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Programming Principles

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By Zheng Yuan
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Variables Naming Conventions

For example, naming two variables first name and last name

  • Camel Case :point_right: firstName, lastName
  • Snake Case :point_right: first_name, last_name
  • Kebab Case :point_right: first-name, last-name
  • Pascal Case :point_right: FirstName, LastName

Style guides

Floating-point Numbers

FP32

\[12345 = \underbrace{1.2345}_{significand} \times {\underbrace{10}_{base}}\!\!\!\!\!\!\!^{\overbrace{4}^{exponent}}\]
  • IEEE754 Single-Precision Format
  • Sign bit: 1 bit \(\{ 0: +; 1: - \}\)
  • Exponent: 8 bits \([-126, +127]\) (with an offset of 127, -127 (all zeros), and +128 (all ones) are reserved for special numbers)
  • Significand: 24 bits (the 1st bit is always 1, and the rest 23 bits are explicitly stored)

This gives from 6 to 9 significant decimal digits precision.

FP32 to Decimal

FP32

\[value = (-1)^{b_{31}} \times 2^{(b_{30}b_{29} \dots b_{23})_2 - 127} \times (1.b_{22}b_{21} \dots b_{0})_2\]
  1. \(sign = b_{31} = 0\)
  2. \((-1)^{sign} = (-1)^0 = +1 \in \{ -1, +1 \}\)
  3. \(E = (b_{30}b_{29}...b_{23})_2 = (01111100)_2 = (124)_{10} \in \{1, ..., (2^8-1) - 1 \} = \{1, ..., 254\}\)
  4. \(2^{E-127} = 2^{-3} \in \{ 2^{-126}, \dots, 2^{127} \}\)
  5. \((1.b_{22}b_{21} \dots b_{0})_2 = 1 + \sum_{i=1}^{23} b_{23 - i}2^{-i} = 1.25\)
  6. \(value = (+1) \times 2^{-3} \times 1.25 = + 0.15625\)

Decimal to FP32

\[- 10.75 = - (1.01011)_{2} \times 2^3\]
  1. \(sign = b_{31} = 1\)
  2. \((3 + 127)_{10} = (10000010)_2 = (b_{30}b_{29} \dots b_{23})_2\)
  3. \((1.b_{22}b_{21} \dots b_{0})_2 = (1.01011 \underbrace{0 \dots 0}_{18})_2\)
  4. \(value = 1\ 10000010\ 01011 \underbrace{0 \dots 0}_{18}\)

Reference

Programming and Development, Programming Principles
programming principle
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