1 files changed, 132 insertions, 0 deletions
diff --git a/Modules/_decimal/libmpdec/numbertheory.c b/Modules/_decimal/libmpdec/numbertheory.c
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+++ b/Modules/_decimal/libmpdec/numbertheory.c
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+/*
+ * Copyright (c) 2008-2012 Stefan Krah. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+
+#include "mpdecimal.h"
+#include <stdlib.h>
+#include <assert.h>
+#include "bits.h"
+#include "umodarith.h"
+#include "numbertheory.h"
+
+
+/* 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;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+
+    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;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    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;
+#ifdef PPRO
+    double dmod;
+    uint32_t dinvmod[3];
+#endif
+    mpd_uint_t kernel;
+
+    SETMODULUS(modnum);
+    kernel = _mpd_getkernel(3, sign, modnum);
+
+    w3table[0] = 1;
+    w3table[1] = kernel;
+    w3table[2] = POWMOD(kernel, 2);
+}
+
+