vendor/bc/3.0.2

1 files changed, 2837 insertions, 0 deletions

diff --git a/src/num.c b/src/num.c
new file mode 100644
index 000000000000..ac255295e970
--- /dev/null
+++ b/src/num.c
@@ -0,0 +1,2837 @@
+/*
+ * *****************************************************************************
+ *
+ * Copyright (c) 2018-2020 Gavin D. Howard and contributors.
+ *
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice, this
+ *   list of conditions and the following disclaimer.
+ *
+ * * 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 COPYRIGHT HOLDERS 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 COPYRIGHT HOLDER 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.
+ *
+ * *****************************************************************************
+ *
+ * Code for the number type.
+ *
+ */
+
+#include <assert.h>
+#include <ctype.h>
+#include <stdbool.h>
+#include <stdlib.h>
+#include <string.h>
+#include <setjmp.h>
+#include <limits.h>
+
+#include <status.h>
+#include <num.h>
+#include <rand.h>
+#include <vm.h>
+
+static void bc_num_m(BcNum *a, BcNum *b, BcNum *restrict c, size_t scale);
+
+static inline ssize_t bc_num_neg(size_t n, bool neg) {
+	return (((ssize_t) n) ^ -((ssize_t) neg)) + neg;
+}
+
+ssize_t bc_num_cmpZero(const BcNum *n) {
+	return bc_num_neg((n)->len != 0, (n)->neg);
+}
+
+static inline size_t bc_num_int(const BcNum *n) {
+	return n->len ? n->len - n->rdx : 0;
+}
+
+static void bc_num_expand(BcNum *restrict n, size_t req) {
+
+	assert(n != NULL);
+
+	req = req >= BC_NUM_DEF_SIZE ? req : BC_NUM_DEF_SIZE;
+
+	if (req > n->cap) {
+
+		BC_SIG_LOCK;
+
+		n->num = bc_vm_realloc(n->num, BC_NUM_SIZE(req));
+		n->cap = req;
+
+		BC_SIG_UNLOCK;
+	}
+}
+
+static void bc_num_setToZero(BcNum *restrict n, size_t scale) {
+	assert(n != NULL);
+	n->scale = scale;
+	n->len = n->rdx = 0;
+	n->neg = false;
+}
+
+static inline void bc_num_zero(BcNum *restrict n) {
+	bc_num_setToZero(n, 0);
+}
+
+void bc_num_one(BcNum *restrict n) {
+	bc_num_zero(n);
+	n->len = 1;
+	n->num[0] = 1;
+}
+
+static void bc_num_clean(BcNum *restrict n) {
+
+	while (BC_NUM_NONZERO(n) && !n->num[n->len - 1]) n->len -= 1;
+
+	if (BC_NUM_ZERO(n)) {
+		n->neg = false;
+		n->rdx = 0;
+	}
+	else if (n->len < n->rdx) n->len = n->rdx;
+}
+
+static size_t bc_num_log10(size_t i) {
+	size_t len;
+	for (len = 1; i; i /= BC_BASE, ++len);
+	assert(len - 1 <= BC_BASE_DIGS + 1);
+	return len - 1;
+}
+
+static inline size_t bc_num_zeroDigits(const BcDig *n) {
+	assert(*n >= 0);
+	assert(((size_t) *n) < BC_BASE_POW);
+	return BC_BASE_DIGS - bc_num_log10((size_t) *n);
+}
+
+static size_t bc_num_intDigits(const BcNum *n) {
+	size_t digits = bc_num_int(n) * BC_BASE_DIGS;
+	if (digits > 0) digits -= bc_num_zeroDigits(n->num + n->len - 1);
+	return digits;
+}
+
+static size_t bc_num_nonzeroLen(const BcNum *restrict n) {
+	size_t i, len = n->len;
+	assert(len == n->rdx);
+	for (i = len - 1; i < len && !n->num[i]; --i);
+	assert(i + 1 > 0);
+	return i + 1;
+}
+
+static BcDig bc_num_addDigits(BcDig a, BcDig b, bool *carry) {
+
+	assert(((BcBigDig) BC_BASE_POW) * 2 == ((BcDig) BC_BASE_POW) * 2);
+	assert(a < BC_BASE_POW);
+	assert(b < BC_BASE_POW);
+
+	a += b + *carry;
+	*carry = (a >= BC_BASE_POW);
+	if (*carry) a -= BC_BASE_POW;
+
+	assert(a >= 0);
+	assert(a < BC_BASE_POW);
+
+	return a;
+}
+
+static BcDig bc_num_subDigits(BcDig a, BcDig b, bool *carry) {
+
+	assert(a < BC_BASE_POW);
+	assert(b < BC_BASE_POW);
+
+	b += *carry;
+	*carry = (a < b);
+	if (*carry) a += BC_BASE_POW;
+
+	assert(a - b >= 0);
+	assert(a - b < BC_BASE_POW);
+
+	return a - b;
+}
+
+static void bc_num_addArrays(BcDig *restrict a, const BcDig *restrict b,
+                             size_t len)
+{
+	size_t i;
+	bool carry = false;
+
+	for (i = 0; i < len; ++i) a[i] = bc_num_addDigits(a[i], b[i], &carry);
+
+	for (; carry; ++i) a[i] = bc_num_addDigits(a[i], 0, &carry);
+}
+
+static void bc_num_subArrays(BcDig *restrict a, const BcDig *restrict b,
+                             size_t len)
+{
+	size_t i;
+	bool carry = false;
+
+	for (i = 0; i < len; ++i) a[i] = bc_num_subDigits(a[i], b[i], &carry);
+
+	for (; carry; ++i) a[i] = bc_num_subDigits(a[i], 0, &carry);
+}
+
+static void bc_num_mulArray(const BcNum *restrict a, BcBigDig b,
+                            BcNum *restrict c)
+{
+	size_t i;
+	BcBigDig carry = 0;
+
+	assert(b <= BC_BASE_POW);
+
+	if (a->len + 1 > c->cap) bc_num_expand(c, a->len + 1);
+
+	memset(c->num, 0, BC_NUM_SIZE(c->cap));
+
+	for (i = 0; i < a->len; ++i) {
+		BcBigDig in = ((BcBigDig) a->num[i]) * b + carry;
+		c->num[i] = in % BC_BASE_POW;
+		carry = in / BC_BASE_POW;
+	}
+
+	assert(carry < BC_BASE_POW);
+	c->num[i] = (BcDig) carry;
+	c->len = a->len;
+	c->len += (carry != 0);
+
+	bc_num_clean(c);
+
+	assert(!c->neg || BC_NUM_NONZERO(c));
+	assert(c->rdx <= c->len || !c->len);
+	assert(!c->len || c->num[c->len - 1] || c->rdx == c->len);
+}
+
+static void bc_num_divArray(const BcNum *restrict a, BcBigDig b,
+                            BcNum *restrict c, BcBigDig *rem)
+{
+	size_t i;
+	BcBigDig carry = 0;
+
+	assert(c->cap >= a->len);
+
+	for (i = a->len - 1; i < a->len; --i) {
+		BcBigDig in = ((BcBigDig) a->num[i]) + carry * BC_BASE_POW;
+		assert(in / b < BC_BASE_POW);
+		c->num[i] = (BcDig) (in / b);
+		carry = in % b;
+	}
+
+	c->len = a->len;
+	bc_num_clean(c);
+	*rem = carry;
+
+	assert(!c->neg || BC_NUM_NONZERO(c));
+	assert(c->rdx <= c->len || !c->len);
+	assert(!c->len || c->num[c->len - 1] || c->rdx == c->len);
+}
+
+static ssize_t bc_num_compare(const BcDig *restrict a, const BcDig *restrict b,
+                              size_t len)
+{
+	size_t i;
+	BcDig c = 0;
+	for (i = len - 1; i < len && !(c = a[i] - b[i]); --i);
+	return bc_num_neg(i + 1, c < 0);
+}
+
+ssize_t bc_num_cmp(const BcNum *a, const BcNum *b) {
+
+	size_t i, min, a_int, b_int, diff;
+	BcDig *max_num, *min_num;
+	bool a_max, neg = false;
+	ssize_t cmp;
+
+	assert(a != NULL && b != NULL);
+
+	if (a == b) return 0;
+	if (BC_NUM_ZERO(a)) return bc_num_neg(b->len != 0, !b->neg);
+	if (BC_NUM_ZERO(b)) return bc_num_cmpZero(a);
+	if (a->neg) {
+		if (b->neg) neg = true;
+		else return -1;
+	}
+	else if (b->neg) return 1;
+
+	a_int = bc_num_int(a);
+	b_int = bc_num_int(b);
+	a_int -= b_int;
+
+	if (a_int) return neg ? -((ssize_t) a_int) : (ssize_t) a_int;
+
+	a_max = (a->rdx > b->rdx);
+
+	if (a_max) {
+		min = b->rdx;
+		diff = a->rdx - b->rdx;
+		max_num = a->num + diff;
+		min_num = b->num;
+	}
+	else {
+		min = a->rdx;
+		diff = b->rdx - a->rdx;
+		max_num = b->num + diff;
+		min_num = a->num;
+	}
+
+	cmp = bc_num_compare(max_num, min_num, b_int + min);
+
+	if (cmp) return bc_num_neg((size_t) cmp, !a_max == !neg);
+
+	for (max_num -= diff, i = diff - 1; i < diff; --i) {
+		if (max_num[i]) return bc_num_neg(1, !a_max == !neg);
+	}
+
+	return 0;
+}
+
+void bc_num_truncate(BcNum *restrict n, size_t places) {
+
+	size_t places_rdx;
+
+	if (!places) return;
+
+	places_rdx = n->rdx ? n->rdx - BC_NUM_RDX(n->scale - places) : 0;
+	assert(places <= n->scale && (BC_NUM_ZERO(n) || places_rdx <= n->len));
+
+	n->scale -= places;
+	n->rdx -= places_rdx;
+
+	if (BC_NUM_NONZERO(n)) {
+
+		size_t pow;
+
+		pow = n->scale % BC_BASE_DIGS;
+		pow = pow ? BC_BASE_DIGS - pow : 0;
+		pow = bc_num_pow10[pow];
+
+		n->len -= places_rdx;
+		memmove(n->num, n->num + places_rdx, BC_NUM_SIZE(n->len));
+
+		// Clear the lower part of the last digit.
