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xenocara/app/xedit/lisp/mp/mpi.c

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Importing from X.Org 7.2RC2
2006-11-25 13:07:29 -07:00
/*
* Copyright (c) 2002 by The XFree86 Project, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE XFREE86 PROJECT BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
* OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
* Except as contained in this notice, the name of the XFree86 Project shall
* not be used in advertising or otherwise to promote the sale, use or other
* dealings in this Software without prior written authorization from the
* XFree86 Project.
*
* Author: Paulo César Pereira de Andrade
*/
/* $XFree86: xc/programs/xedit/lisp/mp/mpi.c,v 1.12 2002/11/20 07:44:43 paulo Exp $ */
#include "mp.h"
#ifdef __UNIXOS2__
# define finite(x) isfinite(x)
#endif
/*
* Prototypes
*/
/* do the hard work of mpi_add and mpi_sub */
static void mpi_addsub(mpi *rop, mpi *op1, mpi *op2, int sub);
/* logical functions implementation */
static INLINE BNS mpi_logic(BNS op1, BNS op2, BNS op);
static void mpi_log(mpi *rop, mpi *op1, mpi *op2, BNS op);
/* internal mpi_seti, whithout memory allocation */
static void _mpi_seti(mpi *rop, long si);
/*
* Initialization
*/
static BNS onedig[1] = { 1 };
static mpi mpone = { 1, 1, 0, (BNS*)&onedig };
/*
* Implementation
*/
void
mpi_init(mpi *op)
{
op->sign = 0;
op->size = op->alloc = 1;
op->digs = mp_malloc(sizeof(BNS));
op->digs[0] = 0;
}
void
mpi_clear(mpi *op)
{
op->sign = 0;
op->size = op->alloc = 0;
mp_free(op->digs);
}
void
mpi_set(mpi *rop, mpi *op)
{
if (rop != op) {
if (rop->alloc < op->size) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * op->size);
rop->alloc = op->size;
}
rop->size = op->size;
memcpy(rop->digs, op->digs, sizeof(BNS) * op->size);
rop->sign = op->sign;
}
}
void
mpi_seti(mpi *rop, long si)
{
unsigned long ui;
int sign = si < 0;
int size;
if (si == MINSLONG) {
ui = MINSLONG;
size = 2;
}
else {
if (sign)
ui = -si;
else
ui = si;
if (ui < CARRY)
size = 1;
else
size = 2;
}
if (rop->alloc < size) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * size);
rop->alloc = size;
}
rop->size = size;
/* store data in small mp integer */
rop->digs[0] = (BNS)ui;
if (size > 1)
rop->digs[1] = (BNS)(ui >> BNSBITS);
rop->size = size;
/* adjust result sign */
rop->sign = sign;
}
static void
_mpi_seti(mpi *rop, long si)
{
unsigned long ui;
int sign = si < 0;
int size;
if (si == MINSLONG) {
ui = MINSLONG;
size = 2;
}
else {
if (sign)
ui = -si;
else
ui = si;
if (ui < CARRY)
size = 1;
else
size = 2;
}
rop->digs[0] = (BNS)ui;
if (size > 1)
rop->digs[1] = (BNS)(ui >> BNSBITS);
rop->size = size;
rop->sign = sign;
}
void
mpi_setd(mpi *rop, double d)
{
long i;
double mantissa;
int shift, exponent;
BNI size;
if (isnan(d))
d = 0.0;
else if (!finite(d))
d = copysign(1.0, d) * DBL_MAX;
/* check if number is larger than 1 */
if (fabs(d) < 1.0) {
rop->digs[0] = 0;
rop->size = 1;
rop->sign = d < 0.0;
return;
}
mantissa = frexp(d, &exponent);
if (mantissa < 0)
mantissa = -mantissa;
size = (exponent + (BNSBITS - 1)) / BNSBITS;
shift = BNSBITS - (exponent & (BNSBITS - 1));
/* adjust amount of memory */
if (rop->alloc < size) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * size);
rop->alloc = size;
}
rop->size = size;
/* adjust the exponent */
if (shift < BNSBITS)
mantissa = ldexp(mantissa, -shift);
/* convert double */
for (i = size - 1; i >= 0 && mantissa != 0.0; i--) {
mantissa = ldexp(mantissa, BNSBITS);
rop->digs[i] = (BNS)mantissa;
mantissa -= rop->digs[i];
}
for (; i >= 0; i--)
rop->digs[i] = 0;
/* normalize */
if (size > 1 && rop->digs[size - 1] == 0)
--rop->size;
rop->sign = d < 0.0;
}
/* how many BNS in the given base, log(base) / log(CARRY) */
#ifdef LONG64
static double str_bases[37] = {
0.0000000000000000, 0.0000000000000000, 0.0312500000000000,
0.0495300781475362, 0.0625000000000000, 0.0725602529652301,
0.0807800781475362, 0.0877298413143002, 0.0937500000000000,
