common/bignum/bignumimpl.c

	bignumimpl.c revision 7c478bd95313f5f23a4c958a745db2134aa03244
/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License, Version 1.0 only
 * (the "License").  You may not use this file except in compliance
 * with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */
/*
 * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#pragma ident   "%Z%%M% %I% %E% SMI"

#define big_div_pos_fast big_div_pos

#include "bignum.h"

/*
 * Configuration guide
 * -------------------
 *
 * There are 4 preprocessor symbols used to configure the bignum
 * implementation.  This file contains no logic to configure based on
 * processor; we leave that to the Makefiles to specify.
 *
 * USE_FLOATING_POINT
 *   Meaning: There is support for a fast floating-point implementation of
 *   Montgomery multiply.
 *
 * PSR_MUL
 *   Meaning: There are processor-specific versions of the low level
 *   functions to implement big_mul.  Those functions are: big_mul_set_vec,
 *   big_mul_add_vec, big_mul_vec, and big_sqr_vec.  PSR_MUL implies support
 *   for all 4 functions.  You cannot pick and choose which subset of these
 *   functions to support; that would lead to a rat's nest of #ifdefs.
 *
 * HWCAP
 *   Meaning: Call multiply support functions through a function pointer.
 *   On x86, there are multiple implementations for differnt hardware
 *   capabilities, such as MMX, SSE2, etc.  Tests are made at run-time, when
 *   a function is first used.  So, the support functions are called through
 *   a function pointer.  There is no need for that on Sparc, because there
 *   is only one implementation; support functions are called directly.
 *   Later, if there were some new VIS instruction, or something, and a
 *   run-time test were needed, rather than variant kernel modules and
 *   libraries, then HWCAP would be defined for Sparc, as well.
 *
 * UMUL64
 *   Meaning: It is safe to use generic C code that assumes the existence
 *   of a 32 x 32 --> 64 bit unsigned multiply.  If this is not defined,
 *   then the generic code for big_mul_add_vec() must necessarily be very slow,
 *   because it must fall back to using 16 x 16 --> 32 bit multiplication.
 *
 */


#ifdef  _KERNEL

#include <sys/types.h>
#include <sys/kmem.h>
#include <sys/param.h>
#include <sys/sunddi.h>

#define big_malloc(size)    kmem_alloc(size, KM_NOSLEEP)
#define big_free(ptr, size) kmem_free(ptr, size)

void *
big_realloc(void *from, size_t oldsize, size_t newsize)
{
    void *rv;

    rv = kmem_alloc(newsize, KM_NOSLEEP);
    if (rv != NULL)
        bcopy(from, rv, oldsize);
    kmem_free(from, oldsize);
    return (rv);
}

#else   /* _KERNEL */

#include <stdlib.h>
#include <stdio.h>

#ifndef MALLOC_DEBUG

#define big_malloc(size)    malloc(size)
#define big_free(ptr, size) free(ptr)

#else

void
big_free(void *ptr, size_t size)
{
    printf("freed %d bytes at %p\n", size, ptr);
    free(ptr);
}

void *
big_malloc(size_t size)
{
    void *rv;
    rv = malloc(size);
    printf("malloced %d bytes, addr:%p\n", size, rv);
    return (rv);
}
#endif /* MALLOC_DEBUG */

#define big_realloc(x, y, z) realloc((x), (z))

void
printbignum(char *aname, BIGNUM *a)
{
    int i;

    (void) printf("\n%s\n%d\n", aname, a->sign*a->len);
    for (i = a->len - 1; i >= 0; i--) {
        (void) printf("%08x ", a->value[i]);
        if ((i % 8 == 0) && (i != 0))
            (void) printf("\n");
    }
    (void) printf("\n");
}

#endif  /* _KERNEL */


/* size in 32-bit words */
BIG_ERR_CODE
big_init(BIGNUM *number, int size)
{
    number->value = big_malloc(sizeof (uint32_t) * size);
    if (number->value == NULL) {
        return (BIG_NO_MEM);
    }
    number->size = size;
    number->len = 0;
    number->sign = 1;
    number->malloced = 1;
    return (BIG_OK);
}

/* size in 32-bit words */
BIG_ERR_CODE
big_init1(BIGNUM *number, int size, uint32_t *buf, int bufsize)
{
    if ((buf == NULL) || (size > bufsize)) {
        number->value = big_malloc(sizeof (uint32_t) * size);
        if (number->value == NULL) {
            return (BIG_NO_MEM);
        }
        number->size = size;
        number->malloced = 1;
    } else {
        number->value = buf;
        number->size = bufsize;
        number->malloced = 0;
    }
        number->len = 0;
        number->sign = 1;

    return (BIG_OK);
}

void
big_finish(BIGNUM *number)
{
    if (number->malloced == 1) {
        big_free(number->value, sizeof (uint32_t) * number->size);
        number->malloced = 0;
    }
}

/*
 *  bn->size should be at least (len + 3) / 4
 * converts from byte-big-endian format to bignum format (words in
 * little endian order, but bytes within the words big endian)
 */
void
bytestring2bignum(BIGNUM *bn, uchar_t *kn, size_t len)
{
    int     i, j, offs;
    uint32_t    word;
    uchar_t     *knwordp;

#ifdef  _LP64
    /* LINTED */
    offs = (uint32_t)len % sizeof (uint32_t);
    /* LINTED */
    bn->len = (uint32_t)len / sizeof (uint32_t);
    /* LINTED */
    for (i = 0; i < (uint32_t)len / sizeof (uint32_t); i++) {
#else   /* !_LP64 */
    offs = len % sizeof (uint32_t);
    bn->len = len / sizeof (uint32_t);
    for (i = 0; i < len / sizeof (uint32_t); i++) {
#endif  /* _LP64 */
        knwordp = &(kn[len - sizeof (uint32_t) * (i + 1)]);
        word = knwordp[0];
        for (j = 1; j < sizeof (uint32_t); j++) {
            word = (word << 8)+ knwordp[j];
        }
        bn->value[i] = word;
    }
    if (offs > 0) {
        word = kn[0];
        for (i = 1; i < offs; i++) word = (word << 8) + kn[i];
        bn->value[bn->len++] = word;
    }
    while ((bn->len > 1) && (bn->value[bn->len-1] == 0)) {
        bn->len --;
    }
}

/*
 * copies the least significant len bytes if
 * len < bn->len * sizeof (uint32_t)
 * converts from bignum format to byte-big-endian format.
 * bignum format is words in little endian order,
 * but bytes within words in native byte order.
 */
void
bignum2bytestring(uchar_t *kn, BIGNUM *bn, size_t len)
{
    int     i, j, offs;
    uint32_t    word;

    if (len < sizeof (uint32_t) * bn->len) {
#ifdef  _LP64
        /* LINTED */
        for (i = 0; i < (uint32_t)len / sizeof (uint32_t); i++) {
#else   /* !_LP64 */
        for (i = 0; i < len / sizeof (uint32_t); i++) {
#endif  /* _LP64 */
            word = bn->value[i];
            for (j = 0; j < sizeof (uint32_t); j++) {
                kn[len - sizeof (uint32_t) * i - j - 1] =
                    word & 0xff;
                word = word >> 8;
            }
        }
#ifdef  _LP64
        /* LINTED */
        offs = (uint32_t)len % sizeof (uint32_t);
#else   /* !_LP64 */
        offs = len % sizeof (uint32_t);
#endif  /* _LP64 */
        if (offs > 0) {
            word = bn->value[len / sizeof (uint32_t)];
#ifdef  _LP64
                /* LINTED */
                for (i =  (uint32_t)len % sizeof (uint32_t);
                i > 0; i --) {
#else   /* !_LP64 */
                for (i = len % sizeof (uint32_t); i > 0; i --) {
#endif  /* _LP64 */
                    kn[i - 1] = word & 0xff;
                    word = word >> 8;
                }
        }
    } else {
        for (i = 0; i < bn->len; i++) {
            word = bn->value[i];
            for (j = 0; j < sizeof (uint32_t); j++) {
                kn[len - sizeof (uint32_t) * i - j - 1] =
                    word & 0xff;
                word = word >> 8;
            }
        }
#ifdef  _LP64
        /* LINTED */
        for (i = 0; i < (uint32_t)len - sizeof (uint32_t) * bn->len;
            i++) {
#else   /* !_LP64 */
        for (i = 0; i < len - sizeof (uint32_t) * bn->len; i++) {
#endif  /* _LP64 */
            kn[i] = 0;
        }
    }
}


int
big_bitlength(BIGNUM *a)
{
    int     l, b;
    uint32_t    c;

    l = a->len - 1;
    while ((l > 0) && (a->value[l] == 0)) {
        l--;
    }
    b = sizeof (uint32_t) * 8;
    c = a->value[l];
    while ((b > 1) && ((c & 0x80000000) == 0)) {
        c = c << 1;
        b--;
    }
    return (l * (int)sizeof (uint32_t) * 8 + b);
}


BIG_ERR_CODE
big_copy(BIGNUM *dest, BIGNUM *src)
{
    uint32_t *newptr;
    int i, len;

    len = src->len;
    while ((len > 1) && (src->value[len - 1] == 0))
        len--;
    src->len = len;
    if (dest->size < len) {
        if (dest->malloced == 1) {
            newptr = (uint32_t *)big_realloc(dest->value,
                sizeof (uint32_t) * dest->size,
                sizeof (uint32_t) * len);
        } else {
            newptr = (uint32_t *)
                big_malloc(sizeof (uint32_t) * len);
            if (newptr != NULL) dest->malloced = 1;
        }
        if (newptr == NULL)
            return (BIG_NO_MEM);
        dest->value = newptr;
        dest->size = len;
    }
    dest->len = len;
    dest->sign = src->sign;
    for (i = 0; i < len; i++) dest->value[i] = src->value[i];

    return (BIG_OK);
}


BIG_ERR_CODE
big_extend(BIGNUM *number, int size)
{
    uint32_t    *newptr;
    int     i;

    if (number->size >= size)
        return (BIG_OK);
    if (number->malloced) {
        number->value =
            big_realloc(number->value,
            sizeof (uint32_t) * number->size,
            sizeof (uint32_t) * size);
    } else {
        newptr = big_malloc(sizeof (uint32_t) * size);
        if (newptr != NULL) {
            for (i = 0; i < number->size; i++) {
                newptr[i] = number->value[i];
            }
        }
        number->value = newptr;
    }

    if (number->value == NULL)
        return (BIG_NO_MEM);

    number->size = size;
    number->malloced = 1;
    return (BIG_OK);
}


int
big_is_zero(BIGNUM *n)
{
    int i, result;

    result = 1;
    for (i = 0; i < n->len; i++)
        if (n->value[i] != 0) result = 0;
    return (result);
}


