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https://github.com/jgaeddert/liquid-fpm

fixed-point math library for embedded signal processing
https://github.com/jgaeddert/liquid-fpm

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fixed-point math library for embedded signal processing

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README 

        

liquid-fpm : Software-Defined Radio Fixed-Point Math Library

============================================================



*NOTE:* This repository has been incorporated as a branch in the main

liquid-dsp repository here:

[https://github.com/jgaeddert/liquid-dsp](https://github.com/jgaeddert/liquid-dsp)



liquidfpm is a flexible fixed-point math library developed for efficient

computational software-defined radio.



Build:



    $ ./bootstrap.sh

    $ ./configure

    $ make



Install:



    # make install



Run tests:



    $ make test



Run benchmarks:



    $ make bench



## ANGULAR REPRESENTATION ##



## INTERFACES ##



Reference



    N : total number of bits in the data type (e.g. 32)

    I : total number of integer bits, including sign

    F : total number of fractional bits



Regular constants



    name                value                   description

    qtype_min                                   minimum representable value

    qtype_max                                   maximum representable value

    qtype_one           1                       one

    qtype_pi                                    pi (angular)

    qtype_2pi                                   2*pi (angular)

    qtype_pi_by_2                               pi/2 (angular)

    qtype_angle_scalarf 3.14159 / 2^(I-2)       angular <-> scalar relationship



Mathematical constants (genlib/genlib.constants.c)



    name                value                   description

    qtype_E             2.71828182845905        e

    qtype_LOG2E         1.44269504088896        log2(e)

    qtype_LOG10E        0.434294481903252       log10(e)

    qtype_LN2           0.693147180559945       log(2)

    qtype_LN10          2.30258509299405        log(10)

    qtype_PI            3.14159265358979        pi (actual)

    qtype_PI_2          1.57079632679490        pi/2

    qtype_PI_4          0.785398163397448       pi/4

    qtype_1_PI          0.318309886183791       1/pi

    qtype_2_PI          0.636619772367581       2/pi

    qtype_2_SQRTPI      1.12837916709551        2/sqrt(pi)

    qtype_SQRT2         1.41421356237310        sqrt(2)

    qtype_SQRT1_2       0.707106781186547       1/sqrt(2)



Fixed-point/Floating-point conversion



    qtype_fixed_to_float            convert fixed-point value to floating-point value

    qtype_float_to_fixed            convert floating-point value to fixed-point value

    qtype_angle_fixed_to_float      convert fixed-point angle to floating-point angle

    qtype_angle_float_to_fixed      convert floating-point value to fixed-point angle



