from math import log2, ceil, floor

BW = 5
BE = 3
EO = 1

BM = BW-BE
BO = BM-EO   # BW-BE-EO
EXP_MAX = 2**BE-1
R_MIN = ufp_to_r(EXP_MAX, 1, BW, BE, EO)


def r_to_ufp(r, BW, BE, EO):
    BM = BW-BE
    BO = BM-EO   # BW-BE-EO
    EXP_MAX = 2**BE-1
    R_MIN = ufp_to_r(EXP_MAX, 1, BW, BE, EO)

    if r<R_MIN: # Small values
        ee = EXP_MAX
        mm = 0
        return ee, mm
        
    aa = floor(BM - log2(r))
    aa = max(min(aa, EXP_MAX+BO), BO)
    ee = aa - BO
    
    mm = round(r*2**aa)
    return ee, mm
    

def ufp_to_r(ee, mm, BW, BE, EO):
    BM = BW-BE
    BO = BM-EO   # BW-BE-EO
    
    r = mm * 2**(-BO-ee)
    return r


for mm in range(2**BM):
    for ee in range(2**BE):
        r_exp =  ufp_to_r(ee, mm, BW, BE, EO)
        ee_exp, mm_exp = r_to_ufp(r_exp, BW, BE, EO)
        r_exp2 = ufp_to_r(ee_exp, mm_exp, BW, BE, EO)
        #print("r={} r_exp={} mm={} ee={}".format(r, r_exp, mm_exp, ee_exp))

        print("mm={} ee={} r={}  ".format(mm, ee, r_exp))
        print("mm={} ee={} r={}  ".format(mm_exp, ee_exp, r_exp2))
        print("---------------------------------------------------")


r=1.5625e-2        
#r=3.1249999999999997e-2
ee, mm = r_to_ufp(r, BW, BE, EO)
r2 = ufp_to_r(ee, mm, BW, BE, EO)