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blender/extern/verse/dist/v_bignum.c

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/*
* Routines for big (thousands of bits) unsigned integers, and
* doing simple maths operations on them. Written by Emil Brink.
*
* Part of the Verse core, see license details elsewhere.
*
* Bignums are represented as vectors of VBigDig (unsigned short),
* where the first element holds the length of the number in such
* digits. So a 32-bit number would be { 2, low, high }; digits are
* in little-endian format.
*
* Verse's uint16 and uint32 types are *not* used, since there is no
* need to limit the bits. If your machine has 32-bit shorts and 64-
* bit ints, this code should cope.
*
* By using unsigned shorts, which are assumed to be half the size of
* an unsigned int, we can easily do intermediary steps in int-sized
* variables, and thus get space for manual carry-management.
*
* This is the second incarnation of this code, the first one used
* a fixed 2,048-bit VBigNum structure passed by value. It had to be
* replaced since it was too weak for the desired functionality. Now,
* there's roughly 1,5 weeks of time gone into this code, which still
* means it's optimized for simplicity rather than speed.
*
* There has been neither time nor interest to meditate over FFTs and
* Karatsubas. Reasonable improvements are of course welcome, although
* this code *should* not be a bottleneck. Famous last words...
*
* In general, these routines do not do a lot of error checking, they
* assume you know what you're doing. Numbers must have >0 digits.
*/
#include <ctype.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "v_randgen.h"
#include "v_bignum.h"
#define MAX_DIG ((1UL << V_BIGBITS) - 1)
/* ----------------------------------------------------------------------------------------- */
/* Some routines need temporary storage to hold a term or two (the multi-
* plier, for instance). Since we don't want to use malloc()/free(), let's
* just have a bunch of digits that it's possible to allocate from in a
* stack-like manner.
*/
static VBigDig heap[2048 + 32];
static unsigned int heap_pos;
/* Allocate a number of <n> digits, returning it un-initialized. */
static VBigDig * bignum_alloc(unsigned int n)
{
VBigDig *y;
if(heap_pos + n > sizeof heap / sizeof *heap)
{
printf("Out of memory in bignum heap -- unbalanced calls?\n");
return NULL;
}
y = heap + heap_pos;
heap_pos += n + 1;
*y = n;
return y;
}
/* Free a number previously allocated by bignum_allow() above. MUST match in sequences. */
static void bignum_free(const VBigDig *x)
{
heap_pos -= *x + 1;
}
/* ----------------------------------------------------------------------------------------- */
/* Set x from bits. External representation is big-endian byte array. */
void v_bignum_raw_import(VBigDig *x, const void *bits)
{
const unsigned char *bytes = bits;
int i;
for(i = *x++ - 1; i >= 0; i--)
{
x[i] = ((VBigDig) *bytes++) << 8;
x[i] |= *bytes++;
}
}
/* Set bits to value of x. External representation is big-endian byte array. */
void v_bignum_raw_export(const VBigDig *x, void *bits)
{
unsigned char *bytes = bits;
int i;
for(i = *x++ - 1; i >= 0; i--)
{
*bytes++ = x[i] >> 8;
*bytes++ = x[i];
}
}
/* ----------------------------------------------------------------------------------------- */
/* Assigns x = 0. */
void v_bignum_set_zero(VBigDig *x)
{
memset(x + 1, 0, *x * sizeof *x);
}
/* Assigns x = 1. */
void v_bignum_set_one(VBigDig *x)