+		if (BC_NUM_NONZERO(n)) n->num[0] -= n->num[0] % (BcDig) pow;
+
+		bc_num_clean(n);
+	}
+}
+
+static void bc_num_extend(BcNum *restrict n, size_t places) {
+
+	size_t places_rdx;
+
+	if (!places) return;
+	if (BC_NUM_ZERO(n)) {
+		n->scale += places;
+		return;
+	}
+
+	places_rdx = BC_NUM_RDX(places + n->scale) - n->rdx;
+
+	if (places_rdx) {
+		bc_num_expand(n, bc_vm_growSize(n->len, places_rdx));
+		memmove(n->num + places_rdx, n->num, BC_NUM_SIZE(n->len));
+		memset(n->num, 0, BC_NUM_SIZE(places_rdx));
+	}
+
+	n->rdx += places_rdx;
+	n->scale += places;
+	n->len += places_rdx;
+
+	assert(n->rdx == BC_NUM_RDX(n->scale));
+}
+
+static void bc_num_retireMul(BcNum *restrict n, size_t scale,
+                             bool neg1, bool neg2)
+{
+	if (n->scale < scale) bc_num_extend(n, scale - n->scale);
+	else bc_num_truncate(n, n->scale - scale);
+
+	bc_num_clean(n);
+	if (BC_NUM_NONZERO(n)) n->neg = (!neg1 != !neg2);
+}
+
+static void bc_num_split(const BcNum *restrict n, size_t idx,
+                         BcNum *restrict a, BcNum *restrict b)
+{
+	assert(BC_NUM_ZERO(a));
+	assert(BC_NUM_ZERO(b));
+
+	if (idx < n->len) {
+
+		b->len = n->len - idx;
+		a->len = idx;
+		a->scale = a->rdx = b->scale = b->rdx = 0;
+
+		assert(a->cap >= a->len);
+		assert(b->cap >= b->len);
+
+		memcpy(b->num, n->num + idx, BC_NUM_SIZE(b->len));
+		memcpy(a->num, n->num, BC_NUM_SIZE(idx));
+
+		bc_num_clean(b);
+	}
+	else bc_num_copy(a, n);
+
+	bc_num_clean(a);
+}
+
+static size_t bc_num_shiftZero(BcNum *restrict n) {
+
+	size_t i;
+
+	assert(!n->rdx || BC_NUM_ZERO(n));
+
+	for (i = 0; i < n->len && !n->num[i]; ++i);
+
+	n->len -= i;
+	n->num += i;
+
+	return i;
+}
+
+static void bc_num_unshiftZero(BcNum *restrict n, size_t places_rdx) {
+	n->len += places_rdx;
+	n->num -= places_rdx;
+}
+
+static void bc_num_shift(BcNum *restrict n, BcBigDig dig) {
+
+	size_t i, len = n->len;
+	BcBigDig carry = 0, pow;
+	BcDig *ptr = n->num;
+
+	assert(dig < BC_BASE_DIGS);
+
+	pow = bc_num_pow10[dig];
+	dig = bc_num_pow10[BC_BASE_DIGS - dig];
+
+	for (i = len - 1; i < len; --i) {
+		BcBigDig in, temp;
+		in = ((BcBigDig) ptr[i]);
+		temp = carry * dig;
+		carry = in % pow;
+		ptr[i] = ((BcDig) (in / pow)) + (BcDig) temp;
+	}
+
+	assert(!carry);
+}
+
+static void bc_num_shiftLeft(BcNum *restrict n, size_t places) {
+
+	BcBigDig dig;
+	size_t places_rdx;
+	bool shift;
+
+	if (!places) return;
+	if (places > n->scale) {
+		size_t size = bc_vm_growSize(BC_NUM_RDX(places - n->scale), n->len);
+		if (size > SIZE_MAX - 1) bc_vm_err(BC_ERROR_MATH_OVERFLOW);
+	}
+	if (BC_NUM_ZERO(n)) {
+		if (n->scale >= places) n->scale -= places;
+		else n->scale = 0;
+		return;
+	}
+
+	dig = (BcBigDig) (places % BC_BASE_DIGS);
+	shift = (dig != 0);
+	places_rdx = BC_NUM_RDX(places);
+
+	if (n->scale) {
+
+		if (n->rdx >= places_rdx) {
+
+			size_t mod = n->scale % BC_BASE_DIGS, revdig;
+
+			mod = mod ? mod : BC_BASE_DIGS;
+			revdig = dig ? BC_BASE_DIGS - dig : 0;
+
+			if (mod + revdig > BC_BASE_DIGS) places_rdx = 1;
+			else places_rdx = 0;
+		}
+		else places_rdx -= n->rdx;
+	}
+
+	if (places_rdx) {
+		bc_num_expand(n, bc_vm_growSize(n->len, places_rdx));
+		memmove(n->num + places_rdx, n->num, BC_NUM_SIZE(n->len));
+		memset(n->num, 0, BC_NUM_SIZE(places_rdx));
+		n->len += places_rdx;
+	}
+
+	if (places > n->scale) n->scale = n->rdx = 0;
+	else {
+		n->scale -= places;
+		n->rdx = BC_NUM_RDX(n->scale);
+	}
+
+	if (shift) bc_num_shift(n, BC_BASE_DIGS - dig);
+
+	bc_num_clean(n);
+}
+
+static void bc_num_shiftRight(BcNum *restrict n, size_t places) {
+
+	BcBigDig dig;
+	size_t places_rdx, scale, scale_mod, int_len, expand;
+	bool shift;
+
+	if (!places) return;
+	if (BC_NUM_ZERO(n)) {
+		n->scale += places;
+		bc_num_expand(n, BC_NUM_RDX(n->scale));
+		return;
+	}
+
+	dig = (BcBigDig) (places % BC_BASE_DIGS);
+	shift = (dig != 0);
+	scale = n->scale;
+	scale_mod = scale % BC_BASE_DIGS;
+	scale_mod = scale_mod ? scale_mod : BC_BASE_DIGS;
+	int_len = bc_num_int(n);
+	places_rdx = BC_NUM_RDX(places);
+
+	if (scale_mod + dig > BC_BASE_DIGS) {
+		expand = places_rdx - 1;
+		places_rdx = 1;
+	}
+	else {
+		expand = places_rdx;
+		places_rdx = 0;
+	}
+
+	if (expand > int_len) expand -= int_len;
+	else expand = 0;
+
+	bc_num_extend(n, places_rdx * BC_BASE_DIGS);
+	bc_num_expand(n, bc_vm_growSize(expand, n->len));
+	memset(n->num + n->len, 0, BC_NUM_SIZE(expand));
+	n->len += expand;
+	n->scale = n->rdx = 0;
+
+	if (shift) bc_num_shift(n, dig);
+
+	n->scale = scale + places;
+	n->rdx = BC_NUM_RDX(n->scale);
+
+	bc_num_clean(n);
+
+	assert(n->rdx <= n->len && n->len <= n->cap);
+	assert(n->rdx == BC_NUM_RDX(n->scale));
+}
+
+static void bc_num_inv(BcNum *a, BcNum *b, size_t scale) {
+
+	BcNum one;
+	BcDig num[2];
+
+	assert(BC_NUM_NONZERO(a));
+
+	bc_num_setup(&one, num, sizeof(num) / sizeof(BcDig));
+	bc_num_one(&one);
+
+	bc_num_div(&one, a, b, scale);
+}
+
+#if BC_ENABLE_EXTRA_MATH
+static void bc_num_intop(const BcNum *a, const BcNum *b, BcNum *restrict c,
+                         BcBigDig *v)
+{
+	if (BC_ERR(b->rdx)) bc_vm_err(BC_ERROR_MATH_NON_INTEGER);
+	bc_num_copy(c, a);
+	bc_num_bigdig(b, v);
+}
+#endif // BC_ENABLE_EXTRA_MATH
+
+static void bc_num_as(BcNum *a, BcNum *b, BcNum *restrict c, size_t sub) {
+
+	BcDig *ptr_c, *ptr_l, *ptr_r;
+	size_t i, min_rdx, max_rdx, diff, a_int, b_int, min_len, max_len, max_int;
+	size_t len_l, len_r;
+	bool b_neg, do_sub, do_rev_sub, carry;
+
+	// Because this function doesn't need to use scale (per the bc spec),
+	// I am hijacking it to say whether it's doing an add or a subtract.
+	// Convert substraction to addition of negative second operand.
+
+	if (BC_NUM_ZERO(b)) {
+		bc_num_copy(c, a);
+		return;
+	}
+	if (BC_NUM_ZERO(a)) {
+		bc_num_copy(c, b);
+		c->neg = (b->neg != sub);
+		return;
+	}
+
+	// Invert sign of b if it is to be subtracted. This operation must
+	// preced the tests for any of the operands being zero.
+	b_neg = (b->neg != sub);
+
+	// Actually add the numbers if their signs are equal, else subtract.
+	do_sub = (a->neg != b_neg);
+
+	a_int = bc_num_int(a);
+	b_int = bc_num_int(b);
+	max_int = BC_MAX(a_int, b_int);
+
+	min_rdx = BC_MIN(a->rdx, b->rdx);
+	max_rdx = BC_MAX(a->rdx, b->rdx);
+	diff = max_rdx - min_rdx;
+
+	max_len = max_int + max_rdx;
+
+	if (do_sub) {
+
+		// Check whether b has to be subtracted from a or a from b.
+		if (a_int != b_int) do_rev_sub = (a_int < b_int);
+		else if (a->rdx > b->rdx)
+			do_rev_sub = (bc_num_compare(a->num + diff, b->num, b->len) < 0);
+		else
+			do_rev_sub = (bc_num_compare(a->num, b->num + diff, a->len) <= 0);
+	}
+	else {
+
+		// The result array of the addition might come out one element
+		// longer than the bigger of the operand arrays.
+		max_len += 1;
+		do_rev_sub = (a_int < b_int);
+	}
+
+	assert(max_len <= c->cap);
+
+	if (do_rev_sub) {
+		ptr_l = b->num;
+		ptr_r = a->num;
+		len_l = b->len;
+		len_r = a->len;
+	}
+	else {
+		ptr_l = a->num;
+		ptr_r = b->num;
+		len_l = a->len;
+		len_r = b->len;
+	}
+
+	ptr_c = c->num;
+	carry = false;
+
+	if (diff) {
+
+		// If the rdx values of the operands do not match, the result will
+		// have low end elements that are the positive or negative trailing
+		// elements of the operand with higher rdx value.
+		if ((a->rdx > b->rdx) != do_rev_sub) {
+
+			// !do_rev_sub && a->rdx > b->rdx || do_rev_sub && b->rdx > a->rdx
+			// The left operand has BcDig values that need to be copied,
+			// either from a or from b (in case of a reversed subtraction).
+			memcpy(ptr_c, ptr_l, BC_NUM_SIZE(diff));
+			ptr_l += diff;
+			len_l -= diff;
+		}
+		else {
+
+			// The right operand has BcDig values that need to be copied
+			// or subtracted from zero (in case of a subtraction).
+			if (do_sub) {
+
+				// do_sub (do_rev_sub && a->rdx > b->rdx ||
+				// !do_rev_sub && b->rdx > a->rdx)
+				for (i = 0; i < diff; i++)
+					ptr_c[i] = bc_num_subDigits(0, ptr_r[i], &carry);
+			}
+			else {
+
+				// !do_sub && b->rdx > a->rdx
+				memcpy(ptr_c, ptr_r, BC_NUM_SIZE(diff));
+			}
+
+			ptr_r += diff;
+			len_r -= diff;
+		}
+
+		ptr_c += diff;
+	}
+
+	min_len = BC_MIN(len_l, len_r);
+
+	// After dealing with possible low array elements that depend on only one
+	// operand, the actual add or subtract can be performed as if the rdx of
+	// both operands was the same.
+	// Inlining takes care of eliminating constant zero arguments to
+	// addDigit/subDigit (checked in disassembly of resulting bc binary
+	// compiled with gcc and clang).
+	if (do_sub) {
+		for (i = 0; i < min_len; ++i)
+			ptr_c[i] = bc_num_subDigits(ptr_l[i], ptr_r[i], &carry);
+		for (; i < len_l; ++i) ptr_c[i] = bc_num_subDigits(ptr_l[i], 0, &carry);
+	}
+	else {
+		for (i = 0; i < min_len; ++i)
+			ptr_c[i] = bc_num_addDigits(ptr_l[i], ptr_r[i], &carry);
+		for (; i < len_l; ++i) ptr_c[i] = bc_num_addDigits(ptr_l[i], 0, &carry);
+		ptr_c[i] = bc_num_addDigits(0, 0, &carry);
+	}
+
+	assert(carry == false);
+
+	// The result has the same sign as a, unless the operation was a
+	// reverse subtraction (b - a).
