int bdAdd(T w, T u, T v)
/* Compute w = u + v, w#v*/
{
size_t dig_size;
DIGIT_T carry;
assert(w && u && v);
/* Check for cheaper option */
if (v->ndigits == 1)
return bdShortAdd(w, u, v->digits[0]);
/* Make sure u and v are the same size */
dig_size = max(u->ndigits, v->ndigits);
bd_resize(v, dig_size);
bd_resize(u, dig_size);
/* Now make sure w is big enough for sum (incl carry) */
bd_resize(w, dig_size + 1);
/* Finally, do the business */
carry = mpAdd(w->digits, u->digits, v->digits, dig_size);
/* Make sure we've set the right size for w */
if (carry)
{
w->digits[dig_size] = carry;
w->ndigits = dig_size + 1;
}
else
w->ndigits = mpSizeof(w->digits, dig_size);
return carry;
}
int main(void)
{
BIGD u, v, w, q, r, p, b, a;
BIGD n, e, m, c, z, mz, cz, t;
bdigit_t overflow;
int cmp, res;
unsigned char ff[64], bytes[16];
int i, mc, jac;
size_t nbytes;
char s[128];
/* MSVC memory leak checking stuff */
#if _MSC_VER >= 1100
_CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_LEAK_CHECK_DF);
_CrtSetReportMode( _CRT_WARN, _CRTDBG_MODE_FILE );
_CrtSetReportFile( _CRT_WARN, _CRTDBG_FILE_STDOUT );
_CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE );
_CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDOUT );
#endif
printf("Tests for BIGD functions\n");
/* Initialise */
u = bdNew();
v = bdNew();
w = bdNew();
p = bdNew();
q = bdNew();
r = bdNew();
printf("SIMPLE ARITHMETIC OPERATIONS...\n");
pr_msg("At start w=", w);
assert(bdIsZero(w));
/* Addition */
/* 1 + 1 = 2 */
bdSetShort(u, 1);
bdSetShort(v, 1);
bdAdd(w, u, v);
pr_msg("1+1=", w);
assert(bdShortCmp(w, 2) == 0);
/* Add with digit overflow */
bdSetShort(u, 0xffffffff);
bdSetShort(v, 0xffffffff);
bdAdd(w, u, v);
pr_msg("ffffffff+ffffffff=", w);
/* ffffffff+ffffffff=00000001 fffffffe */
assert(bdSizeof(w) == 2);
/* Bigger random digits */
bdSetRandTest(u, 10);
bdSetRandTest(v, 10);
bdAdd(w, u, v);
pr_msg("u=\n", u);
pr_msg("v=\n", v);
pr_msg("w=u+v=\n", w);
/* Subtract */
bdSubtract(r, w, v);
pr_msg("w-v=\n", r);
assert(bdCompare(r, u) == 0);
/* Multiplication */
/* 2 * 3 = 6 */
bdSetShort(u, 2);
bdSetShort(v, 3);
bdMultiply(w, u, v);
pr_msg("2 * 3=", w);
assert(bdShortCmp(w, 6) == 0);
bdSetShort(u, 0xffffffff);
bdSetShort(v, 0xffffffff);
bdMultiply(w, u, v);
pr_msg("ffffffff*ffffffff=", w);
/* ffffffff*ffffffff=fffffffe 00000001 */
assert(bdGetBit(w, 0) == 1);
/* Use ShortMult */
bdShortMult(p, u, 0xffffffff);
pr_msg("(Short)ffffffff*ffffffff=", p);
assert(bdCompare(p, w) == 0);
/* Use larger random u, v */
bdSetRandTest(u, 10);
bdSetRandTest(v, 20);
pr_msg("u=\n", u);
pr_msg("v=\n", v);
/* Use ShortMult by one: w = v * 1 */
bdShortMult(w, v, 1);
pr_msg("(Short)v*1=\n", w);
assert(bdCompare(w, v) == 0);
/* Use ShortMult by two */