{
int i;
for(i = *x++ - 1, *x++ = 1; i > 0; i--)
*x++ = 0;
}
/* Assigns x = y. */
void v_bignum_set_digit(VBigDig *x, VBigDig y)
{
v_bignum_set_zero(x);
x[1] = y;
}
/* Assigns x = <string>, with string in decimal ASCII. Kind of slow. */
void v_bignum_set_string(VBigDig *x, const char *string)
{
unsigned int d;
v_bignum_set_zero(x);
for(; *string && isdigit(*string); string++)
{
v_bignum_mul_digit(x, 10);
d = *string - '0';
v_bignum_add_digit(x, d);
}
}
/* Assigns x = <string>, with string in hexadecimal ASCII. */
void v_bignum_set_string_hex(VBigDig *x, const char *string)
{
unsigned int d;
if(string[0] == '0' && (string[1] == 'x' || string[1] == 'X'))
string += 2;
v_bignum_set_zero(x);
for(; *string && isxdigit(*string); string++)
{
v_bignum_bit_shift_left(x, 4);
d = tolower(*string) - '0';
if(d > 9)
d -= ('a' - '0') - 10;
x[1] |= (d & 0xF);
}
}
/* Performs x = y, taking care to handle different precisions correctly by truncating. */
void v_bignum_set_bignum(VBigDig *x, const VBigDig *y)
{
int xs, ys, i, s;
xs = x[0];
ys = y[0];
if(xs == ys) /* For same sizes, just memcpy() and be done. */
{
memcpy(x + 1, y + 1, xs * sizeof *x);
return;
}
else if(ys > xs)
s = xs;
else
s = ys;
/* Copy as many digits as will fit, and clear any remaining high digits. */
for(i = 1; i <= s; i++)
x[i] = y[i];
for(; i <= xs; i++)
x[i] = 0;
}
/* Performs x = y[msb:msb-bits], right-adjusting the result. */
void v_bignum_set_bignum_part(VBigDig *x, const VBigDig *y, unsigned int msb, unsigned int bits)
{
int i, bit;
v_bignum_set_zero(x);
if(y == NULL || msb > (y[0] * (CHAR_BIT * sizeof *x)))
return;
for(i = 0; i < bits; i++)
{
bit = msb - (bits - 1) + i;
if(v_bignum_bit_test(y, bit))
v_bignum_bit_set(x, i);
}
}
/* Set x to a random bunch of bits. Should use a real random source. */
void v_bignum_set_random(VBigDig *x, VRandGen *gen)
{
unsigned int s = *x++;
if(gen != NULL)
v_randgen_get(gen, x, s * sizeof *x);
else
{
fprintf(stderr, "** Warning: Calling v_bignum_set_random() without VRandGen is potentially expensive\n");
if((gen = v_randgen_new()) != NULL)
{
v_randgen_get(gen, x, s * sizeof *x);
v_randgen_destroy(gen);
}
else
fprintf(stderr, __FILE__ ": Couldn't create random number generator\n");
}
}
/* Print x in hexadecimal, with 0x prefix but no linefeed. */
void v_bignum_print_hex(const VBigDig *x)
{
int i, s = *x;
printf("0x");
for(i = 0; i < s; i++)
printf("%04X", x[s - i]);
}
/* Print x in hexadecimal, with linefeed. */
void v_bignum_print_hex_lf(const VBigDig *x)
{
v_bignum_print_hex(x);
printf("\n");
}
/* ----------------------------------------------------------------------------------------- */
/* x = ~x. */
void v_bignum_not(VBigDig *x)
{
unsigned int i, s = *x++;
for(i = 0; i < s; i++)
x[i] = ~x[i];
}
int v_bignum_bit_test(const VBigDig *x, unsigned int bit)
{
unsigned int slot = bit / (CHAR_BIT * sizeof *x), m = 1 << (bit % (CHAR_BIT * sizeof *x));
if(slot < x[0])
return (x[slot + 1] & m) != 0;
return 0;
}
/* Compute x |= (1 << bit). */
void v_bignum_bit_set(VBigDig *x, unsigned int bit)
{
unsigned int slot, m;
if(bit >= (*x * (CHAR_BIT * sizeof *x)))
return;
slot = bit / (CHAR_BIT * sizeof *x);
m = 1 << (bit % (CHAR_BIT * sizeof *x));
x[1 + slot] |= m;
}
/* Returns index of most signifant '1' bit of x, or -1 if x == 0. */
int v_bignum_bit_msb(const VBigDig *x)
{
int i;
unsigned int s = *x++;
for(i = s - 1; i >= 0; i--)
{
if(x[i] != 0)
{
int bit = (i + 1) * (CHAR_BIT * sizeof *x) - 1;
VBigDig d = x[i], mask;
