FR_Math: A C Language Fixed-Point Math Library for Embedded Systems

See: Documentation & Guide — for API reference, examples, fixed-point primer, build instructions.

FR_Math is a compact, integer-only fixed-point math library built for systems where floating point is too slow, too big, or unavailable. Designed for embedded targets ranging from legacy 16 MHz 68k processors to modern Cortex-M and RISC-V cores, it provides a full suite of math primitives — trigonometry, logarithms, roots, transforms, and signal generators — while remaining deterministic, portable, and small.

Unlike most fixed-point libraries, FR_Math lets the caller choose the binary point (radix) per operation, trading precision and range explicitly instead of locking into a single format. Pure C with C++ wrappers — compiles cleanly under C99, C11, C17, C++11 and later. Compiles under Arduino, PlatformIO, Espressif, many older embedded targets.
Zero dependencies beyond <stdint.h>.

Note qf_math is the float32 version of this library with the same functions. If you have floating point support on your platform and want a faster, lighter version of libm consider that library.

Measured accuracy

Errors below are measured at Q16.16 (s15.16). All functions accept any radix — Q16.16 is just the reference point for the table.

At other radixes (3-bit, 24-bit, etc.) accuracy will differ due to the number of fractional bits available.

Function	Max err (%)*	Avg err (%)	Note
sin/cos (BAM)	0.1526	0.0030	very fast binary angle trig
sin/cos (deg)	0.1526	0.0029	degree input trig fns
sin/cos (rad)	0.1828	0.0033	radian (traditional) trig
tan (BAM)	0.5823	0.0008	binary angle tangent; ±maxint at poles
tan (deg)	0.5311	0.0008	degree input tangent; saturated at poles
tan (rad)	0.0386	0.0001	radian (traditional) tangent
asin / acos	0.7771	0.0280	reverse trig, radian output
atan2	0.2564	0.0237	reverse tangent, always safe
atan	0.2425	0.0155	reverse tangent, accepts up to maxint
sqrt	0.0000	0.0000	Round-to-nearest
log2	0.0116	0.0016	shift/add only for speed
pow2	0.0018	0.0004	shift/add only for speed
ln, log10	0.0004	0.0000	shift/add only for speed
exp	0.0003	0.0000	shift/add only for speed
exp_fast	0.0009	0.0001	Shift-only scaling
pow10	0.0005	0.0000	shift/add only for speed
pow10_fast	0.0022	0.0002	Shift-only scaling
hypot (exact)	0.0000	0.0000	Uses 64-bit intermediate
hypot_fast8 (8-seg)	0.0915	0.0320	Shift-only, no multiply

*Relative error; reference clamped to 1% of full-scale output.

What's in the box

Area	Functions
Arithmetic	FR_ADD, FR_SUB, FR_DIV, FR_DIV32, FR_MOD, FR_FixMuls, FR_FixMulSat, FR_CHRDX
Utility	FR_MIN, FR_MAX, FR_CLAMP, FR_ABS, FR_SGN
Trig (degree)	fr_sin_deg, fr_cos_deg, fr_tan_deg, FR_SinI, FR_CosI, FR_TanI
Trig (radian/BAM)	fr_sin, fr_cos, fr_tan, fr_sin_bam, fr_cos_bam, fr_tan_bam
Inverse trig	FR_atan, FR_atan2, FR_asin, FR_acos
Log / exp	FR_log2, FR_ln, FR_log10, FR_pow2, FR_EXP, FR_POW10, FR_EXP_FAST, FR_POW10_FAST, FR_MULK28
Roots	FR_sqrt, FR_hypot, FR_hypot_fast8
Wave generators	fr_wave_sqr, fr_wave_pwm, fr_wave_tri, fr_wave_saw, fr_wave_tri_morph, fr_wave_noise
Envelope	fr_adsr_init, fr_adsr_trigger, fr_adsr_release, fr_adsr_step
2D transforms	FR_Matrix2D_CPT (mul, add, sub, det, inv, setrotate, XFormPtI, XFormPtI16)
Formatted output	FR_printNumD, FR_printNumF, FR_printNumH, FR_numstr

Compiled library size (FR_math.c only, -Os)

.text section sizes, all code + internal tables, ROMable. Sorted 8-bit → 64-bit.

Target	Lean	Core	Full
AVR ATmega328P (8-bit)	9.2 KB	12.8 KB	15.4 KB
68HC11 (8-bit)	13.3 KB	18.4 KB	22.6 KB
MSP430 (16-bit)	7.8 KB	10.7 KB	12.8 KB
Xtensa LX7 (ESP32-S3)	2.9 KB	4.2 KB	5.3 KB
Cortex-M4 (32-bit)	3.3 KB	4.4 KB	5.5 KB
Cortex-M0 (32-bit)	3.4 KB	4.5 KB	5.7 KB
RISC-V rv32	4.1 KB	5.5 KB	6.8 KB
Xtensa LX106 (ESP8266)	4.2 KB	5.8 KB	7.3 KB
m68k (32-bit)	4.4 KB	6.2 KB	7.8 KB
MIPS32	4.7 KB	6.6 KB	8.7 KB
x86-32	5.3 KB	7.2 KB	9.2 KB
RISC-V rv64	4.0 KB	5.5 KB	6.8 KB
x86-64 (GCC)	4.6 KB	6.1 KB	8.0 KB
AArch64 (ARM64)	4.8 KB	6.6 KB	8.7 KB