cosmopolitan/dsp/core/getintegercoefficients.c

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/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│
╞══════════════════════════════════════════════════════════════════════════════╡
│ Copyright 2020 Justine Alexandra Roberts Tunney │
│ │
│ This program is free software; you can redistribute it and/or modify │
│ it under the terms of the GNU General Public License as published by │
│ the Free Software Foundation; version 2 of the License. │
│ │
│ This program is distributed in the hope that it will be useful, but │
│ WITHOUT ANY WARRANTY; without even the implied warranty of │
│ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU │
│ General Public License for more details. │
│ │
│ You should have received a copy of the GNU General Public License │
│ along with this program; if not, write to the Free Software │
│ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA │
│ 02110-1301 USA │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "dsp/core/q.h"
#include "libc/assert.h"
#include "libc/dce.h"
#include "libc/limits.h"
#include "libc/macros.h"
#include "libc/math.h"
#include "libc/str/str.h"
/**
* Precomputes integers that can replace floating-point operands.
*
* “G-d made the integers, all else is the work of man.
* — Leopold Kronecker
*
* This function shifts the decimal point to the left:
*
* 𝑛ᵢ ← ROUND[𝑐ᵢ × 2ᵐ] + φᵢ
*
* With extra effort to compute φ which is normally all zeroes but gives
* us better rounding when it isn't. It's assumed optimized coefficients
* will be used like this:
*
* (Σᵢ𝑥ᵢ𝑛ᵢ + 2⁽ᵐ⁻¹⁾) / 2ᵐ where 𝑥∈[𝐿,𝐻] and 𝑖∈[0,6)
*
* Intended to compute this
*
* ROUND[Σᵢ𝑥ᵢ𝑐ᵢ]
*
* As accurately or approximately as you want it to be. Popular scaling
* factors are 7, 15, 16, 22, and 31. Building this code under MODE=tiny
* will DCE the math.
*
* @param N receives optimized integers
* @param C provides ideal coefficients
* @param M is log₂ scaling factor, e.g. 7
* @param L is minimum input data size, e.g. 0
* @param H is maximum input data size, e.g. 255
* @return sum of errors for all inputs
* @see en.wikipedia.org/wiki/Binary_scaling
* @see o/tool/build/coefficients.com
* @cost ~300ns
*/
long GetIntegerCoefficients(long N[static 6], const double C[static 6], long M,
long L, long H) {
int i;
int j[6], J[6];
int O[6] = {0};
int S[3] = {0, -1, +1};
double R[6], K[6], D[6], HM, HL, least, error;
least = 1;
HM = 1L << M;
HL = H - L + 1;
assert(H >= L);
assert(HL <= HM);
for (i = 0; i < 6; ++i) {
least *= HL;
if (fabs(C[i]) > DBL_MIN) {
J[i] = ARRAYLEN(S);
R[i] = C[i] * HM;
K[i] = rint(R[i]);
N[i] = K[i];
} else {
J[i] = 1;
R[i] = 0;
K[i] = 0;
N[i] = 0;
}
}
if (!NoDebug() && least > 1) {
for (j[0] = 0; j[0] < J[0]; ++j[0]) {
for (j[1] = 0; j[1] < J[1]; ++j[1]) {
for (j[2] = 0; j[2] < J[2]; ++j[2]) {
for (j[3] = 0; j[3] < J[3]; ++j[3]) {
for (j[4] = 0; j[4] < J[4]; ++j[4]) {
for (j[5] = 0; j[5] < J[5]; ++j[5]) {
for (i = 0; i < ARRAYLEN(J); ++i) {
D[i] = S[j[i]] + K[i] - R[i];
}
if ((error = DifferSumSq(D, L, H) / HM) < least) {
least = error;
memcpy(O, j, sizeof(j));
}
}
}
}
}
}
}
for (i = 0; i < 6; ++i) {
N[i] += S[O[i]];
}
}
return lround(least);
}