bdShortMult(w, u, 2);
pr_msg("(Short)u*2=\n", w);
assert(bdIsEven(w));
/* Big multiplication */
bdMultiply(w, u, v);
pr_msg("w=u*v=\n", w);
/* Divide expecting q = w/v == u and r = w%v == 0 */
bdDivide(q, r, w, v);
pr_msg("w/v=\n", q);
pr_msg("w%v=", r);
assert(bdIsEqual(q, u));
assert(bdShortCmp(r, 0) == 0);
/* Modulo */
bdIncrement(w);
bdModulo(r, w, v);
pr_msg("w+1 mod v=", r);
assert(bdShortCmp(r, 1) == 0);
bdDecrement(w);
bdModulo(r, w, u);
pr_msg("w+1-1 mod u=", r);
assert(bdShortCmp(r, 0) == 0);
/* Use a short divisor q=w/2 */
bdShortDiv(q, r, w, 2);
pr_msg("(ShortDiv)w/2=\n", q);
pr_msg("(ShortDiv)w%2=", r);
printf("w is %s\n", bdIsOdd(w) ? "ODD" : "EVEN");
bdShortMod(r, w, 2);
pr_msg("w mod 2=", r);
bdIncrement(w);
printf("w+1 is %s\n", bdIsOdd(w) ? "ODD" : "EVEN");
bdShortMod(r, w, 2);
pr_msg("++w mod 2=", r);
bdDecrement(w);
/* Check with short mult u = q*2 */
bdShortMult(u, q, 2);
pr_msg("(ShortMult) (w/2) * 2=\n", u);
printf("SQUARE AND SQUARE ROOT...\n");
/* Square a random number w = u^2 */
bdSetRandTest(u, 10);
pr_msg("random u=\n", u);
bdSquare(w, u);
pr_msg("(Square) u^2=", w);
/* check against product p = u * u */
bdMultiply(p, u, u);
pr_msg("u*u=", p);
assert(bdIsEqual(p, w));
/* Compute integer square root [new in v2.1] */
bdSqrt(p, w);
pr_msg("sqrt(w)=", p);
assert(bdIsEqual(p, u));
printf("MODULAR ARITHMETIC...\n");
/* Check that (u mod n + v mod n) mod n == (u+v) mod n */
bdSetRandTest(u, 10);
bdSetRandTest(v, 10);
bdSetRandTest(w, 10);
pr_msg("(Modulo)\nNew random u=", u);
pr_msg("v=", v);
pr_msg("w=", w);
/* r = u mod w */
bdModulo(r, u, w);
/* q = v mod w */
bdModulo(q, v, w);
/* q = u mod n + v mod n */
bdAdd(q, q, r);
/* r = (u mod w + v mod w) mod w */
bdModulo(r, q, w);
pr_msg("(u mod w + v mod w) mod w=\n", r);
/* q = (u+v) mod w */
bdSetEqual(p, u);
bdAdd(p, p, v);
bdModulo(q, p, w);
pr_msg("(u+v) mod w=\n", q);
assert(bdIsEqual(r, q));
/* Clear and start again */
bdSetZero(u);
bdSetZero(v);
bdSetZero(w);
printf("ARITHMETIC BOUNDARY CONDITIONS...\n");
/* This causes Divide algorithm to `Add Back' with 32-bit digits
See Knuth 4.3.1 Algorithm D Step D6 */
printf("Check `Add Back' in Divide algorithm\n");
bdConvFromHex(u, "7fffffff 80000001 00000000 00000000");
bdConvFromHex(v, "00000000 80000000 80000002 00000005");
bdDivide(q, r, u, v);
pr_msg("u=", u);
pr_msg("v=", v);
pr_msg("q=u/v=", q);
pr_msg("r=u mod v=", r);
/* check that qv + r = u */
bdMultiply(w, q, v);
bdAdd(w, w, r);
pr_msg("qv+r=", w);
assert(bdIsEqual(w, u));
/* And check that r = u mod v >= (1-2/b)v
See Knuth 4.3.1 Exercise 21 */
bdConvFromHex(p, "1 00000000");
bdSetEqual(w, p);
bdShortSub(w, w, 2);
bdMultiply(u, w, v);
bdDivide(q, w, u, p);
pr_msg("(1-2/b)=", q);
cmp = bdCompare(r, q);