0.0990601562950723, 0.1038102529652301, 0.1081072380824156,
0.1120300781475362, 0.1156387411919092, 0.1189798413143002,
0.1220903311127662, 0.1250000000000000, 0.1277332137890731,
0.1303101562950723, 0.1327477347951120, 0.1350602529652300,
0.1372599194618363, 0.1393572380824156, 0.1413613111267817,
0.1432800781475362, 0.1451205059304602, 0.1468887411919092,
0.1485902344426084, 0.1502298413143002, 0.1518119060977367,
0.1533403311127662, 0.1548186346995899, 0.1562500000000000,
0.1576373162299517, 0.1589832137890731, 0.1602900942795302,
0.1615601562950723,
};
#else
static double str_bases[37] = {
0.0000000000000000, 0.0000000000000000, 0.0625000000000000,
0.0990601562950723, 0.1250000000000000, 0.1451205059304602,
0.1615601562950723, 0.1754596826286003, 0.1875000000000000,
0.1981203125901446, 0.2076205059304602, 0.2162144761648311,
0.2240601562950723, 0.2312774823838183, 0.2379596826286003,
0.2441806622255325, 0.2500000000000000, 0.2554664275781462,
0.2606203125901445, 0.2654954695902241, 0.2701205059304602,
0.2745198389236725, 0.2787144761648311, 0.2827226222535633,
0.2865601562950723, 0.2902410118609203, 0.2937774823838183,
0.2971804688852168, 0.3004596826286003, 0.3036238121954733,
0.3066806622255324, 0.3096372693991797, 0.3125000000000000,
0.3152746324599034, 0.3179664275781462, 0.3205801885590604,
0.3231203125901446,
};
#endif
void
mpi_setstr(mpi *rop, char *str, int base)
{
long i; /* counter */
int sign; /* result sign */
BNI carry; /* carry value */
BNI value; /* temporary value */
BNI size; /* size of result */
char *ptr; /* end of valid input */
/* initialization */
sign = 0;
carry = 0;
/* skip leading spaces */
while (isspace(*str))
++str;
/* check if sign supplied */
if (*str == '-') {
sign = 1;
++str;
}
else if (*str == '+')
++str;
/* skip leading zeros */
while (*str == '0')
++str;
ptr = str;
while (*ptr) {
if (*ptr >= '0' && *ptr <= '9') {
if (*ptr - '0' >= base)
break;
}
else if (*ptr >= 'A' && *ptr <= 'Z') {
if (*ptr - 'A' + 10 >= base)
break;
}
else if (*ptr >= 'a' && *ptr <= 'z') {
if (*ptr - 'a' + 10 >= base)
break;
}
else
break;
++ptr;
}
/* resulting size */
size = (ptr - str) * str_bases[base] + 1;
/* make sure rop has enough storage */
if (rop->alloc < size) {
rop->digs = mp_realloc(rop->digs, size * sizeof(BNS));
rop->alloc = size;
}
rop->size = size;
/* initialize rop to zero */
memset(rop->digs, '\0', size * sizeof(BNS));
/* set result sign */
rop->sign = sign;
/* convert string */
for (; str < ptr; str++) {
value = *str;
if (islower(value))
value = toupper(value);
value = value > '9' ? value - 'A' + 10 : value - '0';
value += rop->digs[0] * base;
carry = value >> BNSBITS;
rop->digs[0] = (BNS)value;
for (i = 1; i < size; i++) {
value = (BNI)rop->digs[i] * base + carry;
carry = value >> BNSBITS;
rop->digs[i] = (BNS)value;
}
}
/* normalize */
if (rop->size > 1 && rop->digs[rop->size - 1] == 0)
--rop->size;
}
void
mpi_add(mpi *rop, mpi *op1, mpi *op2)
{
mpi_addsub(rop, op1, op2, 0);
}
void
mpi_addi(mpi *rop, mpi *op1, long op2)
{
BNS digs[2];
mpi op;
op.digs = (BNS*)digs;
_mpi_seti(&op, op2);
mpi_addsub(rop, op1, &op, 0);
}
void
mpi_sub(mpi *rop, mpi *op1, mpi *op2)
{
mpi_addsub(rop, op1, op2, 1);
}
void
mpi_subi(mpi *rop, mpi *op1, long op2)
{
BNS digs[2];
mpi op;
op.digs = (BNS*)digs;
_mpi_seti(&op, op2);
mpi_addsub(rop, op1, &op, 1);
}
static void
mpi_addsub(mpi *rop, mpi *op1, mpi *op2, int sub)
{
long xlen; /* maximum result size */
if (sub ^ (op1->sign == op2->sign)) {
/* plus one for possible carry */
xlen = MAX(op1->size, op2->size) + 1;
if (rop->alloc < xlen) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * xlen);
rop->alloc = xlen;
}
rop->size = mp_add(rop->digs, op1->digs, op2->digs,
op1->size, op2->size);
rop->sign = op1->sign;
}
else {
long cmp; /* check for larger operator */
cmp = mpi_cmpabs(op1, op2);
if (cmp == 0) {
rop->digs[0] = 0;
rop->size = 1;
rop->sign = 0;
}
else {
xlen = MAX(op1->size, op2->size);
if (rop->alloc < xlen) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * xlen);
rop->alloc = xlen;
}
