qf_math

Quick Float Math — fast approximate float routines for ARM Cortex-M, RISC-V, Xtensa/ESP32, and any target with IEEE-754 single precision. Trig, log, exp, sqrt, hypot, waveform generators, and ADSR envelope in one translation unit — no dependencies, no libm required.

Browse the docs

Quick start — include, compile, and use every major function category
API reference — every public function, macro, and constant
Algorithms — how the approximations work
Integration guide — Makefile, CMake, PlatformIO, ESP-IDF, Arduino
qf_math vs fr_math — float vs fixed-point comparison
Float math tradeoffs — libm, qf_math, fixed-point, DSP, and vendor-tuned libraries

Source & benchmarks

github.com/deftio/qf_math — source, tests, multi-library comparison harness, MCU benchmark snapshots (ESP32-S3, Pico 2 ARM & RISC-V).

See BENCHMARK_REPORT.md and BENCHMARK_CROSSPLATFORM.md for full comparison matrices.

Sister library: fr_math (fixed-point)

No hardware FPU? Use fr_math — same API family, pure integer math, 16-bit platform support. Same function coverage, different numeric domain.

Accuracy vs libm

Peak error measured against C double reference over 8000-sample grids. These numbers are architecture-independent — the same lookup tables produce the same errors on every target.

Function	Metric	Peak error
`qf_sin()`	% of full-scale (±1)	0.0019%
`qf_cos()`	% of full-scale (±1)	0.0019%
`qf_tan()`	absolute	0.30
`qf_asin()`	absolute radians	0.00047
`qf_acos()`	absolute radians	0.00047
`qf_atan2()`	absolute radians	0.0013
`qf_log2()`	relative %	0.0016%
`qf_exp()`	relative %	0.00034%
`qf_sqrt()`	relative %	0.00047%
`qf_hypot()`	relative %	0.00047%
`qf_pow()`	relative %	0.00038%

Speed vs libm — on real MCUs

Ratio of libm wall-clock time to qf_math time for the same function. > 1 = qf_math is faster. Data from compare/ benchmark snapshots using benchmark_core.c on real hardware.

Function	ESP32-S3 (Xtensa, FPU)	Pico 2 ARM (Cortex-M33)	Pico 2 RISC-V (Hazard3)
`qf_sin()`	4.30×	3.25×	4.10×
`qf_cos()`	4.39×	2.95×	3.95×
`qf_tan()`	3.56×	2.59×	5.45×
`qf_atan2()`	2.65×	0.71×	1.93×
`qf_log2()`	2.49×	0.94×	1.91×
`qf_exp()`	1.55×	0.51×	1.86×
`qf_sqrt()`	1.07×	16.81×	0.96×
`qf_hypot()`	2.56×	12.26×	1.63×
`qf_pow()`	2.36×	2.43×	2.87×

Microbenchmark ratios from compare/QF_MATH_ARCH_SPEED.md. sqrt is hard to beat on cores with a hardware VSQRT instruction. Full multi-library comparison (libfixmath, fr_math, FastTrig, ESP-DSP) in BENCHMARK_CROSSPLATFORM.md.

Minimal include

#include "qf_math.h"

qf y   = qf_sin(1.0f);       /* radians */
qf len = qf_hypot(dx, dy);
qf dB  = 20.0f * qf_log10(v / ref);