Robert Allan James
36389e9d4a
Adds q48_reduce_angle() (range-reduce a signed Q48.16 angle into [-PI_Q48, PI_Q48] via one integer division plus a bounded fix-up loop) and q48_sin_approx/q48_cos_approx (Taylor series, terms n=3,5,7,9,11 for sin and n=2,4,6,8,10 for cos, early exit below 10). Q.SIN/Q.COS registered as FORTH words in q48_words.c, same pattern as Q.LOG/Q.EXP/Q.SQRT. Found mid-implementation: this codebase has two independent Q48.16 implementations -- src/word_source/q48_16_words.c (hosted/vendored) and src/starkernel/math/q48_16.c (kernel-only; the kernel build does not compile the former at all). The hosted build linked fine after the first pass; the kernel build failed with undefined references until the same two functions were added to both .c files and both q48_16.h headers (include/q48_16.h and include/starkernel/q48_16.h). Not fixed at the root -- Q.LOG/Q.EXP/Q.SQRT already had this same four-file duplication, unremarked until now -- just navigated correctly for this item. Verified live on amd64 via serial injection: sin/cos at 0, +-pi/2, pi, and 3pi (range-reduction across multiple turns) all match expected values within Taylor-series truncation error (<0.2%). All three architectures boot clean to ok> with the DoE completing; dict_hash identical across all three (0x291a660b05fa7b52). FABRIC.md item 4.3.3a marked done with full acceptance evidence.
298 lines
8.8 KiB
C
298 lines
8.8 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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#ifndef Q48_16_H
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#define Q48_16_H
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#include <stdint.h>
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/* ============================================================================
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* Q48.16 Fixed-Point Arithmetic
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* ============================================================================
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*
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* Format: uint64_t with fixed decimal point after bit 15
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* - Bits 0-15: Fractional part (1/65536 resolution)
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* - Bits 16-63: Integer part (up to 2^48-1)
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*
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* Example: 0x00010000 = 1.0, 0x00018000 = 1.5, 0x00010001 = 1 + 1/65536
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*
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* All operations are integer-only: no floating-point, no transcendental functions.
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* Used for inference engine calculations (variance, regression, diagnostics).
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*
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* Why Q48.16?
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* - 48-bit integer range: 0 to 281,474,976,710,655 (enough for VM metrics)
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* - 16-bit fractional: ~0.0000152 resolution (precise enough for statistical calculations)
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* - Perfect fit for 64-bit uint64_t: efficient on modern CPUs
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*/
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typedef uint64_t q48_16_t;
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/* ============================================================================
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* Core Arithmetic Operations (All Q48.16 ↔ Q48.16)
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* ============================================================================
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*/
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/*
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* @brief Multiply two Q48.16 values, keeping result in Q48.16
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*
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* Math: (a / 2^16) * (b / 2^16) * 2^16 = (a * b) / 2^16
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* Returns: (a * b) >> 16
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*
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* @param a First Q48.16 operand
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* @param b Second Q48.16 operand
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* @return (a * b) >> 16 in Q48.16 format
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*/
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q48_16_t q48_mul(q48_16_t a, q48_16_t b);
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/*
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* @brief Divide two Q48.16 values, keeping result in Q48.16
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*
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* Math: (a / 2^16) / (b / 2^16) * 2^16 = (a << 16) / b
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* Returns: (a << 16) / b
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*
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* @param a Dividend in Q48.16
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* @param b Divisor in Q48.16 (non-zero)
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* @return (a << 16) / b in Q48.16 format
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*/
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q48_16_t q48_div(q48_16_t a, q48_16_t b);
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/* Guard: skip static inlines already provided by include/starkernel/q48_16.h
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* (both headers share the same definitions; STARKERNEL_Q48_16_H is defined
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* by the kernel version so we avoid -Werror redefinition in mixed builds). */
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#ifndef STARKERNEL_Q48_16_H
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/**
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* @brief Add two Q48.16 values
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*
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* Math: (a / 2^16) + (b / 2^16) = (a + b) / 2^16
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* Returns: a + b (no shift needed, both have same scaling)
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*
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* @param a First Q48.16 operand
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* @param b Second Q48.16 operand
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* @return a + b in Q48.16 format
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*/
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static inline q48_16_t q48_add(q48_16_t a, q48_16_t b) {
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return a + b;
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}
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/**
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* @brief Subtract two Q48.16 values
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*
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* Math: (a / 2^16) - (b / 2^16) = (a - b) / 2^16
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* Returns: a - b (no shift needed)
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*
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* @param a Minuend in Q48.16
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* @param b Subtrahend in Q48.16
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* @return a - b in Q48.16 format
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*/
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static inline q48_16_t q48_sub(q48_16_t a, q48_16_t b) {
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return a - b;
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}
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/**
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* @brief Absolute value of Q48.16
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*
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* @param a Q48.16 value
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* @return |a| in Q48.16 format
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*/
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static inline q48_16_t q48_abs(q48_16_t a) {
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return (a < 0x8000000000000000ULL) ? a : (0ULL - a);
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}
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/* ============================================================================
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* Conversion Operations (u64 ↔ Q48.16)
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* ============================================================================
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*/
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/**
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* @brief Convert unsigned 64-bit integer to Q48.16
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*
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* Math: u * 2^16 (shift left by 16 bits)
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* Example: q48_from_u64(1) = 0x10000 (1.0 in Q48.16)
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*
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* @param u Unsigned 64-bit integer (max 2^48-1 to avoid overflow)
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* @return u << 16 in Q48.16 format
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*/
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static inline q48_16_t q48_from_u64(uint64_t u) {
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return u << 16;
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}
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/**
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* @brief Convert Q48.16 to unsigned 64-bit integer (truncate fractional)
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*
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* Math: q / 2^16 (shift right by 16 bits)
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* Example: q48_to_u64(0x10000) = 1
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*
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* @param q Q48.16 value
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* @return q >> 16 as unsigned 64-bit integer
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*/
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static inline uint64_t q48_to_u64(q48_16_t q) {
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return q >> 16;
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}
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#endif /* STARKERNEL_Q48_16_H */
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/*
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* @brief Convert double to Q48.16 (for testing/initialization only)
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*
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* NOT used in inference engine (inference is integer-only).
