text: /*
   * 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 += (BNI)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]) << BNSBITS) + ndigs[npos - 1]) /
  			 ddigs[dpos]);
  
  	while ((value = ((BNI)(ndigs[npos]) << BNSBITS) + 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(BNS));
      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);
  }
  