Releases

Release highlights. For the full per-symbol change log, see release_notes.md in the repo.

v2.0.8 — 2026

Tangent accuracy rewrite and trig rounding fix.

• BAM-native tangent: new fr_tan_bam(u16 bam) with 65-entry octant table (130 bytes). No 64-bit math. FR_TanI, FR_Tan, fr_tan are now thin wrappers.
• Round-to-nearest fix: radian/degree trig wrappers now round instead of truncating when converting to BAM. Peak error drops from ~1.03% to 0.16% on the radian path, matching BAM-native accuracy.
• Conversion macro trimming: FR_DEG2BAM and FR_RAD2BAM reduced to ~18–21 bits (from ~28 bits). Verified: no measurable accuracy impact.
• FR_TRIG_MINVAL fixed: now -FR_TRIG_MAXVAL (was -FR_TRIG_MASK)

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v2.0.7 — 2026

README restructure, accuracy table cleanup, expanded cross-compile support.

• FR_CORE_ONLY convenience define — single #define strips both print helpers and wave generators
• Accuracy table cleanup — removed LSB column (percent error is the user-facing metric)
• New cross-compile targets — RP2040 (Cortex-M0+), STM32 (Cortex-M4), 68HC11, MIPS32 added to Docker build
• Three-column size table — Lean / Core / Full for every target, sorted 8-bit → 64-bit
• scripts/crossbuild_sizes.sh — consolidated script: Docker build, CSV + markdown output, doc patching
• README reordered and cleaned up: accuracy table first, badges as standard markdown, concise build flavor descriptions

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v2.0.6 — 2026

Accuracy improvements, lean-build options, library cleanup.

• FR_acos boundary fix — 12x better accuracy near ±1.0 via deferred quantization
• FR_atan2 rewrite — asin/acos + hypot_fast8, 0.41% peak error (was 20% in libfixmath)
• Lean build guards — FR_NO_PRINT (~1.3 KB) and FR_NO_WAVES (~0.6 KB) for ROM-constrained targets
• Removed FR_hypot_fast (4-segment) — FR_hypot_fast8 is strictly better; 4-seg was dead weight
• libfixmath comparison benchmark added to repo (compare_lfm/)

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v2.0.5 — 2026

Release pipeline fixes. Fixed squash-merge divergence handling and on-master push/CI sequencing in tools/make_release.sh.

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v2.0.4 — 2026

CI fix release. Fixed release.yml coverage step, release pipeline auto-commits badge/version changes, removed conflicting auto-release job from ci.yml.

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v2.0.3 — 2026

CI and release pipeline cleanup. Guided release script (tools/make_release.sh) that validates, merges, tags, and publishes to PlatformIO and ESP-IDF in one flow.

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v2.0.2 — 2026

Embedded library publishing support. No functional changes to the math library — adds Arduino, PlatformIO, and ESP-IDF package manager integration.

• Arduino Library Manager, PlatformIO Registry, and ESP-IDF Component Registry metadata files
• Reorganized examples with focused Arduino .ino sketches
• Added llms.txt and agents.md for AI coding agents
• Tag-triggered release workflow (.github/workflows/release.yml)

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v2.0.1 — 2026

Precision and accuracy release. All changes are backward-compatible with v2.0.0 except where noted.

Trig output precision

• fr_cos_bam / fr_sin_bam now return s15.16 (was s0.15). Exact values at cardinal angles: cos(0°) = 65536, cos(90°) = 0. FR_TRIG_ONE = 65536.
• FR_TanI / fr_tan return s15.16 (was s16.15). Saturation is now ±INT32_MAX.
• All wrappers updated: FR_Cos, FR_Sin, FR_CosI, FR_SinI, FR_TanI, FR_Tan.

Inverse trig now returns radians

• FR_acos, FR_asin, FR_atan gain an out_radix parameter and return radians at that radix (was degrees as s16).
• FR_atan2(y, x, out_radix) also returns radians.
• FR_BAM2RAD macro corrected (was off by a factor of 1024).