for(mask = 1 << (CHAR_BIT * sizeof *x - 1); mask != 0; mask >>= 1, bit--)
{
if(d & mask)
return bit;
}
}
}
return -1;
}
int v_bignum_bit_size(const VBigDig *x)
{
return *x * V_BIGBITS;
}
/* Perform x <<= count. */
void v_bignum_bit_shift_left(VBigDig *x, unsigned int count)
{
unsigned int t, carry, s = *x++;
register int i;
if(count >= CHAR_BIT * sizeof *x) /* Shift whole digits. */
{
unsigned int places = count / (CHAR_BIT * sizeof *x);
for(i = s - 1; i >= places; i--)
x[i] = x[i - places];
for(; i >= 0; i--) /* Clear out the LSBs. */
x[i] = 0;
count -= places * (CHAR_BIT * sizeof *x);
if(count == 0)
return;
}
/* Shift bits. */
for(i = carry = 0; i < s; i++)
{
t = (x[i] << count) | carry;
x[i] = t;
carry = t >> (CHAR_BIT * sizeof *x);
}
}
/* Perform x <<= 1. This is a frequent operation so it can have its own function. */
void v_bignum_bit_shift_left_1(VBigDig *x)
{
register unsigned int t, carry, s = *x++, i;
/* Shift bits. */
for(i = carry = 0; i < s; i++)
{
t = (x[i] << 1) | carry;
x[i] = t;
carry = t >> (CHAR_BIT * sizeof *x);
}
}
/* Perform x >>= count. */
void v_bignum_bit_shift_right(VBigDig *x, unsigned int count)
{
unsigned int t, carry, s = *x++;
int i;
/* Shift entire digits first. */
if(count >= CHAR_BIT * sizeof *x)
{
unsigned int places = count / (CHAR_BIT * sizeof *x);
if(places > s)
{
memset(x, 0, s * sizeof *x);
return;
}
for(i = 0; i < s - places; i++)
x[i] = x[i + places];
for(; i < s; i++)
x[i] = 0;
count -= places * CHAR_BIT * sizeof *x;
if(count == 0)
return;
}
/* Shift any remaining bits. */
for(i = s - 1, carry = 0; i >= 0; i--)
{
t = x[i] << (CHAR_BIT * sizeof *x);
t >>= count;
t |= carry;
carry = (t & MAX_DIG) << (CHAR_BIT * sizeof *x);
x[i] = t >> (CHAR_BIT * sizeof *x);
}
}
/* ----------------------------------------------------------------------------------------- */
/* Return x == 0. */
int v_bignum_eq_zero(const VBigDig *x)
{
unsigned int i, s = *x++;
for(i = 0; i < s; i++)
if(x[i])
return 0;
return 1;
}
/* Return x == 1. */
int v_bignum_eq_one(const VBigDig *x)
{
unsigned int i, s = *x++;
if(x[0] != 1)
return 0;
for(i = 1; i < s; i++)
if(x[i])
return 0;
return 1;
}
/* Returns x == y, handling different lengths properly. */
int v_bignum_eq(const VBigDig *x, const VBigDig *y)
{
unsigned int i, xs, ys, cs;
if(x == y) /* Quick test thanks to pointer representation. */
return 1;
xs = *x++;
ys = *y++;
if(xs == ys) /* Same size? Then let's be quick about this. */
return memcmp(x, y, xs * sizeof *x) == 0;
else
{
cs = xs < ys ? xs : ys; /* Common size. */
if(memcmp(x, y, cs * sizeof *x) == 0)
{
const VBigDig *l;
if(cs == xs) /* y is longer. */
l = y, i = ys - 1;
else
l = x, i = xs - 1;
for(; i > cs; i--)
if(l[i])
return 0;
return 1;
}
}
return 0;
}
/* Returns x >= y. */
int v_bignum_gte(const VBigDig *x, const VBigDig *y)
{
unsigned int xs, ys;
int i, j, k;
if(x == y)
return 1;
/* Find indexes of highest-most used digit in each of the numbers. */
xs = *x++;
ys = *y++;
for(i = xs - 1; i >= 0; i--)
if(x[i] != 0)
break;
for(j = ys - 1; j >= 0; j--)
if(y[j] != 0)
break;
/* Both zero? */
if(i < 0 && j < 0)
return 1;
/* Quick answers exists for different-sized numbers. Find them. */
if(i < j)
return 0;
if(i > j)
return 1;
/* Compare digit by digit. */
for(k = i; k >= 0; k--)
{
if(x[k] < y[k])
return 0;
if(x[k] > y[k])
return 1;
}
return x[k] >= y[k];
}
/* ----------------------------------------------------------------------------------------- */
/* Computes x += y. */
void v_bignum_add_digit(VBigDig *x, VBigDig y)