BIG_ERR_CODE
big_add_abs(BIGNUM *result, BIGNUM *aa, BIGNUM *bb)
{
    int i, shorter, longer;
    uint32_t cy, ai;
    uint32_t *r, *a, *b, *c;
    BIG_ERR_CODE err;

    if (aa->len > bb->len) {
        shorter = bb->len;
        longer = aa->len;
        c = aa->value;
    } else {
        shorter = aa->len;
        longer = bb->len;
        c = bb->value;
    }
    if (result->size < longer + 1) {
        err = big_extend(result, longer + 1);
        if (err != BIG_OK)
            return (err);
    }

    r = result->value;
    a = aa->value;
    b = bb->value;
    cy = 0;
    for (i = 0; i < shorter; i++) {
        ai = a[i];
        r[i] = ai + b[i] + cy;
        if (r[i] > ai) cy = 0;
        else if (r[i] < ai) cy = 1;
    }
    for (; i < longer; i++) {
        ai = c[i];
        r[i] = ai + cy;
        if (r[i] >= ai) cy = 0;
    }
    if (cy == 1) {
        r[i] = cy;
        result->len = longer + 1;
    } else {
        result->len = longer;
    }
    result->sign = 1;
    return (BIG_OK);
}


/* caller must make sure that result has at least len words allocated */
void
big_sub_vec(uint32_t *r, uint32_t *a, uint32_t *b, int len)
{
    int i;
    uint32_t cy, ai;

    cy = 1;
    for (i = 0; i < len; i++) {
        ai = a[i];
        r[i] = ai + (~b[i]) + cy;
        if (r[i] > ai) cy = 0;
        else if (r[i] < ai) cy = 1;
    }
}


/* result=aa-bb  it is assumed that aa>=bb */
BIG_ERR_CODE
big_sub_pos(BIGNUM *result, BIGNUM *aa, BIGNUM *bb)
{
    int i, shorter;
    uint32_t cy, ai;
    uint32_t *r, *a, *b;
    BIG_ERR_CODE err;

    if (aa->len > bb->len) shorter = bb->len;
    else shorter = aa->len;
    if (result->size < aa->len) {
        err = big_extend(result, aa->len);
        if (err != BIG_OK)
            return (err);
    }

    r = result->value;
    a = aa->value;
    b = bb->value;
    result->len = aa->len;
    cy = 1;
    for (i = 0; i < shorter; i++) {
        ai = a[i];
        r[i] = ai + (~b[i]) + cy;
        if (r[i] > ai) cy = 0;
        else if (r[i] < ai) cy = 1;
    }
    for (; i < aa->len; i++) {
        ai = a[i];
        r[i] = ai + (~0) + cy;
        if (r[i] < ai) cy = 1;
    }
    result->sign = 1;
    if (cy == 0)
        return (BIG_INVALID_ARGS);
    else
        return (BIG_OK);
}


/* returns -1 if |aa|<|bb|, 0 if |aa|==|bb| 1 if |aa|>|bb| */
int
big_cmp_abs(BIGNUM *aa, BIGNUM *bb)
{
    int i;

    if (aa->len > bb->len) {
        for (i = aa->len - 1; i > bb->len - 1; i--) {
            if (aa->value[i] > 0)
                return (1);
        }
    } else if (aa->len < bb->len) {
        for (i = bb->len - 1; i > aa->len - 1; i--) {
            if (bb->value[i] > 0)
                return (-1);
        }
    } else i = aa->len-1;
    for (; i >= 0; i--) {
        if (aa->value[i] > bb->value[i])
            return (1);
        else if (aa->value[i] < bb->value[i])
            return (-1);
    }

    return (0);
}


BIG_ERR_CODE
big_sub(BIGNUM *result, BIGNUM *aa, BIGNUM *bb)
{
    BIG_ERR_CODE err;

    if ((bb->sign == -1) && (aa->sign == 1)) {
        if ((err = big_add_abs(result, aa, bb)) != BIG_OK)
            return (err);
        result->sign = 1;
    } else if ((aa->sign == -1) && (bb->sign == 1)) {
        if ((err = big_add_abs(result, aa, bb)) != BIG_OK)
            return (err);
        result->sign = -1;
    } else if ((aa->sign == 1) && (bb->sign == 1)) {
        if (big_cmp_abs(aa, bb) >= 0) {
            if ((err = big_sub_pos(result, aa, bb)) != BIG_OK)
                return (err);
            result->sign = 1;
        } else {
            if ((err = big_sub_pos(result, bb, aa)) != BIG_OK)
                return (err);
            result->sign = -1;
        }
    } else {
        if (big_cmp_abs(aa, bb) >= 0) {
            if ((err = big_sub_pos(result, aa, bb)) != BIG_OK)
                return (err);
            result->sign = -1;
        } else {
            if ((err = big_sub_pos(result, bb, aa)) != BIG_OK)
                return (err);
            result->sign = 1;
        }
    }
    return (BIG_OK);
}


BIG_ERR_CODE
big_add(BIGNUM *result, BIGNUM *aa, BIGNUM *bb)
{
    BIG_ERR_CODE err;

    if ((bb->sign == -1) && (aa->sign == -1)) {
        if ((err = big_add_abs(result, aa, bb)) != BIG_OK)
            return (err);
        result->sign = -1;
    } else if ((aa->sign == 1) && (bb->sign == 1)) {
        if ((err = big_add_abs(result, aa, bb)) != BIG_OK)
            return (err);
        result->sign = 1;
    } else if ((aa->sign == 1) && (bb->sign == -1)) {
        if (big_cmp_abs(aa, bb) >= 0) {
            if ((err = big_sub_pos(result, aa, bb)) != BIG_OK)
                return (err);
            result->sign = 1;
        } else {
            if ((err = big_sub_pos(result, bb, aa)) != BIG_OK)
                return (err);
            result->sign = -1;
        }
    } else {
        if (big_cmp_abs(aa, bb) >= 0) {
            if ((err = big_sub_pos(result, aa, bb)) != BIG_OK)
                return (err);
            result->sign = -1;
        } else {
            if ((err = big_sub_pos(result, bb, aa)) != BIG_OK)
                return (err);
            result->sign = 1;
        }
    }
    return (BIG_OK);
}


/* result = aa/2 aa must be positive */
BIG_ERR_CODE
big_half_pos(BIGNUM *result, BIGNUM *aa)
{
    BIG_ERR_CODE err;
    int i;
    uint32_t cy, cy1;
    uint32_t *a, *r;

    if (result->size < aa->len) {
        err = big_extend(result, aa->len);
        if (err != BIG_OK)
            return (err);
    }

    result->len = aa->len;
    a = aa->value;
    r = result->value;
    cy = 0;
    for (i = aa->len-1; i >= 0; i--) {
        cy1 = a[i] << 31;
        r[i] = (cy|(a[i] >> 1));
        cy = cy1;
    }
    if (r[result->len-1] == 0) result->len--;
    return (BIG_OK);
}

/* result  =  aa*2 aa must be positive */
BIG_ERR_CODE
big_double(BIGNUM *result, BIGNUM *aa)
{
    BIG_ERR_CODE err;
    int i, rsize;
    uint32_t cy, cy1;
    uint32_t *a, *r;

    if ((aa->len > 0) && ((aa->value[aa->len - 1] & 0x80000000) != 0))
        rsize = aa->len + 1;
    else rsize = aa->len;

    if (result->size < rsize) {
        err = big_extend(result, rsize);
        if (err != BIG_OK)
            return (err);
    }

    a = aa->value;
    r = result->value;
    if (rsize == aa->len + 1) r[rsize - 1] = 1;
    cy = 0;
    for (i = 0; i < aa->len; i++) {
        cy1 = a[i] >> 31;
        r[i] = (cy | (a[i] << 1));
        cy = cy1;
    }
    result->len = rsize;
    return (BIG_OK);
}

/* returns aa mod b, aa must be nonneg, b must be a max 16-bit integer */
uint32_t
big_mod16_pos(BIGNUM *aa, uint32_t b)
{
    int i;
    uint32_t rem;

    if (aa->len == 0)
        return (0);
    rem = aa->value[aa->len - 1] % b;
    for (i = aa->len - 2; i >= 0; i--) {
        rem = ((rem << 16) | (aa->value[i] >> 16)) % b;
        rem = ((rem << 16) | (aa->value[i] & 0xffff)) % b;
    }
    return (rem);
}


/*
 * result = aa - (2^32)^lendiff * bb
 * result->size should be at least aa->len at entry
 * aa, bb, and result should be positive
 */
void
big_sub_pos_high(BIGNUM *result, BIGNUM *aa, BIGNUM *bb)
{
    int i, lendiff;
    BIGNUM res1, aa1;

    lendiff = aa->len - bb->len;
    res1.size = result->size - lendiff;
    res1.malloced = 0;
    res1.value = result->value + lendiff;
    aa1.size = aa->size - lendiff;
    aa1.value = aa->value + lendiff;
    aa1.len = bb->len;
    aa1.sign = 1;
    (void) big_sub_pos(&res1, &aa1, bb);
    if (result->value != aa->value) {
        for (i = 0; i < lendiff; i++) {
            result->value[i] = aa->value[i];
        }
    }
    result->len = aa->len;
}


/*
 * returns 1, 0, or -1 depending on whether |aa| > , ==, or <
 *                          (2^32)^lendiff * |bb|
 * aa->len should be >= bb->len
 */
int
big_cmp_abs_high(BIGNUM *aa, BIGNUM *bb)
{
    int lendiff;
    BIGNUM aa1;

    lendiff = aa->len - bb->len;
    aa1.len = bb->len;
    aa1.size = aa->size - lendiff;
    aa1.malloced = 0;
    aa1.value = aa->value + lendiff;
    return (big_cmp_abs(&aa1, bb));
}


/*
 * result = aa * b where b is a max. 16-bit positive integer.
 * result should have enough space allocated.
 */
void
big_mul16_low(BIGNUM *result, BIGNUM *aa, uint32_t b)
{
    int i;
    uint32_t t1, t2, ai, cy;
    uint32_t *a, *r;

    a = aa->value;
    r = result->value;
    cy = 0;
    for (i = 0; i < aa->len; i++) {
        ai = a[i];
        t1 = (ai & 0xffff) * b + cy;
        t2 = (ai >> 16) * b + (t1 >> 16);
        r[i] = (t1 & 0xffff) | (t2 << 16);
        cy = t2 >> 16;
    }
    r[i] = cy;
    result->len = aa->len + 1;
    result->sign = aa->sign;
}


/*
 * result = aa * b * 2^16 where b is a max. 16-bit positive integer.
 * result should have enough space allocated.
 */
void
big_mul16_high(BIGNUM *result, BIGNUM *aa, uint32_t b)
{
    int i;
    uint32_t t1, t2, ai, cy, ri;
    uint32_t *a, *r;

    a = aa->value;
    r = result->value;
    cy = 0;
    ri = 0;
    for (i = 0; i < aa->len; i++) {
        ai = a[i];
        t1 = (ai & 0xffff) * b + cy;
        t2 = (ai >> 16) * b + (t1 >> 16);
        r[i] = (t1 << 16) + ri;
        ri = t2 & 0xffff;
        cy = t2 >> 16;
    }
    r[i] = (cy << 16) + ri;
    result->len = aa->len + 1;
    result->sign = aa->sign;
}

/* it is assumed that result->size is big enough */
void
big_shiftleft(BIGNUM *result, BIGNUM *aa, int offs)
{
    int i;
    uint32_t cy, ai;

    if (offs == 0) {
        if (result != aa) {
            (void) big_copy(result, aa);
        }
        return;
    }
    cy = 0;
    for (i = 0; i < aa->len; i++) {
        ai = aa->value[i];
        result->value[i] = (ai << offs) | cy;
        cy = ai >> (32 - offs);
    }
    if (cy != 0) {
        result->len = aa->len + 1;
        result->value[result->len - 1] = cy;
    } else {
        result->len = aa->len;
    }
    result->sign = aa->sign;
}

/* it is assumed that result->size is big enough */
void
big_shiftright(BIGNUM *result, BIGNUM *aa, int offs)
{
    int i;
    uint32_t cy, ai;

    if (offs == 0) {
        if (result != aa) {
            (void) big_copy(result, aa);
        }
        return;
    }
    cy = aa->value[0] >> offs;
    for (i = 1; i < aa->len; i++) {
        ai = aa->value[i];
        result->value[i-1] = (ai << (32 - offs)) | cy;
        cy = ai >> offs;
    }
    result->len = aa->len;
    result->value[result->len - 1] = cy;
    result->sign = aa->sign;
}


/*
 * result = aa/bb   remainder = aa mod bb
 * it is assumed that aa and bb are positive
 */
BIG_ERR_CODE
big_div_pos_fast(BIGNUM *result, BIGNUM *remainder, BIGNUM *aa, BIGNUM *bb)
{
    BIG_ERR_CODE err;
    int i, alen, blen, tlen, rlen, offs;
    uint32_t higha, highb, coeff;
    uint64_t highb64;
    uint32_t *a, *b;
    BIGNUM bbhigh, bblow, tresult, tmp1, tmp2;
    uint32_t tmp1value[BIGTMPSIZE];
    uint32_t tmp2value[BIGTMPSIZE];
    uint32_t tresultvalue[BIGTMPSIZE];
    uint32_t bblowvalue[BIGTMPSIZE];
    uint32_t bbhighvalue[BIGTMPSIZE];

    a = aa->value;
    b = bb->value;
    alen = aa->len;
    blen = bb->len;
    while ((alen > 1) && (a[alen - 1] == 0)) alen = alen - 1;
    aa->len = alen;
    while ((blen > 1) && (b[blen - 1] == 0)) blen = blen - 1;
    bb->len = blen;
    if ((blen == 1) && (b[0] == 0))
        return (BIG_DIV_BY_0);

    if (big_cmp_abs(aa, bb) < 0) {
        if ((remainder != NULL) &&
            ((err = big_copy(remainder, aa)) != BIG_OK))
            return (err);
        if (result != NULL) {
            result->len = 1;
            result->sign = 1;
            result->value[0] = 0;
        }
        return (BIG_OK);
    }

    if ((err = big_init1(&bblow, blen + 1,
        bblowvalue, arraysize(bblowvalue))) != BIG_OK)
        return (err);

    if ((err = big_init1(&bbhigh, blen + 1,
        bbhighvalue, arraysize(bbhighvalue))) != BIG_OK)
        goto ret1;

    if ((err = big_init1(&tmp1, alen + 2,
        tmp1value, arraysize(tmp1value))) != BIG_OK)
        goto ret2;

    if ((err = big_init1(&tmp2, blen + 2,
        tmp2value, arraysize(tmp2value))) != BIG_OK)
        goto ret3;

    if ((err = big_init1(&tresult, alen - blen + 2,
        tresultvalue, arraysize(tresultvalue))) != BIG_OK)
        goto ret4;

    offs = 0;
    if (blen > 1) {
        highb64 = (((uint64_t)(b[blen - 1])) << 32) |
            ((uint64_t)(b[blen - 2]));
    } else {
        highb64 = (((uint64_t)(b[blen - 1])) << 32);
    }
    if (highb64 >= 0x1000000000000ull) {
        highb64 = highb64 >> 16;
        offs = 16;
    }
    while ((highb64 & 0x800000000000ull) == 0) {
        highb64 = highb64 << 1;
        offs++;
    }
#ifdef  _LP64
    /* LINTED */
    highb = (highb64 >> 32) & 0xffffffff;
#else   /* !_LP64 */
    highb = highb64 >> 32;
#endif  /* _LP64 */

    big_shiftleft(&bblow, bb, offs);
    if (offs <= 15) {
        big_shiftleft(&bbhigh, &bblow, 16);
    } else {
        big_shiftright(&bbhigh, &bblow, 16);
    }
    if (bbhigh.value[bbhigh.len - 1] == 0) {
        bbhigh.len--;
    } else {
        bbhigh.value[bbhigh.len] = 0;
    }

    big_shiftleft(&tmp1, aa, offs);
    rlen = tmp1.len - bblow.len + 1;
    tresult.len = rlen;

    tmp1.len++;
    tlen = tmp1.len;
    tmp1.value[tmp1.len - 1] = 0;
    for (i = 0; i < rlen; i++) {
        higha = (tmp1.value[tlen - 1] << 16) +
            (tmp1.value[tlen - 2] >> 16);
        coeff = higha / (highb + 1);
        big_mul16_high(&tmp2, &bblow, coeff);
        big_sub_pos_high(&tmp1, &tmp1, &tmp2);
        bbhigh.len++;
        while (tmp1.value[tlen - 1] > 0) {
            big_sub_pos_high(&tmp1, &tmp1, &bbhigh);
            coeff++;
        }
        bbhigh.len--;
        tlen--;
        tmp1.len--;
        while (big_cmp_abs_high(&tmp1, &bbhigh) >= 0) {
            big_sub_pos_high(&tmp1, &tmp1, &bbhigh);
            coeff++;
        }
        tresult.value[rlen - i - 1] = coeff << 16;
        higha = tmp1.value[tlen - 1];
        coeff = higha / (highb + 1);
        big_mul16_low(&tmp2, &bblow, coeff);
        tmp2.len--;
        big_sub_pos_high(&tmp1, &tmp1, &tmp2);
        while (big_cmp_abs_high(&tmp1, &bblow) >= 0) {
            big_sub_pos_high(&tmp1, &tmp1, &bblow);
            coeff++;
        }
        tresult.value[rlen - i - 1] =
            tresult.value[rlen - i - 1] + coeff;
    }

    big_shiftright(&tmp1, &tmp1, offs);

    err = BIG_OK;

    if ((remainder != NULL) &&
        ((err = big_copy(remainder, &tmp1)) != BIG_OK))
        goto ret;

    if (result != NULL)
        err = big_copy(result, &tresult);

ret:
    big_finish(&tresult);
ret4:
    big_finish(&tmp1);
ret3:
    big_finish(&tmp2);
ret2:
    big_finish(&bbhigh);
ret1:
    big_finish(&bblow);
    return (err);
}

/*
 * If there is no processor-specific integer implementation of
 * the lower level multiply functions, then this code is provided
 * for big_mul_set_vec(), big_mul_add_vec(), big_mul_vec() and
 * big_sqr_vec().
 *
 * There are two generic implementations.  One that assumes that
 * there is hardware and C compiler support for a 32 x 32 --> 64
 * bit unsigned multiply, but otherwise is not specific to any
 * processor, platform, or ISA.
 *
 * The other makes very few assumptions about hardware capabilities.
 * It does not even assume that there is any implementation of a
 * 32 x 32 --> 64 bit multiply that is accessible to C code and
 * appropriate to use.  It falls constructs 32 x 32 --> 64 bit
 * multiplies from 16 x 16 --> 32 bit multiplies.
 *
 */

#if !defined(PSR_MUL)

#ifdef UMUL64

#define UNROLL8

#define MUL_SET_VEC_ROUND_PREFETCH(R) \
    p = pf * d; \
    pf = (uint64_t)a[R+1]; \
    t = p + cy; \
    r[R] = (uint32_t)t; \
    cy = t >> 32

#define MUL_SET_VEC_ROUND_NOPREFETCH(R) \
    p = pf * d; \
    t = p + cy; \
    r[R] = (uint32_t)t; \
    cy = t >> 32

#define MUL_ADD_VEC_ROUND_PREFETCH(R) \
    t = (uint64_t)r[R]; \
    p = pf * d; \
    pf = (uint64_t)a[R+1]; \
    t = p + t + cy; \
    r[R] = (uint32_t)t; \
    cy = t >> 32

#define MUL_ADD_VEC_ROUND_NOPREFETCH(R) \
    t = (uint64_t)r[R]; \
    p = pf * d; \
    t = p + t + cy; \
    r[R] = (uint32_t)t; \
    cy = t >> 32

#ifdef UNROLL8

#define UNROLL 8

/*
 * r = a * b
 * where r and a are vectors; b is a single 32-bit digit
 */

uint32_t
big_mul_set_vec(uint32_t *r, uint32_t *a, int len, uint32_t b)
{
    uint64_t d, pf, p, t, cy;

    if (len == 0)
        return (0);
    cy = 0;
    d = (uint64_t)b;
    pf = (uint64_t)a[0];
    while (len > UNROLL) {
        MUL_SET_VEC_ROUND_PREFETCH(0);
        MUL_SET_VEC_ROUND_PREFETCH(1);
        MUL_SET_VEC_ROUND_PREFETCH(2);
        MUL_SET_VEC_ROUND_PREFETCH(3);
        MUL_SET_VEC_ROUND_PREFETCH(4);
        MUL_SET_VEC_ROUND_PREFETCH(5);
        MUL_SET_VEC_ROUND_PREFETCH(6);
        MUL_SET_VEC_ROUND_PREFETCH(7);
        r += UNROLL;
        a += UNROLL;
        len -= UNROLL;
    }
    if (len == UNROLL) {
        MUL_SET_VEC_ROUND_PREFETCH(0);
        MUL_SET_VEC_ROUND_PREFETCH(1);
        MUL_SET_VEC_ROUND_PREFETCH(2);
        MUL_SET_VEC_ROUND_PREFETCH(3);
        MUL_SET_VEC_ROUND_PREFETCH(4);
        MUL_SET_VEC_ROUND_PREFETCH(5);
        MUL_SET_VEC_ROUND_PREFETCH(6);
        MUL_SET_VEC_ROUND_NOPREFETCH(7);
        return ((uint32_t)cy);
    }
    while (len > 1) {
        MUL_SET_VEC_ROUND_PREFETCH(0);
        ++r;
        ++a;
        --len;
    }
    if (len > 0) {
        MUL_SET_VEC_ROUND_NOPREFETCH(0);
    }
    return ((uint32_t)cy);
}

/*
 * r += a * b
 * where r and a are vectors; b is a single 32-bit digit
 */

uint32_t
big_mul_add_vec(uint32_t *r, uint32_t *a, int len, uint32_t b)
{
    uint64_t d, pf, p, t, cy;

    if (len == 0)
        return (0);
    cy = 0;
    d = (uint64_t)b;
    pf = (uint64_t)a[0];
    while (len > 8) {
        MUL_ADD_VEC_ROUND_PREFETCH(0);
        MUL_ADD_VEC_ROUND_PREFETCH(1);
        MUL_ADD_VEC_ROUND_PREFETCH(2);
        MUL_ADD_VEC_ROUND_PREFETCH(3);
        MUL_ADD_VEC_ROUND_PREFETCH(4);
        MUL_ADD_VEC_ROUND_PREFETCH(5);
        MUL_ADD_VEC_ROUND_PREFETCH(6);
        MUL_ADD_VEC_ROUND_PREFETCH(7);
        r += 8;
        a += 8;
        len -= 8;
    }
    if (len == 8) {
        MUL_ADD_VEC_ROUND_PREFETCH(0);
        MUL_ADD_VEC_ROUND_PREFETCH(1);
        MUL_ADD_VEC_ROUND_PREFETCH(2);
        MUL_ADD_VEC_ROUND_PREFETCH(3);
        MUL_ADD_VEC_ROUND_PREFETCH(4);
        MUL_ADD_VEC_ROUND_PREFETCH(5);
        MUL_ADD_VEC_ROUND_PREFETCH(6);
        MUL_ADD_VEC_ROUND_NOPREFETCH(7);
        return ((uint32_t)cy);
    }
    while (len > 1) {
        MUL_ADD_VEC_ROUND_PREFETCH(0);
        ++r;
        ++a;
        --len;
    }
    if (len > 0) {
        MUL_ADD_VEC_ROUND_NOPREFETCH(0);
    }
    return ((uint32_t)cy);
}
#endif /* UNROLL8 */

void
big_sqr_vec(uint32_t *r, uint32_t *a, int len)
{
    uint32_t *tr, *ta;
    int tlen, row, col;
    uint64_t p, s, t, t2, cy;
    uint32_t d;

    tr = r + 1;
    ta = a;
    tlen = len - 1;
    tr[tlen] = big_mul_set_vec(tr, ta + 1, tlen, ta[0]);
    while (--tlen > 0) {
        tr += 2;
        ++ta;
        tr[tlen] = big_mul_add_vec(tr, ta + 1, tlen, ta[0]);
    }
    s = (uint64_t)a[0];
    s = s * s;
    r[0] = (uint32_t)s;
    cy = s >> 32;
    p = ((uint64_t)r[1] << 1) + cy;
    r[1] = (uint32_t)p;
    cy = p >> 32;
    row = 1;
    col = 2;
    while (row < len) {
        s = (uint64_t)a[row];
        s = s * s;
        p = (uint64_t)r[col] << 1;
        t = p + s;
        d = (uint32_t)t;
        t2 = (uint64_t)d + cy;
        r[col] = (uint32_t)t2;
        cy = (t >> 32) + (t2 >> 32);
        if (row == len - 1)
            break;
        p = ((uint64_t)r[col+1] << 1) + cy;
        r[col+1] = (uint32_t)p;
        cy = p >> 32;
        ++row;
        col += 2;
    }
    r[col+1] = (uint32_t)cy;
}

#else /* ! UMUL64 */

/*
 * r = r + a * digit, r and a are vectors of length len
 * returns the carry digit
 */
uint32_t
big_mul_add_vec(uint32_t *r, uint32_t *a, int len, uint32_t digit)
{
    uint32_t cy, cy1, retcy, dlow, dhigh;
    int i;

    cy1 = 0;
    dlow = digit & 0xffff;
    dhigh = digit >> 16;
    for (i = 0; i < len; i++) {
        cy = (cy1 >> 16) + dlow * (a[i] & 0xffff) + (r[i] & 0xffff);
        cy1 = (cy >> 16) + dlow * (a[i]>>16) + (r[i] >> 16);
        r[i] = (cy & 0xffff) | (cy1 << 16);
    }
    retcy = cy1 >> 16;

    cy1 = r[0] & 0xffff;
    for (i = 0; i < len - 1; i++) {
        cy = (cy1 >> 16) + dhigh * (a[i] & 0xffff) + (r[i] >> 16);
        r[i] = (cy1 & 0xffff) | (cy << 16);
        cy1 = (cy >> 16) + dhigh * (a[i] >> 16) + (r[i + 1] & 0xffff);
    }
    cy = (cy1 >> 16) + dhigh * (a[len - 1] & 0xffff) + (r[len - 1] >> 16);
    r[len - 1] = (cy1 & 0xffff) | (cy << 16);
    retcy = (cy >> 16) + dhigh * (a[len - 1] >> 16) + retcy;

    return (retcy);
}

/*
 * r = a * digit, r and a are vectors of length len
 * returns the carry digit
 */
uint32_t
big_mul_set_vec(uint32_t *r, uint32_t *a, int len, uint32_t digit)
{
    return (big_mul_add_vec(r, a, len, digit));
}

void
big_sqr_vec(uint32_t *r, uint32_t *a, int len)
{
    int i;

    r[len] = big_mul_set_vec(r, a, len, a[0]);
    for (i = 1; i < len; ++i)
        r[len + i] = big_mul_add_vec(r+i, a, len, a[i]);
}

#endif /* UMUL64 */

void
big_mul_vec(uint32_t *r, uint32_t *a, int alen, uint32_t *b, int blen)
{
    int i;

    r[alen] = big_mul_set_vec(r, a, alen, b[0]);
    for (i = 1; i < blen; ++i)
        r[alen + i] = big_mul_add_vec(r+i, a, alen, b[i]);
}


#endif /* ! PSR_MUL */


/*
 * result = aa * bb  result->value should be big enough to hold the result
 *
 * Implementation: Standard grammar school algorithm
 *
 */

BIG_ERR_CODE
big_mul(BIGNUM *result, BIGNUM *aa, BIGNUM *bb)
{
    BIGNUM tmp1;
    uint32_t tmp1value[BIGTMPSIZE];
    uint32_t *r, *t, *a, *b;
    BIG_ERR_CODE err;
    int i, alen, blen, rsize, sign, diff;

    if (aa == bb) {
        diff = 0;
    } else {
        diff = big_cmp_abs(aa, bb);
        if (diff < 0) {
            BIGNUM *tt;
            tt = aa;
            aa = bb;
            bb = tt;
        }
    }
    a = aa->value;
    b = bb->value;
    alen = aa->len;
    blen = bb->len;
    while ((alen > 1) && (a[alen - 1] == 0)) alen--;
    aa->len = alen;
    while ((blen > 1) && (b[blen - 1] == 0)) blen--;
    bb->len = blen;

    rsize = alen + blen;
    if (result->size < rsize) {
        err = big_extend(result, rsize);
        if (err != BIG_OK)
            return (err);
        /* aa or bb might be an alias to result */
        a = aa->value;
        b = bb->value;
    }
    r = result->value;

    if (((alen == 1) && (a[0] == 0)) || ((blen == 1) && (b[0] == 0))) {
        result->len = 1;
        result->sign = 1;
        r[0] = 0;
        return (BIG_OK);
    }
    sign = aa->sign * bb->sign;
    if ((alen == 1) && (a[0] == 1)) {
        for (i = 0; i < blen; i++) r[i] = b[i];
        result->len = blen;
        result->sign = sign;
        return (BIG_OK);
    }
    if ((blen == 1) && (b[0] == 1)) {
        for (i = 0; i < alen; i++) r[i] = a[i];
        result->len = alen;
        result->sign = sign;
        return (BIG_OK);
    }

    err = big_init1(&tmp1, rsize, tmp1value, arraysize(tmp1value));
    if (err != BIG_OK)
        return (err);
    t = tmp1.value;
    for (i = 0; i < rsize; i++) t[i] = 0;

    if (diff == 0 && alen > 2)
        BIG_SQR_VEC(t, a, alen);
    else if (blen > 0)
        BIG_MUL_VEC(t, a, alen, b, blen);
    if (t[rsize - 1] == 0)
        --rsize;
    tmp1.len = rsize;
    if ((err = big_copy(result, &tmp1)) != BIG_OK)
        return (err);

    result->sign = sign;

    if (tmp1.malloced) big_finish(&tmp1);

    return (BIG_OK);
}


/*
 * caller must ensure that  a < n,  b < n  and  ret->size >=  2 * n->len + 1
 * and that ret is not n
 */
BIG_ERR_CODE
big_mont_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, BIGNUM *n, uint32_t n0)
{
    int i, j, nlen, needsubtract;
    uint32_t *nn, *rr;
    uint32_t digit, c;
    BIG_ERR_CODE err;

    nlen = n->len;
    nn = n->value;

    rr = ret->value;

    if ((err = big_mul(ret, a, b)) != BIG_OK)
        return (err);

