Decimals

Math Operations

• Some arithmetic operators don’t work the same as floats or integers:
  • // or % → also divmod()
  • n = d * (n // d) + (n % d) still satisfied.
  • But for integers → a // b = floor(a/b); For Decimals → a // b = trunc(a/b) , 對於正數來說並不影響 但對於負數來說就有差異

• How this integer division was defined in decimal class?

  1. 確認正負號
  2. 取絕對值進行除法
  3. 持續由分子減去分母直到分母大於分子
  4. return 減去的次數, 並加上正負號

  

• n = d * (n // d) + (n % d) still satisfied.

import decimal
from decimal import Decimal

x = -10
y = 3
print(x//y, x % y)
print(divmod(x, y))
print(x == y * (x//y) + (x % y))

# -4 2
# (-4, 2)
# True

a = Decimal('-10')
b = Decimal('3')
print(a//b, x % b)
print(divmod(a, b))
print(a == b * (a//b) + (a % b))

# -3 -1
# (Decimal('-3'), Decimal('-1'))
# True

• Other Mathematical Operations

  • Decimal class defines a bunch of various mathematical operations, such as sqrt, logs, etc
  • But not all functions defined, trigonometric functions

  help(decimal)
  

• Can use the math module But Decimal objects will be cast to float.
  • lose the whole precision mechanism that made us use Decimal objects in the first place
  • Usually will want to use the math functions defined in the Decimal class if they are available
  • Although you can use the math function of the math module, be aware that the math module functions will cast the Decimal numbers to floats when it performs the various operations. So, if the precision is important (which it probably is if you decided to use Decimal numbers in the first place), choose the math functions of the Decimal class over those of the math module.

import decimal
import math
from decimal import Decimal

decimal.getcontext().prec = 28

x = 0.01
x_dec = Decimal('0.01')
root = math.sqrt(x)
root_mixed = math.sqrt(x_dec)
root_dec = x_dec.sqrt(x_dec)

print(format(root, '1.27f'))
print(format(root_mixed, '1.27f'))
print(format(root_dec, '1.27f'))
# 0.100000000000000005551115123
# 0.100000000000000005551115123
# 0.100000000000000000000000000

print(format(root * root, '1.27f'))
print(format(root_mixed * root_mixed, '1.27f'))
print(format(root_dec * root_dec, '1.27f'))
# 0.010000000000000001942890293
# 0.010000000000000001942890293
# 0.010000000000000000000000000