Bryan Batten / s16math

16 bit fixed point precision with basic math, logarithms, trigonometric functions, and exponentiation. Available in binary and decimal resolutions. Re-entrant, thread safe, fully interruptible.

Fork of s16math by Bryan Batten

DESCRIPTION.txt@1:ab4d55399b01, 2014-09-03 (annotated)

Committer:
bbatten
Date:
Wed Sep 03 17:12:36 2014 +0000
Revision:
1:ab4d55399b01
Parent:
0:306417d5f0a0 
16 bit fixed point precision with basic math, logarithms, trigonometric; functions, and exponentiation. Available in binary and decimal; resolutions. Re-entrant, thread safe, fully interruptible.

Who changed what in which revision?

UserRevisionLine numberNew contents of line
bbatten 0:306417d5f0a0 1 Description
bbatten 0:306417d5f0a0 2
bbatten 0:306417d5f0a0 3 s16math is a compact library of 16 bit fixed point[1] math functions
bbatten 0:306417d5f0a0 4 for microcontroller - MCU - environments without fixed or floating
bbatten 0:306417d5f0a0 5 point hardware.
bbatten 0:306417d5f0a0 6
bbatten 0:306417d5f0a0 7 The development platform is Debian Linux running on an X86 machine
bbatten 0:306417d5f0a0 8 using basic GNU/Linux cross compilation development tools. The package
bbatten 0:306417d5f0a0 9 provides tools to build deployable object versions of the library for a
bbatten 0:306417d5f0a0 10 variety of targets.
bbatten 0:306417d5f0a0 11
bbatten 0:306417d5f0a0 12 Capabilities are focused on processor and memory constrained embedded
bbatten 0:306417d5f0a0 13 applications such as resource limited battery powered sensors and
bbatten 0:306417d5f0a0 14 wearable medical devices. MCUs such as the HC08, HC11, 8051, Z80, and
bbatten 0:306417d5f0a0 15 ARM machines operating in 16-bit mode are supported, maximizing use of
bbatten 0:306417d5f0a0 16 limited MCU registers while minimizing the software overhead of 32 and
bbatten 0:306417d5f0a0 17 64 bit operations.
bbatten 0:306417d5f0a0 18
bbatten 0:306417d5f0a0 19 The trigonometric and math functions make the library well suited for
bbatten 0:306417d5f0a0 20 software defined radio - SDR - signal management requirements.
bbatten 0:306417d5f0a0 21
bbatten 0:306417d5f0a0 22 The virtual fixed point format provides 65,536 discrete signed values
bbatten 0:306417d5f0a0 23 between -32768 and +32767 inclusive, with an equivalent decimal fixed
bbatten 0:306417d5f0a0 24 point range of -327.68 through +327.67. If binary resolution is used,
bbatten 0:306417d5f0a0 25 the range is -256.000 through +255.127 (see text on dot (".") notation
bbatten 0:306417d5f0a0 26 below). If your application requires numbers outside this range, then
bbatten 0:306417d5f0a0 27 this masterpiece - alas - is not for you.
bbatten 0:306417d5f0a0 28
bbatten 0:306417d5f0a0 29 Machine level integers are treated as virtual fixed point[1] numbers
bbatten 0:306417d5f0a0 30 with sign, integer, and fractional parts specified in either decimal or
bbatten 0:306417d5f0a0 31 Qm.n[2] format. The most significant bit is the sign bit, leaving 15
bbatten 0:306417d5f0a0 32 bits to be allocated between the integer and the fractional components.
bbatten 0:306417d5f0a0 33
bbatten 0:306417d5f0a0 34 Numbers are a ratio of two integers: the numerator is kept in storage,
bbatten 0:306417d5f0a0 35 the denominator is implied and is equal to either a power of 10 or a
bbatten 0:306417d5f0a0 36 power of 2. The integer and fractional parts are given by the integer
bbatten 0:306417d5f0a0 37 division of the whole number by the denominator: the integer portion is
bbatten 0:306417d5f0a0 38 the quotient and the fractional part is the remainder. A dot (".")
bbatten 0:306417d5f0a0 39 notation is used to separate the integer and fractional portions of the
bbatten 0:306417d5f0a0 40 number when it is displayed.
bbatten 0:306417d5f0a0 41
bbatten 0:306417d5f0a0 42 If exact fractional powers of ten are desired, then a decimal format
bbatten 0:306417d5f0a0 43 should be used[1]. This provides more range than the binary format, but
bbatten 0:306417d5f0a0 44 less resolution.
bbatten 0:306417d5f0a0 45
bbatten 0:306417d5f0a0 46 So where the denominator is 100, the number 30 is treated as 30/100, or
bbatten 0:306417d5f0a0 47 2.30; 250 is treated as 250/100, or 2.50. In this library, denominators
bbatten 0:306417d5f0a0 48 of 10, 100, and 1000 are used.
bbatten 0:306417d5f0a0 49
bbatten 0:306417d5f0a0 50 In Qm.n format 'm' is the number of bits in the integer portion of the
bbatten 0:306417d5f0a0 51 number, and 'n' is the number of bits in the fractional part. The
bbatten 0:306417d5f0a0 52 denominator is a constant equal to 2^n[2].
bbatten 0:306417d5f0a0 53
bbatten 0:306417d5f0a0 54 So where n is 6, 2^n is 64, and the number 30 is treated as 30/64
bbatten 0:306417d5f0a0 55 (0.30); 250 is treated as 250/64, or 3 58/64 (3.58). Where n is 7, 2^n
bbatten 0:306417d5f0a0 56 is 128, and the number 30 is treated as 30/128 (0.030); 250 is treated
bbatten 0:306417d5f0a0 57 as 250/128, or 1 122/128 (1.122) etc. In this library, Q11.4, Q8.7, and
bbatten 0:306417d5f0a0 58 Q6.9 formats are used.
bbatten 0:306417d5f0a0 59
bbatten 0:306417d5f0a0 60 The advantage of the Qm.n format is that the rounding operations needed
bbatten 0:306417d5f0a0 61 to preserve precision may be done with bit shifts instead of division
bbatten 0:306417d5f0a0 62 and multiplication, which can significantly boost performance and save
bbatten 0:306417d5f0a0 63 code overhead in machines without integer multiplication and division
bbatten 0:306417d5f0a0 64 hardware.
bbatten 0:306417d5f0a0 65
bbatten 0:306417d5f0a0 66 Installation
bbatten 0:306417d5f0a0 67
bbatten 0:306417d5f0a0 68 The download file unpacks into a directory named "eval". So change to
bbatten 0:306417d5f0a0 69 the directory where you wish to install it, download the zip file and
bbatten 0:306417d5f0a0 70 unzip it.
bbatten 0:306417d5f0a0 71
bbatten 0:306417d5f0a0 72 You should now see the subdirectory "eval". Go there. Peruse README.
bbatten 0:306417d5f0a0 73 Alternately, point your browser to eval/html and peruse README.html.
bbatten 0:306417d5f0a0 74 Proceed thence.
bbatten 0:306417d5f0a0 75
bbatten 0:306417d5f0a0 76 [1] Fixed-point arithmetic
bbatten 0:306417d5f0a0 77 http://en.wikipedia.org/wiki/Fixed-point_arithmetic
bbatten 0:306417d5f0a0 78
bbatten 0:306417d5f0a0 79 [2] Q (number format)
bbatten 0:306417d5f0a0 80 http://en.wikipedia.org/wiki/Q_%28number_format%29
bbatten 0:306417d5f0a0 81 # vi:set expandtab: