/**CFile***********************************************************************

  FileName    [epd.c]

  PackageName [epd]

  Synopsis    [Arithmetic functions with extended double precision.]

  Description []

  SeeAlso     []

  Author      [In-Ho Moon]

  Copyright [ This file was created at the University of Colorado at
  Boulder.  The University of Colorado at Boulder makes no warranty
  about the suitability of this software for any purpose.  It is
  presented on an AS IS basis.]

  Revision    [$Id: epd.c,v 1.1.1.1 2003/02/24 22:23:57 wjiang Exp $]

******************************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "util_hack.h"
#include "epd.h"


/**Function********************************************************************

  Synopsis    [Allocates an EpDouble struct.]

  Description [Allocates an EpDouble struct.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
EpDouble *
EpdAlloc()
{
  EpDouble    *epd;

  epd = ALLOC(EpDouble, 1);
  return(epd);
}


/**Function********************************************************************

  Synopsis    [Compares two EpDouble struct.]

  Description [Compares two EpDouble struct.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
EpdCmp(const char *key1, const char *key2)
{
  EpDouble *epd1 = (EpDouble *) key1;
  EpDouble *epd2 = (EpDouble *) key2;
  if (epd1->type.value != epd2->type.value ||
      epd1->exponent != epd2->exponent) {
    return(1);
  }
  return(0);
}


/**Function********************************************************************

  Synopsis    [Frees an EpDouble struct.]

  Description [Frees an EpDouble struct.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdFree(EpDouble *epd)
{
  FREE(epd);
}


/**Function********************************************************************

  Synopsis    [Multiplies two arbitrary precision double values.]

  Description [Multiplies two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdGetString(EpDouble *epd, char *str)
{
  double    value;
  int        exponent;
  char        *pos;

  if (IsNanDouble(epd->type.value)) {
    sprintf(str, "NaN");
    return;
  } else if (IsInfDouble(epd->type.value)) {
    if (epd->type.bits.sign == 1)
      sprintf(str, "-Inf");
    else
      sprintf(str, "Inf");
    return;
  }

  assert(epd->type.bits.exponent == EPD_MAX_BIN ||
     epd->type.bits.exponent == 0);

  EpdGetValueAndDecimalExponent(epd, &value, &exponent);
  sprintf(str, "%e", value);
  pos = strstr(str, "e");
  if (exponent >= 0) {
    if (exponent < 10)
      sprintf(pos + 1, "+0%d", exponent);
    else
      sprintf(pos + 1, "+%d", exponent);
  } else {
    exponent *= -1;
    if (exponent < 10)
      sprintf(pos + 1, "-0%d", exponent);
    else
      sprintf(pos + 1, "-%d", exponent);
  }
}


/**Function********************************************************************

  Synopsis    [Converts double to EpDouble struct.]

  Description [Converts double to EpDouble struct.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdConvert(double value, EpDouble *epd)
{
  epd->type.value = value;
  epd->exponent = 0;
  EpdNormalize(epd);
}


/**Function********************************************************************

  Synopsis    [Multiplies two arbitrary precision double values.]

  Description [Multiplies two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdMultiply(EpDouble *epd1, double value)
{
  EpDouble    epd2;
  double    tmp;
  int        exponent;

  if (EpdIsNan(epd1) || IsNanDouble(value)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || IsInfDouble(value)) {
    int    sign;

    EpdConvert(value, &epd2);
    sign = epd1->type.bits.sign ^ epd2.type.bits.sign;
    EpdMakeInf(epd1, sign);
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);

  EpdConvert(value, &epd2);
  tmp = epd1->type.value * epd2.type.value;
  exponent = epd1->exponent + epd2.exponent;
  epd1->type.value = tmp;
  epd1->exponent = exponent;
  EpdNormalize(epd1);
}


/**Function********************************************************************

  Synopsis    [Multiplies two arbitrary precision double values.]

