Floating Point Numbers comparison #203

data/learning.yml

@@ -22,6 +22,11 @@ books:
       - link: /learn/quickstart/organising_code
       - link: /learn/quickstart/derived_types
 
+  - title: Floating Point Numbers comparison
+  description: Learn how to handle rounding errors in floating-point numbers, use them in if and for loops, and make robust comparisons using tolerance in Fortran.
+  category: Getting started
+  link: /learn/Floating_Point_Numbers_comparison
+
   - title: Building programs
     description: How to use the compiler to build an executable program
     category: Getting started

source/learn/Floating_Point_Numbers_comparison.md

@@ -0,0 +1,76 @@
+# Floating-Point Tolerance and Precision in Fortran
+
+Floating-point numbers like `0.1` cannot be represented exactly in binary because their binary form is infinite and repeating. Due to the limited precision of floating-point formats (like 32-bit or 64-bit), these numbers are rounded off to fit within the constrained number of bits.
+This rounding can lead to small errors in representation and calculations. 
+
+To ensure reliable comparisons, it is better to use **tolerance** to check whether two numbers are close enough rather than comparing them directly.
+
+## Handling Floating-Point Comparisons
+
+Here’s an example of how to use a tolerance value in Fortran:
+
+### Example: Using Tolerance
+```fortran
+real(dp) :: tol
+tol = 10 * epsilon(1.0_dp)  ! epsilon returns the smallest number such that 1.0 + epsilon > 1.0
+
+if (abs(x - y) < tol) then
+    print *, "Effectively Equal"
+else
+    print *, "Not Equal"
+end if
+```
+
+In this example:
+- The **tolerance** value is derived using either `epsilon()` or a manually defined small value.
+- Instead of checking `x == y`, we compare the absolute difference `abs(x - y)` to the tolerance.
+
+---
+
+## Avoiding Floating-Point Precision Issues
+
+Sometimes, directly incrementing floating-point numbers can cause cumulative rounding errors. 
+Instead, use **integer iterators** and convert them to floating-point values within the loop.
+
+### Example: Using Integer Iterators
+```fortran
+integer :: i
+real(dp) :: step, value
+step = 0.1_dp
+
+do i = 0, 10
+   value = i * step
+   print *, value
+end do
+```
+
+In this example:
+- The step size is defined as `0.1` in double precision.
+- The loop uses integers (`i`) to avoid compounding errors when iterating.
+
+---
+
+## Why Use Tolerance?
+
+Due to rounding errors, numbers like `0.1 + 0.2` may not exactly equal `0.3`. Direct comparisons fail in such cases:
+```fortran
+if (a + b == c) then
+   print *, "Equal"
+else
+   print *, "Not Equal"
+end if
+```
+Instead, use a tolerance to make approximate comparisons:
+```fortran
+if (abs((a + b) - c) < tol) then
+   print *, "Approximately Equal"
+else
+   print *, "Not Equal"
+end if
+```
+
+---
+
+
+
+