if (cmp > 0) {
rop->size = mp_sub(rop->digs, op1->digs, op2->digs,
op1->size, op2->size);
rop->sign = op1->sign;
}
else {
rop->size = mp_sub(rop->digs, op2->digs, op1->digs,
op2->size, op1->size);
rop->sign = sub ^ op2->sign;
}
}
}
}
void
mpi_mul(mpi *rop, mpi *op1, mpi *op2)
{
int sign; /* sign flag */
BNS *digs; /* result data */
long xsize; /* result size */
/* get result sign */
sign = op1->sign ^ op2->sign;
/* check for special cases */
if (op1->size == 1) {
if (*op1->digs == 0) {
/* multiply by 0 */
mpi_seti(rop, 0);
return;
}
else if (*op1->digs == 1) {
/* multiply by +-1 */
if (rop->alloc < op2->size) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * op2->size);
rop->alloc = op2->size;
}
rop->size = op2->size;
memmove(rop->digs, op2->digs, sizeof(BNS) * op2->size);
rop->sign = op2->size > 1 || *op2->digs ? sign : 0;
return;
}
}
else if (op2->size == 1) {
if (*op2->digs == 0) {
/* multiply by 0 */
mpi_seti(rop, 0);
return;
}
else if (*op2->digs == 1) {
/* multiply by +-1 */
if (rop->alloc < op1->size) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * op1->size);
rop->alloc = op1->size;
}
rop->size = op1->size;
memmove(rop->digs, op1->digs, sizeof(BNS) * op1->size);
rop->sign = op1->size > 1 || *op1->digs ? sign : 0;
return;
}
}
/* allocate result data and set it to zero */
xsize = op1->size + op2->size;
if (rop->digs == op1->digs || rop->digs == op2->digs)
/* rop is also an operand */
digs = mp_calloc(1, sizeof(BNS) * xsize);
else {
if (rop->alloc < xsize) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * xsize);
rop->alloc = xsize;
}
digs = rop->digs;
memset(digs, '\0', sizeof(BNS) * xsize);
}
/* multiply operands */
xsize = mp_mul(digs, op1->digs, op2->digs, op1->size, op2->size);
/* store result in rop */
if (digs != rop->digs) {
/* if rop was an operand, free old data */
mp_free(rop->digs);
rop->digs = digs;
}
rop->size = xsize;
/* set result sign */
rop->sign = sign;
}
void
mpi_muli(mpi *rop, mpi *op1, long op2)
{
BNS digs[2];
mpi op;
op.digs = (BNS*)digs;
_mpi_seti(&op, op2);
mpi_mul(rop, op1, &op);
}
void
mpi_div(mpi *rop, mpi *num, mpi *den)
{
mpi_divqr(rop, NULL, num, den);
}
void
mpi_rem(mpi *rop, mpi *num, mpi *den)
{
mpi_divqr(NULL, rop, num, den);
}
/*
* Could/should be changed to not allocate qdigs if qrop is NULL
* Performance wouldn't suffer too much with a test on every loop iteration.
*/
void
mpi_divqr(mpi *qrop, mpi *rrop, mpi *num, mpi *den)
{
long i, j; /* counters */
int qsign; /* sign of quotient */
int rsign; /* sign of remainder */
BNI qsize; /* size of quotient */
BNI rsize; /* size of remainder */
BNS qest; /* estimative of quotient value */
BNS *qdigs, *rdigs; /* work copy or result */
BNS *ndigs, *ddigs; /* work copy or divisor and dividend */
BNI value; /* temporary result */
long svalue; /* signed temporary result (2's complement) */
BNS carry, scarry, denorm; /* carry and normalization */
BNI dpos, npos; /* offsets in data */
/* get signs */
rsign = num->sign;
qsign = rsign ^ den->sign;
/* check for special case */
if (num->size < den->size) {
/* quotient is zero and remainder is numerator */
if (rrop && rrop->digs != num->digs) {
if (rrop->alloc < num->size) {
rrop->digs = mp_realloc(rrop->digs, sizeof(BNS) * num->size);
rrop->alloc = num->size;
}
rrop->size = num->size;
memcpy(rrop->digs, num->digs, sizeof(BNS) * num->size);
rrop->sign = rsign;
}
if (qrop)
mpi_seti(qrop, 0);
return;
}
/* estimate result sizes */
rsize = den->size;
qsize = num->size - den->size + 1;
/* offsets */
npos = num->size - 1;
dpos = den->size - 1;
/* allocate space for quotient and remainder */
if (qrop == NULL || qrop->digs == num->digs || qrop->digs == den->digs)
qdigs = mp_calloc(1, sizeof(BNS) * qsize);
else {
if (qrop->alloc < qsize) {
qrop->digs = mp_realloc(qrop->digs, sizeof(BNS) * qsize);
qrop->alloc = qsize;
}
memset(qrop->digs, '\0', sizeof(BNS) * qsize);
qdigs = qrop->digs;
}
if (rrop) {
if (rrop->digs == num->digs || rrop->digs == den->digs)
rdigs = mp_calloc(1, sizeof(BNS) * rsize);
