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fixed-point math library for embedded signal processing

branch: master
README.md

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

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
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