+	c->neg = (a->neg != (do_sub && do_rev_sub));
+	c->len = max_len;
+	c->rdx = max_rdx;
+	c->scale = BC_MAX(a->scale, b->scale);
+
+	bc_num_clean(c);
+}
+
+static void bc_num_m_simp(const BcNum *a, const BcNum *b, BcNum *restrict c)
+{
+	size_t i, alen = a->len, blen = b->len, clen;
+	BcDig *ptr_a = a->num, *ptr_b = b->num, *ptr_c;
+	BcBigDig sum = 0, carry = 0;
+
+	assert(sizeof(sum) >= sizeof(BcDig) * 2);
+	assert(!a->rdx && !b->rdx);
+
+	clen = bc_vm_growSize(alen, blen);
+	bc_num_expand(c, bc_vm_growSize(clen, 1));
+
+	ptr_c = c->num;
+	memset(ptr_c, 0, BC_NUM_SIZE(c->cap));
+
+	for (i = 0; i < clen; ++i) {
+
+		ssize_t sidx = (ssize_t) (i - blen + 1);
+		size_t j = (size_t) BC_MAX(0, sidx), k = BC_MIN(i, blen - 1);
+
+		for (; j < alen && k < blen; ++j, --k) {
+
+			sum += ((BcBigDig) ptr_a[j]) * ((BcBigDig) ptr_b[k]);
+
+			if (sum >= ((BcBigDig) BC_BASE_POW) * BC_BASE_POW) {
+				carry += sum / BC_BASE_POW;
+				sum %= BC_BASE_POW;
+			}
+		}
+
+		if (sum >= BC_BASE_POW) {
+			carry += sum / BC_BASE_POW;
+			sum %= BC_BASE_POW;
+		}
+
+		ptr_c[i] = (BcDig) sum;
+		assert(ptr_c[i] < BC_BASE_POW);
+		sum = carry;
+		carry = 0;
+	}
+
+	// This should always be true because there should be no carry on the last
+	// digit; multiplication never goes above the sum of both lengths.
+	assert(!sum);
+
+	c->len = clen;
+}
+
+static void bc_num_shiftAddSub(BcNum *restrict n, const BcNum *restrict a,
+                               size_t shift, BcNumShiftAddOp op)
+{
+	assert(n->len >= shift + a->len);
+	assert(!n->rdx && !a->rdx);
+	op(n->num + shift, a->num, a->len);
+}
+
+static void bc_num_k(BcNum *a, BcNum *b, BcNum *restrict c) {
+
+	size_t max, max2, total;
+	BcNum l1, h1, l2, h2, m2, m1, z0, z1, z2, temp;
+	BcDig *digs, *dig_ptr;
+	BcNumShiftAddOp op;
+	bool aone = BC_NUM_ONE(a);
+
+	assert(BC_NUM_ZERO(c));
+
+	if (BC_NUM_ZERO(a) || BC_NUM_ZERO(b)) return;
+	if (aone || BC_NUM_ONE(b)) {
+		bc_num_copy(c, aone ? b : a);
+		if ((aone && a->neg) || b->neg) c->neg = !c->neg;
+		return;
+	}
+	if (a->len < BC_NUM_KARATSUBA_LEN || b->len < BC_NUM_KARATSUBA_LEN) {
+		bc_num_m_simp(a, b, c);
+		return;
+	}
+
+	max = BC_MAX(a->len, b->len);
+	max = BC_MAX(max, BC_NUM_DEF_SIZE);
+	max2 = (max + 1) / 2;
+
+	total = bc_vm_arraySize(BC_NUM_KARATSUBA_ALLOCS, max);
+
+	BC_SIG_LOCK;
+
+	digs = dig_ptr = bc_vm_malloc(BC_NUM_SIZE(total));
+
+	bc_num_setup(&l1, dig_ptr, max);
+	dig_ptr += max;
+	bc_num_setup(&h1, dig_ptr, max);
+	dig_ptr += max;
+	bc_num_setup(&l2, dig_ptr, max);
+	dig_ptr += max;
+	bc_num_setup(&h2, dig_ptr, max);
+	dig_ptr += max;
+	bc_num_setup(&m1, dig_ptr, max);
+	dig_ptr += max;
+	bc_num_setup(&m2, dig_ptr, max);
+	max = bc_vm_growSize(max, 1);
+	bc_num_init(&z0, max);
+	bc_num_init(&z1, max);
+	bc_num_init(&z2, max);
+	max = bc_vm_growSize(max, max) + 1;
+	bc_num_init(&temp, max);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_split(a, max2, &l1, &h1);
+	bc_num_split(b, max2, &l2, &h2);
+
+	bc_num_expand(c, max);
+	c->len = max;
+	memset(c->num, 0, BC_NUM_SIZE(c->len));
+
+	bc_num_sub(&h1, &l1, &m1, 0);
+	bc_num_sub(&l2, &h2, &m2, 0);
+
+	if (BC_NUM_NONZERO(&h1) && BC_NUM_NONZERO(&h2)) {
+
+		bc_num_m(&h1, &h2, &z2, 0);
+		bc_num_clean(&z2);
+
+		bc_num_shiftAddSub(c, &z2, max2 * 2, bc_num_addArrays);
+		bc_num_shiftAddSub(c, &z2, max2, bc_num_addArrays);
+	}
+
+	if (BC_NUM_NONZERO(&l1) && BC_NUM_NONZERO(&l2)) {
+
+		bc_num_m(&l1, &l2, &z0, 0);
+		bc_num_clean(&z0);
+
+		bc_num_shiftAddSub(c, &z0, max2, bc_num_addArrays);
+		bc_num_shiftAddSub(c, &z0, 0, bc_num_addArrays);
+	}
+
+	if (BC_NUM_NONZERO(&m1) && BC_NUM_NONZERO(&m2)) {
+
+		bc_num_m(&m1, &m2, &z1, 0);
+		bc_num_clean(&z1);
+
+		op = (m1.neg != m2.neg) ? bc_num_subArrays : bc_num_addArrays;
+		bc_num_shiftAddSub(c, &z1, max2, op);
+	}
+
+err:
+	BC_SIG_MAYLOCK;
+	free(digs);
+	bc_num_free(&temp);
+	bc_num_free(&z2);
+	bc_num_free(&z1);
+	bc_num_free(&z0);
+	BC_LONGJMP_CONT;
+}
+
+static void bc_num_m(BcNum *a, BcNum *b, BcNum *restrict c, size_t scale) {
+
+	BcNum cpa, cpb;
+	size_t ascale, bscale, ardx, brdx, azero = 0, bzero = 0, zero, len, rscale;
+
+	bc_num_zero(c);
+	ascale = a->scale;
+	bscale = b->scale;
+	scale = BC_MAX(scale, ascale);
+	scale = BC_MAX(scale, bscale);
+
+	rscale = ascale + bscale;
+	scale = BC_MIN(rscale, scale);
+
+	if ((a->len == 1 || b->len == 1) && !a->rdx && !b->rdx) {
+
+		BcNum *operand;
+		BcBigDig dig;
+
+		if (a->len == 1) {
+			dig = (BcBigDig) a->num[0];
+			operand = b;
+		}
+		else {
+			dig = (BcBigDig) b->num[0];
+			operand = a;
+		}
+
+		bc_num_mulArray(operand, dig, c);
+
+		if (BC_NUM_NONZERO(c)) c->neg = (a->neg != b->neg);
+
+		return;
+	}
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&cpa, a->len + a->rdx);
+	bc_num_init(&cpb, b->len + b->rdx);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_copy(&cpa, a);
+	bc_num_copy(&cpb, b);
+
+	cpa.neg = cpb.neg = false;
+
+	ardx = cpa.rdx * BC_BASE_DIGS;
+	bc_num_shiftLeft(&cpa, ardx);
+
+	brdx = cpb.rdx * BC_BASE_DIGS;
+	bc_num_shiftLeft(&cpb, brdx);
+
+	// We need to reset the jump here because azero and bzero are used in the
+	// cleanup, and local variables are not guaranteed to be the same after a
+	// jump.
+	BC_SIG_LOCK;
+
+	BC_UNSETJMP;
+
+	azero = bc_num_shiftZero(&cpa);
+	bzero = bc_num_shiftZero(&cpb);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_clean(&cpa);
+	bc_num_clean(&cpb);
+
+	bc_num_k(&cpa, &cpb, c);
+
+	zero = bc_vm_growSize(azero, bzero);
+	len = bc_vm_growSize(c->len, zero);
+
+	bc_num_expand(c, len);
+	bc_num_shiftLeft(c, (len - c->len) * BC_BASE_DIGS);
+	bc_num_shiftRight(c, ardx + brdx);
+
+	bc_num_retireMul(c, scale, a->neg, b->neg);
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_unshiftZero(&cpb, bzero);
+	bc_num_free(&cpb);
+	bc_num_unshiftZero(&cpa, azero);
+	bc_num_free(&cpa);
+	BC_LONGJMP_CONT;
+}
+
+static bool bc_num_nonZeroDig(BcDig *restrict a, size_t len) {
+	size_t i;
+	bool nonzero = false;
+	for (i = len - 1; !nonzero && i < len; --i) nonzero = (a[i] != 0);
+	return nonzero;
+}
+
+static ssize_t bc_num_divCmp(const BcDig *a, const BcNum *b, size_t len) {
+
+	ssize_t cmp;
+
+	if (b->len > len && a[len]) cmp = bc_num_compare(a, b->num, len + 1);
+	else if (b->len <= len) {
+		if (a[len]) cmp = 1;
+		else cmp = bc_num_compare(a, b->num, len);
+	}
+	else cmp = -1;
+
+	return cmp;
+}
+
+static void bc_num_divExtend(BcNum *restrict a, BcNum *restrict b,
+                             BcBigDig divisor)
+{
+	size_t pow;
+
+	assert(divisor < BC_BASE_POW);
+
+	pow = BC_BASE_DIGS - bc_num_log10((size_t) divisor);
+
+	bc_num_shiftLeft(a, pow);
+	bc_num_shiftLeft(b, pow);
+}
+
+static void bc_num_d_long(BcNum *restrict a, BcNum *restrict b,
+                          BcNum *restrict c, size_t scale)
+{
+	BcBigDig divisor;
+	size_t len, end, i, rdx;
+	BcNum cpb;
+	bool nonzero = false;
+
+	assert(b->len < a->len);
+	len = b->len;
+	end = a->len - len;
+	assert(len >= 1);
+
+	bc_num_expand(c, a->len);
+	memset(c->num, 0, c->cap * sizeof(BcDig));
+
+	c->rdx = a->rdx;
+	c->scale = a->scale;
+	c->len = a->len;
+
+	divisor = (BcBigDig) b->num[len - 1];
+
+	if (len > 1 && bc_num_nonZeroDig(b->num, len - 1)) {
+
+		nonzero = (divisor > 1 << ((10 * BC_BASE_DIGS) / 6 + 1));
+
+		if (!nonzero) {
+
+			bc_num_divExtend(a, b, divisor);
+
+			len = BC_MAX(a->len, b->len);
+			bc_num_expand(a, len + 1);
+
+			if (len + 1 > a->len) a->len = len + 1;
+
+			len = b->len;
+			end = a->len - len;
+			divisor = (BcBigDig) b->num[len - 1];
+
+			nonzero = bc_num_nonZeroDig(b->num, len - 1);
+		}
+	}
+
+	divisor += nonzero;
+
+	bc_num_expand(c, a->len);
+	memset(c->num, 0, BC_NUM_SIZE(c->cap));
+
+	assert(c->scale >= scale);
+	rdx = c->rdx - BC_NUM_RDX(scale);
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&cpb, len + 1);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	i = end - 1;
+
+	for (; i < end && i >= rdx && BC_NUM_NONZERO(a); --i) {
+
+		ssize_t cmp;
+		BcDig *n;
+		BcBigDig result;
+
+		n = a->num + i;
+		assert(n >= a->num);
+		result = 0;
+
+		cmp = bc_num_divCmp(n, b, len);
+
+		while (cmp >= 0) {
+
+			BcBigDig n1, dividend, q;
+
+			n1 = (BcBigDig) n[len];
+			dividend = n1 * BC_BASE_POW + (BcBigDig) n[len - 1];
+			q = (dividend / divisor);
+
+			if (q <= 1) {
+				q = 1;
+				bc_num_subArrays(n, b->num, len);
+			}
+			else {
+
+				assert(q <= BC_BASE_POW);
+
+				bc_num_mulArray(b, (BcBigDig) q, &cpb);
+				bc_num_subArrays(n, cpb.num, cpb.len);
+			}
+
+			result += q;
+			assert(result <= BC_BASE_POW);
+
+			if (nonzero) cmp = bc_num_divCmp(n, b, len);
+			else cmp = -1;
+		}
+
+		assert(result < BC_BASE_POW);
+
+		c->num[i] = (BcDig) result;
+	}
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&cpb);
+	BC_LONGJMP_CONT;
+}
+
+static void bc_num_d(BcNum *a, BcNum *b, BcNum *restrict c, size_t scale) {
+
+	size_t len;
+	BcNum cpa, cpb;
+
+	if (BC_NUM_ZERO(b)) bc_vm_err(BC_ERROR_MATH_DIVIDE_BY_ZERO);
+	if (BC_NUM_ZERO(a)) {
+		bc_num_setToZero(c, scale);
+		return;
+	}
+	if (BC_NUM_ONE(b)) {
+		bc_num_copy(c, a);
+		bc_num_retireMul(c, scale, a->neg, b->neg);
+		return;
+	}
+	if (!a->rdx && !b->rdx && b->len == 1 && !scale) {
+		BcBigDig rem;
+		bc_num_divArray(a, (BcBigDig) b->num[0], c, &rem);
+		bc_num_retireMul(c, scale, a->neg, b->neg);
+		return;
+	}
+
+	len = bc_num_mulReq(a, b, scale);
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&cpa, len);
+	bc_num_copy(&cpa, a);
+	bc_num_createCopy(&cpb, b);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	len = b->len;
+
+	if (len > cpa.len) {
+		bc_num_expand(&cpa, bc_vm_growSize(len, 2));
+		bc_num_extend(&cpa, (len - cpa.len) * BC_BASE_DIGS);
+	}
+
+	cpa.scale = cpa.rdx * BC_BASE_DIGS;
+
+	bc_num_extend(&cpa, b->scale);
+	cpa.rdx -= BC_NUM_RDX(b->scale);
+	cpa.scale = cpa.rdx * BC_BASE_DIGS;
+
+	if (scale > cpa.scale) {
+		bc_num_extend(&cpa, scale);
+		cpa.scale = cpa.rdx * BC_BASE_DIGS;
+	}
+
+	if (cpa.cap == cpa.len) bc_num_expand(&cpa, bc_vm_growSize(cpa.len, 1));
+
+	// We want an extra zero in front to make things simpler.