else {
if (rrop->alloc < rsize) {
rrop->digs = mp_realloc(rrop->digs, sizeof(BNS) * rsize);
rrop->alloc = rsize;
}
memset(rrop->digs, '\0', sizeof(BNS) * rsize);
rdigs = rrop->digs;
}
}
else
rdigs = NULL; /* fix gcc warning */
/* special case, only one word in divisor */
if (dpos == 0) {
for (carry = 0, i = npos; i >= 0; i--) {
value = ((BNI)carry << BNSBITS) + num->digs[i];
qdigs[i] = (BNS)(value / den->digs[0]);
carry = (BNS)(value % den->digs[0]);
}
if (rrop)
rdigs[0] = carry;
goto mpi_divqr_done;
}
/* make work copy of numerator */
ndigs = mp_malloc(sizeof(BNS) * (num->size + 1));
/* allocate one extra word an update offset */
memcpy(ndigs, num->digs, sizeof(BNS) * num->size);
ndigs[num->size] = 0;
++npos;
/* normalize */
denorm = (BNS)((BNI)CARRY / ((BNI)(den->digs[dpos]) + 1));
if (denorm > 1) {
/* i <= num->size because ndigs has an extra word */
for (carry = 0, i = 0; i <= num->size; i++) {
value = ndigs[i] * (BNI)denorm + carry;
ndigs[i] = (BNS)value;
carry = (BNS)(value >> BNSBITS);
}
/* make work copy of denominator */
ddigs = mp_malloc(sizeof(BNS) * den->size);
memcpy(ddigs, den->digs, sizeof(BNS) * den->size);
for (carry = 0, i = 0; i < den->size; i++) {
value = ddigs[i] * (BNI)denorm + carry;
ddigs[i] = (BNS)value;
carry = (BNS)(value >> BNSBITS);
}
}
else
/* only allocate copy of denominator if going to change it */
ddigs = den->digs;
/* divide mp integers */
for (j = qsize - 1; j >= 0; j--, npos--) {
/* estimate quotient */
if (ndigs[npos] == ddigs[dpos])
qest = (BNS)SMASK;
else
qest = (BNS)((((BNI)(ndigs[npos]) << 16) + ndigs[npos - 1]) /
ddigs[dpos]);
while ((value = ((BNI)(ndigs[npos]) << 16) + ndigs[npos - 1] -
qest * (BNI)(ddigs[dpos])) < CARRY &&
ddigs[dpos - 1] * (BNI)qest >
(value << BNSBITS) + ndigs[npos - 2])
--qest;
/* multiply and subtract */
carry = scarry = 0;
for (i = 0; i < den->size; i++) {
value = qest * (BNI)ddigs[i] + carry;
carry = (BNS)(value >> BNSBITS);
svalue = (long)ndigs[npos - dpos + i - 1] - (long)(value & SMASK) -
(long)scarry;
ndigs[npos - dpos + i - 1] = (BNS)svalue;
scarry = svalue < 0;
}
svalue = (long)ndigs[npos] - (long)(carry & SMASK) - (long)scarry;
ndigs[npos] = (BNS)svalue;
if (svalue & LMASK) {
/* quotient too big */
--qest;
carry = 0;
for (i = 0; i < den->size; i++) {
value = ndigs[npos - dpos + i - 1] + (BNI)carry + (BNI)ddigs[i];
ndigs[npos - dpos + i - 1] = (BNS)value;
carry = (BNS)(value >> BNSBITS);
}
ndigs[npos] += carry;
}
qdigs[j] = qest;
}
/* calculate remainder */
if (rrop) {
for (carry = 0, j = dpos; j >= 0; j--) {
value = ((BNI)carry << BNSBITS) + ndigs[j];
rdigs[j] = (BNS)(value / denorm);
carry = (BNS)(value % denorm);
}
}
mp_free(ndigs);
if (ddigs != den->digs)
mp_free(ddigs);
mpi_divqr_done:
if (rrop) {
if (rrop->digs != rdigs)
mp_free(rrop->digs);
/* normalize remainder */
for (i = rsize - 1; i >= 0; i--)
if (rdigs[i] != 0)
break;
if (i != rsize - 1) {
if (i < 0) {
rsign = 0;
rsize = 1;
}
else
rsize = i + 1;
}
rrop->digs = rdigs;
rrop->sign = rsign;
rrop->size = rsize;
}
/* normalize quotient */
if (qrop) {
if (qrop->digs != qdigs)
mp_free(qrop->digs);
for (i = qsize - 1; i >= 0; i--)
if (qdigs[i] != 0)
break;
if (i != qsize - 1) {
if (i < 0) {
qsign = 0;
qsize = 1;
}
else
qsize = i + 1;
}
qrop->digs = qdigs;
qrop->sign = qsign;
qrop->size = qsize;
}
else
mp_free(qdigs);
}
long
mpi_divqri(mpi *qrop, mpi *num, long den)
{
BNS ddigs[2];
mpi dop, rrop;
long remainder;
dop.digs = (BNS*)ddigs;
_mpi_seti(&dop, den);
memset(&rrop, '\0', sizeof(mpi));
mpi_init(&rrop);
mpi_divqr(qrop, &rrop, num, &dop);
remainder = rrop.digs[0];
if (rrop.size > 1)
remainder |= (BNI)(rrop.digs[1]) << BNSBITS;
if (rrop.sign)
remainder = -remainder;
mpi_clear(&rrop);
return (remainder);
}
void
mpi_divi(mpi *rop, mpi *num, long den)
{
BNS ddigs[2];
mpi dop;
dop.digs = (BNS*)ddigs;
_mpi_seti(&dop, den);
mpi_divqr(rop, NULL, num, &dop);
}
long
mpi_remi(mpi *num, long den)
{
return (mpi_divqri(NULL, num, den));
}
void
mpi_mod(mpi *rop, mpi *num, mpi *den)
{
mpi_rem(rop, num, den);
