Python - floats approximations

# author: Bartlomiej "furas" Burek (https://blog.furas.pl)
# 2017.04.03

'''
floats approximations
'''

# -----------------------------------------------------------------------------

def example_0():
    '''
    floats can keep only aproximations
    and Python can display rounded values which look correctly
    but it uses aproximations in calculations which give incorrect results

    0.1 + 0.2 == 0.3  =>  False

          0.1  =>  0.1000000000000000055511151231257827021181583404541015625
          0.2  =>  0.2000000000000000111022302462515654042363166809082031250
          0.3  =>  0.2999999999999999888977697537484345957636833190917968750
    0.1 + 0.2  =>  0.3000000000000000444089209850062616169452667236328125000
    '''

    print('========== example 0 ==========')

    print('0.1 + 0.2 == 0.3', ' => ', 0.1 + 0.2 == 0.3 ) # False
    print()
    print('      0.1', ' => ', '%.55f' % 0.1)
    print('      0.2', ' => ', '%.55f' % 0.2)
    print('      0.3', ' => ', '%.55f' % 0.3)
    print('0.1 + 0.2', ' => ', '%.55f' % (0.1+0.2))

# -----------------------------------------------------------------------------

def example_1():
    '''
    replace floats with integers to get better results (precision: 100)
    number % divider  ==> ( (number*100) % (divider*100) ) / 100
    '''

    print('========== example 1 ==========')

    print('1050 % 0.05                        ', ' => ', 1050 % 0.05 )
    print('((1050 * 100) % (0.05 * 100)) / 100', ' => ', ((1050 * 100) % (0.05 * 100)) / 100 )
    print('(105000%5)/100                     ', ' => ', (105000%5)/100 )

# -----------------------------------------------------------------------------
# another examples
# -----------------------------------------------------------------------------

def example_2():
    '''
    replace floats with integers to get better results (precision: 100)
    number % divider  ==> ( (number*100) % (divider*10) ) / 100
    '''

    print('========== example 2 ==========')

    for d in [0.3, 0.4, 0.5, 0.6, 0.7, 0.05]:

        print('--- x %', d, '---')
        print()
        print('--+-----+-----+-----------------------')
        print('x | int |round| float ')
        print('--+-----+-----+-----------------------')

        for x in range(10):
            print( x, '|', ((x*100) % (d*100)) / 100, '|', round(x%d, 1), '|', x%d )

        print('--+-----+-----+-----------------------')
        print()

# -----------------------------------------------------------------------------

def example_3():
    '''
    `math.fmod` - it seems not useful

    `numpy` can make opertion on all elements in array
    but it seems it has the same problem with floats
    '''

    print()
    print('=== math.fmod ===')
    print()

    import math

    for d in [0.3, 0.4, 0.5, 0.6, 0.7, 0.05]:
        print('--- x %', d, '---')
        print()
        print('--+-----------------------')
        print('x | fmod ')
        print('--+-----------------------')

        for x in range(10):
            print( x, '|', math.fmod(x, d) )

        print('--+-----------------------')
        print()

# -----------------------------------------------------------------------------

def example_4():
    '''
    numpy has float16, float32, float64
    (https://docs.scipy.org/doc/numpy/user/basics.types.html)
    and float32 gives True for 0.1 + 0.2 == 0.3
    but float16 and float64 give False
    '''

    import numpy as np

    print('========== example 4 - numpy ==========')

    print()
    print('--- 0.1 + 0.2 == 0.3 ---')
    print()

    a16 = np.float16(0.1) # you can use string np.float16("0.1")
    b16 = np.float16(0.2) # you can use string np.float16("0.2")
    c16 = a16 + b16
    d16 = np.float16(0.3) # you can use string np.float16("0.3")

    print('float16:', a16, b16, c16, d16, ' => ', c16 == d16) # 0.1 0.2 0.3 0.3 True

    a32 = np.float32(0.1) # you can use string np.float32("0.1")
    b32 = np.float32(0.2) # you can use string np.float32("0.2")
    c32 = a32 + b32
    d32 = np.float32(0.3) # you can use string np.float32("0.3")

    print('float32:', a32, b32, c32, d32, ' => ', c32 == d32) # 0.1 0.2 0.3 0.3 True

    a64 = np.float64(0.1) # you can use string np.float64("0.1")
    b64 = np.float64(0.2) # you can use string np.float64("0.2")
    c64 = a64 + b64
    d64 = np.float64(0.3) # you can use string np.float64("0.3")

    print('float64:', a64, b64, c64, d64, ' => ', c64 == d64) # 0.1 0.2 0.3 0.3 False

    print()
    print('--- 1050 % d ---')
    print()

    print('int % float16:', 1050 % np.float16(0.05), 'round:', round(1050 % np.float16(0.05), 2)) # 0.00640869140625
    print('int % float32:', 1050 % np.float32(0.05), 'round:', round(1050 % np.float32(0.05), 2)) # 0.0499843545258
    print('int % float64:', 1050 % np.float64(0.05), 'round:', round(1050 % np.float64(0.05), 2)) # 0.0499999999999
    print()
    print('float16 % float16:', np.float16(1050) % np.float16(0.05), 'round:', round(np.float16(1050) % np.float16(0.05), 2)) # 0.0064087
    print('float32 % float32:', np.float32(1050) % np.float32(0.05), 'round:', round(np.float32(1050) % np.float32(0.05), 2)) # 0.0499844
    print('float64 % float64:', np.float64(1050) % np.float64(0.05), 'round:', round(np.float64(1050) % np.float64(0.05), 2)) # 0.0499999999999

# -----------------------------------------------------------------------------

def example_5():

    import numpy as np

    for d in [0.3, 0.4, 0.5, 0.6, 0.7, 0.05]:
        print()

        for x in range(10):
            print()
            print('---', x, '%', d, '=', ((x*100) % (d*100)) / 100, '---------')
            print('int % f16 |', x % np.float16(d))
            print('int % f32 |', x % np.float32(d))
            print('int % f64 |', x % np.float64(d))
            print('----------+---')
            print('f16 % f16 |', np.float16(x) % np.float16(d))
            print('f32 % f32 |', np.float32(x) % np.float32(d))
            print('f64 % f64 |', np.float64(x) % np.float64(d))
            print('----------+-----------------')
        print()

# -----------------------------------------------------------------------------

example_0() # 0.1 + 0.2 == 0.3
example_1() # x % 0.05
example_2() # x % 0.05
example_3() # math.fmod()
example_4() # numpy float16/float32/float64
example_5() # numpy float16/float32/float64