+	cpa.num[cpa.len++] = 0;
+
+	if (cpa.rdx == cpa.len) cpa.len = bc_num_nonzeroLen(&cpa);
+	if (cpb.rdx == cpb.len) cpb.len = bc_num_nonzeroLen(&cpb);
+	cpb.scale = cpb.rdx = 0;
+
+	bc_num_d_long(&cpa, &cpb, c, scale);
+
+	bc_num_retireMul(c, scale, a->neg, b->neg);
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&cpb);
+	bc_num_free(&cpa);
+	BC_LONGJMP_CONT;
+}
+
+static void bc_num_r(BcNum *a, BcNum *b, BcNum *restrict c,
+                     BcNum *restrict d, size_t scale, size_t ts)
+{
+	BcNum temp;
+	bool neg;
+
+	if (BC_NUM_ZERO(b)) bc_vm_err(BC_ERROR_MATH_DIVIDE_BY_ZERO);
+	if (BC_NUM_ZERO(a)) {
+		bc_num_setToZero(c, ts);
+		bc_num_setToZero(d, ts);
+		return;
+	}
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&temp, d->cap);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_d(a, b, c, scale);
+
+	if (scale) scale = ts + 1;
+
+	bc_num_m(c, b, &temp, scale);
+	bc_num_sub(a, &temp, d, scale);
+
+	if (ts > d->scale && BC_NUM_NONZERO(d)) bc_num_extend(d, ts - d->scale);
+
+	neg = d->neg;
+	bc_num_retireMul(d, ts, a->neg, b->neg);
+	d->neg = BC_NUM_NONZERO(d) ? neg : false;
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&temp);
+	BC_LONGJMP_CONT;
+}
+
+static void bc_num_rem(BcNum *a, BcNum *b, BcNum *restrict c, size_t scale) {
+
+	BcNum c1;
+	size_t ts;
+
+	ts = bc_vm_growSize(scale, b->scale);
+	ts = BC_MAX(ts, a->scale);
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&c1, bc_num_mulReq(a, b, ts));
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_r(a, b, &c1, c, scale, ts);
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&c1);
+	BC_LONGJMP_CONT;
+}
+
+static void bc_num_p(BcNum *a, BcNum *b, BcNum *restrict c, size_t scale) {
+
+	BcNum copy;
+	BcBigDig pow = 0;
+	size_t i, powrdx, resrdx;
+	bool neg, zero;
+
+	if (BC_ERR(b->rdx)) bc_vm_err(BC_ERROR_MATH_NON_INTEGER);
+
+	if (BC_NUM_ZERO(b)) {
+		bc_num_one(c);
+		return;
+	}
+	if (BC_NUM_ZERO(a)) {
+		if (b->neg) bc_vm_err(BC_ERROR_MATH_DIVIDE_BY_ZERO);
+		bc_num_setToZero(c, scale);
+		return;
+	}
+	if (BC_NUM_ONE(b)) {
+		if (!b->neg) bc_num_copy(c, a);
+		else bc_num_inv(a, c, scale);
+		return;
+	}
+
+	BC_SIG_LOCK;
+
+	neg = b->neg;
+	b->neg = false;
+	bc_num_bigdig(b, &pow);
+	b->neg = neg;
+
+	bc_num_createCopy(&copy, a);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	if (!neg) {
+		size_t max = BC_MAX(scale, a->scale), scalepow = a->scale * pow;
+		scale = BC_MIN(scalepow, max);
+	}
+
+	for (powrdx = a->scale; !(pow & 1); pow >>= 1) {
+		powrdx <<= 1;
+		bc_num_mul(&copy, &copy, &copy, powrdx);
+	}
+
+	bc_num_copy(c, &copy);
+	resrdx = powrdx;
+
+	while (pow >>= 1) {
+
+		powrdx <<= 1;
+		bc_num_mul(&copy, &copy, &copy, powrdx);
+
+		if (pow & 1) {
+			resrdx += powrdx;
+			bc_num_mul(c, &copy, c, resrdx);
+		}
+	}
+
+	if (neg) bc_num_inv(c, c, scale);
+
+	if (c->scale > scale) bc_num_truncate(c, c->scale - scale);
+
+	// We can't use bc_num_clean() here.
+	for (zero = true, i = 0; zero && i < c->len; ++i) zero = !c->num[i];
+	if (zero) bc_num_setToZero(c, scale);
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&copy);
+	BC_LONGJMP_CONT;
+}
+
+#if BC_ENABLE_EXTRA_MATH
+static void bc_num_place(BcNum *a, BcNum *b, BcNum *restrict c, size_t scale) {
+
+	BcBigDig val = 0;
+
+	BC_UNUSED(scale);
+
+	bc_num_intop(a, b, c, &val);
+
+	if (val < c->scale) bc_num_truncate(c, c->scale - val);
+	else if (val > c->scale) bc_num_extend(c, val - c->scale);
+}
+
+static void bc_num_left(BcNum *a, BcNum *b, BcNum *restrict c, size_t scale) {
+
+	BcBigDig val = 0;
+
+	BC_UNUSED(scale);
+
+	bc_num_intop(a, b, c, &val);
+
+	bc_num_shiftLeft(c, (size_t) val);
+}
+
+static void bc_num_right(BcNum *a, BcNum *b, BcNum *restrict c, size_t scale) {
+
+	BcBigDig val = 0;
+
+	BC_UNUSED(scale);
+
+	bc_num_intop(a, b, c, &val);
+
+	if (BC_NUM_ZERO(c)) return;
+
+	bc_num_shiftRight(c, (size_t) val);
+}
+#endif // BC_ENABLE_EXTRA_MATH
+
+static void bc_num_binary(BcNum *a, BcNum *b, BcNum *c, size_t scale,
+                          BcNumBinaryOp op, size_t req)
+{
+	BcNum num2, *ptr_a, *ptr_b;
+	bool init = false;
+
+	assert(a != NULL && b != NULL && c != NULL && op != NULL);
+
+	BC_SIG_LOCK;
+
+	if (c == a) {
+
+		ptr_a = &num2;
+
+		memcpy(ptr_a, c, sizeof(BcNum));
+		init = true;
+	}
+	else ptr_a = a;
+
+	if (c == b) {
+
+		ptr_b = &num2;
+
+		if (c != a) {
+			memcpy(ptr_b, c, sizeof(BcNum));
+			init = true;
+		}
+	}
+	else ptr_b = b;
+
+	if (init) {
+
+		bc_num_init(c, req);
+
+		BC_SETJMP_LOCKED(err);
+		BC_SIG_UNLOCK;
+	}
+	else {
+		BC_SIG_UNLOCK;
+		bc_num_expand(c, req);
+	}
+
+	op(ptr_a, ptr_b, c, scale);
+
+	assert(!c->neg || BC_NUM_NONZERO(c));
+	assert(c->rdx <= c->len || !c->len);
+	assert(!c->len || c->num[c->len - 1] || c->rdx == c->len);
+
+err:
+	if (init) {
+		BC_SIG_MAYLOCK;
+		bc_num_free(&num2);
+		BC_LONGJMP_CONT;
+	}
+}
+
+#ifndef NDEBUG
+static bool bc_num_strValid(const char *val) {
+
+	bool radix = false;
+	size_t i, len = strlen(val);
+
+	if (!len) return true;
+
+	for (i = 0; i < len; ++i) {
+
+		BcDig c = val[i];
+
+		if (c == '.') {
+
+			if (radix) return false;
+
+			radix = true;
+			continue;
+		}
+
+		if (!(isdigit(c) || isupper(c))) return false;
+	}
+
+	return true;
+}
+#endif // NDEBUG
+
+static BcBigDig bc_num_parseChar(char c, size_t base_t) {
+
+	if (isupper(c)) {
+		c = BC_NUM_NUM_LETTER(c);
+		c = ((size_t) c) >= base_t ? (char) base_t - 1 : c;
+	}
+	else c -= '0';
+
+	return (BcBigDig) (uchar) c;
+}
+
+static void bc_num_parseDecimal(BcNum *restrict n, const char *restrict val) {
+
+	size_t len, i, temp, mod;
+	const char *ptr;
+	bool zero = true, rdx;
+
+	for (i = 0; val[i] == '0'; ++i);
+
+	val += i;
+	assert(!val[0] || isalnum(val[0]) || val[0] == '.');
+
+	// All 0's. We can just return, since this
+	// procedure expects a virgin (already 0) BcNum.
