[fsbl] add fsbl for cv181x/cv180x
Change-Id: I6809bc5016d4bc148f62be2ed3f8e928ec111f19
This commit is contained in:
sam.xiang
208
fsbl/lib/BigDigits/t_spExtras.c
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208
fsbl/lib/BigDigits/t_spExtras.c
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/* $Id: t_spExtras.c $ */
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/***** BEGIN LICENSE BLOCK *****
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*
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* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/.
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*
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* Copyright (c) 2001-15 David Ireland, D.I. Management Services Pty Limited
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* <http://www.di-mgt.com.au/bigdigits.html>. All rights reserved.
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*
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***** END LICENSE BLOCK *****/
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/*
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* Last updated:
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* $Date: 2015-10-22 10:23:00 $
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* $Revision: 2.5.0 $
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* $Author: dai $
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*/
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/* Some tests for `extra' single-precision functions
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-- some tests assume word size >= 32 bits
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*/
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#include <stdio.h>
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#include <assert.h>
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#include "bigdigits.h"
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#include "spExtras.h"
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#ifndef NELEMS
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#define NELEMS(x) ((sizeof(x)) / (sizeof((x)[0])))
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#endif /* NELEMS */
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static int is_in_list(DIGIT_T a, DIGIT_T *list, size_t n)
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/* Returns true (1) if a is in list of n elements; else false (0) */
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{
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size_t i;
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int result = 0;
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for (i = 0; i < n; i++)
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{
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if (a == list[i])
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{
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result = 1;
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break;
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}
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}
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return result;
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}
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int main(void)
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{
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DIGIT_T x, y, g;
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DIGIT_T m, e, n, c, z, t;
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DIGIT_T p, v, u, w, a, q;
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int res, i, ntries;
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DIGIT_T primes32[] = { 5, 17, 65, 99 };
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DIGIT_T primes16[] = { 15, 17, 39 };
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/* Test greatest common divisor (gcd) */
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printf("Test spGcd:\n");
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/* simple one */
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x = 15; y = 27;
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g = spGcd(x, y);
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printf("gcd(%" PRIuBIGD ", %" PRIuBIGD ") = %" PRIuBIGD "\n", x, y, g);
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assert(g == 3);
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/* contrived using small primes */
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x = 53 * 37; y = 53 * 83;
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g = spGcd(x, y);
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printf("gcd(%" PRIuBIGD ", %" PRIuBIGD ") = %" PRIuBIGD "\n", x, y, g);
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assert(g == 53);
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/* contrived using bigger primes */
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x = 0x0345 * 0xfedc; y = 0xfedc * 0x0871;
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g = spGcd(x, y);
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printf("gcd(0x%" PRIxBIGD ", 0x%" PRIxBIGD ") = 0x%" PRIxBIGD "\n", x, y, g);
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assert(g == 0xfedc);
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/* Known primes: 2^16-15, 2^32-5 */
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y = 0x10000 - 15;
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x = spSimpleRand(1, y);
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g = spGcd(x, y);
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printf("gcd(0x%" PRIxBIGD ", 0x%" PRIxBIGD ") = %" PRIxBIGD "\n", x, y, g);
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assert(g == 1);
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y = 0xffffffff - 5 + 1;
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x = spSimpleRand(1, y);
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g = spGcd(x, y);
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printf("gcd(0x%" PRIxBIGD ", 0x%" PRIxBIGD ") = %" PRIxBIGD "\n", x, y, g);
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assert(g == 1);
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/* Test spModExp */
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printf("Test spModExp:\n");
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/* Verify that (m^e mod n).(z^e mod n) == (m.z)^e mod n
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for random m, e, n, z */
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/* Generate some random numbers */
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n = spSimpleRand(MAX_DIGIT / 2, MAX_DIGIT);
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m = spSimpleRand(1, n -1);
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e = spSimpleRand(1, n -1);
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z = spSimpleRand(1, n -1);
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/* Compute c = m^e mod n */
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spModExp(&c, m, e, n);
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printf("c=m^e mod n=%" PRIxBIGD "^%" PRIxBIGD " mod %" PRIxBIGD "=%" PRIxBIGD "\n", m, e, n, c);
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/* Compute x = c.z^e mod n */
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printf("z=%" PRIxBIGD "\n", z);
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spModExp(&t, z, e, n);
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spModMult(&x, c, t, n);
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printf("x = c.z^e mod n = %" PRIxBIGD "\n", x);
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/* Compute y = (m.z)^e mod n */
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spModMult(&t, m, z, n);