Basic arithmetic functions



    qtype_sign(x)       sign of x = x / |x|

    qtype_abs(x)        |x|

    qtype_add(x,y)      x+y

    qtype_sub(x,y)      x-y

    qtype_mul(x,y)      x*y

    qtype_div(x,y)      x/y

    qtype_inv(x,n)      1/x with n iterations

    qtype_ratio(a,b,n)  integer ratio a/b with n iterations



Pre-C99 functions



    qtype_acos

    qtype_atan

    qtype_atan2

    qtype_ceil

    qtype_cos

    qtype_cosh

    qtype_exp

    qtype_fabs

    qtype_floor

    qtype_fmod

    qtype_frexp

    qtype_ldexp

    qtype_log

    qtype_log10

    qtype_modf

    qtype_pow

    qtype_sin

    qtype_sinh

    qtype_sqrt

    qtype_tan

    qtype_tanh



C99 functions



    qtype_acosh

    qtype_asinh

    qtype_atanh

    qtype_cbrt

    qtype_copysign

    qtype_erf

    qtype_erfc

    qtype_exp2

    qtype_expm1

    qtype_fdim

    qtype_fma

    qtype_fmax

    qtype_fmin

    qtype_hypot

    qtype_ilogb

    qtype_lgamma

    qtype_llrint

    qtype_lrint

    qtype_llround

    qtype_lround

    qtype_log1p

    qtype_log2

    qtype_logb

    qtype_nan

    qtype_nearbyint

    qtype_nextafter

    qtype_nexttoward

    qtype_remainder

    qtype_remquo

    qtype_rint

    qtype_round

    qtype_scalbln

    qtype_scalbn

    qtype_tgamma

    qtype_trunc



Additional functions



    qtype_lngamma

    qtype_besseli0

    qtype_besselj0

    qtype_sinc

    qtype_kaiser



Complex arithmetic



    cqtype_add(x,y)         x+y

    cqtype_sub(x,y)         x-y

    cqtype_mul(x,y)         x*y

    cqtype_mul_scalar(x,c)  x*c

    cqtype_div(x,y)         x/y

    cqtype_div_scalar(x,c)  x/c

    cqtype_inv(x)           1/x



Complex trig



    cqtype_cabs

    cqtype_cacos

    cqtype_cacosh

    cqtype_carg

    cqtype_casin

    cqtype_casinh

    cqtype_catan

    cqtype_catanh

    cqtype_ccos

    cqtype_ccosh

    cqtype_cexp

    cqtype_cimag

    cqtype_clog

    cqtype_conj

    cqtype_cpow

    cqtype_cproj

    cqtype_creal

    cqtype_csin

    cqtype_csinh

    cqtype_csqrt

    cqtype_ctan

    cqtype_ctanh



 * Function declaration exists but no function definition (not yet implemented)



## Build Description ##



gentab (auto-generated tables)

Some of the algorithms in liquid-fpm (such as the CORDICs) use tables

which are automatically generated at build-time.

These are located in the gentab/ subdirectory.



For example,



    script:     gentab/gentab.sincos.cordic.c

    program:    gentab/gentab.sincos.cordic

    source:     gentab/sincos.cordic.$(qtype).c

    object:     gentab/sincos.cordic.$(qtype).o



where the makefile key $(qtype) is given by configure.ac (default is "q32")



genlib (auto-generated assembly objects)

Several of the low-level arithmetic functions (such as multiplication

of two fixed-point numbers) can be computed faster by taking advantage

of architecture-specific hardware instructions.

These functions are generated automatically given the precision...



## Configuring Precision ##



The bit-precision of the fixed-point type is defined in two places:



configure.ac

    QTYPE                   : name of variables (e.g. "q32")

    QTYPE_INTBITS           : number of bits in integer component (e.g. "7")

    QTYPE_FRACBITS          : number of bits in fractional component (e.g. "25")

include/liquidfpm.h

    LIQUIDFPM_MANGLE        : name-mangling macro (e.g. LIQUIDFPM_CONCAT(q32,name))

    LIQUIDFPM_DEFINE_API    : interface macro



The default name for the data types are:

    q32_t   : fixed-point 32-bit data type

    cq32_t  : complex 2-valued (real,imag) 32-bit data type

    q32f_t  : floating-point 2-valued (base,frac) data type (internal use)



Limitations:

Due to some arithmetic constants required for computation in certain

algorithms, not all precisions are possible.  For example, the sinh|cosh

CORDIC requires initialization on kp_inv=1.207497... which needs at least 2

integer bits representation (not including the sign bit).  As a result, this

excludes data types such as Q1.31 format from running properly for these

functions. The library will configure and compile for such precisions, however

the unit tests might (and probaby will) fail.



## Specific Build Targets ##



Here is a list of the specific build targets



    all             :   everything: libliquidfpm shared object library

    check           :   generate autotest program and execute

    bench           :   generate benchmark program and execute



    distclean       :   clean everything, including configuration headers, and makefile

    clean           :   clean all ojbect files and shared library

    clean-genlib    :   clean only the auto-generated assembly sources and objects

    clean-gentab    :   clean only the auto-generated table sources and objects

    clean-bench     :   clean only the benchmark files

    clean-autotest  :   clean only the autotest files



    test            :   generate debugging test and execute