  Description [Multiplies two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdMultiply2(EpDouble *epd1, EpDouble *epd2)
{
  double    value;
  int        exponent;

  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
    EpdMakeInf(epd1, sign);
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);
  assert(epd2->type.bits.exponent == EPD_MAX_BIN);

  value = epd1->type.value * epd2->type.value;
  exponent = epd1->exponent + epd2->exponent;
  epd1->type.value = value;
  epd1->exponent = exponent;
  EpdNormalize(epd1);
}


/**Function********************************************************************

  Synopsis    [Multiplies two arbitrary precision double values.]

  Description [Multiplies two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdMultiply2Decimal(EpDouble *epd1, EpDouble *epd2)
{
  double    value;
  int        exponent;

  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
    EpdMakeInf(epd1, sign);
    return;
  }

  value = epd1->type.value * epd2->type.value;
  exponent = epd1->exponent + epd2->exponent;
  epd1->type.value = value;
  epd1->exponent = exponent;
  EpdNormalizeDecimal(epd1);
}


/**Function********************************************************************

  Synopsis    [Multiplies two arbitrary precision double values.]

  Description [Multiplies two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdMultiply3(EpDouble *epd1, EpDouble *epd2, EpDouble *epd3)
{
  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
    EpdMakeInf(epd3, sign);
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);
  assert(epd2->type.bits.exponent == EPD_MAX_BIN);

  epd3->type.value = epd1->type.value * epd2->type.value;
  epd3->exponent = epd1->exponent + epd2->exponent;
  EpdNormalize(epd3);
}


/**Function********************************************************************

  Synopsis    [Multiplies two arbitrary precision double values.]

  Description [Multiplies two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdMultiply3Decimal(EpDouble *epd1, EpDouble *epd2, EpDouble *epd3)
{
  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
    EpdMakeInf(epd3, sign);
    return;
  }

  epd3->type.value = epd1->type.value * epd2->type.value;
  epd3->exponent = epd1->exponent + epd2->exponent;
  EpdNormalizeDecimal(epd3);
}


/**Function********************************************************************

  Synopsis    [Divides two arbitrary precision double values.]

  Description [Divides two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdDivide(EpDouble *epd1, double value)
{
  EpDouble    epd2;
  double    tmp;
  int        exponent;

  if (EpdIsNan(epd1) || IsNanDouble(value)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || IsInfDouble(value)) {
    int    sign;

    EpdConvert(value, &epd2);
    if (EpdIsInf(epd1) && IsInfDouble(value)) {
      EpdMakeNan(epd1);
    } else if (EpdIsInf(epd1)) {
      sign = epd1->type.bits.sign ^ epd2.type.bits.sign;
      EpdMakeInf(epd1, sign);
    } else {
      sign = epd1->type.bits.sign ^ epd2.type.bits.sign;
      EpdMakeZero(epd1, sign);
    }
    return;
  }

  if (value == 0.0) {
    EpdMakeNan(epd1);
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);

  EpdConvert(value, &epd2);
  tmp = epd1->type.value / epd2.type.value;
  exponent = epd1->exponent - epd2.exponent;
  epd1->type.value = tmp;
  epd1->exponent = exponent;
  EpdNormalize(epd1);
}


/**Function********************************************************************

  Synopsis    [Divides two arbitrary precision double values.]

  Description [Divides two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdDivide2(EpDouble *epd1, EpDouble *epd2)
{
  double    value;
  int        exponent;

  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    if (EpdIsInf(epd1) && EpdIsInf(epd2)) {
      EpdMakeNan(epd1);
    } else if (EpdIsInf(epd1)) {
      sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
      EpdMakeInf(epd1, sign);
    } else {
      sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
      EpdMakeZero(epd1, sign);
    }
    return;
  }

  if (epd2->type.value == 0.0) {
    EpdMakeNan(epd1);
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);
  assert(epd2->type.bits.exponent == EPD_MAX_BIN);

  value = epd1->type.value / epd2->type.value;
  exponent = epd1->exponent - epd2->exponent;
  epd1->type.value = value;
  epd1->exponent = exponent;
  EpdNormalize(epd1);
}


/**Function********************************************************************

  Synopsis    [Divides two arbitrary precision double values.]

