Floating-Point Operations Ali Taheri Sharif University of - - PowerPoint PPT Presentation

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floating point operations

Floating-Point Operations Ali Taheri Sharif University of - - PowerPoint PPT Presentation

Jan 01, 2024 116 likes •187 views

Fu Fundamentals of Pr Programming (Py Python) Floating-Point Operations Ali Taheri Sharif University of Technology Fall 2018 Outline 1. Fixed-Point Representation 2. Floating-Point Representation 3. Arithmetic Errors 4. The math Module

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SLIDE 1

Fu Fundamentals of Pr Programming (Py Python)

Floating-Point Operations

Ali Taheri Sharif University of Technology

Fall 2018

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SLIDE 2

Outline

1. Fixed-Point Representation
2. Floating-Point Representation
3. Arithmetic Errors
4. The math Module

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ALI TAHERI - FUNDAMENTALS OF PROGRAMMING [PYTHON] Fall 2018

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SLIDE 3

Fixed-Point

The number of bits before and after the decimal point is fixed

Example: 98.75

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ALI TAHERI - FUNDAMENTALS OF PROGRAMMING [PYTHON] Fall 2018

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SLIDE 4

Floating-Point

Supports a trade-off between range and precision

IEEE 754 Standard:

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ALI TAHERI - FUNDAMENTALS OF PROGRAMMING [PYTHON] Fall 2018

𝒕𝒋𝒉𝒐𝒋𝒈𝒋𝒅𝒃𝒐𝒆 ∗ 𝒄𝒃𝒕𝒇𝒇𝒚𝒒𝒑𝒐𝒇𝒐𝒖

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SLIDE 5

Arithmetic Errors

When dealing with floating-point numbers, the result of calculation may not be necessarily correct: You should be careful when doing comparisons:

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ALI TAHERI - FUNDAMENTALS OF PROGRAMMING [PYTHON] Fall 2018

0.1 + 0.1 + 0.1 == 0.3 7/5 - 1 == 2/5 1 - 1/3 == 2/3

abs(a-b) < 1e-4

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SLIDE 6

The math module

Implements many of the IEEE functions for complex mathematical operations using floating point values, including logarithms and trigonometric operations. The import keyword enables us to include additional modules into our program

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ALI TAHERI - FUNDAMENTALS OF PROGRAMMING [PYTHON] Fall 2018

import math