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Initial port of the IQMath Library, obtained from TI MSPM0 SDK.

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IQMath Library

The IQmath Library is a collection of highly optimized and high-precision mathematical functions for C programmers to seamlessly port a floating-point algorithm into fixed-point code on chips without a floating-point unit (FPU). These routines are typically used in computationally intensive real-time applications where optimal execution speed, high accuracy and ultra-low energy are critical. By using the IQmath library, it is possible to achieve execution speeds considerably faster and energy consumption considerably lower than equivalent code written using floating-point math.

The IQmath library provides functions for use with 32-bit data types and high accuracy.

IQmath Data Types

The IQmath library uses a 32-bit fixed-point signed number (i.e. int32_t) as its basic data type. The IQ format of this fixed-point number can range from IQ1 to IQ30, where the IQ format number indicates the number of fractional bits. The IQ format value is stored as an integer with an implied scale based on the IQ format and the number of fractional bits. The equation below shows how a IQ format decimal number $x_{iq}$ is stored using an integer value $x_i$ with an implied scale, where $n$ represents the number of fractional bits.

$$ IQ_n(x_{iq}) = x_i * 2^{-n} $$

For example the IQ24 value of 3.625 is stored as an integer value of 60817408, shown in the equation below.

$$ IQ_{24}(3.625) = 60817408 * 2^{-24} $$

C typedefs are provided for the various IQ formats, and these IQmath data types should be used in preference to the underlying “int32_t” data type to make it clear which variables are in IQ format.

The following table provides the characteristics of the various IQ formats:

Type Integer Bits Fractional Bits Min Range Max Range Resolution
_iq30 2 30 -2 1.999 999 999 0.000 000 001
_iq29 3 29 -4 3.999 999 998 0.000 000 002
_iq28 4 28 -8 7.999 999 996 0.000 000 004
_iq27 5 27 -16 15.999 999 993 0.000 000 007
_iq26 6 26 -32 31.999 999 985 0.000 000 015
_iq25 7 25 -64 63.999 999 970 0.000 000 030
_iq24 8 24 -128 127.999 999 940 0.000 000 060
_iq23 9 23 -256 255.999 999 881 0.000 000 119
_iq22 10 22 -512 511.999 999 762 0.000 000 238
_iq21 11 21 -1,024 1,023.999 999 523 0.000 000 477
_iq20 12 20 -2,048 2,047.999 999 046 0.000 000 954
_iq19 13 19 -4,096 4,095.999 998 093 0.000 001 907
_iq18 14 18 -8,192 8,191.999 996 185 0.000 003 815
_iq17 15 17 -16,384 16,383.999 992 371 0.000 007 629
_iq16 16 16 -32,768 32,767.999 984 741 0.000 015 259
_iq15 17 15 -65,536 65,535.999 969 483 0.000 030 518
_iq14 18 14 -131,072 131,071.999 938 965 0.000 061 035
_iq13 19 13 -262,144 262,143.999 877 930 0.000 122 070
_iq12 20 12 -524,288 524,287.999 755 859 0.000 244 141
_iq11 21 11 -1,048,576 1,048,575.999 511 720 0.000 488 281
_iq10 22 10 -2,097,152 2,097,151.999 023 440 0.000 976 563
_iq9 23 9 -4,194,304 4,194,303.998 046 880 0.001 953 125
_iq8 24 8 -8,388,608 8,388,607.996 093 750 0.003 906 250
_iq7 25 7 -16,777,216 16,777,215.992 187 500 0.007 812 500
_iq6 26 6 -33,554,432 33,554,431.984 375 000 0.015 625 000
_iq5 27 5 -67,108,864 67,108,863.968 750 000 0.031 250 000
_iq4 28 4 -134,217,728 134,217,727.937 500 000 0.062 500 000
_iq3 29 3 -268,435,456 268,435,455.875 000 000 0.125 000 000
_iq2 30 2 -536,870,912 536,870,911.750 000 000 0.250 000 000
_iq1 31 1 -1,073,741,824 1,073,741,823.500 000 000 0.500 000 000

API Guide

IQmath includes five types of routines:

  • Format conversion functions: methods to convert numbers to and from the various formats.
  • Arithmetic functions: methods to perform basic arithmetic (addition, subtraction, multiplication, division).
  • Trigonometric functions: methods to perform trigonometric functions (sin, cos, atan, and so on).
  • Mathematical functions: methods to perform advanced arithmetic (square root, ex , and so on).
  • Miscellaneous: miscellaneous methods (saturation and absolute value).

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Initial port of the IQMath Library, obtained from TI MSPM0 SDK.

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