    rr = ret->value;
    for (i = ret->len; i < 2 * nlen + 1; i++) rr[i] = 0;
    for (i = 0; i < nlen; i++) {
        digit = rr[i];
        digit = digit * n0;

        c = BIG_MUL_ADD_VEC(rr + i, nn, nlen, digit);
        j = i + nlen;
        rr[j] += c;
        while (rr[j] < c) {
            rr[j + 1] += 1;
            j++;
            c = 1;
        }
    }

    needsubtract = 0;
    if ((rr[2 * nlen]  != 0))
        needsubtract = 1;
    else {
        for (i = 2 * nlen - 1; i >= nlen; i--) {
            if (rr[i] > nn[i - nlen]) {
                needsubtract = 1;
                break;
            } else if (rr[i] < nn[i - nlen]) break;
        }
    }
    if (needsubtract)
        big_sub_vec(rr, rr + nlen, nn, nlen);
    else {
        for (i = 0; i < nlen; i++)
            rr[i] = rr[i + nlen];
    }
    for (i = nlen - 1; (i >= 0) && (rr[i] == 0); i--);
    ret->len = i+1;

    return (BIG_OK);
}

uint32_t
big_n0(uint32_t n)
{
    int i;
    uint32_t result, tmp;

    result = 0;
    tmp = 0xffffffff;
    for (i = 0; i < 32; i++) {
        if ((tmp & 1) == 1) {
            result = (result >> 1) | 0x80000000;
            tmp = tmp - n;
        } else  result = (result>>1);
        tmp = tmp >> 1;
    }

    return (result);
}


int
big_numbits(BIGNUM *n)
{
    int i, j;
    uint32_t t;

    for (i = n->len - 1; i > 0; i--)
        if (n->value[i] != 0) break;
    t = n->value[i];
    for (j = 32; j > 0; j--) {
        if ((t & 0x80000000) == 0)
            t = t << 1;
        else
            return (32 * i + j);
    }
    return (0);
}

/* caller must make sure that a < n */
BIG_ERR_CODE
big_mont_rr(BIGNUM *result, BIGNUM *n)
{
    BIGNUM rr;
    uint32_t rrvalue[BIGTMPSIZE];
    int len, i;
    BIG_ERR_CODE err;

    rr.malloced = 0;
    len = n->len;

    if ((err = big_init1(&rr, 2 * len + 1,
        rrvalue, arraysize(rrvalue))) != BIG_OK)
        return (err);

    for (i = 0; i < 2 * len; i++) rr.value[i] = 0;
    rr.value[2 * len] = 1;
    rr.len = 2 * len + 1;
    if ((err = big_div_pos(NULL, &rr, &rr, n)) != BIG_OK)
        goto ret;
    err = big_copy(result, &rr);
ret:
    if (rr.malloced) big_finish(&rr);
    return (err);
}

/* caller must make sure that a < n */
BIG_ERR_CODE
big_mont_conv(BIGNUM *result, BIGNUM *a, BIGNUM *n, uint32_t n0, BIGNUM *n_rr)
{
    BIGNUM rr;
    uint32_t rrvalue[BIGTMPSIZE];
    int len, i;
    BIG_ERR_CODE err;

    rr.malloced = 0;
    len = n->len;

    if ((err = big_init1(&rr, 2 * len + 1, rrvalue, arraysize(rrvalue)))
        != BIG_OK)
            return (err);

    if (n_rr == NULL) {
        for (i = 0; i < 2 * len; i++) rr.value[i] = 0;
        rr.value[2 * len] = 1;
        rr.len = 2 * len + 1;
        if ((err = big_div_pos(NULL, &rr, &rr, n)) != BIG_OK)
            goto ret;
        n_rr = &rr;
    }

    if ((err = big_mont_mul(&rr, n_rr, a, n, n0)) != BIG_OK)
        goto ret;
    err = big_copy(result, &rr);
ret:
    if (rr.malloced) big_finish(&rr);
    return (err);
}


#define MAX_EXP_BIT_GROUP_SIZE 6
#define APOWERS_MAX_SIZE (1 << (MAX_EXP_BIT_GROUP_SIZE - 1))

#ifdef USE_FLOATING_POINT

/*
 * This version makes use of floating point for performance.
 */
static BIG_ERR_CODE
_big_modexp(BIGNUM *result, BIGNUM *a, BIGNUM *e, BIGNUM *n, BIGNUM *n_rr)
{
    BIGNUM ma, tmp, rr;
    uint32_t mavalue[BIGTMPSIZE];
    uint32_t tmpvalue[BIGTMPSIZE];
    uint32_t rrvalue[BIGTMPSIZE];
    int i, j, k, l, m, p, bit, bitind, bitcount, nlen;
    BIG_ERR_CODE err;
    uint32_t n0;
    double dn0;
    double *dn, *dt, *d16r, *d32r;
    uint32_t *nint, *prod;
    double *apowers[APOWERS_MAX_SIZE];
    int nbits, groupbits, apowerssize;

    nbits = big_numbits(e);
    if (nbits < 50) {
        groupbits = 1;
        apowerssize = 1;
    } else {
        groupbits = MAX_EXP_BIT_GROUP_SIZE;
        apowerssize = 1 << (groupbits - 1);
    }

    if ((err = big_init1(&ma, n->len, mavalue, arraysize(mavalue))) !=
        BIG_OK)
        return (err);
    ma.len = 1;
    ma.value[0] = 0;

    if ((err = big_init1(&tmp, 2 * n->len + 1,
        tmpvalue, arraysize(tmpvalue))) != BIG_OK)
        goto ret1;
    tmp.len = 1;
    tmp.value[0] = 0;

    rr.malloced = 0;
    if (n_rr == NULL) {
        if ((err = big_init1(&rr, 2 * n->len + 1,
            rrvalue, arraysize(rrvalue))) != BIG_OK)
            goto ret2;
        if (big_mont_rr(&rr, n) != BIG_OK)
            goto ret2;
        n_rr = &rr;
    }

    n0 = big_n0(n->value[0]);

    if (big_cmp_abs(a, n) > 0) {
        if ((err = big_div_pos(NULL, &ma, a, n)) != BIG_OK)
            goto ret2;
        err = big_mont_conv(&ma, &ma, n, n0, n_rr);
    } else {
        err = big_mont_conv(&ma, a, n, n0, n_rr);
    }
    if (err != BIG_OK)
        goto ret3;

    tmp.len = 1;
    tmp.value[0] = 1;
    if ((err = big_mont_conv(&tmp, &tmp, n, n0, n_rr)) != BIG_OK)
        goto ret3;

    nlen = n->len;
    dn0 = (double)(n0 & 0xffff);

    dn = dt = d16r = d32r = NULL;
    nint = prod = NULL;
    for (i = 0; i < apowerssize; i++) {
        apowers[i] = NULL;
    }

    if ((dn = big_malloc(nlen * sizeof (double))) == NULL) {
        err = BIG_NO_MEM;
        goto ret;
    }
    if ((dt = big_malloc((4 * nlen + 2) * sizeof (double))) == NULL) {
        err = BIG_NO_MEM;
        goto ret;
    }
    if ((nint = big_malloc(nlen * sizeof (uint32_t))) == NULL) {
        err = BIG_NO_MEM;
        goto ret;
    }
    if ((prod = big_malloc((nlen + 1) * sizeof (uint32_t))) == NULL) {
        err = BIG_NO_MEM;
        goto ret;
    }
    if ((d16r = big_malloc((2 * nlen + 1) * sizeof (double))) == NULL) {
        err = BIG_NO_MEM;
        goto ret;
    }
    if ((d32r = big_malloc(nlen * sizeof (double))) == NULL) {
        err = BIG_NO_MEM;
        goto ret;
    }
    for (i = 0; i < apowerssize; i++) {
        if ((apowers[i] = big_malloc((2 * nlen + 1) *
            sizeof (double))) == NULL) {
            err = BIG_NO_MEM;
            goto ret;
        }
    }

    for (i = 0; i < ma.len; i++) nint[i] = ma.value[i];
    for (; i < nlen; i++) nint[i] = 0;
    conv_i32_to_d32_and_d16(d32r, apowers[0], nint, nlen);

    for (i = 0; i < n->len; i++) nint[i] = n->value[i];
    for (; i < nlen; i++) nint[i] = 0;
    conv_i32_to_d32(dn, nint, nlen);

    mont_mulf_noconv(prod, d32r, apowers[0], dt, dn, nint, nlen, dn0);
    conv_i32_to_d32(d32r, prod, nlen);
    for (i = 1; i < apowerssize; i++) {
        mont_mulf_noconv(prod, d32r, apowers[i - 1],
            dt, dn, nint, nlen, dn0);
        conv_i32_to_d16(apowers[i], prod, nlen);
    }

    for (i = 0; i < tmp.len; i++) prod[i] = tmp.value[i];
    for (; i < nlen + 1; i++) prod[i] = 0;

    bitind = nbits % 32;
    k = 0;
    l = 0;
    p = 0;
    bitcount = 0;
    for (i = nbits / 32; i >= 0; i--) {
        for (j = bitind - 1; j >= 0; j--) {
            bit = (e->value[i] >> j) & 1;
            if ((bitcount == 0) && (bit == 0)) {
                conv_i32_to_d32_and_d16(d32r, d16r,
                    prod, nlen);
                mont_mulf_noconv(prod, d32r, d16r,
                    dt, dn, nint, nlen, dn0);
            } else {
                bitcount++;
                p = p * 2 + bit;
                if (bit == 1) {
                    k = k + l + 1;
                    l = 0;
                } else {
                    l++;
                }
                if (bitcount == groupbits) {
                    for (m = 0; m < k; m++) {
                        conv_i32_to_d32_and_d16(
                            d32r, d16r,
                            prod, nlen);
                        mont_mulf_noconv(prod, d32r,
                            d16r, dt, dn, nint,
                            nlen, dn0);
                    }
                    conv_i32_to_d32(d32r, prod, nlen);
                    mont_mulf_noconv(prod, d32r,
                        apowers[p >> (l+1)],
                        dt, dn, nint, nlen, dn0);
                    for (m = 0; m < l; m++) {
                        conv_i32_to_d32_and_d16(
                            d32r, d16r,
                            prod, nlen);
                        mont_mulf_noconv(prod, d32r,
                            d16r, dt, dn, nint,
                            nlen, dn0);
                    }
                    k = 0;
                    l = 0;
                    p = 0;
                    bitcount = 0;
                }
            }
        }
        bitind = 32;
    }