+	if (!val[0]) return;
+
+	len = strlen(val);
+
+	ptr = strchr(val, '.');
+	rdx = (ptr != NULL);
+
+	for (i = 0; i < len && (zero = (val[i] == '0' || val[i] == '.')); ++i);
+
+	n->scale = (size_t) (rdx * ((val + len) - (ptr + 1)));
+	n->rdx = BC_NUM_RDX(n->scale);
+
+	i = len - (ptr == val ? 0 : i) - rdx;
+	temp = BC_NUM_ROUND_POW(i);
+	mod = n->scale % BC_BASE_DIGS;
+	i = mod ? BC_BASE_DIGS - mod : 0;
+	n->len = ((temp + i) / BC_BASE_DIGS);
+
+	bc_num_expand(n, n->len);
+	memset(n->num, 0, BC_NUM_SIZE(n->len));
+
+	if (zero) n->len = n->rdx = 0;
+	else {
+
+		BcBigDig exp, pow;
+
+		assert(i <= BC_NUM_BIGDIG_MAX);
+
+		exp = (BcBigDig) i;
+		pow = bc_num_pow10[exp];
+
+		for (i = len - 1; i < len; --i, ++exp) {
+
+			char c = val[i];
+
+			if (c == '.') exp -= 1;
+			else {
+
+				size_t idx = exp / BC_BASE_DIGS;
+
+				if (isupper(c)) c = '9';
+				n->num[idx] += (((BcBigDig) c) - '0') * pow;
+
+				if ((exp + 1) % BC_BASE_DIGS == 0) pow = 1;
+				else pow *= BC_BASE;
+			}
+		}
+	}
+}
+
+static void bc_num_parseBase(BcNum *restrict n, const char *restrict val,
+                             BcBigDig base)
+{
+	BcNum temp, mult1, mult2, result1, result2, *m1, *m2, *ptr;
+	char c = 0;
+	bool zero = true;
+	BcBigDig v;
+	size_t i, digs, len = strlen(val);
+
+	for (i = 0; zero && i < len; ++i) zero = (val[i] == '.' || val[i] == '0');
+	if (zero) return;
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&temp, BC_NUM_BIGDIG_LOG10);
+	bc_num_init(&mult1, BC_NUM_BIGDIG_LOG10);
+
+	BC_SETJMP_LOCKED(int_err);
+
+	BC_SIG_UNLOCK;
+
+	for (i = 0; i < len && (c = val[i]) && c != '.'; ++i) {
+
+		v = bc_num_parseChar(c, base);
+
+		bc_num_mulArray(n, base, &mult1);
+		bc_num_bigdig2num(&temp, v);
+		bc_num_add(&mult1, &temp, n, 0);
+	}
+
+	if (i == len && !(c = val[i])) goto int_err;
+
+	assert(c == '.');
+
+	BC_SIG_LOCK;
+
+	BC_UNSETJMP;
+
+	bc_num_init(&mult2, BC_NUM_BIGDIG_LOG10);
+	bc_num_init(&result1, BC_NUM_DEF_SIZE);
+	bc_num_init(&result2, BC_NUM_DEF_SIZE);
+	bc_num_one(&mult1);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	m1 = &mult1;
+	m2 = &mult2;
+
+	for (i += 1, digs = 0; i < len && (c = val[i]); ++i, ++digs) {
+
+		v = bc_num_parseChar(c, base);
+
+		bc_num_mulArray(&result1, base, &result2);
+
+		bc_num_bigdig2num(&temp, v);
+		bc_num_add(&result2, &temp, &result1, 0);
+		bc_num_mulArray(m1, base, m2);
+
+		if (m2->len < m2->rdx) m2->len = m2->rdx;
+
+		ptr = m1;
+		m1 = m2;
+		m2 = ptr;
+	}
+
+	// This one cannot be a divide by 0 because mult starts out at 1, then is
+	// multiplied by base, and base cannot be 0, so mult cannot be 0.
+	bc_num_div(&result1, m1, &result2, digs * 2);
+	bc_num_truncate(&result2, digs);
+	bc_num_add(n, &result2, n, digs);
+
+	if (BC_NUM_NONZERO(n)) {
+		if (n->scale < digs) bc_num_extend(n, digs - n->scale);
+	}
+	else bc_num_zero(n);
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&result2);
+	bc_num_free(&result1);
+	bc_num_free(&mult2);
+int_err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&mult1);
+	bc_num_free(&temp);
+	BC_LONGJMP_CONT;
+}
+
+static void bc_num_printNewline(void) {
+	if (vm.nchars >= vm.line_len - 1) {
+		bc_vm_putchar('\\');
+		bc_vm_putchar('\n');
+	}
+}
+
+static void bc_num_putchar(int c) {
+	if (c != '\n') bc_num_printNewline();
+	bc_vm_putchar(c);
+}
+
+#if DC_ENABLED
+static void bc_num_printChar(size_t n, size_t len, bool rdx) {
+	BC_UNUSED(rdx);
+	BC_UNUSED(len);
+	assert(len == 1);
+	bc_vm_putchar((uchar) n);
+}
+#endif // DC_ENABLED
+
+static void bc_num_printDigits(size_t n, size_t len, bool rdx) {
+
+	size_t exp, pow;
+
+	bc_num_putchar(rdx ? '.' : ' ');
+
+	for (exp = 0, pow = 1; exp < len - 1; ++exp, pow *= BC_BASE);
+
+	for (exp = 0; exp < len; pow /= BC_BASE, ++exp) {
+		size_t dig = n / pow;
+		n -= dig * pow;
+		bc_num_putchar(((uchar) dig) + '0');
+	}
+}
+
+static void bc_num_printHex(size_t n, size_t len, bool rdx) {
+
+	BC_UNUSED(len);
+
+	assert(len == 1);
+
+	if (rdx) bc_num_putchar('.');
+
+	bc_num_putchar(bc_num_hex_digits[n]);
+}
+
+static void bc_num_printDecimal(const BcNum *restrict n) {
+
+	size_t i, j, rdx = n->rdx;
+	bool zero = true;
+	size_t buffer[BC_BASE_DIGS];
+
+	if (n->neg) bc_num_putchar('-');
+
+	for (i = n->len - 1; i < n->len; --i) {
+
+		BcDig n9 = n->num[i];
+		size_t temp;
+		bool irdx = (i == rdx - 1);
+
+		zero = (zero & !irdx);
+		temp = n->scale % BC_BASE_DIGS;
+		temp = i || !temp ? 0 : BC_BASE_DIGS - temp;
+
+		memset(buffer, 0, BC_BASE_DIGS * sizeof(size_t));
+
+		for (j = 0; n9 && j < BC_BASE_DIGS; ++j) {
+			buffer[j] = n9 % BC_BASE;
+			n9 /= BC_BASE;
+		}
+
+		for (j = BC_BASE_DIGS - 1; j < BC_BASE_DIGS && j >= temp; --j) {
+			bool print_rdx = (irdx & (j == BC_BASE_DIGS - 1));
+			zero = (zero && buffer[j] == 0);
+			if (!zero) bc_num_printHex(buffer[j], 1, print_rdx);
+		}
+	}
+}
+
+#if BC_ENABLE_EXTRA_MATH
+static void bc_num_printExponent(const BcNum *restrict n, bool eng) {
+
+	bool neg = (n->len <= n->rdx);
+	BcNum temp, exp;
+	size_t places, mod;
+	BcDig digs[BC_NUM_BIGDIG_LOG10];
+
+	BC_SIG_LOCK;
+
+	bc_num_createCopy(&temp, n);
+
+	BC_SETJMP_LOCKED(exit);
+
+	BC_SIG_UNLOCK;
+
+	if (neg) {
+
+		size_t i, idx = bc_num_nonzeroLen(n) - 1;
+
+		places = 1;
+
+		for (i = BC_BASE_DIGS - 1; i < BC_BASE_DIGS; --i) {
+			if (bc_num_pow10[i] > (BcBigDig) n->num[idx]) places += 1;
+			else break;
+		}
+
+		places += (n->rdx - (idx + 1)) * BC_BASE_DIGS;
+		mod = places % 3;
+
+		if (eng && mod != 0) places += 3 - mod;
+		bc_num_shiftLeft(&temp, places);
+	}
+	else {
+		places = bc_num_intDigits(n) - 1;
+		mod = places % 3;
+		if (eng && mod != 0) places -= 3 - (3 - mod);
+		bc_num_shiftRight(&temp, places);
+	}
+
+	bc_num_printDecimal(&temp);
+	bc_num_putchar('e');
+
+	if (!places) {
+		bc_num_printHex(0, 1, false);
+		goto exit;
+	}
+
+	if (neg) bc_num_putchar('-');
+
+	bc_num_setup(&exp, digs, BC_NUM_BIGDIG_LOG10);
+	bc_num_bigdig2num(&exp, (BcBigDig) places);
+
+	bc_num_printDecimal(&exp);
+
+exit:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&temp);
+	BC_LONGJMP_CONT;
+}
+#endif // BC_ENABLE_EXTRA_MATH
+
+static void bc_num_printFixup(BcNum *restrict n, BcBigDig rem,
+                              BcBigDig pow, size_t idx)
+{
+	size_t i, len = n->len - idx;
+	BcBigDig acc;
+	BcDig *a = n->num + idx;
+
+	if (len < 2) return;
+
+	for (i = len - 1; i > 0; --i) {
+
+		acc = ((BcBigDig) a[i]) * rem + ((BcBigDig) a[i - 1]);
+		a[i - 1] = (BcDig) (acc % pow);
+		acc /= pow;
+		acc += (BcBigDig) a[i];
+
+		if (acc >= BC_BASE_POW) {
+
+			if (i == len - 1) {
+				len = bc_vm_growSize(len, 1);
+				bc_num_expand(n, bc_vm_growSize(len, idx));
+				a = n->num + idx;
+				a[len - 1] = 0;
+			}
+
+			a[i + 1] += acc / BC_BASE_POW;
+			acc %= BC_BASE_POW;
+		}
+
+		assert(acc < BC_BASE_POW);
+		a[i] = (BcDig) acc;
+	}
+
+	n->len = len + idx;
+}
+
+static void bc_num_printPrepare(BcNum *restrict n, BcBigDig rem,
+                                BcBigDig pow)
+{
+	size_t i;
+
+	for (i = 0; i < n->len; ++i) bc_num_printFixup(n, rem, pow, i);
+
+	for (i = 0; i < n->len; ++i) {
+
+		assert(pow == ((BcBigDig) ((BcDig) pow)));
+
+		if (n->num[i] >= (BcDig) pow) {
+
+			if (i + 1 == n->len) {
+				n->len = bc_vm_growSize(n->len, 1);
+				bc_num_expand(n, n->len);
+				n->num[i + 1] = 0;
+			}
+
+			assert(pow < BC_BASE_POW);
+			n->num[i + 1] += n->num[i] / ((BcDig) pow);
+			n->num[i] %= (BcDig) pow;
+		}
+	}
+}
+
+static void bc_num_printNum(BcNum *restrict n, BcBigDig base,
+                            size_t len, BcNumDigitOp print)
+{
+	BcVec stack;
+	BcNum intp, fracp1, fracp2, digit, flen1, flen2, *n1, *n2, *temp;
+	BcBigDig dig = 0, *ptr, acc, exp;
+	size_t i, j;
+	bool radix;
+	BcDig digit_digs[BC_NUM_BIGDIG_LOG10 + 1];
+
+	assert(base > 1);
+
+	if (BC_NUM_ZERO(n)) {
+		print(0, len, false);
+		return;
+	}
+
+	// This function uses an algorithm that Stefan Esser <se@freebsd.org> came
+	// up with to print the integer part of a number. What it does is convert
+	// intp into a number of the specified base, but it does it directly,
+	// instead of just doing a series of divisions and printing the remainders
+	// in reverse order.
+	//
+	// Let me explain in a bit more detail:
+	//
+	// The algorithm takes the current least significant digit (after intp has
+	// been converted to an integer) and the next to least significant digit,
+	// and it converts the least significant digit into one of the specified
+	// base, putting any overflow into the next to least significant digit. It
+	// iterates through the whole number, from least significant to most
+	// significant, doing this conversion. At the end of that iteration, the
+	// least significant digit is converted, but the others are not, so it
+	// iterates again, starting at the next to least significant digit. It keeps
+	// doing that conversion, skipping one more digit than the last time, until
+	// all digits have been converted. Then it prints them in reverse order.
+	//
+	// That is the gist of the algorithm. It leaves out several things, such as
+	// the fact that digits are not always converted into the specified base,
+	// but into something close, basically a power of the specified base. In
+	// Stefan's words, "You could consider BcDigs to be of base 10^BC_BASE_DIGS
+	// in the normal case and obase^N for the largest value of N that satisfies
+	// obase^N <= 10^BC_BASE_DIGS. [This means that] the result is not in base
+	// "obase", but in base "obase^N", which happens to be printable as a number
+	// of base "obase" without consideration for neighbouring BcDigs." This fact
+	// is what necessitates the existence of the loop later in this function.