if (num->sign ^ den->sign)
mpi_add(rop, rop, den);
}
long
mpi_modi(mpi *num, long den)
{
long remainder;
remainder = mpi_remi(num, den);
if (num->sign ^ (den < 0))
remainder += den;
return (remainder);
}
void
mpi_gcd(mpi *rop, mpi *num, mpi *den)
{
long cmp;
mpi rem;
/* check if result already given */
cmp = mpi_cmpabs(num, den);
/* check if num is equal to den or if num is zero */
if (cmp == 0 || (num->size == 1 && num->digs[0] == 0)) {
mpi_set(rop, den);
rop->sign = 0;
return;
}
/* check if den is not zero */
if (den->size == 1 && den->digs[0] == 0) {
mpi_set(rop, num);
rop->sign = 0;
return;
}
/* don't call mpi_init, relies on realloc(0, size) == malloc(size) */
memset(&rem, '\0', sizeof(mpi));
/* if num larger than den */
if (cmp > 0) {
mpi_rem(&rem, num, den);
if (rem.size == 1 && rem.digs[0] == 0) {
/* exact division */
mpi_set(rop, den);
rop->sign = 0;
mpi_clear(&rem);
return;
}
mpi_set(rop, den);
}
else {
mpi_rem(&rem, den, num);
if (rem.size == 1 && rem.digs[0] == 0) {
/* exact division */
mpi_set(rop, num);
rop->sign = 0;
mpi_clear(&rem);
return;
}
mpi_set(rop, num);
}
/* loop using positive values */
rop->sign = rem.sign = 0;
/* cannot optimize this inverting rem/rop assignment earlier
* because rop mais be an operand */
mpi_swap(rop, &rem);
/* Euclides algorithm */
for (;;) {
mpi_rem(&rem, &rem, rop);
if (rem.size == 1 && rem.digs[0] == 0)
break;
mpi_swap(rop, &rem);
}
mpi_clear(&rem);
}
void
mpi_lcm(mpi *rop, mpi *num, mpi *den)
{
mpi gcd;
/* check for zero operand */
if ((num->size == 1 && num->digs[0] == 0) ||
(den->size == 1 && den->digs[0] == 0)) {
rop->digs[0] = 0;
rop->sign = 0;
return;
}
/* don't call mpi_init, relies on realloc(0, size) == malloc(size) */
memset(&gcd, '\0', sizeof(mpi));
mpi_gcd(&gcd, num, den);
mpi_div(&gcd, den, &gcd);
mpi_mul(rop, &gcd, num);
rop->sign = 0;
mpi_clear(&gcd);
}
void
mpi_pow(mpi *rop, mpi *op, unsigned long exp)
{
mpi zop, top;
if (exp == 2) {
mpi_mul(rop, op, op);
return;
}
/* check for op**0 */
else if (exp == 0) {
rop->digs[0] = 1;
rop->size = 1;
rop->sign = 0;
return;
}
else if (exp == 1) {
mpi_set(rop, op);
return;
}
else if (op->size == 1) {
if (op->digs[0] == 0) {
mpi_seti(rop, 0);
return;
}
else if (op->digs[0] == 1) {
mpi_seti(rop, op->sign && (exp & 1) ? -1 : 1);
return;
}
}
memset(&zop, '\0', sizeof(mpi));
memset(&top, '\0', sizeof(mpi));
mpi_set(&zop, op);
mpi_set(&top, op);
for (--exp; exp; exp >>= 1) {
if (exp & 1)
mpi_mul(&zop, &top, &zop);
mpi_mul(&top, &top, &top);
}
mpi_clear(&top);
rop->sign = zop.sign;
mp_free(rop->digs);
rop->digs = zop.digs;
rop->size = zop.size;
}
/* Find integer root of given number using the iteration
* x{n+1} = ((K-1) * x{n} + N / x{n}^(K-1)) / K
*/
int
mpi_root(mpi *rop, mpi *op, unsigned long nth)
{
long bits, cmp;
int exact;
int sign;
mpi *r, t, temp, quot, old, rem;
sign = op->sign;
/* divide by zero op**1/0 */
if (nth == 0) {
int one = 1, zero = 0;
one = one / zero;
}
/* result is complex */
if (sign && !(nth & 1)) {
int one = 1, zero = 0;
one = one / zero;
}
/* special case op**1/1 = op */
if (nth == 1) {
mpi_set(rop, op);
return (1);
}
bits = mpi_getsize(op, 2) - 2;
if (bits < 0 || bits / nth == 0) {
/* integral root is surely less than 2 */
exact = op->size == 1 && (op->digs[0] == 1 || op->digs[0] == 0);
mpi_seti(rop, sign ? -1 : op->digs[0] == 0 ? 0 : 1);
return (exact == 1);
}
/* initialize */
if (rop != op)
r = rop;
else {
r = &t;
memset(r, '\0', sizeof(mpi));
}
memset(&temp, '\0', sizeof(mpi));
memset(&quot, '\0', sizeof(mpi));
memset(&old, '\0', sizeof(mpi));
memset(&rem, '\0', sizeof(mpi));
if (sign)
r->sign = 0;
/* root aproximation */
mpi_ash(r, op, -(bits - (bits / nth)));
for (;;) {
mpi_pow(&temp, r, nth - 1);
mpi_divqr(&quot, &rem, op, &temp);
cmp = mpi_cmpabs(r, &quot);
if (cmp == 0) {
exact = mpi_cmpi(&rem, 0) == 0;
break;
}
else if (cmp < 0) {
if (mpi_cmpabs(r, &old) == 0) {
exact = 0;
break;
}
mpi_set(&old, r);
}
mpi_muli(&temp, r, nth - 1);
mpi_add(&quot, &quot, &temp);
mpi_divi(r, &quot, nth);
}
mpi_clear(&temp);