    for (m = 0; m < k; m++) {
        conv_i32_to_d32_and_d16(d32r, d16r, prod, nlen);
        mont_mulf_noconv(prod, d32r, d16r, dt, dn, nint, nlen, dn0);
    }
    if (p != 0) {
        conv_i32_to_d32(d32r, prod, nlen);
        mont_mulf_noconv(prod, d32r, apowers[p >> (l + 1)],
            dt, dn, nint, nlen, dn0);
    }
    for (m = 0; m < l; m++) {
        conv_i32_to_d32_and_d16(d32r, d16r, prod, nlen);
        mont_mulf_noconv(prod, d32r, d16r, dt, dn, nint, nlen, dn0);
    }

    ma.value[0] = 1;
    ma.len = 1;
    for (i = 0; i < nlen; i++) tmp.value[i] = prod[i];
    for (i = nlen - 1; (i > 0) && (prod[i] == 0); i--);
    tmp.len = i + 1;
    if ((err = big_mont_mul(&tmp, &tmp, &ma, n, n0)) != BIG_OK)
        goto ret;
    err = big_copy(result, &tmp);
ret:
    for (i = apowerssize - 1; i >= 0; i--) {
        if (apowers[i] != NULL)
            big_free(apowers[i], (2 * nlen + 1) * sizeof (double));
    }
    if (d32r != NULL)
        big_free(d32r, nlen * sizeof (double));
    if (d16r != NULL)
        big_free(d16r, (2 * nlen + 1) * sizeof (double));
    if (prod != NULL)
        big_free(prod, (nlen + 1) * sizeof (uint32_t));
    if (nint != NULL)
        big_free(nint, nlen * sizeof (uint32_t));
    if (dt != NULL)
        big_free(dt, (4 * nlen + 2) * sizeof (double));
    if (dn != NULL)
        big_free(dn, nlen * sizeof (double));

ret3:
    big_finish(&rr);
ret2:
    big_finish(&tmp);
ret1:
    big_finish(&ma);
    return (err);

}

#ifdef _KERNEL

#include <sys/sysmacros.h>
#include <sys/regset.h>
#include <sys/fpu/fpusystm.h>

/* the alignment for block stores to save fp registers */
#define FPR_ALIGN   (64)

extern void big_savefp(kfpu_t *);
extern void big_restorefp(kfpu_t *);

#endif /* _KERNEL */

BIG_ERR_CODE
big_modexp(BIGNUM *result, BIGNUM *a, BIGNUM *e, BIGNUM *n, BIGNUM *n_rr)
{
#ifdef _KERNEL
    BIG_ERR_CODE rv;
    uint8_t fpua[sizeof (kfpu_t) + FPR_ALIGN];
    kfpu_t *fpu;

#ifdef DEBUG
    if (!fpu_exists)
        return (BIG_GENERAL_ERR);
#endif

    fpu =  (kfpu_t *)P2ROUNDUP((uintptr_t)fpua, FPR_ALIGN);
    big_savefp(fpu);

    rv = _big_modexp(result, a, e, n, n_rr);

    big_restorefp(fpu);

    return (rv);
#else
    return (_big_modexp(result, a, e, n, n_rr));
#endif  /* _KERNEL */
}

#else /* ! USE_FLOATING_POINT */

/*
 * This version uses strictly integer math and is safe in the kernel
 * for all platforms.
 */

/*
 * computes a^e mod n
 * assumes a < n, n odd, result->value at least as long as n->value
 */
BIG_ERR_CODE
big_modexp(BIGNUM *result, BIGNUM *a, BIGNUM *e, BIGNUM *n, BIGNUM *n_rr)
{
    BIGNUM ma, tmp, rr;
    uint32_t mavalue[BIGTMPSIZE];
    uint32_t tmpvalue[BIGTMPSIZE];
    uint32_t rrvalue[BIGTMPSIZE];
    BIGNUM apowers[APOWERS_MAX_SIZE];
    int i, j, k, l, m, p,
        bit, bitind, bitcount, groupbits, apowerssize;
    BIG_ERR_CODE err;
    uint32_t n0;

    int nbits;

    nbits = big_numbits(e);
    if (nbits < 50) {
        groupbits = 1;
        apowerssize = 1;
    } else {
        groupbits = MAX_EXP_BIT_GROUP_SIZE;
        apowerssize = 1 << (groupbits - 1);
    }

    if ((err = big_init1(&ma, n->len,
        mavalue, arraysize(mavalue))) != BIG_OK)
        return (err);
    ma.len = 1;
    ma.value[0] = 0;

    if ((err = big_init1(&tmp, 2 * n->len + 1,
        tmpvalue, arraysize(tmpvalue))) != BIG_OK)
        goto ret1;
    tmp.len = 1;
    tmp.value[0] = 1;

    n0 = big_n0(n->value[0]);

    rr.malloced = 0;
    if (n_rr == NULL) {
        if ((err = big_init1(&rr, 2 * n->len + 1,
            rrvalue, arraysize(rrvalue))) != BIG_OK)
            goto ret2;

        if (big_mont_rr(&rr, n) != BIG_OK)
            goto ret3;
        n_rr = &rr;
    }

    for (i = 0; i < apowerssize; i++) apowers[i].malloced = 0;
    for (i = 0; i < apowerssize; i++) {
        if ((err = big_init1(&(apowers[i]), n->len, NULL, 0)) !=
            BIG_OK)
            goto ret;
    }

    if (big_cmp_abs(a, n) > 0) {
        if ((err = big_div_pos(NULL, &ma, a, n)) != BIG_OK)
            goto ret;
        err = big_mont_conv(&ma, &ma, n, n0, n_rr);
    } else {
        err = big_mont_conv(&ma, a, n, n0, n_rr);
    }
    if (err != BIG_OK) goto ret;

    (void) big_copy(&(apowers[0]), &ma);
    if ((err = big_mont_mul(&tmp, &ma, &ma, n, n0)) != BIG_OK)
        goto ret;
    (void) big_copy(&ma, &tmp);

    for (i = 1; i < apowerssize; i++) {
        if ((err = big_mont_mul(&tmp, &ma,
            &(apowers[i-1]), n, n0)) != BIG_OK)
            goto ret;
        (void) big_copy(&apowers[i], &tmp);
    }

    tmp.len = 1;
    tmp.value[0] = 1;
    if ((err = big_mont_conv(&tmp, &tmp, n, n0, n_rr)) != BIG_OK)
        goto ret;

    bitind = nbits % 32;
    k = 0;
    l = 0;
    p = 0;
    bitcount = 0;
    for (i = nbits / 32; i >= 0; i--) {
        for (j = bitind - 1; j >= 0; j--) {
            bit = (e->value[i] >> j) & 1;
            if ((bitcount == 0) && (bit == 0)) {
                if ((err = big_mont_mul(&tmp,
                    &tmp, &tmp, n, n0)) != BIG_OK)
                    goto ret;
            } else {
                bitcount++;
                p = p * 2 + bit;
                if (bit == 1) {
                    k = k + l + 1;
                    l = 0;
                } else {
                    l++;
                }
                if (bitcount == groupbits) {
                    for (m = 0; m < k; m++) {
                        if ((err = big_mont_mul(&tmp,
                            &tmp, &tmp, n, n0)) !=
                            BIG_OK)
                            goto ret;
                    }
                    if ((err = big_mont_mul(&tmp, &tmp,
                        &(apowers[p >> (l + 1)]),
                        n, n0)) != BIG_OK)
                        goto ret;
                    for (m = 0; m < l; m++) {
                        if ((err = big_mont_mul(&tmp,
                            &tmp, &tmp, n, n0)) !=
                            BIG_OK)
                            goto ret;
                    }
                    k = 0;
                    l = 0;
                    p = 0;
                    bitcount = 0;
                }
            }
        }
        bitind = 32;
    }

    for (m = 0; m < k; m++) {
        if ((err = big_mont_mul(&tmp, &tmp, &tmp, n, n0)) != BIG_OK)
            goto ret;
    }
    if (p != 0) {
        if ((err = big_mont_mul(&tmp, &tmp,
            &(apowers[p >> (l + 1)]), n, n0)) != BIG_OK)
            goto ret;
    }
    for (m = 0; m < l; m++) {
        if ((err = big_mont_mul(&tmp, &tmp, &tmp, n, n0)) != BIG_OK)
            goto ret;
    }

    ma.value[0] = 1;
    ma.len = 1;
    if ((err = big_mont_mul(&tmp, &tmp, &ma, n, n0)) != BIG_OK)
        goto ret;
    err = big_copy(result, &tmp);
ret:
    for (i = apowerssize - 1; i >= 0; i--) {
        big_finish(&(apowers[i]));
    }
ret3:
    if (rr.malloced) big_finish(&rr);
ret2:
    if (tmp.malloced) big_finish(&tmp);
ret1:
    if (ma.malloced) big_finish(&ma);
    return (err);
}

#endif /* USE_FLOATING_POINT */


BIG_ERR_CODE
big_modexp_crt(BIGNUM *result, BIGNUM *a, BIGNUM *dmodpminus1,
    BIGNUM *dmodqminus1, BIGNUM *p, BIGNUM *q, BIGNUM *pinvmodq,
    BIGNUM *p_rr, BIGNUM *q_rr)
{
    BIGNUM ap, aq, tmp;
    int alen, biglen, sign;
    BIG_ERR_CODE err;

    if (p->len > q->len) biglen = p->len;
    else biglen = q->len;

    if ((err = big_init1(&ap, p->len, NULL, 0)) != BIG_OK)
        return (err);
    if ((err = big_init1(&aq, q->len, NULL, 0)) != BIG_OK)
        goto ret1;
    if ((err = big_init1(&tmp, biglen + q->len + 1, NULL, 0)) != BIG_OK)
        goto ret2;