printf("u mod v %s (1-2/b)v\n", (cmp >= 0 ? ">=" : "<"));
/* Cope, sort of, with `negative' numbers */
printf("Go ``negative''...\n");
bdSetZero(u);
overflow = bdShortSub(w, u, 2);
pr_msg("w=0-2=", w);
printf("overflow=%" PRIuBIGD "\n", overflow);
overflow = bdIncrement(w);
pr_msg("w+1=", w);
printf("overflow=%" PRIuBIGD "\n", overflow);
overflow = bdIncrement(w);
pr_msg("(Note error!) w+1=", w);
printf("overflow=%" PRIuBIGD "\n", overflow);
bdSetZero(u);
overflow = bdShortAdd(u, u, 1);
pr_msg("u=0+1=", u);
printf("overflow=%" PRIuBIGD "\n", overflow);
bdSetZero(u);
bdSetZero(v);
bdAdd(w, u, v);
pr_msg("0+0=", w);
/* Set u = v = ffff...ffff */
for (i = 0; i < sizeof(ff); i++)
ff[i] = 0xff;
bdConvFromOctets(u, ff, sizeof(ff));
bdConvFromOctets(v, ff, sizeof(ff));
pr_msg("u=", u);
pr_msg("v=", v);
/* Compute u * v */
bdMultiply(w, u, v);
pr_msg("w = u * v =\n", w);
/* Set v = w / u */
bdDivide(v, r, w, u);
pr_msg("v = w / u =\n", v);
pr_msg("rem=", r);
assert(bdIsEqual(u, v));
assert(bdShortCmp(r, 0) == 0);
bdIncrement(u);
bdDecrement(v);
bdMultiply(w, u, v);
pr_msg("w = ++u * --v =\n", w);
bdDivide(w, r, u, v);
pr_msg("q = u / v =", w);
pr_msg("rem=", r);
assert(bdShortCmp(w, 1) == 0);
assert(bdShortCmp(r, 2) == 0);
/* Clear and start again */
bdSetZero(u);
bdSetZero(v);
bdSetZero(w);
bdSetShort(u, 0); /* Fixed [v2.3]: This used to cause an error */
bdPrintDecimal("bdSetShort(u, 0)=> u=", u, "\n");
bdSetShort(v, 3);
bdModulo(w, u, v);
bdPrintDecimal("0 mod 3=", w, "\n");
/* Set a new random value for v */
bdSetRandTest(v, 10);
pr_msg("Random v=\n", v);
bdShortAdd(u, v, 1);
pr_msg("u = v + 1 =\n", u);
cmp = bdCompare(u, v);
printf("bdCompare(u-v) = %d\n", cmp);
assert(cmp > 0);
cmp = bdCompare(v, u);
printf("bdCompare(v-u) = %d\n", cmp);
assert(cmp < 0);
cmp = bdCompare(u, u);
printf("bdCompare(u-u) = %d\n", cmp);
assert(cmp == 0);
/* Compare with short */
bdSetShort(w, 0xfffffffe);
pr_msg("w=", w);
cmp = bdShortCmp(w, 1);
assert(cmp > 0);
printf("bdShortCmp(w-1) = %d\n", cmp);
cmp = bdShortCmp(w, 0xffffffff);
assert(cmp < 0);
printf("bdShortCmp(w-0xffffffff) = %d\n", cmp);
cmp = bdShortCmp(w, 0xfffffffd);
printf("bdShortCmp(w-0xfffffffd) = %d\n", cmp);
assert(cmp > 0);
printf("BIT SHIFT OPERATIONS...\n");
/* Try shifting bits */
pr_msg("w = ", w);
bdFree(&u);
u = bdNew();
bdShiftLeft(u, w, 2);
pr_msg("w << 2 = ", u);
assert(bdGetBit(u, 33) == 1);
bdShiftRight(v, u, 3);
pr_msg("(w << 2) >> 3 = ", v);
assert(bdGetBit(v, 31) == 0);
/* Bigger shift */
bdShiftLeft(u, w, 128);
pr_msg("w << 128 = ", u);
assert(bdGetBit(u, 159) == 1);
bdShiftRight(v, u, 129);
pr_msg("(w << 128) >> 129 = ", v);
assert(bdGetBit(v, 31) == 0);
/* Use a new variable */
b = bdNew();
bdSetZero(b); /* overkill */
bdSetBit(b, 510, 1);
bdSetBit(b, 477, 1);
