/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:4;tab-width:8;coding:utf-8 -*-â
âvi: set net ft=c ts=4 sts=4 sw=4 fenc=utf-8                                :viâ
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â Copyright (c) 2008-2016 Stefan Krah. All rights reserved.                    â
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#include "third_party/python/Modules/_decimal/libmpdec/bits.h"
#include "third_party/python/Modules/_decimal/libmpdec/mpdecimal.h"
#include "third_party/python/Modules/_decimal/libmpdec/numbertheory.h"
#include "third_party/python/Modules/_decimal/libmpdec/umodarith.h"
/* clang-format off */

asm(".ident\t\"\\n\\n\
libmpdec (BSD-2)\\n\
Copyright 2008-2016 Stefan Krah\"");
asm(".include \"libc/disclaimer.inc\"");

/* Bignum: Initialize the Number Theoretic Transform. */

/*
 * Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n)
 * in the Fourier transform. We have w**n == 1 (mod p).
 *    n := transform length.
 *    sign := -1 for forward transform, 1 for backward transform.
 *    modnum := one of {P1, P2, P3}.
 */
mpd_uint_t
_mpd_getkernel(mpd_uint_t n, int sign, int modnum)
{
    mpd_uint_t umod, p, r, xi;
    SETMODULUS(modnum);
    r = mpd_roots[modnum]; /* primitive root of F(p) */
    p = umod;
    xi = (p-1) / n;
    if (sign == -1)
        return POWMOD(r, (p-1-xi));
    else
        return POWMOD(r, xi);
}

/*
 * Initialize and return transform parameters.
 *    n := transform length.
 *    sign := -1 for forward transform, 1 for backward transform.
 *    modnum := one of {P1, P2, P3}.
 */
struct fnt_params *
_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum)
{
    struct fnt_params *tparams;
    mpd_uint_t umod;
    mpd_uint_t kernel, w;
    mpd_uint_t i;
    mpd_size_t nhalf;
    assert(ispower2(n));
    assert(sign == -1 || sign == 1);
    assert(P1 <= modnum && modnum <= P3);
    nhalf = n/2;
    tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));
    if (tparams == NULL) {
        return NULL;
    }
    SETMODULUS(modnum);
    kernel = _mpd_getkernel(n, sign, modnum);
    tparams->modnum = modnum;
    tparams->modulus = umod;
    tparams->kernel = kernel;
    /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */
    w = 1;
    for (i = 0; i < nhalf; i++) {
        tparams->wtable[i] = w;
        w = MULMOD(w, kernel);
    }
    return tparams;
}

/* Initialize wtable of size three. */
void
_mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum)
{
    mpd_uint_t umod;
    mpd_uint_t kernel;
    SETMODULUS(modnum);
    kernel = _mpd_getkernel(3, sign, modnum);
    w3table[0] = 1;
    w3table[1] = kernel;
    w3table[2] = POWMOD(kernel, 2);
}