    /*
     * check whether a is too short - to avoid timing attacks
     */
    alen = a->len;
    while ((alen > p->len) && (a->value[alen - 1] == 0)) {
        alen--;
    }
    if (alen < p->len + q->len) {
        /*
         * a is too short, add p*q to it before
         * taking it modulo p and q
         * this will also affect timing, but this difference
         * does not depend on p or q, only on a
         * (in "normal" operation, this path will never be
         * taken, so it is not a performance penalty
         */
        if ((err = big_mul(&tmp, p, q)) != BIG_OK)
            goto ret;
        if ((err = big_add(&tmp, &tmp, a)) != BIG_OK)
            goto ret;
        if ((err = big_div_pos(NULL, &ap, &tmp, p)) != BIG_OK)
            goto ret;
        if ((err = big_div_pos(NULL, &aq, &tmp, q)) != BIG_OK)
            goto ret;
    } else {
        if ((err = big_div_pos(NULL, &ap, a, p)) != BIG_OK)
            goto ret;
        if ((err = big_div_pos(NULL, &aq, a, q)) != BIG_OK)
            goto ret;
    }

    if ((err = big_modexp(&ap, &ap, dmodpminus1, p, p_rr)) != BIG_OK)
        goto ret;
    if ((err = big_modexp(&aq, &aq, dmodqminus1, q, q_rr)) != BIG_OK)
        goto ret;
    if ((err = big_sub(&tmp, &aq, &ap)) != BIG_OK)
        goto ret;
    if ((err = big_mul(&tmp, &tmp, pinvmodq)) != BIG_OK)
        goto ret;
    sign = tmp.sign;
    tmp.sign = 1;
    if ((err = big_div_pos(NULL, &aq, &tmp, q)) != BIG_OK)
        goto ret;
    if ((sign == -1) && (!big_is_zero(&aq))) {
        (void) big_sub_pos(&aq, q, &aq);
    }
    if ((err = big_mul(&tmp, &aq, p)) != BIG_OK)
        goto ret;
    err = big_add_abs(result, &ap, &tmp);

ret:
    big_finish(&tmp);
ret2:
    big_finish(&aq);
ret1:
    big_finish(&ap);

    return (err);
}


uint32_t onearr[1] = {1};
BIGNUM One = {1, 1, 1, 0, onearr};

uint32_t twoarr[1] = {2};
BIGNUM Two = {1, 1, 1, 0, twoarr};

uint32_t fourarr[1] = {4};
BIGNUM Four = {1, 1, 1, 0, fourarr};

BIG_ERR_CODE
big_sqrt_pos(BIGNUM *result, BIGNUM *n)
{
    BIGNUM *high, *low, *mid, *t;
    BIGNUM t1, t2, t3, prod;
    uint32_t t1value[BIGTMPSIZE];
    uint32_t t2value[BIGTMPSIZE];
    uint32_t t3value[BIGTMPSIZE];
    uint32_t prodvalue[BIGTMPSIZE];
    int i, nbits, diff, nrootbits, highbits;
    BIG_ERR_CODE err;

    nbits = big_numbits(n);

    if ((err = big_init1(&t1, n->len + 1,
        t1value, arraysize(t1value))) != BIG_OK)
        return (err);
    if ((err = big_init1(&t2, n->len + 1,
        t2value, arraysize(t2value))) != BIG_OK)
        goto ret1;
    if ((err = big_init1(&t3, n->len + 1,
        t3value, arraysize(t3value))) != BIG_OK)
        goto ret2;
    if ((err = big_init1(&prod, n->len + 1,
        prodvalue, arraysize(prodvalue))) != BIG_OK)
        goto ret3;

    nrootbits = (nbits + 1) / 2;
    t1.len = t2.len = t3.len = (nrootbits - 1) / 32 + 1;
    for (i = 0; i < t1.len; i++) {
        t1.value[i] = 0;
        t2.value[i] = 0xffffffff;
    }
    highbits = nrootbits - 32 * (t1.len - 1);
    if (highbits == 32) {
        t1.value[t1.len - 1] = 0x80000000;
        t2.value[t2.len - 1] = 0xffffffff;
    } else {
        t1.value[t1.len - 1] = 1 << (highbits - 1);
        t2.value[t2.len - 1] = 2 * t1.value[t1.len - 1] - 1;
    }
    high = &t2;
    low = &t1;
    mid = &t3;

    if ((err = big_mul(&prod, high, high)) != BIG_OK)
        goto ret;
    diff = big_cmp_abs(&prod, n);
    if (diff <= 0) {
        err = big_copy(result, high);
        goto ret;
    }

    (void) big_sub_pos(mid, high, low);
    while (big_cmp_abs(&One, mid) != 0) {
        (void) big_add_abs(mid, high, low);
        (void) big_half_pos(mid, mid);
        if ((err = big_mul(&prod, mid, mid)) != BIG_OK)
            goto ret;
        diff = big_cmp_abs(&prod, n);
        if (diff > 0) {
            t = high;
            high = mid;
            mid = t;
        } else if (diff < 0) {
            t = low;
            low = mid;
            mid = t;
        } else {
            err = big_copy(result, low);
            goto ret;
        }
        (void) big_sub_pos(mid, high, low);
    }

    err = big_copy(result, low);
ret:
    if (prod.malloced) big_finish(&prod);
ret3:
    if (t3.malloced) big_finish(&t3);
ret2:
    if (t2.malloced) big_finish(&t2);
ret1:
    if (t1.malloced) big_finish(&t1);

    return (err);
}


BIG_ERR_CODE
big_Jacobi_pos(int *jac, BIGNUM *nn, BIGNUM *mm)
{
    BIGNUM *t, *tmp2, *m, *n;
    BIGNUM t1, t2, t3;
    uint32_t t1value[BIGTMPSIZE];
    uint32_t t2value[BIGTMPSIZE];
    uint32_t t3value[BIGTMPSIZE];
    int len, err;

    if (big_is_zero(nn) ||
        (((nn->value[0] & 1) | (mm->value[0] & 1)) == 0)) {
        *jac = 0;
        return (BIG_OK);
    }

    if (nn->len > mm->len) len = nn->len;
    else len = mm->len;

    if ((err = big_init1(&t1, len,
        t1value, arraysize(t1value))) != BIG_OK)
        return (err);
    if ((err = big_init1(&t2, len,
        t2value, arraysize(t2value))) != BIG_OK)
        goto ret1;
    if ((err = big_init1(&t3, len,
        t3value, arraysize(t3value))) != BIG_OK)
        goto ret2;

    n = &t1;
    m = &t2;
    tmp2 = &t3;

    (void) big_copy(n, nn);
    (void) big_copy(m, mm);

    *jac = 1;
    while (big_cmp_abs(&One, m) != 0) {
        if (big_is_zero(n)) {
            *jac = 0;
            goto ret;
        }
        if ((m->value[0] & 1) == 0) {
            if (((n->value[0] & 7) == 3) ||
                ((n->value[0] & 7) == 5)) *jac = -*jac;
            (void) big_half_pos(m, m);
        } else if ((n->value[0] & 1) == 0) {
            if (((m->value[0] & 7) == 3) ||
                ((m->value[0] & 7) == 5)) *jac = -*jac;
            (void) big_half_pos(n, n);
        } else {
            if (((m->value[0] & 3) == 3) &&
                ((n->value[0] & 3) == 3)) {
                *jac = -*jac;
            }
            if ((err = big_div_pos(NULL, tmp2, m, n)) != BIG_OK)
                goto ret;
            t = tmp2;
            tmp2 = m;
            m = n;
            n = t;
        }
    }
    err = BIG_OK;

ret:
    if (t3.malloced) big_finish(&t3);
ret2:
    if (t2.malloced) big_finish(&t2);
ret1:
    if (t1.malloced) big_finish(&t1);

    return (err);
}


BIG_ERR_CODE
big_Lucas(BIGNUM *Lkminus1, BIGNUM *Lk, BIGNUM *p, BIGNUM *k, BIGNUM *n)
{
    int m, w, i;
    uint32_t bit;
    BIGNUM ki, tmp, tmp2;
    uint32_t kivalue[BIGTMPSIZE];
    uint32_t tmpvalue[BIGTMPSIZE];
    uint32_t tmp2value[BIGTMPSIZE];
    BIG_ERR_CODE err;

    if (big_cmp_abs(k, &One) == 0) {
        (void) big_copy(Lk, p);
        (void) big_copy(Lkminus1, &Two);
        return (BIG_OK);
    }

    if ((err = big_init1(&ki, k->len + 1,
        kivalue, arraysize(kivalue))) != BIG_OK)
        return (err);

    if ((err = big_init1(&tmp, 2 * n->len +1,
        tmpvalue, arraysize(tmpvalue))) != BIG_OK)
        goto ret1;

    if ((err = big_init1(&tmp2, n->len,
        tmp2value, arraysize(tmp2value))) != BIG_OK)
        goto ret2;

    m = big_numbits(k);
    ki.len = (m - 1) / 32 + 1;
    w = (m - 1) / 32;
    bit = 1 << ((m - 1) % 32);
    for (i = 0; i < ki.len; i++) ki.value[i] = 0;
    ki.value[ki.len - 1] = bit;
    if (big_cmp_abs(k, &ki) != 0)
        (void) big_double(&ki, &ki);
    (void) big_sub_pos(&ki, &ki, k);

    (void) big_copy(Lk, p);
    (void) big_copy(Lkminus1, &Two);

    for (i = 0; i < m; i++) {
        if ((err = big_mul(&tmp, Lk, Lkminus1)) != BIG_OK)
            goto ret;
        (void) big_add_abs(&tmp, &tmp, n);
        (void) big_sub_pos(&tmp, &tmp, p);
        if ((err = big_div_pos(NULL, &tmp2, &tmp, n)) != BIG_OK)
            goto ret;

        if ((ki.value[w] & bit) != 0) {
            if ((err = big_mul(&tmp, Lkminus1, Lkminus1)) !=
                BIG_OK)
                goto ret;
            (void) big_add_abs(&tmp, &tmp, n);
            (void) big_sub_pos(&tmp, &tmp, &Two);
            if ((err = big_div_pos(NULL, Lkminus1, &tmp, n)) !=
                BIG_OK)
                goto ret;
            (void) big_copy(Lk, &tmp2);
        } else {
            if ((err = big_mul(&tmp, Lk, Lk)) != BIG_OK)
                goto ret;
            (void) big_add_abs(&tmp, &tmp, n);
            (void) big_sub_pos(&tmp, &tmp, &Two);
            if ((err = big_div_pos(NULL, Lk, &tmp, n)) != BIG_OK)
                goto ret;
            (void) big_copy(Lkminus1, &tmp2);
        }
        bit = bit >> 1;
        if (bit == 0) {
            bit = 0x80000000;
            w--;
        }
    }

    err = BIG_OK;

ret:
    if (tmp2.malloced) big_finish(&tmp2);
ret2:
    if (tmp.malloced) big_finish(&tmp);
ret1:
    if (ki.malloced) big_finish(&ki);

    return (err);
}


BIG_ERR_CODE
big_isprime_pos(BIGNUM *n)
{
    BIGNUM o, nminus1, tmp, Lkminus1, Lk;
    uint32_t ovalue[BIGTMPSIZE];
    uint32_t nminus1value[BIGTMPSIZE];
    uint32_t tmpvalue[BIGTMPSIZE];
    uint32_t Lkminus1value[BIGTMPSIZE];
    uint32_t Lkvalue[BIGTMPSIZE];
    BIG_ERR_CODE err;
    int e, i, jac;

    if (big_cmp_abs(n, &One) == 0)
        return (BIG_FALSE);
    if (big_cmp_abs(n, &Two) == 0)
        return (BIG_TRUE);
    if ((n->value[0] & 1) == 0)
        return (BIG_FALSE);

    if ((err = big_init1(&o, n->len, ovalue, arraysize(ovalue))) != BIG_OK)
        return (err);

    if ((err = big_init1(&nminus1, n->len,
        nminus1value, arraysize(nminus1value))) != BIG_OK)
        goto ret1;

    if ((err = big_init1(&tmp, 2 * n->len,
        tmpvalue, arraysize(tmpvalue))) != BIG_OK)
        goto ret2;

    if ((err = big_init1(&Lkminus1, n->len,
        Lkminus1value, arraysize(Lkminus1value))) != BIG_OK)
        goto ret3;

    if ((err = big_init1(&Lk, n->len,
        Lkvalue, arraysize(Lkvalue))) != BIG_OK)
        goto ret4;

