Here are 8 key examples highlighting the most important features of the Decimal type in its current state:
from decimojo import dm, Decimal
# The classic floating-point problem
print(0.1 + 0.2) # 0.30000000000000004 (not exactly 0.3)
# Decimal solves this with exact representation
var d1 = Decimal("0.1")
var d2 = Decimal("0.2")
var sum = d1 + d2
print(sum) # Exactly 0.3
# Financial calculation example - computing tax
var price = Decimal("19.99")
var tax_rate = Decimal("0.0725")
var tax = price * tax_rate # Exactly 1.449275
var total = price + tax # Exactly 21.439275
# Addition with different scales
var a = Decimal("123.45")
var b = Decimal("67.8")
print(a + b) # 191.25 (preserves highest precision)
# Subtraction with negative result
var c = Decimal("50")
var d = Decimal("75.25")
print(c - d) # -25.25
# Multiplication with banker's rounding (round to even)
var e = Decimal("12.345")
var f = Decimal("5.67")
print(round(e * f, 2)) # 69.96 (rounds to nearest even)
# Division with banker's rounding
var g = Decimal("10")
var h = Decimal("3")
print(round(g / h, 2)) # 3.33 (rounded banker's style)
# Scale refers to number of decimal places
var d1 = Decimal("123.45")
print(d1.scale()) # 2
# Precision control with explicit rounding
var d2 = Decimal("123.456")
print(d2.round_to_scale(1)) # 123.5 (banker's rounding)
# High precision is preserved (up to 28 decimal places)
var precise = Decimal("0.1234567890123456789012345678")
print(precise) # 0.1234567890123456789012345678
# Negation operator
var pos = Decimal("123.45")
var neg = -pos
print(neg) # -123.45
# Absolute value
var abs_val = abs(Decimal("-987.65"))
print(abs_val) # 987.65
# Sign checking
print(Decimal("-123.45").is_negative()) # True
print(Decimal("0").is_negative()) # False
# Sign preservation in multiplication
print(Decimal("-5") * Decimal("3")) # -15
print(Decimal("-5") * Decimal("-3")) # 15
# Highly accurate square root implementation
var root2 = Decimal("2").sqrt()
print(root2) # 1.4142135623730950488016887242
# Square root of imperfect squares
var root_15_9999 = Decimal("15.9999").sqrt()
print(root_15_9999) # 3.9999874999804686889646053305
# Integer powers with fast binary exponentiation
var cubed = Decimal("3") ** 3
print(cubed) # 27
# Negative powers (reciprocals)
var recip = Decimal("2") ** (-1)
print(recip) # 0.5
# Division by zero is properly caught
try:
var result = Decimal("10") / Decimal("0")
except:
print("Division by zero properly detected")
# Zero raised to negative power
try:
var invalid = Decimal("0") ** (-1)
except:
print("Zero to negative power properly detected")
# Overflow detection and prevention
var max_val = Decimal.MAX()
try:
var overflow = max_val * Decimal("2")
except:
print("Overflow correctly detected")
# Equal values with different scales
var a = Decimal("123.4500")
var b = Decimal("123.45")
print(a == b) # True (numeric value equality)
# Comparison operators
var c = Decimal("100")
var d = Decimal("200")
print(c < d) # True
print(c <= d) # True
print(c > d) # False
print(c >= d) # False
print(c != d) # True
# Monthly loan payment calculation with precise interest
var principal = Decimal("200000") # $200,000 loan
var annual_rate = Decimal("0.05") # 5% interest rate
var monthly_rate = annual_rate / Decimal("12")
var num_payments = Decimal("360") # 30 years
# Monthly payment formula: P * r(1+r)^n/((1+r)^n-1)
var numerator = monthly_rate * (Decimal("1") + monthly_rate) ** 360
var denominator = (Decimal("1") + monthly_rate) ** 360 - Decimal("1")
var payment = principal * (numerator / denominator)
print("Monthly payment: $" + String(round(payment, 2))) # $1,073.64