Rounding improvements

• FR_FixMuls / FR_FixMulSat: add 0.5 LSB (+0x8000) before the >>16 shift. Both now round to nearest instead of truncating.
• FR_sqrt / FR_hypot: the internal fr_isqrt64 now rounds to nearest (remainder > root → +1). Worst-case error drops from <1 LSB to ≤ 0.5 LSB.

Improved exp / log accuracy

• FR_pow2 table expanded from 17 entries (16 segments) to 65 entries (64 segments, 260 bytes). Interpolation error drops by ~16×.
• FR_log2 table expanded from 33 entries to 65 entries (6-bit index / 24-bit interpolation). Worst-case error ≤ 4 LSB at Q16.16.
• FR_MULK28 macro added: multiplies any fixed-point value by a radix-28 constant using a 64-bit intermediate with round-to-nearest. ~9 decimal digits of precision.
• FR_EXP and FR_POW10 now use FR_MULK28 for the base conversion instead of shift-only macros. Much lower error.
• FR_ln and FR_log10 also use FR_MULK28 internally.
• FR_EXP_FAST and FR_POW10_FAST added as shift-only alternatives for 8-bit targets where 64-bit multiply is expensive.
• Four radix-28 constants added: FR_kLOG2E_28, FR_krLOG2E_28, FR_kLOG2_10_28, FR_krLOG2_10_28.

New utility macros

• FR_MIN, FR_MAX, FR_CLAMP — standard min/max/clamp.
• FR_DIV(x, xr, y, yr) — fixed-point division with 64-bit pre-scaling. Now rounds to nearest (≤ 0.5 LSB error) instead of truncating. FR_DIV_TRUNC preserves the old truncating behavior for backward compatibility. FR_DIV32 is the 32-bit-only truncating path.
• FR_MOD(x, xr, y, yr) — fixed-point modulus.

Infrastructure

• Docker cross-compile size report (9 targets).
• sync_version.sh rewrite — FR_MATH_VERSION_HEX is the single source of truth for version numbers.
• CI auto-release job, Dependabot config.
• Documentation audit: 14 errors fixed across header, source, markdown, and HTML docs.

Breaking changes from v2.0.0

Change	v2.0.0	v2.0.1
sin/cos return type	s16 (s0.15)	s32 (s15.16)
sin/cos 1.0 value	32767	65536 (exact)
tan return format	s16.15 (radix 15)	s15.16 (radix 16)
tan saturation	±(32767 << 15)	±INT32_MAX
FR_acos/asin signature	(input, radix) → s16 degrees	(input, radix, out_radix) → s32 radians
FR_atan signature	(input, radix) → s16 degrees	(input, radix, out_radix) → s32 radians
FR_atan2 signature	(y, x) → s16 degrees	(y, x, out_radix) → s32 radians
FR_BAM2RAD	off by 1024× (bug)	correct
FR_DIV rounding	truncates toward zero	rounds to nearest (use FR_DIV_TRUNC for old behavior)

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v2.0.0 — 2026

The first major revision in more than twenty years. v2 is a bug-fix, precision, and feature release with a full test suite and 99% line coverage.

64-bit safety

v1 defined s32 as signed long, which is 64 bits on LP64 platforms (Linux x64, macOS arm64). Every fixed-point path that assumed s32 was exactly 32 bits silently produced wrong results on desktop hosts. v2 migrates all typedefs to <stdint.h> (int8_t…int32_t). C99 is now mandatory.

Numerical fixes

• FR_FixMulSat / FR_FixMuls: rewritten on an int64_t fast path with explicit saturation; v1 had an algebraic bug in the sign-combination logic.
• FR_log2 / FR_ln / FR_log10: new leading-bit-position + 33-entry mantissa table with linear interpolation. v1 returned wrong values for non-power-of-2 inputs.
• FR_pow2 / FR_EXP / FR_POW10: corrected floor-toward-−∞ integer-part extraction. v1 gave wrong answers for negative non-integer inputs.
• FR_atan2: v1 was a placeholder that returned garbage. v2 is a correct octant-reduced arctan with max error ≤ 1°. The vestigial radix argument was dropped.
• FR_atan, FR_Tan, FR_TanI: wiring and overflow fixes.
• FR_printNumD/F/H: fixed undefined behavior on INT_MIN and a broken fraction extraction in the v1 code.
• FR_DEG2RAD / FR_RAD2DEG: macro bodies were swapped in v1. v2 fixes them and adds missing parentheses.