{
unsigned int i, s = *x++, t;
t = x[0] + y;
x[0] = t;
if(t > MAX_DIG)
{
for(i = 1; i < s; i++)
{
if(++x[i])
break;
}
}
}
/* Computes x -= y. */
void v_bignum_sub_digit(VBigDig *x, VBigDig y)
{
unsigned int i, s = *x++, t;
t = x[0] - y;
x[0] = t;
if(t > MAX_DIG)
{
for(i = 1; i < s; i++)
{
x[i]--;
if(x[i] < MAX_DIG)
break;
}
}
}
/* Computes x *= y. */
void v_bignum_mul_digit(VBigDig *x, VBigDig y)
{
unsigned int i, s = *x++, carry, t;
for(i = carry = 0; i < s; i++)
{
t = x[i] * y + carry;
x[i] = t;
carry = t >> (CHAR_BIT * sizeof *x);
}
}
/* ----------------------------------------------------------------------------------------- */
/* Computes x += y. */
void v_bignum_add(VBigDig *x, const VBigDig *y)
{
unsigned int i, xs = *x++, ys = *y++, s, carry, t;
s = xs < ys ? xs : ys;
for(i = carry = 0; i < s; i++)
{
t = x[i] + y[i] + carry;
x[i] = t;
carry = t > MAX_DIG;
}
for(; carry && i < xs; i++)
{
t = x[i] + carry;
x[i] = t;
carry = t > MAX_DIG;
}
}
/* Computes x -= y. */
void v_bignum_sub(VBigDig *x, const VBigDig *y)
{
unsigned int i, xs = *x++, ys = *y++, s, carry, t;
if(x == y)
{
v_bignum_set_zero(x - 1);
return;
}
s = xs < ys ? xs : ys;
for(i = carry = 0; i < s; i++)
{
t = x[i] - y[i] - carry;
x[i] = t;
carry = t > MAX_DIG;
}
for(; carry && i < xs; i++)
{
t = x[i] - carry;
x[i] = t;
carry = t > MAX_DIG;
}
}
/* Compute x *= y, using as many digits as is necessary, then truncating the
* result down. This is Algorithm 14.12 from "Handbook of Applied Cryptography".
*/
void v_bignum_mul(VBigDig *x, const VBigDig *y)
{
int n = *x, t = *y, i, j;
VBigDigs uv = 0, c, w[2048];
memset(w, 0, (n + t + 1) * sizeof *w);
for(i = 0; i < t; i++)
{
c = 0;
for(j = 0; j < n; j++)
{
uv = w[i + j] + x[1 + j] * y[1 + i] + c;
w[i + j] = uv & ((1 << V_BIGBITS) - 1);
c = uv >> V_BIGBITS;
}
w[i + n + 1] = uv >> V_BIGBITS;
}
/* Write low words of w back into x. */
for(i = 0; i < *x; i++)
x[1 + i] = w[i];
}
/* Computes x /= y and remainder = x % y. */
void v_bignum_div(VBigDig *x, const VBigDig *y, VBigDig *remainder)
{
VBigDig *q, *work;
int msbx = v_bignum_bit_msb(x), msby = v_bignum_bit_msb(y), next;
/* Compare magnitudes of inputs, allows quick exits. */
if(msby > msbx)
{
if(remainder != NULL)
v_bignum_set_bignum(remainder, x);
v_bignum_set_zero(x);
return;
}
if(msby < 0)
{
v_bignum_set_zero(x);
return;
}
q = bignum_alloc(*x);
v_bignum_set_zero(q);
work = bignum_alloc(*x);
v_bignum_set_bignum_part(work, x, msbx, msby + 1);
for(next = msbx - (msby + 1); next >= -1; next--)
{
v_bignum_bit_shift_left_1(q);
if(v_bignum_gte(work, y))
{
q[1] |= 1;
v_bignum_sub(work, y);
}
v_bignum_bit_shift_left_1(work);
if(v_bignum_bit_test(x, next))
work[1] |= 1;
}
v_bignum_bit_shift_right(work, 1); /* Undo the last shift (when next==-1). */
if(remainder != NULL)
{
/* printf("div() got remainder ");
v_bignum_print_hex_lf(work);
*/
v_bignum_set_bignum(remainder, work);
}
bignum_free(work);
v_bignum_set_bignum(x, q);
bignum_free(q);
}
/* Computes x %= y. */
void v_bignum_mod(VBigDig *x, const VBigDig *y)
{
int digs;
VBigDig *tmp;
/* printf("computing ");
v_bignum_print_hex(x);
printf("L %% ");
v_bignum_print_hex(y);
*/
digs = *x > *y ? *x : *y;
tmp = bignum_alloc(digs);
v_bignum_div(x, y, tmp);
v_bignum_set_bignum(x, tmp);
bignum_free(tmp);
/* printf("L = ");
v_bignum_print_hex_lf(x);
*/
}
/* Initialize Barrett reduction by computing the "mu" helper value. Defined in
* Handbook of Applied Cryptography algorithm 14.42 as floor(b^2k / m).
*/
const VBigDig * v_bignum_reduce_begin(const VBigDig *m)
{
VBigDig *mu;
int k;
for(k = *m; m[k] == 0; k--)
;
/* printf("k=%d -> digits are 0..%u\n", k, k - 1);
printf("computing mu=floor(65536^%d/", 2 * k);
v_bignum_print_hex(m);
printf(")\n");
*/ mu = bignum_alloc(2 * k + 1);
/* b ^ 2k is just 65536 << 2k, i.e. set bit 16 * 2k. */
v_bignum_set_zero(mu);
v_bignum_bit_set(mu, V_BIGBITS * 2 * k);
/* v_bignum_print_hex_lf(mu);*/
v_bignum_div(mu, m, NULL);
return mu;
}
void v_bignum_reduce_end(const VBigDig *mu)
{
bignum_free(mu);
}
/* Compute x % m, using mu as the helper quantity mu, precomputed by the
* routine above.
*/
void v_bignum_reduce(VBigDig *x, const VBigDig *m, const VBigDig *mu)
{
VBigDig *q, *r1, *r2, *r;
int i, k;
for(k = *m; m[k] == 0; k--)
;
/* Step 1, compute the q helper. */
q = bignum_alloc(*x + *mu - (k - 1)); /* Tighter bound number length (was 2 * *x). */
v_bignum_set_bignum(q, x);
v_bignum_bit_shift_right(q, V_BIGBITS * (k - 1));
v_bignum_mul(q, mu);
v_bignum_bit_shift_right(q, V_BIGBITS * (k + 1));
/* Step 2, initialize. */
r1 = bignum_alloc(*x);
r2 = bignum_alloc(*x);
v_bignum_set_bignum(r1, x);
for(i = k + 1; i < *r1; i++)
r1[i + 1] = 0;
v_bignum_set_bignum(r2, q);
v_bignum_mul(r2, m);
for(i = k + 1; i < *r2; i++)
r2[i + 1] = 0;
r = x;
v_bignum_set_bignum(r, r1);
v_bignum_sub(r, r2);
/* Step 3, make sure r is positive. */
if(v_bignum_bit_test(r, V_BIGBITS * *r - 1))
{
VBigDig *term;
term = bignum_alloc(k + 1 * V_BIGBITS);
v_bignum_set_zero(term);
v_bignum_bit_set(term, V_BIGBITS * (k + 1));
v_bignum_add(r, term);
bignum_free(term);
}
/* Step 4, loop. */
while(v_bignum_gte(r, m))
v_bignum_sub(r, m);
bignum_free(r2);
bignum_free(r1);
bignum_free(q);
}
/* Compute x * x using the algorithm 14.16 from "Handbook of Applied Cryptography".
* Note that since 'w' needs to be double-precision (i.e., 32-bit), we cannot allocate
* it using bignum_alloc() cleanly. Thus the static limit, which should be enough here.
* NOTE: This very much assumes V_BIGBITS == 16.