mpi_clear(&quot);
mpi_clear(&old);
mpi_clear(&rem);
if (r != rop) {
mpi_set(rop, r);
mpi_clear(r);
}
rop->sign = sign;
return (exact);
}
/*
* Find square root using the iteration:
* x{n+1} = (x{n}+N/x{n})/2
*/
int
mpi_sqrt(mpi *rop, mpi *op)
{
long bits, cmp;
int exact;
mpi *r, t, quot, rem, old;
/* result is complex */
if (op->sign) {
int one = 1, zero = 0;
one = one / zero;
}
bits = mpi_getsize(op, 2) - 2;
if (bits < 2) {
/* integral root is surely less than 2 */
exact = op->size == 1 && (op->digs[0] == 1 || op->digs[0] == 0);
mpi_seti(rop, op->digs[0] == 0 ? 0 : 1);
return (exact == 1);
}
/* initialize */
if (rop != op)
r = rop;
else {
r = &t;
memset(r, '\0', sizeof(mpi));
}
memset(&quot, '\0', sizeof(mpi));
memset(&rem, '\0', sizeof(mpi));
memset(&old, '\0', sizeof(mpi));
/* root aproximation */
mpi_ash(r, op, -(bits - (bits / 2)));
for (;;) {
if (mpi_cmpabs(r, &old) == 0) {
exact = 0;
break;
}
mpi_divqr(&quot, &rem, op, r);
cmp = mpi_cmpabs(&quot, r);
if (cmp == 0) {
exact = mpi_cmpi(&rem, 0) == 0;
break;
}
else if (cmp > 0 && rem.size == 1 && rem.digs[0] == 0)
mpi_subi(&quot, &quot, 1);
mpi_set(&old, r);
mpi_add(r, r, &quot);
mpi_ash(r, r, -1);
}
mpi_clear(&quot);
mpi_clear(&rem);
mpi_clear(&old);
if (r != rop) {
mpi_set(rop, r);
mpi_clear(r);
}
return (exact);
}
void
mpi_ash(mpi *rop, mpi *op, long shift)
{
long i; /* counter */
long xsize; /* maximum result size */
BNS *digs;
/* check for 0 shift, multiply/divide by 1 */
if (shift == 0) {
if (rop != op) {
if (rop->alloc < op->size) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * op->size);
rop->alloc = op->size;
}
rop->size = op->size;
memcpy(rop->digs, op->digs, sizeof(BNS) * op->size);
}
return;
}
else if (op->size == 1 && op->digs[0] == 0) {
rop->sign = 0;
rop->size = 1;
rop->digs[0] = 0;
return;
}
/* check shift and initialize */
if (shift > 0)
xsize = op->size + (shift / BNSBITS) + 1;
else {
xsize = op->size - ((-shift) / BNSBITS);
if (xsize <= 0) {
rop->size = 1;
rop->sign = op->sign;
rop->digs[0] = op->sign ? 1 : 0;
return;
}
}
/* allocate/adjust memory for result */
if (rop == op)
digs = mp_malloc(sizeof(BNS) * xsize);
else {
if (rop->alloc < xsize) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * xsize);
rop->alloc = xsize;
}
digs = rop->digs;
}
/* left shift, multiply by power of two */
if (shift > 0)
rop->size = mp_lshift(digs, op->digs, op->size, shift);
/* right shift, divide by power of two */
else {
long carry = 0;
if (op->sign) {
BNI words, bits;
words = -shift / BNSBITS;
bits = -shift % BNSBITS;
for (i = 0; i < words; i++)
carry |= op->digs[xsize + i];
if (!carry) {
for (i = 0; i < bits; i++)
if (op->digs[op->size - xsize] & (1 << i)) {
carry = 1;
break;
}
}
}
rop->size = mp_rshift(digs, op->digs, op->size, -shift);
if (carry)
/* emulates two's complement subtracting 1 from the result */
rop->size = mp_add(digs, digs, mpone.digs, rop->size, 1);
}
if (rop->digs != digs) {
mp_free(rop->digs);
rop->alloc = rop->size;
rop->digs = digs;
}
rop->sign = op->sign;
}
static INLINE BNS
mpi_logic(BNS op1, BNS op2, BNS op)
{
switch (op) {
case '&':
return (op1 & op2);
case '|':
return (op1 | op2);
case '^':
return (op1 ^ op2);
}
return (SMASK);
}
static void
mpi_log(mpi *rop, mpi *op1, mpi *op2, BNS op)
{
long i; /* counter */
long c, c1, c2; /* carry */
BNS *digs, *digs1, *digs2; /* pointers to mp data */
BNI size, size1, size2;
BNS sign, sign1, sign2;
BNS n, n1, n2; /* logical operands */
BNI sum;
/* initialize */
size1 = op1->size;
size2 = op2->size;
sign1 = op1->sign ? SMASK : 0;
sign2 = op2->sign ? SMASK : 0;
sign = mpi_logic(sign1, sign2, op);
size = MAX(size1, size2);
if (sign)
++size;
if (rop->alloc < size) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * size);
rop->alloc = size;
}
digs = rop->digs;
digs1 = op1->digs;
digs2 = op2->digs;
c = c1 = c2 = 1;
/* apply logical operation */
for (i = 0; i < size; i++) {
if (i >= size1)
n1 = sign1;
else if (sign1) {
sum = (BNI)(BNS)(~digs1[i]) + c1;
c1 = (long)(sum >> BNSBITS);
n1 = (BNS)sum;
}
else
