+ /* now add in the addend, if any */
+ if (addend) {
+ BignumDblInt carry = 0;
+ for (i = 1; i <= rlen; i++) {
+ carry += (i <= (int)ret[0] ? ret[i] : 0);
+ carry += (i <= (int)addend[0] ? addend[i] : 0);
+ ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
+ carry >>= BIGNUM_INT_BITS;
+ if (ret[i] != 0 && i > maxspot)
+ maxspot = i;
+ }
+ }
+ ret[0] = maxspot;
+
+ sfree(workspace);
+ return ret;
+}
+
+/*
+ * Non-modular multiplication.
+ */
+Bignum bigmul(Bignum a, Bignum b)
+{
+ return bigmuladd(a, b, NULL);
+}
+
+/*
+ * Create a bignum which is the bitmask covering another one. That
+ * is, the smallest integer which is >= N and is also one less than
+ * a power of two.
+ */
+Bignum bignum_bitmask(Bignum n)
+{
+ Bignum ret = copybn(n);
+ int i;
+ BignumInt j;
+
+ i = ret[0];
+ while (n[i] == 0 && i > 0)
+ i--;
+ if (i <= 0)
+ return ret; /* input was zero */
+ j = 1;
+ while (j < n[i])
+ j = 2 * j + 1;
+ ret[i] = j;
+ while (--i > 0)
+ ret[i] = BIGNUM_INT_MASK;
+ return ret;
+}
+
+/*
+ * Convert a (max 32-bit) long into a bignum.
+ */
+Bignum bignum_from_long(unsigned long nn)
+{
+ Bignum ret;
+ BignumDblInt n = nn;
+
+ ret = newbn(3);
+ ret[1] = (BignumInt)(n & BIGNUM_INT_MASK);
+ ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK);
+ ret[3] = 0;
+ ret[0] = (ret[2] ? 2 : 1);
+ return ret;
+}
+
+/*
+ * Add a long to a bignum.
+ */
+Bignum bignum_add_long(Bignum number, unsigned long addendx)
+{
+ Bignum ret = newbn(number[0] + 1);
+ int i, maxspot = 0;
+ BignumDblInt carry = 0, addend = addendx;
+
+ for (i = 1; i <= (int)ret[0]; i++) {
+ carry += addend & BIGNUM_INT_MASK;
+ carry += (i <= (int)number[0] ? number[i] : 0);
+ addend >>= BIGNUM_INT_BITS;
+ ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
+ carry >>= BIGNUM_INT_BITS;
+ if (ret[i] != 0)
+ maxspot = i;
+ }
+ ret[0] = maxspot;
+ return ret;
+}
+
+/*
+ * Compute the residue of a bignum, modulo a (max 16-bit) short.
+ */
+unsigned short bignum_mod_short(Bignum number, unsigned short modulus)
+{
+ BignumDblInt mod, r;
+ int i;
+
+ r = 0;
+ mod = modulus;
+ for (i = number[0]; i > 0; i--)
+ r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod;
+ return (unsigned short) r;
+}
+
+#ifdef DEBUG
+void diagbn(char *prefix, Bignum md)
+{
+ int i, nibbles, morenibbles;
+ static const char hex[] = "0123456789ABCDEF";
+
+ debug(("%s0x", prefix ? prefix : ""));
+
+ nibbles = (3 + bignum_bitcount(md)) / 4;
+ if (nibbles < 1)
+ nibbles = 1;
+ morenibbles = 4 * md[0] - nibbles;
+ for (i = 0; i < morenibbles; i++)
+ debug(("-"));
+ for (i = nibbles; i--;)
+ debug(("%c",
+ hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF]));
+
+ if (prefix)
+ debug(("\n"));
+}
+#endif
+
+/*
+ * Simple division.
+ */
+Bignum bigdiv(Bignum a, Bignum b)
+{
+ Bignum q = newbn(a[0]);
+ bigdivmod(a, b, NULL, q);
+ return q;
+}
+
+/*
+ * Simple remainder.
+ */
+Bignum bigmod(Bignum a, Bignum b)
+{
+ Bignum r = newbn(b[0]);
+ bigdivmod(a, b, r, NULL);
+ return r;
+}
+
+/*
+ * Greatest common divisor.
+ */
+Bignum biggcd(Bignum av, Bignum bv)
+{
+ Bignum a = copybn(av);
+ Bignum b = copybn(bv);
+
+ while (bignum_cmp(b, Zero) != 0) {
+ Bignum t = newbn(b[0]);
+ bigdivmod(a, b, t, NULL);
+ while (t[0] > 1 && t[t[0]] == 0)
+ t[0]--;
+ freebn(a);
+ a = b;
+ b = t;
+ }
+
+ freebn(b);
+ return a;
+}
+
+/*
+ * Modular inverse, using Euclid's extended algorithm.