bdSetBit(b, 31, 1);
bdSetBit(b, 0, 1);
pr_msg("b=\n", b);
bdSetBit(b, 512, 1);
bdSetBit(b, 31, 0);
pr_msg("b'=\n", b);
printf("Bit 512 is %d\n", bdGetBit(b, 512));
assert(bdGetBit(b, 512) == 1);
printf("Bit 511 is %d\n", bdGetBit(b, 511));
assert(bdGetBit(b, 511) == 0);
assert(bdGetBit(b, 477) == 1);
/* NB one-based bit lengths so expecting 513 */
printf("Bit Length = %u\n", bdBitLength(b));
assert(bdBitLength(b) == 513);
pr_msg("b'=\n", b);
/* Destroy b */
bdFree(&b);
printf("RANDOM NUMBER GENERATION...\n");
/* Create a random number using `my_rand' callback function */
bdRandomSeeded(r, 508, (const unsigned char*)"", 0, my_rand);
pr_msg("random=\n", r);
/* NB bit length may be less than 508 */
printf("%u bits\n", bdBitLength(r));
assert(bdBitLength(r) <= 508);
/* Create a random number using the internal RNG */
bdRandomBits(r, 509);
pr_msg("random=\n", r);
printf("%u bits\n", bdBitLength(r));
assert(bdBitLength(r) <= 509);
printf("PRIME NUMBERS...\n");
/* Generate two random primes */
printf("Generating two primes...\n");
bdGeneratePrime(p, 128, 5, (const unsigned char*)"1", 1, my_rand);
pr_msg("prime p=\n", p);
bdGeneratePrime(q, 128, 5, (const unsigned char*)"abcdef", 6, my_rand);
pr_msg("prime q=\n", q);
/* Check primality with more tests (64 vs 5) */
/* NB vv small chance this could fail */
printf("Checking prime: p ");
res = bdIsPrime(p, 64);
printf("%s\n", (res ? "is OK" : "is NOT prime!!"));
/* And again using Fermat test */
res = fermat_test(p);
if (res == 0) printf("WARNING: p failed Fermat test.\n");
/* w = product pq */
bdMultiply(w, p, q);
pr_msg("pq=\n", w);
/* Product pq should not be prime */
res = bdIsPrime(w, 5);
printf("Composite pq %s\n", (res ? "IS prime" : "is NOT prime"));
assert(res == 0);
/* Check GCD: gcd(pq, p) == p */
bdGcd(r, w, p);
pr_msg("gcd(pq, p) =\n", r);
assert(bdIsEqual(r, p));
/* --Modular inversion-- */
printf("MODULAR INVERSION...\n");
/* set v to be a small random multiplier */
bdSetRandTest(v, 1);
bdIncrement(v); /* Make sure not zero */
pr_msg("multiplier, v=", v);
/* set u = vp - 1 */
bdMultiply(u, v, p);
bdDecrement(u);
pr_msg("p=\n", p);
pr_msg("u = vp - 1 =\n", u);
/* compute w = u^-1 mod p */
res = bdModInv(w, u, p);
pr_msg("w = u^-1 mod p=\n", w);
assert(res == 0);
/* check that wu mod p == 1 */
bdModMult(r, w, u, p);
pr_msg("wu mod p = ", r);
assert(bdShortCmp(r, 1) == 0);
/* Try mod inversion that should fail */
/* Set u = pq so that gcd(u, p) != 1 */
bdMultiply(u, p, q);
res = bdModInv(w, u, p);
printf("w = (pq)^-1 mod p returns (expected) error %d\n", res);
assert(res != 0);
pr_msg("output, w=", w);
/* Do some bit string operations */
printf("BIT STRING OPERATIONS...\n");
/* Use XOR to swop two variables without a temp variable, i.e.
