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And with the math module, we access even more. Abs computes absolute values. Sqrt computes square roots.

**Others** (cos and sin) are trigonometric. When possible, these built-in methods are preferred over custom code. They are tested. They are reliable.

**Abs built-in.** A common math method is abs. This computes absolute values. It removes the negative sign (if there is one) from the number and returns that.

**Note:** When computing a hash code (a number based on data and used for lookup) we sometimes end up with a negative value. Abs fixes that.

**Tip:** The abs method is not part of the math module. Instead, you can use it directly in your programs.

Based on:Python 3Python program that uses abs# Negative number.n = -100.5# Absolute value.print(abs(n))Output100.5

**Floor, ceil.** Two common math functions are floor and ceil. Floor removes the digits past the decimal place. In this example it changes 100.7 to 100.

**Ceil:** This rounds the number up to the next highest one. A ceiling is always above us.

**Tip:** When using methods like floor and ceil, consistency is key. If some parts of the program use these methods, other parts should too.

Python program that imports mathimport math# Fractional number.n = 100.7# Absolute value.print(math.floor(n)) print(math.ceil(n))Output100 101

**Round.** This receives one or two arguments. The second argument tells how many numbers past the decimal point to keep. The final number is rounded up if the next digit is 5 or more.

Python program that uses roundnumber = 1.23456 print(round(number)) print(round(number, 0)) print(round(number, 1)) print(round(number, 2)) print(round(number, 3))Output1 0 digits 1.0 0 digits 1.2 1 digit 1.23 2 digits 1.235 3 digits, last one rounded up to 5

**Sum, fsum.** With sum, we add together the elements in a list. Fsum is a more accurate way to sum floating-point numbers. On integers, the methods are equal. But fsum is better for floats.

**Tip:** Sum and fsum can be used on any iterable collection. This includes the list, tuple and set.

**Caution:** If the iterable contains a non-numeric value, a TypeError will occur. We handle this in an except statement.

**Here:** In this example, the sum() method causes a rounding error to occur. The fsum() method returns a better sum.

Python program that uses sum, fsumimport math# Input list.values = [0.9999999, 1, 2, 3]# Sum values in list.r =sum(values) print(r)# Sum values with fsum.r = math.fsum(values) print(r)Output6.999999900000001 6.9999999

**Truncate.** Truncating a number removes everything past the decimal place. This does not round the number. Instead it just eliminates the fractional part.

**Note:** A positive number becomes smaller with trunc. And a negative number becomes larger.

Python program that uses math.truncimport math# Truncate this value.value1 = 123.45 truncate1 =math.trunc(value1) print(truncate1)# Truncate another value.value2 = 345.67 truncate2 =math.trunc(value2) print(truncate2)Output123 345

**Pow built-in.** Exponentiation multiplies a number by itself a certain number of times. With math.pow we apply this operation. Math.pow is similar to the ** operator.

**But:** When math.pow is applied, the result is always converted to a float. This is not the case with the ** operator.

**Tip:** More examples of using the exponent operator are available on the numbers page.

Python program that uses math.powimport math# Use math.pow method.a =math.pow(2, 3)# Use operator.b = 2 ** 3# Print results.print(a) print(b)Output8.0 8

**Sqrt.** In most programs, we do not need square roots. But when we do, the math.sqrt method is useful. It receives one argument. It returns the square root (in floating-point form).

**Tip:** If your program often uses square roots, a cache or lookup table may be helpful. You could memoize the result of math.sqrt for speed.

Python that uses math.sqrtimport math value1 = 9 value2 = 16 value3 = 100# Use sqrt method.print(math.sqrt(value1)) print(math.sqrt(value2)) print(math.sqrt(value3))Output3.0 4.0 10.0

**Pi, E.** You probably know the approximate values of E and pi. And you could specify these directly in a Python program. But with math.e and math.pi, we avoid this hassle.

Python that uses math.e, piimport math# This returns the value of e.print(math.e)# And this is pi.print(math.pi)Output2.718281828459045 3.141592653589793

**Abs performance.** Are math methods fast? In this program, I tested the abs method versus a simple if-else statement that also computes absolute values.

**Info:** They compute absolute values of the number a. In the results, doing an if-else statement to compute the absolute value was faster.

**But:** The difference here is not relevant to many programs. I recommend using abs() for clearer programs.

Python that benchmarks absimport time print(time.time())# Compute absolute value with abs.a = -1 i = 0whilei < 10000000: b = abs(a) i += 1 print(time.time())# Compute absolute value with if-statement.a = -1 i = 0whilei < 10000000: if a < 0: b = -a else: b = a i += 1 print(time.time())Output1346355970.511 1346355973.081 (Abs =2.57 s) 1346355975.509 (If =2.428 s)

**Compound interest.** Math is used in the real world. Please also check out the compound_interest Python implementation. It uses pow to compute an exponential function.

**Math is everywhere.** It is possible to directly compute mathematical functions. We could add methods that use arithmetic operators. But this adds complexity. It bloats programs.

**Instead,** we can use built-ins. These are found in the default and math modules. This approach is more effective. It is simpler. It makes programs easier to understand and maintain.