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* Provided for testing and diagnostic tools only.
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*
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* @param d Double-precision float
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* @return d * 2^16 as Q48.16
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*/
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q48_16_t q48_from_double(double d);
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/*
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* @brief Convert Q48.16 to double (for testing/diagnostics only)
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*
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* NOT used in inference engine (inference is integer-only).
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* Provided for logging and RStudio dashboard output.
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*
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* @param q Q48.16 value
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* @return q / 2^16 as double
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*/
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double q48_to_double(q48_16_t q);
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/* ============================================================================
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* Approximation Operations (Integer-Only)
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* ============================================================================
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*/
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/*
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* @brief Approximate natural logarithm in Q48.16 (integer-only)
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*
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* Purpose: Required for decay slope inference via exponential fitting
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* Model: ln(heat[t]) = ln(h0) - slope*t
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*
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* Method: Piecewise linear approximation or Newton-Raphson iteration
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* - Input x must be > 0 (assertion check)
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* - Output is ln(x) in Q48.16 format
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* - Precision: ~5% error acceptable (tuning parameter)
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* - No floating-point operations
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*
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* Implementation Strategy:
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* 1. Use bit position (floor(log2(x))) as coarse estimate
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* 2. Refine with Newton iteration (3-4 cycles for Q48.16 precision)
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* 3. Keep all arithmetic in integer space
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*
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* Example: q48_log_approx(65536) = log(1.0) in Q48.16 ≈ 0
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* q48_log_approx(131072) = log(2.0) in Q48.16 ≈ 0x0000B172
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*
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* @param x Value to take logarithm of (x > 0)
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* @return ln(x) in Q48.16 format
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*/
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q48_16_t q48_log_approx(uint64_t x);
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/*
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* @brief Approximate exponential e^x in Q48.16 (integer-only, future use)
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*
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* Purpose: Might be needed for inverse operations or model validation
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* Status: Defined but not required for Phase 1 inference engine
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* Method: Similar to q48_log_approx (piecewise + Newton)
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*
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* @param q Q48.16 exponent
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* @return e^q in Q48.16 format
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*/
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q48_16_t q48_exp_approx(q48_16_t q);
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/*
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* @brief Approximate square root in Q48.16 (integer-only)
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*
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* Purpose: Compute R² (fit quality) for regression diagnostics
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* Method: Newton-Raphson for integer-only sqrt
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*
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* @param q Q48.16 value
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* @return sqrt(q) in Q48.16 format
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*/
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q48_16_t q48_sqrt_approx(q48_16_t q);
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/*
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* @brief Approximate sin(q) in Q48.16 (integer-only, Taylor series)
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*
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* Purpose: Console drawing fabric's CIRCLE/ARC/ELLIPSE (FABRIC.md item 4.3.3b)
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* Method: Range-reduce into [-pi, pi], then Taylor series
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*
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* @param q Angle in Q48.16 format (radians, any magnitude)
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* @return sin(q) in Q48.16 format
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*/
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q48_16_t q48_sin_approx(q48_16_t q);
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/*
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* @brief Approximate cos(q) in Q48.16 (integer-only, Taylor series)
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*
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* Purpose: Console drawing fabric's CIRCLE/ARC/ELLIPSE (FABRIC.md item 4.3.3b)
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* Method: Range-reduce into [-pi, pi], then Taylor series
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*
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* @param q Angle in Q48.16 format (radians, any magnitude)
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* @return cos(q) in Q48.16 format
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*/
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q48_16_t q48_cos_approx(q48_16_t q);
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/* ============================================================================
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* Diagnostic / Testing Utilities
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* ============================================================================
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*/
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/*
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* @brief Pretty-print Q48.16 value to string for debugging
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*
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* Format: "integer.fractional" (e.g., "1.50000")
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* Uses internal static buffer - NOT thread-safe
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*
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* @param q Q48.16 value
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* @return Pointer to static string (valid until next call)
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*/
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const char* q48_to_string(q48_16_t q);
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/*
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* @brief Validate Q48.16 value is within safe range
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*
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* Checks: Does not overflow on mul/div operations
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* Returns: 1 if valid, 0 if risky
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*
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* @param q Q48.16 value
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* @return 1 if safe, 0 if risky
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*/
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int q48_is_valid(q48_16_t q);
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#endif /* Q48_16_H */ |