  Description [Divides two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdDivide3(EpDouble *epd1, EpDouble *epd2, EpDouble *epd3)
{
  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd3);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    if (EpdIsInf(epd1) && EpdIsInf(epd2)) {
      EpdMakeNan(epd3);
    } else if (EpdIsInf(epd1)) {
      sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
      EpdMakeInf(epd3, sign);
    } else {
      sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
      EpdMakeZero(epd3, sign);
    }
    return;
  }

  if (epd2->type.value == 0.0) {
    EpdMakeNan(epd3);
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);
  assert(epd2->type.bits.exponent == EPD_MAX_BIN);

  epd3->type.value = epd1->type.value / epd2->type.value;
  epd3->exponent = epd1->exponent - epd2->exponent;
  EpdNormalize(epd3);
}


/**Function********************************************************************

  Synopsis    [Adds two arbitrary precision double values.]

  Description [Adds two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdAdd(EpDouble *epd1, double value)
{
  EpDouble    epd2;
  double    tmp;
  int        exponent, diff;

  if (EpdIsNan(epd1) || IsNanDouble(value)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || IsInfDouble(value)) {
    int    sign;

    EpdConvert(value, &epd2);
    if (EpdIsInf(epd1) && IsInfDouble(value)) {
      sign = epd1->type.bits.sign ^ epd2.type.bits.sign;
      if (sign == 1)
    EpdMakeNan(epd1);
    } else if (EpdIsInf(&epd2)) {
      EpdCopy(&epd2, epd1);
    }
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);

  EpdConvert(value, &epd2);
  if (epd1->exponent > epd2.exponent) {
    diff = epd1->exponent - epd2.exponent;
    if (diff <= EPD_MAX_BIN)
      tmp = epd1->type.value + epd2.type.value / pow((double)2.0, (double)diff);
    else
      tmp = epd1->type.value;
    exponent = epd1->exponent;
  } else if (epd1->exponent < epd2.exponent) {
    diff = epd2.exponent - epd1->exponent;
    if (diff <= EPD_MAX_BIN)
      tmp = epd1->type.value / pow((double)2.0, (double)diff) + epd2.type.value;
    else
      tmp = epd2.type.value;
    exponent = epd2.exponent;
  } else {
    tmp = epd1->type.value + epd2.type.value;
    exponent = epd1->exponent;
  }
  epd1->type.value = tmp;
  epd1->exponent = exponent;
  EpdNormalize(epd1);
}


/**Function********************************************************************

  Synopsis    [Adds two arbitrary precision double values.]

  Description [Adds two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdAdd2(EpDouble *epd1, EpDouble *epd2)
{
  double    value;
  int        exponent, diff;

  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    if (EpdIsInf(epd1) && EpdIsInf(epd2)) {
      sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
      if (sign == 1)
    EpdMakeNan(epd1);
    } else if (EpdIsInf(epd2)) {
      EpdCopy(epd2, epd1);
    }
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);
  assert(epd2->type.bits.exponent == EPD_MAX_BIN);

  if (epd1->exponent > epd2->exponent) {
    diff = epd1->exponent - epd2->exponent;
    if (diff <= EPD_MAX_BIN) {
      value = epd1->type.value +
        epd2->type.value / pow((double)2.0, (double)diff);
    } else
      value = epd1->type.value;
    exponent = epd1->exponent;
  } else if (epd1->exponent < epd2->exponent) {
    diff = epd2->exponent - epd1->exponent;
    if (diff <= EPD_MAX_BIN) {
      value = epd1->type.value / pow((double)2.0, (double)diff) +
        epd2->type.value;
    } else
      value = epd2->type.value;
    exponent = epd2->exponent;
  } else {
    value = epd1->type.value + epd2->type.value;
    exponent = epd1->exponent;
  }
  epd1->type.value = value;
  epd1->exponent = exponent;
  EpdNormalize(epd1);
}


/**Function********************************************************************

  Synopsis    [Adds two arbitrary precision double values.]