n1 = digs1[i];
if (i >= size2)
n2 = sign2;
else if (sign2) {
sum = (BNI)(BNS)(~digs2[i]) + c2;
c2 = (long)(sum >> BNSBITS);
n2 = (BNS)sum;
}
else
n2 = digs2[i];
n = mpi_logic(n1, n2, op);
if (sign) {
sum = (BNI)(BNS)(~n) + c;
c = (long)(sum >> BNSBITS);
digs[i] = (BNS)sum;
}
else
digs[i] = n;
}
/* normalize */
for (i = size - 1; i >= 0; i--)
if (digs[i] != 0)
break;
if (i != size - 1) {
if (i < 0) {
sign = 0;
size = 1;
}
else
size = i + 1;
}
rop->sign = sign != 0;
rop->size = size;
}
void
mpi_and(mpi *rop, mpi *op1, mpi *op2)
{
mpi_log(rop, op1, op2, '&');
}
void
mpi_ior(mpi *rop, mpi *op1, mpi *op2)
{
mpi_log(rop, op1, op2, '|');
}
void
mpi_xor(mpi *rop, mpi *op1, mpi *op2)
{
mpi_log(rop, op1, op2, '^');
}
void
mpi_com(mpi *rop, mpi *op)
{
static BNS digs[1] = { 1 };
static mpi one = { 0, 1, 1, (BNS*)&digs };
mpi_log(rop, rop, &one, '^');
}
void
mpi_neg(mpi *rop, mpi *op)
{
int sign = op->sign ^ 1;
if (rop->digs != op->digs) {
if (rop->alloc < op->size) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * rop->size);
rop->alloc = op->size;
}
rop->size = op->size;
memcpy(rop->digs, op->digs, sizeof(BNS) * rop->size);
}
rop->sign = sign;
}
void
mpi_abs(mpi *rop, mpi *op)
{
if (rop->digs != op->digs) {
if (rop->alloc < op->size) {
rop->digs = mp_realloc(rop->digs, sizeof(BNS) * rop->size);
rop->alloc = op->size;
}
rop->size = op->size;
memcpy(rop->digs, op->digs, sizeof(BNS) * rop->size);
}
rop->sign = 0;
}
int
mpi_cmp(mpi *op1, mpi *op2)
{
if (op1->sign ^ op2->sign)
return (op1->sign ? -1 : 1);
if (op1->size == op2->size) {
long i, cmp = 0;
for (i = op1->size - 1; i >= 0; i--)
if ((cmp = (long)op1->digs[i] - (long)op2->digs[i]) != 0)
break;
return (cmp == 0 ? 0 : (cmp < 0) ^ op1->sign ? -1 : 1);
}
return ((op1->size < op2->size) ^ op1->sign ? -1 : 1);
}
int
mpi_cmpi(mpi *op1, long op2)
{
long cmp;
if (op1->size > 2)
return (op1->sign ? -1 : 1);
cmp = op1->digs[0];
if (op1->size == 2) {
cmp |= (long)op1->digs[1] << BNSBITS;
if (cmp == MINSLONG)
return (op2 == cmp && op1->sign ? 0 : op1->sign ? -1 : 1);
}
if (op1->sign)
cmp = -cmp;
return (cmp - op2);
}
int
mpi_cmpabs(mpi *op1, mpi *op2)
{
if (op1->size == op2->size) {
long i, cmp = 0;
for (i = op1->size - 1; i >= 0; i--)
if ((cmp = (long)op1->digs[i] - (long)op2->digs[i]) != 0)
break;
return (cmp);
}
return ((op1->size < op2->size) ? -1 : 1);
}
int
mpi_cmpabsi(mpi *op1, long op2)
{
unsigned long cmp;
if (op1->size > 2)
return (1);
cmp = op1->digs[0];
if (op1->size == 2)
cmp |= (unsigned long)op1->digs[1] << BNSBITS;
return (cmp > op2 ? 1 : cmp == op2 ? 0 : -1);
}
int
mpi_sgn(mpi *op)
{
return (op->sign ? -1 : op->size > 1 || op->digs[0] ? 1 : 0);
}
void
mpi_swap(mpi *op1, mpi *op2)
{
if (op1 != op2) {
mpi swap;
memcpy(&swap, op1, sizeof(mpi));
memcpy(op1, op2, sizeof(mpi));
memcpy(op2, &swap, sizeof(mpi));
}
}
int
mpi_fiti(mpi *op)
{
if (op->size == 1)
return (1);
else if (op->size == 2) {
unsigned long value = ((BNI)(op->digs[1]) << BNSBITS) | op->digs[0];
if (value & MINSLONG)
return (op->sign && value == MINSLONG) ? 1 : 0;
return (1);
}
return (0);
}
long
mpi_geti(mpi *op)
{
long value;
value = op->digs[0];
if (op->size > 1)
value |= (BNI)(op->digs[1]) << BNSBITS;
return (op->sign && value != MINSLONG ? -value : value);
}
double
mpi_getd(mpi *op)
{
long i, len;
double d = 0.0;
int exponent;
#define FLOATDIGS sizeof(double) / sizeof(BNS)
switch (op->size) {
case 2:
d = (BNI)(op->digs[1]) << BNSBITS;
case 1:
d += op->digs[0];
return (op->sign ? -d : d);
default:
break;
}
for (i = 0, len = op->size; len > 0 && i < FLOATDIGS; i++)
d = ldexp(d, BNSBITS) + op->digs[--len];
d = frexp(d, &exponent);
if (len > 0)
exponent += len * BNSBITS;
if (d == 0.0)
return (d);
d = ldexp(d, exponent);
return (op->sign ? -d : d);
}
/* how many digits in a given base, floor(log(CARRY) / log(base)) */
#ifdef LONG64
static char dig_bases[37] = {
0, 0, 32, 20, 16, 13, 12, 11, 10, 10, 9, 9, 8, 8, 8, 8,
8, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6,
};
#else
static char dig_bases[37] = {