+	//
+	// The conversion happens in bc_num_printPrepare() where the outer loop
+	// happens and bc_num_printFixup() where the inner loop, or actual
+	// conversion, happens.
+
+	BC_SIG_LOCK;
+
+	bc_vec_init(&stack, sizeof(BcBigDig), NULL);
+	bc_num_init(&fracp1, n->rdx);
+
+	bc_num_createCopy(&intp, n);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_truncate(&intp, intp.scale);
+
+	bc_num_sub(n, &intp, &fracp1, 0);
+
+	if (base != vm.last_base) {
+
+		vm.last_pow = 1;
+		vm.last_exp = 0;
+
+		while (vm.last_pow * base <= BC_BASE_POW) {
+			vm.last_pow *= base;
+			vm.last_exp += 1;
+		}
+
+		vm.last_rem = BC_BASE_POW - vm.last_pow;
+		vm.last_base = base;
+	}
+
+	exp = vm.last_exp;
+
+	if (vm.last_rem != 0) bc_num_printPrepare(&intp, vm.last_rem, vm.last_pow);
+
+	for (i = 0; i < intp.len; ++i) {
+
+		acc = (BcBigDig) intp.num[i];
+
+		for (j = 0; j < exp && (i < intp.len - 1 || acc != 0); ++j)
+		{
+			if (j != exp - 1) {
+				dig = acc % base;
+				acc /= base;
+			}
+			else {
+				dig = acc;
+				acc = 0;
+			}
+
+			assert(dig < base);
+
+			bc_vec_push(&stack, &dig);
+		}
+
+		assert(acc == 0);
+	}
+
+	for (i = 0; i < stack.len; ++i) {
+		ptr = bc_vec_item_rev(&stack, i);
+		assert(ptr != NULL);
+		print(*ptr, len, false);
+	}
+
+	if (!n->scale) goto err;
+
+	BC_SIG_LOCK;
+
+	BC_UNSETJMP;
+
+	bc_num_init(&fracp2, n->rdx);
+	bc_num_setup(&digit, digit_digs, sizeof(digit_digs) / sizeof(BcDig));
+	bc_num_init(&flen1, BC_NUM_BIGDIG_LOG10);
+	bc_num_init(&flen2, BC_NUM_BIGDIG_LOG10);
+
+	BC_SETJMP_LOCKED(frac_err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_one(&flen1);
+
+	radix = true;
+	n1 = &flen1;
+	n2 = &flen2;
+
+	fracp2.scale = n->scale;
+	fracp2.rdx = BC_NUM_RDX(fracp2.scale);
+
+	while (bc_num_intDigits(n1) < n->scale + 1) {
+
+		bc_num_expand(&fracp2, fracp1.len + 1);
+		bc_num_mulArray(&fracp1, base, &fracp2);
+		if (fracp2.len < fracp2.rdx) fracp2.len = fracp2.rdx;
+
+		// fracp is guaranteed to be non-negative and small enough.
+		bc_num_bigdig2(&fracp2, &dig);
+
+		bc_num_bigdig2num(&digit, dig);
+		bc_num_sub(&fracp2, &digit, &fracp1, 0);
+
+		print(dig, len, radix);
+		bc_num_mulArray(n1, base, n2);
+
+		radix = false;
+		temp = n1;
+		n1 = n2;
+		n2 = temp;
+	}
+
+frac_err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&flen2);
+	bc_num_free(&flen1);
+	bc_num_free(&fracp2);
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&fracp1);
+	bc_num_free(&intp);
+	bc_vec_free(&stack);
+	BC_LONGJMP_CONT;
+}
+
+static void bc_num_printBase(BcNum *restrict n, BcBigDig base) {
+
+	size_t width;
+	BcNumDigitOp print;
+	bool neg = n->neg;
+
+	if (neg) bc_num_putchar('-');
+
+	n->neg = false;
+
+	if (base <= BC_NUM_MAX_POSIX_IBASE) {
+		width = 1;
+		print = bc_num_printHex;
+	}
+	else {
+		assert(base <= BC_BASE_POW);
+		width = bc_num_log10(base - 1);
+		print = bc_num_printDigits;
+	}
+
+	bc_num_printNum(n, base, width, print);
+	n->neg = neg;
+}
+
+#if DC_ENABLED
+void bc_num_stream(BcNum *restrict n, BcBigDig base) {
+	bc_num_printNum(n, base, 1, bc_num_printChar);
+}
+#endif // DC_ENABLED
+
+void bc_num_setup(BcNum *restrict n, BcDig *restrict num, size_t cap) {
+	assert(n != NULL);
+	n->num = num;
+	n->cap = cap;
+	bc_num_zero(n);
+}
+
+void bc_num_init(BcNum *restrict n, size_t req) {
+
+	BcDig *num;
+
+	BC_SIG_ASSERT_LOCKED;
+
+	assert(n != NULL);
+
+	req = req >= BC_NUM_DEF_SIZE ? req : BC_NUM_DEF_SIZE;
+
+	if (req == BC_NUM_DEF_SIZE && vm.temps.len) {
+		BcNum *nptr = bc_vec_top(&vm.temps);
+		num = nptr->num;
+		req = nptr->cap;
+		bc_vec_pop(&vm.temps);
+	}
+	else num = bc_vm_malloc(BC_NUM_SIZE(req));
+
+	bc_num_setup(n, num, req);
+}
+
+void bc_num_clear(BcNum *restrict n) {
+	n->num = NULL;
+	n->cap = 0;
+}
+
+void bc_num_free(void *num) {
+
+	BcNum *n = (BcNum*) num;
+
+	BC_SIG_ASSERT_LOCKED;
+
+	assert(n != NULL);
+
+	if (n->cap == BC_NUM_DEF_SIZE) bc_vec_push(&vm.temps, n);
+	else free(n->num);
+}
+
+void bc_num_copy(BcNum *d, const BcNum *s) {
+	assert(d != NULL && s != NULL);
+	if (d == s) return;
+	bc_num_expand(d, s->len);
+	d->len = s->len;
+	d->neg = s->neg;
+	d->rdx = s->rdx;
+	d->scale = s->scale;
+	memcpy(d->num, s->num, BC_NUM_SIZE(d->len));
+}
+
+void bc_num_createCopy(BcNum *d, const BcNum *s) {
+	BC_SIG_ASSERT_LOCKED;
+	bc_num_init(d, s->len);
+	bc_num_copy(d, s);
+}
+
+void bc_num_createFromBigdig(BcNum *n, BcBigDig val) {
+	BC_SIG_ASSERT_LOCKED;
+	bc_num_init(n, (BC_NUM_BIGDIG_LOG10 - 1) / BC_BASE_DIGS + 1);
+	bc_num_bigdig2num(n, val);
+}
+
+size_t bc_num_scale(const BcNum *restrict n) {
+	return n->scale;
+}
+
+size_t bc_num_len(const BcNum *restrict n) {
+
+	size_t len = n->len;
+
+	if (BC_NUM_ZERO(n)) return 0;
+
+	if (n->rdx == len) {
+
+		size_t zero, scale;
+
+		len = bc_num_nonzeroLen(n);
+
+		scale = n->scale % BC_BASE_DIGS;
+		scale = scale ? scale : BC_BASE_DIGS;
+
+		zero = bc_num_zeroDigits(n->num + len - 1);
+
+		len = len * BC_BASE_DIGS - zero - (BC_BASE_DIGS - scale);
+	}
+	else len = bc_num_intDigits(n) + n->scale;
+
+	return len;
+}
+
+void bc_num_parse(BcNum *restrict n, const char *restrict val,
+                  BcBigDig base, bool letter)
+{
+	assert(n != NULL && val != NULL && base);
+	assert(base >= BC_NUM_MIN_BASE && base <= vm.maxes[BC_PROG_GLOBALS_IBASE]);
+	assert(bc_num_strValid(val));
+
+	if (letter) {
+		BcBigDig dig = bc_num_parseChar(val[0], BC_NUM_MAX_LBASE);
+		bc_num_bigdig2num(n, dig);
+	}
+	else if (base == BC_BASE) bc_num_parseDecimal(n, val);
+	else bc_num_parseBase(n, val, base);
+}
+
+void bc_num_print(BcNum *restrict n, BcBigDig base, bool newline) {
+
+	assert(n != NULL);
+	assert(BC_ENABLE_EXTRA_MATH || base >= BC_NUM_MIN_BASE);
+
+	bc_num_printNewline();
+
+	if (BC_NUM_ZERO(n)) bc_num_printHex(0, 1, false);
+	else if (base == BC_BASE) bc_num_printDecimal(n);
+#if BC_ENABLE_EXTRA_MATH
+	else if (base == 0 || base == 1)
+		bc_num_printExponent(n, base != 0);
+#endif // BC_ENABLE_EXTRA_MATH
+	else bc_num_printBase(n, base);
+
+	if (newline) bc_num_putchar('\n');
+}
+
+void bc_num_bigdig2(const BcNum *restrict n, BcBigDig *result) {
+
+	// This function returns no errors because it's guaranteed to succeed if
+	// its preconditions are met. Those preconditions include both parameters
+	// being non-NULL, n being non-negative, and n being less than vm.max. If
+	// all of that is true, then we can just convert without worrying about
+	// negative errors or overflow. We also don't care about signals because
+	// this function should execute in only a few iterations, meaning that
+	// ignoring signals here should be fine.
+
+	BcBigDig r = 0;
+
+	assert(n != NULL && result != NULL);
+	assert(!n->neg);
+	assert(bc_num_cmp(n, &vm.max) < 0);
+	assert(n->len - n->rdx <= 3);
+
+	// There is a small speed win from unrolling the loop here, and since it
+	// only adds 53 bytes, I decided that it was worth it.
+	switch (n->len - n->rdx) {
+		case 3:
+			r = (BcBigDig) n->num[n->rdx + 2];
+			// Fallthrough.
+		case 2:
+			r = r * BC_BASE_POW + (BcBigDig) n->num[n->rdx + 1];
+			// Fallthrough.
+		case 1:
+			r = r * BC_BASE_POW + (BcBigDig) n->num[n->rdx];
+	}
+
+	*result = r;
+}
+
+void bc_num_bigdig(const BcNum *restrict n, BcBigDig *result) {
+
+	assert(n != NULL && result != NULL);
+
+	if (BC_ERR(n->neg)) bc_vm_err(BC_ERROR_MATH_NEGATIVE);
+	if (BC_ERR(bc_num_cmp(n, &vm.max) >= 0))
+		bc_vm_err(BC_ERROR_MATH_OVERFLOW);
+
+	bc_num_bigdig2(n, result);
+}
+
+void bc_num_bigdig2num(BcNum *restrict n, BcBigDig val) {
+
+	BcDig *ptr;
+	size_t i;
+
+	assert(n != NULL);
+
+	bc_num_zero(n);
+
+	if (!val) return;
+
+	bc_num_expand(n, BC_NUM_BIGDIG_LOG10);
+
+	for (ptr = n->num, i = 0; val; ++i, val /= BC_BASE_POW)
+		ptr[i] = val % BC_BASE_POW;
+
+	n->len = i;
+}
+
+#if BC_ENABLE_EXTRA_MATH
+void bc_num_rng(const BcNum *restrict n, BcRNG *rng) {
+
+	BcNum pow, temp, temp2, intn, frac;
+	BcRand state1, state2, inc1, inc2;
+	BcDig pow_num[BC_RAND_NUM_SIZE];
+
+	bc_num_setup(&pow, pow_num, sizeof(pow_num) / sizeof(BcDig));
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&temp, n->len);
+	bc_num_init(&temp2, n->len);
+	bc_num_init(&frac, n->rdx);
+	bc_num_init(&intn, bc_num_int(n));
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_mul(&vm.max, &vm.max, &pow, 0);
+
+	memcpy(frac.num, n->num, BC_NUM_SIZE(n->rdx));
+	frac.len = n->rdx;
+	frac.rdx = n->rdx;
+	frac.scale = n->scale;
+
+	bc_num_mul(&frac, &pow, &temp, 0);
+
+	bc_num_truncate(&temp, temp.scale);
+	bc_num_copy(&frac, &temp);
+
+	memcpy(intn.num, n->num + n->rdx, BC_NUM_SIZE(bc_num_int(n)));
+	intn.len = bc_num_int(n);
+
+	// This assert is here because it has to be true. It is also here to justify
+	// the use of BC_ERROR_SIGNAL_ONLY() on each of the divmod's and mod's
+	// below.
