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
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)
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...
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.
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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