPPRECISION-1),
        pow(FPRADIX,FPPRECISION))
    else
      // Has FPPRECISION digits (bits), the highest
      // of which is always 1 because it's the
      // only nonzero bit
      sm=pow(FPRADIX,FPPRECISION-1)
      s=RNDINTEXC(sm)+sm
    end
    ret=s*1.0*pow(FPRADIX, ex)
    if ret>=lo and ret<=hi: return ret
  end
END METHOD