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spModExp(&y, t, e, n);
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printf("y = (m.z)^e mod n = %" PRIxBIGD "\n", x);
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/* Check they are equal */
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assert(x == y);
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/* Test spModInv */
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printf("Test spModInv:\n");
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/* Use identity that (vp-1)^-1 mod p = p-1
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for prime p and integer v */
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/* known prime */
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p = 0x10000 - 15;
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/* small multiplier */
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v = spSimpleRand(2, 10);
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u = v * p - 1;
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printf("u = vp-1 = %" PRIuBIGD " * %" PRIuBIGD " - 1 = %" PRIuBIGD "\n", v, p, u);
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/* compute w = u^-1 mod p */
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spModInv(&w, u, p);
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printf("w = u^-1 mod p = %" PRIuBIGD "\n", w);
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/* check wu mod p == 1 */
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spModMult(&c, w, u, p);
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printf("Check 1 == wu mod p = %" PRIuBIGD "\n", c);
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assert(c == 1);
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/* Try mod inversion that should fail */
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/* Set u = pq so that gcd(u, p) != 1 */
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q = 31;
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u = p * q;
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printf("p=%" PRIuBIGD " q=%" PRIuBIGD " pq=%" PRIuBIGD "\n", p, q, u);
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printf("gcd(pq, p) = %" PRIuBIGD " (i.e. not 1)\n", spGcd(u, p));
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res = spModInv(&w, u, p);
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printf("w = (pq)^-1 mod p returns error %d (expected 1)\n", res);
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assert(res != 0);
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/* Test spIsPrime */
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printf("Test spIsPrime:\n");
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/* Find primes just less than 2^32. Ref: Knuth p408 */
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for (n = 0xffffffff, a = 1; a < 100; a++, n--)
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{
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if (spIsPrime(n, 50))
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{
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printf("2^32-%" PRIuBIGD " is prime\n", a);
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assert(is_in_list(a, primes32, NELEMS(primes32)));
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}
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}
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/* And just less than 2^16 */
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for (n = 0xffff, a = 1; a < 50; a++, n--)
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{
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if (spIsPrime(n, 50))
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{
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printf("2^16-%" PRIuBIGD " is prime\n", a);
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assert(is_in_list(a, primes16, NELEMS(primes16)));
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}
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}
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/* Generate a random prime < MAX_DIGIT */
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n = spSimpleRand(0, MAX_DIGIT);
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/* make sure odd */
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n |= 0x01;
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/* expect to find a prime approx every lg(n) numbers,
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so for sure within 100 times that */
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ntries = BITS_PER_DIGIT * 100;
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for (i = 0; i < ntries; i++)
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{
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if (spIsPrime(n, 50))
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break;
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n += 2;
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}
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printf("Random prime, n = %" PRIuBIGD " (0x%" PRIxBIGD ")\n", n, n);
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printf("found after %d candidates\n", i+1);
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if (i >= ntries)
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printf("Didn't manage to find a prime in %d tries!\n", ntries);
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else
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assert(spIsPrime(n, 50));
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res = spIsPrime(n, 50);
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printf("spIsPrime(%" PRIuBIGD ") is %s\n", n, (res ? "TRUE" : "FALSE"));
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/* Check using (less accurate) Fermat test (these could fail) */
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w = 2;
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spModExp(&x, w, n-1, n);
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printf("Fermat test: %" PRIxBIGD "^(n-1) mod n = %" PRIxBIGD " (%s)\n", w, x, (x == 1 ? "PASSED" : "FAILED!"));
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w = 3;
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spModExp(&x, w, n-1, n);
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printf("Fermat test: %" PRIxBIGD "^(n-1) mod n = %" PRIxBIGD " (%s)\n", w, x, (x == 1 ? "PASSED" : "FAILED!"));
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w = 5;
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spModExp(&x, w, n-1, n);
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printf("Fermat test: %" PRIxBIGD "^(n-1) mod n = %" PRIxBIGD " (%s)\n", w, x, (x == 1 ? "PASSED" : "FAILED!"));
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/* Try a known Fermat liar (Carmichael number) */
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n = 561;
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printf("Try n = 561 = 3*11*17 (a 'Fermat liar')\n");
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w = 5;
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spModExp(&x, w, n-1, n);
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printf("Fermat test: %" PRIxBIGD "^(n-1) mod n = %" PRIxBIGD " (%s)\n", w, x, (x == 1 ? "PASSED" : "FAILED!"));
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res = spIsPrime(n, 50);
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printf("spIsPrime(%" PRIuBIGD ") is %s\n", n, (res ? "TRUE" : "FALSE"));
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assert(!res);
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return 0;
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}
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