+ */
+Bignum modinv(Bignum number, Bignum modulus)
+{
+ Bignum a = copybn(modulus);
+ Bignum b = copybn(number);
+ Bignum xp = copybn(Zero);
+ Bignum x = copybn(One);
+ int sign = +1;
+
+ while (bignum_cmp(b, One) != 0) {
+ Bignum t = newbn(b[0]);
+ Bignum q = newbn(a[0]);
+ bigdivmod(a, b, t, q);
+ while (t[0] > 1 && t[t[0]] == 0)
+ t[0]--;
+ freebn(a);
+ a = b;
+ b = t;
+ t = xp;
+ xp = x;
+ x = bigmuladd(q, xp, t);
+ sign = -sign;
+ freebn(t);
+ freebn(q);
+ }
+
+ freebn(b);
+ freebn(a);
+ freebn(xp);
+
+ /* now we know that sign * x == 1, and that x < modulus */
+ if (sign < 0) {
+ /* set a new x to be modulus - x */
+ Bignum newx = newbn(modulus[0]);
+ BignumInt carry = 0;
+ int maxspot = 1;
+ int i;
+
+ for (i = 1; i <= (int)newx[0]; i++) {
+ BignumInt aword = (i <= (int)modulus[0] ? modulus[i] : 0);
+ BignumInt bword = (i <= (int)x[0] ? x[i] : 0);
+ newx[i] = aword - bword - carry;
+ bword = ~bword;
+ carry = carry ? (newx[i] >= bword) : (newx[i] > bword);
+ if (newx[i] != 0)
+ maxspot = i;
+ }
+ newx[0] = maxspot;
+ freebn(x);
+ x = newx;
+ }
+
+ /* and return. */
+ return x;
+}
+
+/*
+ * Render a bignum into decimal. Return a malloced string holding
+ * the decimal representation.
+ */
+char *bignum_decimal(Bignum x)
+{
+ int ndigits, ndigit;
+ int i, iszero;
+ BignumDblInt carry;
+ char *ret;
+ BignumInt *workspace;
+
+ /*
+ * First, estimate the number of digits. Since log(10)/log(2)
+ * is just greater than 93/28 (the joys of continued fraction
+ * approximations...) we know that for every 93 bits, we need
+ * at most 28 digits. This will tell us how much to malloc.
+ *
+ * Formally: if x has i bits, that means x is strictly less
+ * than 2^i. Since 2 is less than 10^(28/93), this is less than
+ * 10^(28i/93). We need an integer power of ten, so we must
+ * round up (rounding down might make it less than x again).
+ * Therefore if we multiply the bit count by 28/93, rounding
+ * up, we will have enough digits.
+ *
+ * i=0 (i.e., x=0) is an irritating special case.
+ */
+ i = bignum_bitcount(x);
+ if (!i)
+ ndigits = 1; /* x = 0 */
+ else
+ ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */
+ ndigits++; /* allow for trailing \0 */
+ ret = snewn(ndigits, char);
+
+ /*
+ * Now allocate some workspace to hold the binary form as we
+ * repeatedly divide it by ten. Initialise this to the
+ * big-endian form of the number.
+ */
+ workspace = snewn(x[0], BignumInt);
+ for (i = 0; i < (int)x[0]; i++)
+ workspace[i] = x[x[0] - i];
+
+ /*
+ * Next, write the decimal number starting with the last digit.
+ * We use ordinary short division, dividing 10 into the
+ * workspace.
+ */
+ ndigit = ndigits - 1;
+ ret[ndigit] = '\0';
+ do {
+ iszero = 1;
+ carry = 0;
+ for (i = 0; i < (int)x[0]; i++) {
+ carry = (carry << BIGNUM_INT_BITS) + workspace[i];
+ workspace[i] = (BignumInt) (carry / 10);
+ if (workspace[i])
+ iszero = 0;
+ carry %= 10;
+ }
+ ret[--ndigit] = (char) (carry + '0');
+ } while (!iszero);
+
+ /*
+ * There's a chance we've fallen short of the start of the
+ * string. Correct if so.
+ */
+ if (ndigit > 0)
+ memmove(ret, ret + ndigit, ndigits - ndigit);
+
+ /*
+ * Done.
+ */
+ sfree(workspace);
+ return ret;