a = a XOR b; b = a XOR b; a = a XOR b; */
printf("Swop u and w:\n");
/* Generate 2 random numbers (u,w) each 144 bits long */
bdRandomBits(u, 144);
bdRandomBits(w, 144);
pr_msg("u= ", u);
pr_msg("w= ", w);
/* remember these for later (p=u, q=w) */
bdSetEqual(p, u);
bdSetEqual(q, w);
/* Swop using XOR */
bdXorBits(u, u, w);
bdXorBits(w, u, w);
bdXorBits(u, u, w);
pr_msg("u'=", u);
pr_msg("w'=", w);
/* check they have swopped accurately */
assert(bdIsEqual(u, q));
assert(bdIsEqual(w, p));
/* Try some simple AND and OR ops */
printf("AND and OR ops:\n");
/* Set every even bit in u and every odd bit in v */
bdSetZero(u);
bdSetZero(v);
for (i = 0; i < 144 / 2; i++)
{
bdSetBit(u, (i * 2), 1);
bdSetBit(v, (i * 2) + 1, 1);
}
pr_msg("u= ", u);
pr_msg("v= ", v);
bdAndBits(w, u, v);
pr_msg("u AND v=", w);
/* expected answer = zero */
assert(bdIsZero(w));
bdOrBits(w, u, v);
pr_msg("u OR v= ", w);
/* expected answer p = 2^144 - 1 */
bdSetZero(p);
bdSetBit(p, 144, 1);
bdDecrement(p);
pr_msg("2^144-1=", p);
assert(bdIsEqual(p, w));
/* Invert all bits */
bdSetZero(p);
bdSetZero(q);
bdSetShort(p, 0xfffe);
bdShiftLeft(p, p, 32);
bdShortAdd(p, p, 0xfffe);
pr_msg("p= ", p);
bdNotBits(q, p);
pr_msg("NOT p=", q);
/* check p AND (NOT p) == 0 */
bdAndBits(w, p, q);
pr_msg("p AND (NOT p)=", w);
assert(bdIsZero(w));
/* Compose a 400-bit string by concatenating random 160-bit sections
and then truncating the result */
printf("Bit string concatenation and truncation:\n");
/*
ALGORITHM: (based on a similar one in RFC 2631/ANSI X.42)
Set m' = m/160 where / represents integer division with rounding upwards
Set U = 0
For i = 0 to m' - 1
Set R = FUNC_160 and V = FUNC_160 where FUNC_160 generates a unique 160-bit value
U = U + (R XOR V) * 2^(160 * i)
Form q from U by computing U mod (2^m) and setting the most
significant bit (the 2^(m-1) bit) and the least significant bit to 1.
In terms of boolean operations, q = U OR 2^(m-1) OR 1.
Note that 2^(m-1) < q < 2^m
*/
/* In this example, m=400 and m'=3, and we just generate 160-bit random values */
mc = 3;
bdSetZero(u); /* Set U = 0 */
for (i = 0; i < mc; i++)
{
bdRandomBits(r, 160); /* R = FUNC_160 */
bdRandomBits(v, 160); /* V = FUNC_160 */
bdXorBits(p, r, v); /* p = (R XOR V) */
/* w = p * 2^160i, i.e. shift p left by 160i bits */
bdShiftLeft(w, p, (160 * i));
bdOrBits(u, u, w); /* q = q + w */
printf("w(%d)=", i);
pr_msg("", w);
}
pr_msg("u = w(0)+w(1)+w(2) =\n", u);
bdModPowerOf2(u, 400); /* U = U mod (2^m) */
pr_msg("u = u mod (2^m) = // `ModPowerOf2' \n", u);
/* q = U OR 2^(m-1) OR 1 */
bdSetEqual(q, u); /* q = U */
bdSetBit(q, 400-1, 1); /* q = q OR 2^(m-1) */
bdSetBit(q, 0, 1); /* q = q OR 1 */
pr_msg("q = u OR 2^(m-1) OR 1 =\n", q);
/* Check that 2^(m-1) < q < 2^m */
printf("BitLength(q)=%d\n", bdBitLength(q));
bdSetZero(p);
bdSetBit(p, 400-1, 1); /* p = 2^(m-1) */
assert(bdCompare(p, q) < 1); /* p < q */
bdSetZero(r);
bdSetBit(r, 400, 1); /* r = 2^m */
assert(bdCompare(q, r) < 1); /* q < r */
printf("OK, checked that 2^(m-1) < q < 2^m\n");
/* Create a new set for Modular exponentiation test */
printf("MODULAR EXPONENTIATION...\n");
n = bdNew();
e = bdNew();
m = bdNew();
c = bdNew();
z = bdNew();
mz = bdNew();
cz = bdNew();
t = bdNew();
/* n is a prime modulus */
printf("Generating a prime...\n");
bdGeneratePrime(n, 513, 5, NULL, 0, my_rand);
pr_msg("prime n=\n", n);
printf("bdBitLength(n)=%u bdSizeof(n)=%u\n", bdBitLength(n), bdSizeof(n));
/* Check primality using Fermat test */
res = fermat_test(n);
if (res == 0) printf("WARNING: n failed Fermat test.\n");
/* exponent e is a single random digit */
bdSetShort(e, bdRandDigit());
pr_msg("e=", e);
/* base m is some random number m < n */
bdSetRandTest(m, bdSizeof(n) - 1);
pr_msg("random m=\n", m);
/* Compute c = m^e mod n */
bdModExp(c, m, e, n);
pr_msg("c = m^e mod n =\n", c);
/* Now use a random z and check that
c.z^e == (m.z)^e (mod n) */
bdSetRandTest(z, bdSizeof(n));
pr_msg("random z=\n", z);
/* Compute cz = c.z^e mod n (Note use of temp t) */
bdModExp(t, z, e, n);
bdModMult(cz, c, t, n);
pr_msg("c.z^e mod n=\n", cz);
/* Compute mz = (m.z)^e mod n */
bdModMult(t, m, z, n);
bdModExp(mz, t, e, n);
pr_msg("(m.z)^e mod n==\n", mz);
if (!bdIsEqual(mz, cz))
printf("ERROR: (c.z^e == (m.z)^e (mod n) DOES NOT MATCH m'\n");
else
printf("c.z^e == (m.z)^e (mod n) checks OK\n");
assert(bdIsEqual(mz, cz));
/* Do some conversions with hex and decimal strings */
bdSetZero(u);
bdConvFromHex(u, "DeadBeefCafeBabeBeddedDefacedDeafBeadFacade");
pr_msg("From Hex: ", u);
bdConvToHex(u, s, sizeof(s));
printf("To Hex: %s\n", s);
bdConvFromDecimal(u, "1234567890123456789012345678901234567890");
pr_msg("From Decimal: ", u);
bdConvToDecimal(u, s, sizeof(s));
printf("To Decimal: %s\n", s);
cmp = strcmp(s, "1234567890123456789012345678901234567890");
assert(cmp == 0);
/* 987654321 x 81 = 80000000001 */
bdConvFromDecimal(u, "987654321");
bdShortMult(v, u, 81);
bdConvToDecimal(v, s, sizeof(s));
printf("987654321 x 81 = %s\n", s);
cmp = strcmp(s, "80000000001");
assert(cmp == 0);
/* 123456789 x 9 + 10 = 1111111111 */
bdConvFromDecimal(u, "123456789");
bdShortMult(v, u, 9);
bdShortAdd(w, v, 10);
bdConvToDecimal(w, s, sizeof(s));
printf("123456789 x 9 + 10 = %s\n", s);
cmp = strcmp(s, "1111111111");
assert(cmp == 0);
/* Convert an empty decimal string to a BIGD */
bdSetShort(u, 0xfdfdfdfd);
bdConvFromDecimal(u, "");
pr_msg("bdConvFromDecimal(u, '')=", u);
assert(bdIsZero(u));
/* ditto an empty hex string */
bdSetShort(u, 0xfdfdfdfd);
bdConvFromHex(u, "");
pr_msg("bdConvFromHex(u, '')=", u);
assert(bdIsZero(u));
/* Convert zero BIGD value to a decimal string */
bdSetZero(u);
bdConvToDecimal(u, s, sizeof(s));
printf("Decimal zero = '%s'\n", s);
cmp = strcmp(s, "0");
assert(cmp == 0);
/* ditto to a hex string */
bdConvToHex(u, s, sizeof(s));
printf("Hex zero = '%s'\n", s);
cmp = strcmp(s, "0");
assert(cmp == 0);
/* Convert a zero BIGD to an array of octets */
memset(bytes, 0xdf, sizeof(bytes));
bdSetZero(u);
nbytes = bdConvToOctets(u, bytes, sizeof(bytes));
printf("bdConvToOctets returns %d: ", nbytes);
/* show that all bytes are zero */
pr_bytesmsg("", bytes, sizeof(bytes));
assert(0 == bytes[sizeof(bytes)-1] && 0 == bytes[0]);
/* Convert an zero-length array of octets to a BIGD */
bdSetShort(u, 0xfdfdfdfd);
bdConvFromOctets(u, bytes, 0);
pr_msg("bdConvFromOctets(nbytes=0)=", u);
assert(bdIsZero(u));
bdFree(&n);
/* Try computing some Jacobi and Legendre symbol values */
a = bdNew();
n = bdNew();
bdSetShort(a, 158);
bdSetShort(n, 235);
jac = bdJacobi(a, n);
printf("Jacobi(158, 235)=%d\n", jac);
assert(-1 == jac);
bdSetShort(a, 2183);
bdSetShort(n, 9907);
jac = bdJacobi(a, n);
printf("Jacobi(2183, 9907)=%d\n", jac);
assert(1 == jac);
bdSetShort(a, 1001);
jac = bdJacobi(a, n);
printf("Jacobi(1001, 9907)=%d\n", jac);
assert(-1 == jac);
bdShortMult(a, n, 10000);
jac = bdJacobi(a, n);
printf("Jacobi(10000 * 9907, 9907)=%d\n", jac);
assert(0 == jac);
printf("SQUARE AND SQUARE ROOT...\n");
/* Square a random number w = u^2 */
bdSetRandTest(u, 10);
bdPrintHex("random u=\n", u, "\n");
bdSquare(w, u);
bdPrintHex("(Square) u^2=", w, "\n");
/* check against product p = u * u */
bdMultiply(p, u, u);
bdPrintHex("u*u=", p, "\n");
assert(bdIsEqual(p, w));
/* and check against power function */
bdPower(p, u, 2);
bdPrintHex("u power 2=", p, "\n");
assert(bdIsEqual(p, w));
/* Compute integer square root [new in v2.1] */
bdSqrt(p, w);
bdPrintHex("sqrt(u^2)=", p, "\n");
assert(bdIsEqual(p, u));
/* Now test sqrt(u^2 - 1) */
bdDecrement(w);
bdPrintHex("u^2-1=", w, "\n");
bdSqrt(r, w);
bdPrintHex("sqrt(u^2-1)=", r, "\n");
/* Check difference is 1 */
bdSubtract(q, p, r);
bdPrintHex("difference=", q, " (expected 1)\n");
assert(bdShortCmp(q, 1) == 0);
printf("\nCUBE AND CUBE ROOT...\n");
/* Cube a random number w = u^2 */
bdPrintHex("u=", u, "\n");
bdSquare(v, u);
bdMultiply(w, v, u);
bdPrintHex("(Cube) u^3=", w, "\n");
/* Check that power function works */
bdPower(v, u, 0);
bdPrintHex("u^0=", v, "\n");
bdPower(v, u, 1);
bdPrintHex("u^1=", v, "\n");
bdPower(v, u, 3);
bdPrintHex("(Power) u^3=", v, "\n");
assert(bdIsEqual(v, w));
/* Compute integer cube root (new in [v2.3]) */
bdCubeRoot(p, w);
bdPrintHex("cuberoot(u^3)=", p, "\n");
assert(bdIsEqual(p, u));
/* Now test cuberoot(u^2 - 1) */
bdDecrement(w);
bdPrintHex("u^3-1=", w, "\n");
bdCubeRoot(r, w);
bdPrintHex("cuberoot(u^3-1)=", r, "\n");
/* Check difference is 1 */
bdSubtract(q, p, r);
bdPrintHex("difference=", q, " (expected 1)\n");
assert(bdShortCmp(q, 1) == 0);
/* Finally, show the current version number */
printf("\nVERSION=%d\n", bdVersion());
/* Clear up */
bdFree(&u);
bdFree(&v);
bdFree(&w);
bdFree(&q);
bdFree(&r);
bdFree(&p);
bdFree(&a);
bdFree(&n);
bdFree(&e);
bdFree(&m);
bdFree(&c);
bdFree(&z);
bdFree(&mz);
bdFree(&cz);
bdFree(&t);
printf("OK, successfully completed tests.\n");
return 0;
}
int bdIncrement(T a)
/* Sets a = a + 1, returns carry */
{
assert(a);
return bdShortAdd(a, a, 1);
}