92 lines
2.9 KiB
C
92 lines
2.9 KiB
C
/*
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StarForth — Steady-State Virtual Machine Runtime
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Copyright (c) 2023–2025 Robert A. James
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All rights reserved.
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This file is part of the StarForth project.
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Licensed under the StarForth License, Version 1.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at:
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https://github.com/star.4th@proton.me/StarForth/LICENSE.txt
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This software is provided "AS IS", WITHOUT WARRANTY OF ANY KIND,
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express or implied, including but not limited to the warranties of
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merchantability, fitness for a particular purpose, and noninfringement.
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See the License for the specific language governing permissions and
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limitations under the License.
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StarForth — Steady-State Virtual Machine Runtime
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Copyright (c) 2023–2025 Robert A. James
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All rights reserved.
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This file is part of the StarForth project.
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Licensed under the StarForth License, Version 1.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at:
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https://github.com/star.4th@proton.me/StarForth/LICENSE.txt
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This software is provided "AS IS", WITHOUT WARRANTY OF ANY KIND,
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express or implied, including but not limited to the warranties of
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merchantability, fitness for a particular purpose, and noninfringement.
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See the License for the specific language governing permissions and
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limitations under the License.
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*/
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/*
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* math_portable.h
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*
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* Portable C99 math functions in Q48.16 64-bit fixed-point format.
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* Suitable for embedded environments with no libm
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* (HISTORICAL: also L4Re, through mid-2026; removed as an active target).
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* All arithmetic is integer-only for maximum performance.
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*
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* Q48.16 Format:
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* - 48-bit signed integer + 16-bit fractional part
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* - Precision: 2^-16 ≈ 0.0000153 (nanoseconds)
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* - Range: ±140 trillion ns (≈ 4.4 years)
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*
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* Functions:
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* sqrt_q48(x) - Square root of Q48.16 value via Newton-Raphson
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* erf_q48(x) - Error function of Q48.16 value (dimensionless)
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*/
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#ifndef MATH_PORTABLE_H
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#define MATH_PORTABLE_H
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#include <stdint.h>
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#define Q48_SCALE (1LL << 16) /* 65536 */
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/**
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* Square root in Q48.16 fixed-point
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* Input: x in Q48.16 format
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* Output: sqrt(x) in Q48.16 format
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* Uses Newton-Raphson: x_{n+1} = (x_n + a/x_n) / 2
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* Converges in ~10-15 iterations
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* Returns 0 for negative inputs (guard against domain error)
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*/
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int64_t sqrt_q48(int64_t x);
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/**
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* Error function in Q48.16 fixed-point
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* Input: x in Q48.16 format (dimensionless Z-score)
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* Output: erf(x) in Q48.16 format (range: -Q48_SCALE to +Q48_SCALE)
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* Uses Abramowitz & Stegun approximation (7.1.26)
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* Maximum error: 1.5e-7 relative to floating-point erf
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* Properties:
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* - erf(0) = 0
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* - erf(-x) = -erf(x) (odd function)
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* - erf(x) approaches ±Q48_SCALE for large |x|
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*/
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int64_t erf_q48(int64_t x);
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#endif /* MATH_PORTABLE_H */
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