# Ruby Math Examples: floor, ceil, round and truncate

*Use mathematical functions like floor, ceil and truncate. Compute square roots.***Math.** A stone tablet is covered in dust. On it you read an inscription. It also has some mathematical markings but you start feeling sleepy.

**In Ruby** we invoke built-in Math functions. Sqrt returns a square root. The sin, cos and tan methods relate parts of a triangle. There are two constants: PI and E.

**Constants.** Here we call Math methods and use Math constants. This program uses sqrt() on 9, which returns 3. It also prints PI, equal to 3.14, and E, equal to 2.71.

**Methods:** Please notice how the Math methods, such as sqrt(), use a period after Math.

**Constants:** To access constants in a module, like PI, we use the Math::PI syntax. Math::E uses the same syntax.

**Ruby program that uses Math**
*# Use sqrt.
# ... Square root of 9 is 3.
*x = __Math.sqrt__(*9*)
puts x*
# Use pi.
*puts __Math::PI__*
# Use e.
*puts __Math::E__
**Output**
3.0
3.141592653589793
2.718281828459045

**Absolute values.** These are never negative. The abs method takes absolute values of numbers. It is not part of the Math class—we do not use the Math module name here.

**Result:** If the number is negative, abs will return a positive version. It also handles floating point numbers.

**Ruby program that uses abs**
*# Take absolute values.
*value = *-1*
puts value.__abs__
value = *-1.1*
puts value.__abs__
value = *1*
puts value.__abs__
**Output**
1
1.1
1

**Sin, cos and tan.** Trigonometric functions are available in the Math module. These provide standard results—the cos of zero, for example, is 1.

**Quote:** In mathematics, the trigonometric functions [are] functions of an angle. They relate the angles of a triangle to the lengths of its sides.

Trigonometric functions: Wikipedia**Ruby program that uses sin, cos and tan**
*# Math provides sin, cos and tan methods.
*puts Math::sin(*0*)
puts Math::cos(*0*)
puts Math::tan(*0*)
**Output**
0.0
1.0
0.0

**Memoization.** Sometimes Math methods, and more complex calculations involving many calls, are slow. We can use a memoization approach to avoid calculating the same thing twice.

**Here:** We use a cache (a Hash) and check to see if it contains the square root of the argument.

Hash**Then:** We fetch the square root from the Hash, avoiding sqrt, when possible. We reduce an operation to a lookup.

**Tip:** For slow computations, this can improve performance. But it will make fast computations slower than before.

**Ruby program that uses memoization, sqrt**
def __check_sqrt__(a, cache)*
# See if the cache contains a square root for this argument.
*if cache.key?(a)
return cache[a]
end*
# Compute square root and memoize it.
*cache[a] = Math.sqrt(a)
return cache[a]
end*
# Use memoize square root method with Hash.
*cache = Hash.new()
puts __check_sqrt__(*9*, cache)
puts __check_sqrt__(*9*, cache)
**Output**
3.0
3.0

**Floor, ceil.** The floor and ceil methods are not part of the Math module. We call them directly on a number instance. Here we set a number to 1.1 and use floor and ceil.

**Info:** Floor changes 1.1 to 1, and ceil changes 1.1 to 2. The methods go lower and higher to the next integer.

**Ruby program that uses floor, ceil**
number = *1.1*
puts number*
# Use floor to remove the fractional part.
*result1 = number.__floor__
puts result1*
# Use ceil to move to the next highest integer.
*result2 = number.__ceil__
puts result2
**Output**
*1.1*
1
2

**Truncate.** A number can have a fractional part. The number 1.99 has a fractional part of ".99." With truncate the fractional part is eliminated from the number.

**And:** No other changes are made. Truncate can work on positive or negative numbers.

**Ruby program that uses truncate**
number = *1.99*
puts number*
# Truncate removes the fractional part.
*result = number.__truncate__
puts result*
# Negative numbers can be truncated too.
*number = *-1.99*
puts number.__truncate__
**Output**
1.99
1
-1

**Round.** On Floats we can use the round() method. This returns the nearest integral value to the value stored by the float. It may move the total value lower or higher.

**Ruby program that uses round**
number_a = 1.234
number_b = -1.234
number_c = 1.99
number_d = -1.99
puts *":::ROUND number_a, number_b :::"**
# Use round method.
*puts number_a.__round__
puts number_b.__round__
puts *":::ROUND number_c, number_d :::"**
# The nearest integer is returned.
*puts number_c.__round__
puts number_d.__round__
**Output**
:::ROUND number_a, number_b :::
1
-1
:::ROUND number_c, number_d :::
2
-2

**Fibonacci numbers.** In the Fibonacci sequence, each number is equal to the two previous numbers added together. This sequence occurs often in nature. And we can compute it with an iterator.

Fibonacci

**A summary.** Certain mathematical methods, such as sqrt() and trigonometric identities, are rarely implemented in user code. Ruby provides these methods.

**As an optimization,** we can cache their results in a lookup table. This classic optimization is known as memoization. A function remembers its previous results by argument.

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