nthroot_1.c

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/**
 *  Copyright (C) 2026 HJimmyK(Jericho Knox)
 *
 *  This file is part of LAMMP.
 *
 *  LAMMP is free software: you can redistribute it and/or modify it under
 *  the terms of the GNU Lesser General Public License (LGPL) as published
 *   by the Free Software Foundation; either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed WITHOUT ANY WARRANTY.
 *
 *  See <https://www.gnu.org/licenses/>.
 */
 
#include <math.h>
 
#include "../../../include/lammp/numth.h"
 
 
static inline ulong pow_n(ulong x, ulong n) {
    ulong ret = 1;
    for (ulong i = 0; i < n; ++i) {
        ret *= x;
    }
    return ret;
}
 
static const float inv_table[] = {
    0.200000000000000, 0.166666666666667, 0.142857142857143, 0.125000000000000, 0.111111111111111, 0.100000000000000,
    0.090909090909091, 0.083333333333333, 0.076923076923077, 0.071428571428571, 0.066666666666667, 0.062500000000000,
    0.058823529411765, 0.055555555555556, 0.052631578947368, 0.050000000000000, 0.047619047619048, 0.045454545454545,
    0.043478260869565, 0.041666666666667, 0.040000000000000, 0.038461538461538, 0.037037037037037, 0.035714285714286,
    0.034482758620690, 0.033333333333333, 0.032258064516129, 0.031250000000000, 0.030303030303030, 0.029411764705882,
    0.028571428571429, 0.027777777777778, 0.027027027027027, 0.026315789473684, 0.025641025641026, 0.025000000000000,
};
 
/* This table has the max possible base for a given root. For n >= 4,
   max_base[n-4] = floor(UWORD_MAX^(1/n)).*/
static const uint16_t max_base[] = {
    65535, 7131, 1625, 565, 255, 138, 84, 56, 40, 30, 23, 19, 15, 13, 11, 10, 9, 8, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 3,
    3,     3,    3,    3,   3,   3,   3,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2};
 
ulong lmmp_nthroot_ulong_(ulong n, ulong root) {
    ulong x, currval, base, upper_limit;
 
    if (n == 0 || root == 0)
        return 0;
    if (root == 1)
        return n;
    if (root == 2)
        return lmmp_sqrt_ulong_(n);
    if (root == 3)
        return lmmp_cbrt_ulong_(n);
 
    if (root >= LIMB_BITS || n < (1ULL << root))
        return 1;
 
    /* n <= upper_limit^root */
    upper_limit = max_base[root - 4];
 
    if (upper_limit == 2)
        return upper_limit;
 
    /* upper_limit = 2 for root >= 41 */
    lmmp_debug_assert(root <= 40);
 
    if (root == 4)
        x = sqrt(sqrt(n));
    else
        x = expf(inv_table[root - 5] * logf(n));
 
    base = x;
 
    if (base >= upper_limit)
        base = upper_limit - 1;
 
    currval = pow_n(base, root);
    if (currval == n)
        return base;
 
    while (currval <= n) {
        base++;
        currval = pow_n(base, root);
        if (base == upper_limit)
            break;
    }
 
    while (currval > n) {
        base--;
        currval = pow_n(base, root);
    }
 
    return base;
}