Ch2.2.2 Floating Point Numbers

Floating Point Numbers

  • Floating point numbers provide the way around the limitations of binary integers.
  • Floating point numbers are capable of storing noninteger values, such as 2.71828182845905, 3.14159265358979, and 0.25.
  • How many significant digits shown below?

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Floating Point Numbers

  • Floating point numbers provide the way around the limitations of binary integers.
  • Floating point numbers are capable of storing noninteger values, such as 2.71828182845905, 3.14159265358979, and 0.25.
  • How many significant digits shown below? (Ans = 5)

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Floating Point Numbers

  • Floating point numbers can store much larger numbers.
  • R defaults to storing numerical data as floating point data.
2^31

[1] 2147483648

2^30

[1] 1073741824

Floating Point Numbers: Double Precision

  • There are several standards for floating point.
  • We focus on double precision, or just double.
  • It has approximately double the storage space (64 bits) than standard floating point format (32 bits).

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Floating Point Numbers: Double Precision

  • Compare with single precision.

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Floating Point Numbers: Single Precision

  • Compare with single precision.
  • See next slide for more details.

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Floating Point Numbers: Single Precision

  • Exponent range split to allow for positive and negative exponents on base.
  • Thus exponent on 2 has “-127” for this reason
256/2

[1] 128

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Floating Point Numbers: Single Precision

  • The C float data type is sometimes called single precision.
  • R includes a function to convert a number to a single precision value.
  • Underlying data type within R is still double precision.
  • R can interact with languages that support single precision data types.