*/
void v_bignum_square_half(VBigDig *x)
{
VBigDigs w[256], uv, c, ouv;
int t = *x / 2, i, j, high;
if(t == 0)
return;
for(; x[t] == 0; t--)
;
memset(w, 0, 2 * t * sizeof *w); /* Clear digits of w. */
/* printf("print %lu, ", ++count);
v_bignum_print_hex(x);
printf("*");
v_bignum_print_hex(x);
*/ for(i = 0; i < t; i++)
{
/* printf("computing w[%d]: %lX + %lX * %lX\n", 2 * i, w[2 * i], x[1 + i], x[1 + i]);*/
uv = w[2 * i] + x[1 + i] * x[1 + i];
/* printf("setting w[%d]=%X [before]\n", 2 * i, uv & 0xffff);*/
w[2 * i] = uv & 0xffff;
c = uv >> V_BIGBITS;
/* printf("uv before=%X, c=%X\n", uv, c);*/
high = 0;
for(j = i + 1; j < t; j++)
{
/* printf("computing uv=%X+2*%X*%X+%X\n", w[i + j], x[1 + j], x[1 + i], c);*/
uv = x[1 + j] * x[1 + i];
high = (uv & 0x80000000) != 0;
uv *= 2;
ouv = uv; /* Addition below might wrap and generate high bit. */
uv += w[i + j] + c;
/* printf("ouv=0x%lX uv=0x%lX\n", ouv, uv);*/
high |= uv < ouv;
/* printf("setting w[%d]=%lX [inner] uv=%lX high=%d c=%X\n", i + j, uv & 0xffff, uv, high, c);*/
w[i + j] = uv & 0xffff;
c = (uv >> V_BIGBITS) | (high << V_BIGBITS);
}
/* printf("setting w[%d] to %X [after]\n", i + t, (uv >> 16) | (high << 16));*/
w[i + t] = (uv >> V_BIGBITS) | (high << V_BIGBITS);
}
/* printf("w=0x");
for(i = *x - 1; i >= 0; i--)
printf("%04X.", w[i]);
printf("\n");
*/ /* Write low words of w back into x, trashing it with the square. */
for(i = 0; i < 2 * t; i++)
x[1 + i] = w[i];
for(; i < *x; i++)
x[1 + i] = 0;
/* printf("==");
v_bignum_print_hex_lf(x);
*/
}
/* Computes x = (x^y) % n, where ^ denotes exponentiation. */
void v_bignum_pow_mod(VBigDig *x, const VBigDig *y, const VBigDig *n)
{
VBigDig *tmp;
const VBigDig *mu;
int i, k;
/* printf("computing pow(");
v_bignum_print_hex(x);
printf("L,");
v_bignum_print_hex(y);
printf("L,");
v_bignum_print_hex(n);
printf("L)\n");
*/
tmp = bignum_alloc(2 * *x); /* Squaring needs twice the bits, or lossage occurs. */
v_bignum_set_bignum(tmp, x);
k = v_bignum_bit_msb(y);
mu = v_bignum_reduce_begin(n);
for(i = k - 1; i >= 0; i--)
{
v_bignum_square_half(tmp);
v_bignum_reduce(tmp, n, mu);
if(v_bignum_bit_test(y, i))
{
v_bignum_mul(tmp, x);
v_bignum_reduce(tmp, n, mu);
}
}
v_bignum_set_bignum(x, tmp);
v_bignum_reduce_end(mu);
bignum_free(tmp);
}
/* ----------------------------------------------------------------------------------------- */
#if defined STANDALONE
int main(void)
{
VBigDig VBIGNUM(x, 3648), VBIGNUM(y, 128), VBIGNUM(z, 128);
printf("MAX_DIG=%u\n", MAX_DIG);
v_bignum_set_string_hex(x, "0x433864FE0F8FAC180FF1BC3A5BFD0C5566F6B11679E27294EDCC43056EB73EE118415E0CD6E6519509476EB21341ED0328BA7B14E0ED80D5E100A4549C5202B57B4CF17A74987631B6BA896C0DBA2095A7EDE5B9C4B4EEFCD1B9EF8474BCB7FBD0F64B549625D444847ED1FCB7F8050EB4F22794F694A0FAC6DFFB781C264B227966840185F9216484F6A7954741CB11FC14DEC2937EAD2CE640FD9A4339706BDB5BC355079C2F2F7994669DFA5B20C50D957A676E67C86835037078323A0BDAD3686B8E638749F327A7AD433C0D18BCD2FC970D125914C7FBEE061290A0F0F3572E207");
v_bignum_set_bignum(y, x);
v_bignum_set_digit(z, 77);
printf("x:");
v_bignum_print_hex_lf(x);
printf("y:");
v_bignum_print_hex_lf(y);
printf("r:");
v_bignum_print_hex_lf(z);
v_bignum_pow_mod(x, y, z);
printf(" =");
v_bignum_print_hex_lf(x);
return 0;
}
#endif /* STANDALONE */
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