+	assert(BC_NUM_NONZERO(&vm.max));
+
+	if (BC_NUM_NONZERO(&frac)) {
+
+		bc_num_divmod(&frac, &vm.max, &temp, &temp2, 0);
+
+		// frac is guaranteed to be smaller than vm.max * vm.max (pow).
+		// This means that when dividing frac by vm.max, as above, the
+		// quotient and remainder are both guaranteed to be less than vm.max,
+		// which means we can use bc_num_bigdig2() here and not worry about
+		// overflow.
+		bc_num_bigdig2(&temp2, (BcBigDig*) &state1);
+		bc_num_bigdig2(&temp, (BcBigDig*) &state2);
+	}
+	else state1 = state2 = 0;
+
+	if (BC_NUM_NONZERO(&intn)) {
+
+		bc_num_divmod(&intn, &vm.max, &temp, &temp2, 0);
+
+		// Because temp2 is the mod of vm.max, from above, it is guaranteed
+		// to be small enough to use bc_num_bigdig2().
+		bc_num_bigdig2(&temp2, (BcBigDig*) &inc1);
+
+		if (bc_num_cmp(&temp, &vm.max) >= 0) {
+			bc_num_copy(&temp2, &temp);
+			bc_num_mod(&temp2, &vm.max, &temp, 0);
+		}
+
+		// The if statement above ensures that temp is less than vm.max, which
+		// means that we can use bc_num_bigdig2() here.
+		bc_num_bigdig2(&temp, (BcBigDig*) &inc2);
+	}
+	else inc1 = inc2 = 0;
+
+	bc_rand_seed(rng, state1, state2, inc1, inc2);
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&intn);
+	bc_num_free(&frac);
+	bc_num_free(&temp2);
+	bc_num_free(&temp);
+	BC_LONGJMP_CONT;
+}
+
+void bc_num_createFromRNG(BcNum *restrict n, BcRNG *rng) {
+
+	BcRand s1, s2, i1, i2;
+	BcNum pow, conv, temp1, temp2, temp3;
+	BcDig pow_num[BC_RAND_NUM_SIZE];
+	BcDig temp1_num[BC_RAND_NUM_SIZE], temp2_num[BC_RAND_NUM_SIZE];
+	BcDig conv_num[BC_NUM_BIGDIG_LOG10];
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&temp3, 2 * BC_RAND_NUM_SIZE);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_setup(&pow, pow_num, sizeof(pow_num) / sizeof(BcDig));
+	bc_num_setup(&temp1, temp1_num, sizeof(temp1_num) / sizeof(BcDig));
+	bc_num_setup(&temp2, temp2_num, sizeof(temp2_num) / sizeof(BcDig));
+	bc_num_setup(&conv, conv_num, sizeof(conv_num) / sizeof(BcDig));
+
+	// This assert is here because it has to be true. It is also here to justify
+	// the assumption that pow is not zero.
+	assert(BC_NUM_NONZERO(&vm.max));
+
+	bc_num_mul(&vm.max, &vm.max, &pow, 0);
+
+	// Because this is true, we can just use BC_ERROR_SIGNAL_ONLY() below when
+	// dividing by pow.
+	assert(BC_NUM_NONZERO(&pow));
+
+	bc_rand_getRands(rng, &s1, &s2, &i1, &i2);
+
+	bc_num_bigdig2num(&conv, (BcBigDig) s2);
+
+	bc_num_mul(&conv, &vm.max, &temp1, 0);
+
+	bc_num_bigdig2num(&conv, (BcBigDig) s1);
+
+	bc_num_add(&conv, &temp1, &temp2, 0);
+
+	bc_num_div(&temp2, &pow, &temp3, BC_RAND_STATE_BITS);
+
+	bc_num_bigdig2num(&conv, (BcBigDig) i2);
+
+	bc_num_mul(&conv, &vm.max, &temp1, 0);
+
+	bc_num_bigdig2num(&conv, (BcBigDig) i1);
+
+	bc_num_add(&conv, &temp1, &temp2, 0);
+
+	bc_num_add(&temp2, &temp3, n, 0);
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&temp3);
+	BC_LONGJMP_CONT;
+}
+
+void bc_num_irand(const BcNum *restrict a, BcNum *restrict b,
+                  BcRNG *restrict rng)
+{
+	BcRand r;
+	BcBigDig modl;
+	BcNum pow, pow2, cp, cp2, mod, temp1, temp2, rand;
+	BcNum *p1, *p2, *t1, *t2, *c1, *c2, *tmp;
+	BcDig rand_num[BC_NUM_BIGDIG_LOG10];
+	bool carry;
+	ssize_t cmp;
+
+	assert(a != b);
+
+	if (BC_ERR(a->neg)) bc_vm_err(BC_ERROR_MATH_NEGATIVE);
+	if (BC_ERR(a->rdx)) bc_vm_err(BC_ERROR_MATH_NON_INTEGER);
+	if (BC_NUM_ZERO(a) || BC_NUM_ONE(a)) return;
+
+	cmp = bc_num_cmp(a, &vm.max);
+
+	if (cmp <= 0) {
+
+		BcRand bits = 0;
+
+		if (cmp < 0) bc_num_bigdig2(a, (BcBigDig*) &bits);
+
+		// This condition means that bits is a power of 2. In that case, we
+		// can just grab a full-size int and mask out the unneeded bits.
+		// Also, this condition says that 0 is a power of 2, which works for
+		// us, since a value of 0 means a == rng->max. The bitmask will mask
+		// nothing in that case as well.
+		if (!(bits & (bits - 1))) r = bc_rand_int(rng) & (bits - 1);
+		else r = bc_rand_bounded(rng, bits);
+
+		// We made sure that r is less than vm.max,
+		// so we can use bc_num_bigdig2() here.
+		bc_num_bigdig2num(b, r);
+
+		return;
+	}
+
+	// In the case where a is less than rng->max, we have to make sure we have
+	// an exclusive bound. This ensures that it happens. (See below.)
+	carry = (cmp < 0);
+
+	BC_SIG_LOCK;
+
+	bc_num_createCopy(&cp, a);
+
+	bc_num_init(&cp2, cp.len);
+	bc_num_init(&mod, BC_NUM_BIGDIG_LOG10);
+	bc_num_init(&temp1, BC_NUM_DEF_SIZE);
+	bc_num_init(&temp2, BC_NUM_DEF_SIZE);
+	bc_num_init(&pow2, BC_NUM_DEF_SIZE);
+	bc_num_init(&pow, BC_NUM_DEF_SIZE);
+	bc_num_one(&pow);
+	bc_num_setup(&rand, rand_num, sizeof(rand_num) / sizeof(BcDig));
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	p1 = &pow;
+	p2 = &pow2;
+	t1 = &temp1;
+	t2 = &temp2;
+	c1 = &cp;
+	c2 = &cp2;
+
+	// This assert is here because it has to be true. It is also here to justify
+	// the use of BC_ERROR_SIGNAL_ONLY() on each of the divmod's and mod's
+	// below.
+	assert(BC_NUM_NONZERO(&vm.max));
+
+	while (BC_NUM_NONZERO(c1)) {
+
+		bc_num_divmod(c1, &vm.max, c2, &mod, 0);
+
+		// Because mod is the mod of vm.max, it is guaranteed to be smaller,
+		// which means we can use bc_num_bigdig2() here.
+		bc_num_bigdig(&mod, &modl);
+
+		if (bc_num_cmp(c1, &vm.max) < 0) {
+
+			// In this case, if there is no carry, then we know we can generate
+			// an integer *equal* to modl. Thus, we add one if there is no
+			// carry. Otherwise, we add zero, and we are still bounded properly.
+			// Since the last portion is guaranteed to be greater than 1, we
+			// know modl isn't 0 unless there is no carry.