0, 0, 16, 10, 8, 6, 6, 5, 5, 5, 4, 4, 4, 4, 4, 4,
4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3,
};
#endif
/* how many digits per bit in a given base, log(2) / log(base) */
static double bit_bases[37] = {
0.0000000000000000, 0.0000000000000000, 1.0000000000000000,
0.6309297535714575, 0.5000000000000000, 0.4306765580733931,
0.3868528072345416, 0.3562071871080222, 0.3333333333333334,
0.3154648767857287, 0.3010299956639811, 0.2890648263178878,
0.2789429456511298, 0.2702381544273197, 0.2626495350371936,
0.2559580248098155, 0.2500000000000000, 0.2446505421182260,
0.2398124665681315, 0.2354089133666382, 0.2313782131597592,
0.2276702486969530, 0.2242438242175754, 0.2210647294575037,
0.2181042919855316, 0.2153382790366965, 0.2127460535533632,
0.2103099178571525, 0.2080145976765095, 0.2058468324604344,
0.2037950470905062, 0.2018490865820999, 0.2000000000000000,
0.1982398631705605, 0.1965616322328226, 0.1949590218937863,
0.1934264036172708,
};
/* normalization base for string conversion, pow(base, dig_bases[base]) & ~CARRY */
#ifdef LONG64
static BNS big_bases[37] = {
0x00000001, 0x00000001, 0x00000000, 0xCFD41B91, 0x00000000, 0x48C27395,
0x81BF1000, 0x75DB9C97, 0x40000000, 0xCFD41B91, 0x3B9ACA00, 0x8C8B6D2B,
0x19A10000, 0x309F1021, 0x57F6C100, 0x98C29B81, 0x00000000, 0x18754571,
0x247DBC80, 0x3547667B, 0x4C4B4000, 0x6B5A6E1D, 0x94ACE180, 0xCAF18367,
0x0B640000, 0x0E8D4A51, 0x1269AE40, 0x17179149, 0x1CB91000, 0x23744899,
0x2B73A840, 0x34E63B41, 0x40000000, 0x4CFA3CC1, 0x5C13D840, 0x6D91B519,
0x81BF1000,
};
#else
static BNS big_bases[37] = {
0x0001, 0x0001, 0x0000, 0xE6A9, 0x0000, 0x3D09, 0xB640, 0x41A7, 0x8000,
0xE6A9, 0x2710, 0x3931, 0x5100, 0x6F91, 0x9610, 0xC5C1, 0x0000, 0x1331,
0x16C8, 0x1ACB, 0x1F40, 0x242D, 0x2998, 0x2F87, 0x3600, 0x3D09, 0x44A8,
0x4CE3, 0x55C0, 0x5F45, 0x6978, 0x745F, 0x8000, 0x8C61, 0x9988, 0xA77B,
0xb640,
};
#endif
unsigned long
mpi_getsize(mpi *op, int base)
{
unsigned long value, bits;
value = op->digs[op->size - 1];
/* count leading bits */
if (value) {
unsigned long count, carry;
for (count = 0, carry = CARRY >> 1; carry; count++, carry >>= 1)
if (value & carry)
break;
bits = BNSBITS - count;
}
else
bits = 0;
return ((bits + (op->size - 1) * BNSBITS) * bit_bases[base] + 1);
}
char *
mpi_getstr(char *str, mpi *op, int base)
{
long i; /* counter */
BNS *digs, *xdigs; /* copy of op data */
BNI size; /* size of op */
BNI digits; /* digits per word in given base */
BNI bigbase; /* big base of given base */
BNI strsize; /* size of resulting string */
char *cp; /* pointer in str for conversion */
/* initialize */
size = op->size;
strsize = mpi_getsize(op, base) + op->sign + 1;
if (str == NULL)
str = mp_malloc(strsize);
/* check for zero */
if (size == 1 && op->digs[0] == 0) {
str[0] = '0';
str[1] = '\0';
return (str);
}
digits = dig_bases[base];
bigbase = big_bases[base];
cp = str + strsize;
*--cp = '\0';
/* make copy of op data and adjust digs */
xdigs = mp_malloc(size * sizeof(BNS));
memcpy(xdigs, op->digs, size * sizeof(unsigned short));
digs = xdigs + size - 1;
/* convert to string */
for (;;) {
long count = -1;
BNI value;
BNS quotient, remainder = 0;
/* if power of two base */
if ((base & (base - 1)) == 0) {
for (i = 0; i < size; i++) {
quotient = remainder;
remainder = digs[-i];
digs[-i] = quotient;
if (count < 0 && quotient)
count = i;
}
}
else {
for (i = 0; i < size; i++) {
value = digs[-i] + ((BNI)remainder << BNSBITS);
quotient = (BNS)(value / bigbase);
remainder = (BNS)(value % bigbase);
digs[-i] = quotient;
if (count < 0 && quotient)
count = i;
}
}
quotient = remainder;
for (i = 0; i < digits; i++) {
if (quotient == 0 && count < 0)
break;
remainder = quotient % base;
quotient /= base;
*--cp = remainder < 10 ? remainder + '0' : remainder - 10 + 'A';
}
if (count < 0)
break;
digs -= count;
size -= count;
}
/* adjust sign */
if (op->sign)
*--cp = '-';
/* remove any extra characters */
if (cp > str)
strcpy(str, cp);
mp_free(xdigs);
return (str);
}
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