    (void) big_sub_pos(&o, n, &One);    /* cannot fail */
    (void) big_copy(&nminus1, &o);      /* cannot fail */
    e = 0;
    while ((o.value[0] & 1) == 0) {
        e++;
        (void) big_half_pos(&o, &o);  /* cannot fail */
    }
    if ((err = big_modexp(&tmp, &Two, &o, n, NULL)) != BIG_OK)
        goto ret;
    i = 0;
    while ((i < e) &&
        (big_cmp_abs(&tmp, &One) != 0) &&
        (big_cmp_abs(&tmp, &nminus1) != 0)) {
        if ((err = big_modexp(&tmp, &tmp, &Two, n, NULL)) !=  BIG_OK)
            goto ret;
        i++;
    }
    if (!((big_cmp_abs(&tmp, &nminus1) == 0) ||
        ((i == 0) && (big_cmp_abs(&tmp, &One) == 0)))) {
        err = BIG_FALSE;
        goto ret;
    }

    if ((err = big_sqrt_pos(&tmp, n)) != BIG_OK)
        goto ret;
    if ((err = big_mul(&tmp, &tmp, &tmp)) != BIG_OK)
        goto ret;
    if (big_cmp_abs(&tmp, n) == 0) {
        err = BIG_FALSE;
        goto ret;
    }

    (void) big_copy(&o, &Two);
    do {
        (void) big_add_abs(&o, &o, &One);
        if ((err = big_mul(&tmp, &o, &o)) != BIG_OK)
            goto ret;
        (void) big_sub_pos(&tmp, &tmp, &Four);
        if ((err = big_Jacobi_pos(&jac, &tmp, n)) != BIG_OK)
            goto ret;
    } while (jac != -1);

    (void) big_add_abs(&tmp, n, &One);
    if ((err = big_Lucas(&Lkminus1, &Lk, &o, &tmp, n)) != BIG_OK)
        goto ret;
    if ((big_cmp_abs(&Lkminus1, &o) == 0) && (big_cmp_abs(&Lk, &Two) == 0))
        err = BIG_TRUE;
    else err = BIG_FALSE;

ret:
    if (Lk.malloced) big_finish(&Lk);
ret4:
    if (Lkminus1.malloced) big_finish(&Lkminus1);
ret3:
    if (tmp.malloced) big_finish(&tmp);
ret2:
    if (nminus1.malloced) big_finish(&nminus1);
ret1:
    if (o.malloced) big_finish(&o);

    return (err);
}


#define SIEVESIZE 1000

uint32_t smallprimes[] =
{
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
51, 53, 59, 61, 67, 71, 73, 79, 83, 89, 91, 97
};


BIG_ERR_CODE
big_nextprime_pos(BIGNUM *result, BIGNUM *n)
{
    BIG_ERR_CODE err;
    int sieve[SIEVESIZE];
    int i;
    uint32_t off, p;

    if ((err = big_copy(result, n)) != BIG_OK)
        return (err);
    result->value[0] |= 1;
    /* LINTED */
    while (1) {
        for (i = 0; i < SIEVESIZE; i++) sieve[i] = 0;
        for (i = 0;
            i < sizeof (smallprimes) / sizeof (uint32_t); i++) {
            p = smallprimes[i];
            off = big_mod16_pos(result, p);
            off = p - off;
            if ((off % 2) == 1) off = off + p;
            off = off/2;
            while (off < SIEVESIZE) {
                sieve[off] = 1;
                off = off + p;
            }
        }

        for (i = 0; i < SIEVESIZE; i++) {
            if (sieve[i] == 0) {
                err = big_isprime_pos(result);
                if (err != BIG_FALSE) {
                    if (err != BIG_TRUE)
                        return (err);
                    else
                        return (BIG_OK);
                }

            }
            if ((err = big_add_abs(result, result, &Two)) !=
                BIG_OK)
                return (err);
        }
    }
    return (BIG_OK);
}


BIG_ERR_CODE
big_nextprime_pos_slow(BIGNUM *result, BIGNUM *n)
{
    BIG_ERR_CODE err;


    if ((err = big_copy(result, n)) != BIG_OK)
        return (err);
    result->value[0] |= 1;
    while ((err = big_isprime_pos(result)) != BIG_TRUE) {
        if (err != BIG_FALSE)
            return (err);
        if ((err = big_add_abs(result, result, &Two)) != BIG_OK)
            return (err);
    }
    return (BIG_OK);
}


/*
 * given m and e, computes the rest in the equation
 * gcd(m, e) = cm * m + ce * e
 */
BIG_ERR_CODE
big_ext_gcd_pos(BIGNUM *gcd, BIGNUM *cm, BIGNUM *ce, BIGNUM *m, BIGNUM *e)
{
    BIGNUM *xi, *ri, *riminus1, *riminus2, *t,
        *vmi, *vei, *vmiminus1, *veiminus1;
    BIGNUM t1, t2, t3, t4, t5, t6, t7, t8, tmp;
    uint32_t t1value[BIGTMPSIZE];
    uint32_t t2value[BIGTMPSIZE];
    uint32_t t3value[BIGTMPSIZE];
    uint32_t t4value[BIGTMPSIZE];
    uint32_t t5value[BIGTMPSIZE];
    uint32_t t6value[BIGTMPSIZE];
    uint32_t t7value[BIGTMPSIZE];
    uint32_t t8value[BIGTMPSIZE];
    uint32_t tmpvalue[BIGTMPSIZE];
    BIG_ERR_CODE err;
    int len;

    if (big_cmp_abs(m, e) >= 0) len = m->len;
    else len = e->len;

    if ((err = big_init1(&t1, len,
        t1value, arraysize(t1value))) != BIG_OK)
        return (err);
    if ((err = big_init1(&t2, len,
        t2value, arraysize(t2value))) != BIG_OK)
            goto ret1;
    if ((err = big_init1(&t3, len,
        t3value, arraysize(t3value))) != BIG_OK)
            goto ret2;
    if ((err = big_init1(&t4, len,
        t4value, arraysize(t3value))) != BIG_OK)
            goto ret3;
    if ((err = big_init1(&t5, len,
        t5value, arraysize(t5value))) != BIG_OK)
            goto ret4;
    if ((err = big_init1(&t6, len,
        t6value, arraysize(t6value))) != BIG_OK)
            goto ret5;
    if ((err = big_init1(&t7, len,
        t7value, arraysize(t7value))) != BIG_OK)
            goto ret6;
    if ((err = big_init1(&t8, len,
        t8value, arraysize(t8value))) != BIG_OK)
            goto ret7;

    if ((err = big_init1(&tmp, 2 * len,
        tmpvalue, arraysize(tmpvalue))) != BIG_OK)
        goto ret8;

    ri = &t1;
    ri->value[0] = 1;
    ri->len = 1;
    xi = &t2;
    riminus1 = &t3;
    riminus2 = &t4;
    vmi = &t5;
    vei = &t6;
    vmiminus1 = &t7;
    veiminus1 = &t8;

    (void) big_copy(vmiminus1, &One);
    (void) big_copy(vmi, &One);
    (void) big_copy(veiminus1, &One);
    (void) big_copy(xi, &One);
    vei->len = 1;
    vei->value[0] = 0;

    (void) big_copy(riminus1, m);
    (void) big_copy(ri, e);

    while (!big_is_zero(ri)) {
        t = riminus2;
        riminus2 = riminus1;
        riminus1 = ri;
        ri = t;
        if ((err = big_mul(&tmp, vmi, xi)) != BIG_OK)
            goto ret;
        if ((err = big_sub(vmiminus1, vmiminus1, &tmp)) != BIG_OK)
            goto ret;
        t = vmiminus1;
        vmiminus1 = vmi;
        vmi = t;
        if ((err = big_mul(&tmp, vei, xi)) != BIG_OK)
            goto ret;
        if ((err = big_sub(veiminus1, veiminus1, &tmp)) != BIG_OK)
            goto ret;
        t = veiminus1;
        veiminus1 = vei;
        vei = t;
        if ((err = big_div_pos(xi, ri, riminus2, riminus1)) != BIG_OK)
            goto ret;
    }
    if ((gcd != NULL) && ((err = big_copy(gcd, riminus1)) != BIG_OK))
        goto ret;
    if ((cm != NULL) && ((err = big_copy(cm, vmi)) != BIG_OK))
        goto ret;
    if (ce != NULL)
        err = big_copy(ce, vei);
ret:
    if (tmp.malloced) big_finish(&tmp);
ret8:
    if (t8.malloced) big_finish(&t8);
ret7:
    if (t7.malloced) big_finish(&t7);
ret6:
    if (t6.malloced) big_finish(&t6);
ret5:
    if (t5.malloced) big_finish(&t5);
ret4:
    if (t4.malloced) big_finish(&t4);
ret3:
    if (t3.malloced) big_finish(&t3);
ret2:
    if (t2.malloced) big_finish(&t2);
ret1:
    if (t1.malloced) big_finish(&t1);

    return (err);
}