+			modl += !carry;
+
+			if (modl == 1) r = 0;
+			else if (!modl) r = bc_rand_int(rng);
+			else r = bc_rand_bounded(rng, (BcRand) modl);
+		}
+		else {
+			if (modl) modl -= carry;
+			r = bc_rand_int(rng);
+			carry = (r >= (BcRand) modl);
+		}
+
+		bc_num_bigdig2num(&rand, r);
+
+		bc_num_mul(&rand, p1, p2, 0);
+		bc_num_add(p2, t1, t2, 0);
+
+		if (BC_NUM_NONZERO(c2)) {
+
+			bc_num_mul(&vm.max, p1, p2, 0);
+
+			tmp = p1;
+			p1 = p2;
+			p2 = tmp;
+
+			tmp = c1;
+			c1 = c2;
+			c2 = tmp;
+		}
+		else c1 = c2;
+
+		tmp = t1;
+		t1 = t2;
+		t2 = tmp;
+	}
+
+	bc_num_copy(b, t1);
+	bc_num_clean(b);
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&pow);
+	bc_num_free(&pow2);
+	bc_num_free(&temp2);
+	bc_num_free(&temp1);
+	bc_num_free(&mod);
+	bc_num_free(&cp2);
+	bc_num_free(&cp);
+	BC_LONGJMP_CONT;
+}
+#endif // BC_ENABLE_EXTRA_MATH
+
+size_t bc_num_addReq(const BcNum *a, const BcNum *b, size_t scale) {
+
+	size_t aint, bint, ardx, brdx;
+
+	BC_UNUSED(scale);
+
+	ardx = a->rdx;
+	aint = bc_num_int(a);
+	assert(aint <= a->len && ardx <= a->len);
+
+	brdx = b->rdx;
+	bint = bc_num_int(b);
+	assert(bint <= b->len && brdx <= b->len);
+
+	ardx = BC_MAX(ardx, brdx);
+	aint = BC_MAX(aint, bint);
+
+	return bc_vm_growSize(bc_vm_growSize(ardx, aint), 1);
+}
+
+size_t bc_num_mulReq(const BcNum *a, const BcNum *b, size_t scale) {
+	size_t max, rdx;
+	rdx = bc_vm_growSize(a->rdx, b->rdx);
+	max = BC_NUM_RDX(scale);
+	max = bc_vm_growSize(BC_MAX(max, rdx), 1);
+	rdx = bc_vm_growSize(bc_vm_growSize(bc_num_int(a), bc_num_int(b)), max);
+	return rdx;
+}
+
+size_t bc_num_powReq(const BcNum *a, const BcNum *b, size_t scale) {
+	BC_UNUSED(scale);
+	return bc_vm_growSize(bc_vm_growSize(a->len, b->len), 1);
+}
+
+#if BC_ENABLE_EXTRA_MATH
+size_t bc_num_placesReq(const BcNum *a, const BcNum *b, size_t scale) {
+	BC_UNUSED(scale);
+	return a->len + b->len - a->rdx - b->rdx;
+}
+#endif // BC_ENABLE_EXTRA_MATH
+
+void bc_num_add(BcNum *a, BcNum *b, BcNum *c, size_t scale) {
+	bc_num_binary(a, b, c, false, bc_num_as, bc_num_addReq(a, b, scale));
+}
+
+void bc_num_sub(BcNum *a, BcNum *b, BcNum *c, size_t scale) {
+	bc_num_binary(a, b, c, true, bc_num_as, bc_num_addReq(a, b, scale));
+}
+
+void bc_num_mul(BcNum *a, BcNum *b, BcNum *c, size_t scale) {
+	bc_num_binary(a, b, c, scale, bc_num_m, bc_num_mulReq(a, b, scale));
+}
+
+void bc_num_div(BcNum *a, BcNum *b, BcNum *c, size_t scale) {
+	bc_num_binary(a, b, c, scale, bc_num_d, bc_num_mulReq(a, b, scale));
+}
+
+void bc_num_mod(BcNum *a, BcNum *b, BcNum *c, size_t scale) {
+	bc_num_binary(a, b, c, scale, bc_num_rem, bc_num_mulReq(a, b, scale));
+}
+
+void bc_num_pow(BcNum *a, BcNum *b, BcNum *c, size_t scale) {
+	bc_num_binary(a, b, c, scale, bc_num_p, bc_num_powReq(a, b, scale));
+}
+
+#if BC_ENABLE_EXTRA_MATH
+void bc_num_places(BcNum *a, BcNum *b, BcNum *c, size_t scale) {
+	bc_num_binary(a, b, c, scale, bc_num_place, bc_num_placesReq(a, b, scale));
+}
+
+void bc_num_lshift(BcNum *a, BcNum *b, BcNum *c, size_t scale) {
+	bc_num_binary(a, b, c, scale, bc_num_left, bc_num_placesReq(a, b, scale));
+}
+
+void bc_num_rshift(BcNum *a, BcNum *b, BcNum *c, size_t scale) {
+	bc_num_binary(a, b, c, scale, bc_num_right, bc_num_placesReq(a, b, scale));
+}
+#endif // BC_ENABLE_EXTRA_MATH
+
+void bc_num_sqrt(BcNum *restrict a, BcNum *restrict b, size_t scale) {
+
+	BcNum num1, num2, half, f, fprime, *x0, *x1, *temp;
+	size_t pow, len, rdx, req, digs, digs1, digs2, resscale;
+	BcDig half_digs[1];
+
+	assert(a != NULL && b != NULL && a != b);
+
+	if (BC_ERR(a->neg)) bc_vm_err(BC_ERROR_MATH_NEGATIVE);
+
+	if (a->scale > scale) scale = a->scale;
+
+	len = bc_vm_growSize(bc_num_intDigits(a), 1);
+	rdx = BC_NUM_RDX(scale);
+	req = bc_vm_growSize(BC_MAX(rdx, a->rdx), len >> 1);
+
+	BC_SIG_LOCK;
+
+	bc_num_init(b, bc_vm_growSize(req, 1));
+
+	BC_SIG_UNLOCK;
+
+	if (BC_NUM_ZERO(a)) {
+		bc_num_setToZero(b, scale);
+		return;
+	}
+	if (BC_NUM_ONE(a)) {
+		bc_num_one(b);
+		bc_num_extend(b, scale);
+		return;
+	}
+
+	rdx = BC_NUM_RDX(scale);
+	rdx = BC_MAX(rdx, a->rdx);
+	len = bc_vm_growSize(a->len, rdx);
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&num1, len);
+	bc_num_init(&num2, len);
+	bc_num_setup(&half, half_digs, sizeof(half_digs) / sizeof(BcDig));
+
+	bc_num_one(&half);
+	half.num[0] = BC_BASE_POW / 2;
+	half.len = 1;
+	half.rdx = 1;
+	half.scale = 1;
+
+	bc_num_init(&f, len);
+	bc_num_init(&fprime, len);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	x0 = &num1;
+	x1 = &num2;
+
+	bc_num_one(x0);
+	pow = bc_num_intDigits(a);
+
+	if (pow) {
+
+		if (pow & 1) x0->num[0] = 2;
+		else x0->num[0] = 6;
+
+		pow -= 2 - (pow & 1);
+		bc_num_shiftLeft(x0, pow / 2);
+	}
+
+	x0->scale = x0->rdx = digs = digs1 = digs2 = 0;
+	resscale = (scale + BC_BASE_DIGS) + 2;
+
+	while (bc_num_cmp(x1, x0)) {
+
+		assert(BC_NUM_NONZERO(x0));
+
+		bc_num_div(a, x0, &f, resscale);
+		bc_num_add(x0, &f, &fprime, resscale);
+		bc_num_mul(&fprime, &half, x1, resscale);
+
+		temp = x0;
+		x0 = x1;
+		x1 = temp;
+	}
+
+	bc_num_copy(b, x0);
+	if (b->scale > scale) bc_num_truncate(b, b->scale - scale);
+
+	assert(!b->neg || BC_NUM_NONZERO(b));
+	assert(b->rdx <= b->len || !b->len);
+	assert(!b->len || b->num[b->len - 1] || b->rdx == b->len);
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&fprime);
+	bc_num_free(&f);
+	bc_num_free(&num2);
+	bc_num_free(&num1);
+	BC_LONGJMP_CONT;
+}
+
+void bc_num_divmod(BcNum *a, BcNum *b, BcNum *c, BcNum *d, size_t scale) {
+
+	BcNum num2, *ptr_a;
+	bool init = false;
+	size_t ts, len;
+
+	ts = BC_MAX(scale + b->scale, a->scale);
+	len = bc_num_mulReq(a, b, ts);
+
+	assert(a != NULL && b != NULL && c != NULL && d != NULL);
+	assert(c != d && a != d && b != d && b != c);
+
+	if (c == a) {
+
+		memcpy(&num2, c, sizeof(BcNum));
+		ptr_a = &num2;
+
+		BC_SIG_LOCK;
+
+		bc_num_init(c, len);
+
+		init = true;
+
+		BC_SETJMP_LOCKED(err);
+
+		BC_SIG_UNLOCK;
+	}
+	else {
+		ptr_a = a;
+		bc_num_expand(c, len);
+	}
+
+	if (BC_NUM_NONZERO(a) && !a->rdx && !b->rdx && b->len == 1 && !scale) {
+
+		BcBigDig rem;
+
+		bc_num_divArray(ptr_a, (BcBigDig) b->num[0], c, &rem);
+
+		assert(rem < BC_BASE_POW);
+
+		d->num[0] = (BcDig) rem;
+		d->len = (rem != 0);
+	}
+	else bc_num_r(ptr_a, b, c, d, scale, ts);
+
+	assert(!c->neg || BC_NUM_NONZERO(c));
+	assert(c->rdx <= c->len || !c->len);
+	assert(!c->len || c->num[c->len - 1] || c->rdx == c->len);
+	assert(!d->neg || BC_NUM_NONZERO(d));
+	assert(d->rdx <= d->len || !d->len);
+	assert(!d->len || d->num[d->len - 1] || d->rdx == d->len);
+
+err:
+	if (init) {
+		BC_SIG_MAYLOCK;
+		bc_num_free(&num2);
+		BC_LONGJMP_CONT;
+	}
+}
+
+#if DC_ENABLED
+void bc_num_modexp(BcNum *a, BcNum *b, BcNum *c, BcNum *restrict d) {
+
+	BcNum base, exp, two, temp;
+	BcDig two_digs[2];
+
+	assert(a != NULL && b != NULL && c != NULL && d != NULL);
+	assert(a != d && b != d && c != d);
+
+	if (BC_ERR(BC_NUM_ZERO(c))) bc_vm_err(BC_ERROR_MATH_DIVIDE_BY_ZERO);
+	if (BC_ERR(b->neg)) bc_vm_err(BC_ERROR_MATH_NEGATIVE);
+	if (BC_ERR(a->rdx || b->rdx || c->rdx))
+		bc_vm_err(BC_ERROR_MATH_NON_INTEGER);
+
+	bc_num_expand(d, c->len);
+
+	BC_SIG_LOCK;
+
+	bc_num_init(&base, c->len);
+	bc_num_setup(&two, two_digs, sizeof(two_digs) / sizeof(BcDig));
+	bc_num_init(&temp, b->len + 1);
+	bc_num_createCopy(&exp, b);
+
+	BC_SETJMP_LOCKED(err);
+
+	BC_SIG_UNLOCK;
+
+	bc_num_one(&two);
+	two.num[0] = 2;
+	bc_num_one(d);
+
+	// We already checked for 0.
+	bc_num_rem(a, c, &base, 0);
+
+	while (BC_NUM_NONZERO(&exp)) {
+
+		// Num two cannot be 0, so no errors.
+		bc_num_divmod(&exp, &two, &exp, &temp, 0);
+
+		if (BC_NUM_ONE(&temp) && !temp.neg) {
+
+			bc_num_mul(d, &base, &temp, 0);
+
+			// We already checked for 0.
+			bc_num_rem(&temp, c, d, 0);
+		}
+
+		bc_num_mul(&base, &base, &temp, 0);
+
+		// We already checked for 0.
+		bc_num_rem(&temp, c, &base, 0);
+	}
+
+err:
+	BC_SIG_MAYLOCK;
+	bc_num_free(&exp);
+	bc_num_free(&temp);
+	bc_num_free(&base);
+	BC_LONGJMP_CONT;
+	assert(!d->neg || d->len);
+	assert(!d->len || d->num[d->len - 1] || d->rdx == d->len);
+}
+#endif // DC_ENABLED
+
+#if BC_DEBUG_CODE
+void bc_num_printDebug(const BcNum *n, const char *name, bool emptyline) {
+	bc_file_puts(&vm.fout, name);
+	bc_file_puts(&vm.fout, ": ");
+	bc_num_printDecimal(n);
+	bc_file_putchar(&vm.fout, '\n');
+	if (emptyline) bc_file_putchar(&vm.fout, '\n');
+	vm.nchars = 0;
+}
+
+void bc_num_printDigs(const BcDig *n, size_t len, bool emptyline) {
+
+	size_t i;
+
+	for (i = len - 1; i < len; --i)
+		bc_file_printf(&vm.fout, " %lu", (unsigned long) n[i]);
+
+	bc_file_putchar(&vm.fout, '\n');
+	if (emptyline) bc_file_putchar(&vm.fout, '\n');
+	vm.nchars = 0;
+}
+
+void bc_num_printWithDigs(const BcNum *n, const char *name, bool emptyline) {
+	bc_file_puts(&vm.fout, name);
+	bc_file_printf(&vm.fout, " len: %zu, rdx: %zu, scale: %zu\n",
+	               name, n->len, n->rdx, n->scale);
+	bc_num_printDigs(n->num, n->len, emptyline);
+}
+
+void bc_num_dump(const char *varname, const BcNum *n) {
+
+	ulong i, scale = n->scale;
+
+	bc_file_printf(&vm.ferr, "\n%s = %s", varname,
+	               n->len ? (n->neg ? "-" : "+") : "0 ");
+
+	for (i = n->len - 1; i < n->len; --i) {
+
+		if (i + 1 == n->rdx) bc_file_puts(&vm.ferr, ". ");
+
+		if (scale / BC_BASE_DIGS != n->rdx - i - 1)
+			bc_file_printf(&vm.ferr, "%lu ", (unsigned long) n->num[i]);
+		else {
+
+			int mod = scale % BC_BASE_DIGS;
+			int d = BC_BASE_DIGS - mod;
+			BcDig div;
+
+			if (mod != 0) {
+				div = n->num[i] / ((BcDig) bc_num_pow10[(ulong) d]);
+				bc_file_printf(&vm.ferr, "%lu", (unsigned long) div);
+			}
+
+			div = n->num[i] % ((BcDig) bc_num_pow10[(ulong) d]);
+			bc_file_printf(&vm.ferr, " ' %lu ", (unsigned long) div);
+		}
+	}
+
+	bc_file_printf(&vm.ferr, "(%zu | %zu.%zu / %zu) %lu\n",
+	               n->scale, n->len, n->rdx, n->cap,
+	               (unsigned long) (void*) n->num);
+}
+#endif // BC_DEBUG_CODE