New functionality

• Radian-native trig: fr_sin, fr_cos, fr_tan, fr_sin_bam, fr_cos_bam, fr_sin_deg, fr_cos_deg. Uses a new 129-entry quadrant cosine table with round-to-nearest linear interpolation. Max error ≤ 1 LSB of s0.15 (~3e−5).
• BAM macros: FR_DEG2BAM, FR_BAM2DEG, FR_RAD2BAM, FR_BAM2RAD. BAM (16 bits per full circle) is the natural integer representation for phase accumulators and gives zero quantization at the wraparound.
• Square root and hypot: FR_sqrt uses a digit-by-digit integer isqrt on int64_t; FR_hypot computes sqrt(x² + y²) with no intermediate overflow across the full s32 range.
• Wave generator family: fr_wave_sqr, fr_wave_pwm, fr_wave_tri, fr_wave_saw, fr_wave_tri_morph, fr_wave_noise. All are stateless and take a u16 BAM phase. Suitable for embedded audio, LFOs, and control signals.
• ADSR envelope generator: linear-segment attack/decay/sustain/release with s1.30 internal state so very long durations at high sample rates still have non-zero per-sample increments.
• Compile-time table size: -DFR_TRIG_TABLE_BITS=8 doubles table precision at the cost of a larger (257-entry) table. Default is 7 / 129 entries.

New documentation

• API Reference — complete per-symbol reference with inputs, outputs, radix handling, and worst-case error.
• CONTRIBUTING.md — PR expectations, portability rules, commit format.
• tools/interp_analysis.html — interactive Chart.js comparison of seven interpolation methods on the trig table.
• This documentation site (the one you’re reading).

Breaking changes

• FR_NUM(i, f, r) → FR_NUM(i, f, d, r). The v1 form was broken (it ignored f entirely), so any caller was already getting wrong results.
• FR_atan2(y, x, radix) → FR_atan2(y, x). The radix parameter was vestigial.
• FR_RESULT and the FR_E_* codes are gone. inv() returns bool; add() / sub() / setrotate() return void. Math functions use named sentinels FR_DOMAIN_ERROR, FR_OVERFLOW_POS, FR_OVERFLOW_NEG.
• FR_SQUARE and FR_FIXMUL32u removed — use FR_FixMuls / FR_FixMulSat, which now have an int64_t fast path and work at any radix.
• FR_NO_INT64 and FR_NO_STDINT build flags removed. Every modern C99 toolchain ships <stdint.h> and 64-bit arithmetic.

Test suite

v2 ships with a full test suite covering 99% of library source lines, plus a characterization suite (test_tdd.cpp) that pins numerical behavior to bit-exact reference values.

v1.0.3 — 2025

Test-coverage release. Overall line coverage went from 4% to 72% with four new test files (test_comprehensive.c, test_overflow_saturation.c, test_full_coverage.c, test_2d_complete.cpp). Added a GitHub Actions CI with multi-platform (Linux, macOS) and multi-compiler (gcc, clang) matrices, cross-compilation for ARM and RISC-V, and 32-bit compatibility testing.

Also fixed a broken FR_atan implementation, corrected FR_PI / FR_2PI / FR_E declarations to use const, and fixed XFormPtI test assumptions.

v1.02 — first public release

Basic fixed-point operations, 2D transforms, and integer-degree trigonometry. This is the version that shipped inside the original Palm Pilot Inkstorm application.

v1.01 — internal development

Naming conventions cleanup and an initial test framework. Never released publicly.

Timeline

FR_Math has been in continuous service since 2000, when it was written to run 2D graphics transforms on 16 MHz 68k Palm Pilots for Trumpetsoft’s Inkstorm. It has since been ported to ARM, x86, MIPS, RISC-V, and a menagerie of 8- and 16-bit embedded targets. The current release has a full test suite, a bit-exact numerical specification, and CI on every push.