  Description [Adds two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdAdd3(EpDouble *epd1, EpDouble *epd2, EpDouble *epd3)
{
  double    value;
  int        exponent, diff;

  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd3);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    if (EpdIsInf(epd1) && EpdIsInf(epd2)) {
      sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
      if (sign == 1)
    EpdMakeNan(epd3);
      else
    EpdCopy(epd1, epd3);
    } else if (EpdIsInf(epd1)) {
      EpdCopy(epd1, epd3);
    } else {
      EpdCopy(epd2, epd3);
    }
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);
  assert(epd2->type.bits.exponent == EPD_MAX_BIN);

  if (epd1->exponent > epd2->exponent) {
    diff = epd1->exponent - epd2->exponent;
    if (diff <= EPD_MAX_BIN) {
      value = epd1->type.value +
        epd2->type.value / pow((double)2.0, (double)diff);
    } else
      value = epd1->type.value;
    exponent = epd1->exponent;
  } else if (epd1->exponent < epd2->exponent) {
    diff = epd2->exponent - epd1->exponent;
    if (diff <= EPD_MAX_BIN) {
      value = epd1->type.value / pow((double)2.0, (double)diff) +
        epd2->type.value;
    } else
      value = epd2->type.value;
    exponent = epd2->exponent;
  } else {
    value = epd1->type.value + epd2->type.value;
    exponent = epd1->exponent;
  }
  epd3->type.value = value;
  epd3->exponent = exponent;
  EpdNormalize(epd3);
}


/**Function********************************************************************

  Synopsis    [Subtracts two arbitrary precision double values.]

  Description [Subtracts two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdSubtract(EpDouble *epd1, double value)
{
  EpDouble    epd2;
  double    tmp;
  int        exponent, diff;

  if (EpdIsNan(epd1) || IsNanDouble(value)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || IsInfDouble(value)) {
    int    sign;

    EpdConvert(value, &epd2);
    if (EpdIsInf(epd1) && IsInfDouble(value)) {
      sign = epd1->type.bits.sign ^ epd2.type.bits.sign;
      if (sign == 0)
    EpdMakeNan(epd1);
    } else if (EpdIsInf(&epd2)) {
      EpdCopy(&epd2, epd1);
    }
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);

  EpdConvert(value, &epd2);
  if (epd1->exponent > epd2.exponent) {
    diff = epd1->exponent - epd2.exponent;
    if (diff <= EPD_MAX_BIN)
      tmp = epd1->type.value - epd2.type.value / pow((double)2.0, (double)diff);
    else
      tmp = epd1->type.value;
    exponent = epd1->exponent;
  } else if (epd1->exponent < epd2.exponent) {
    diff = epd2.exponent - epd1->exponent;
    if (diff <= EPD_MAX_BIN)
      tmp = epd1->type.value / pow((double)2.0, (double)diff) - epd2.type.value;
    else
      tmp = epd2.type.value * (double)(-1.0);
    exponent = epd2.exponent;
  } else {
    tmp = epd1->type.value - epd2.type.value;
    exponent = epd1->exponent;
  }
  epd1->type.value = tmp;
  epd1->exponent = exponent;
  EpdNormalize(epd1);
}


/**Function********************************************************************

  Synopsis    [Subtracts two arbitrary precision double values.]

  Description [Subtracts two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdSubtract2(EpDouble *epd1, EpDouble *epd2)
{
  double    value;
  int        exponent, diff;

  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd1);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    if (EpdIsInf(epd1) && EpdIsInf(epd2)) {
      sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
      if (sign == 0)
    EpdMakeNan(epd1);
    } else if (EpdIsInf(epd2)) {
      EpdCopy(epd2, epd1);
    }
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);
  assert(epd2->type.bits.exponent == EPD_MAX_BIN);

  if (epd1->exponent > epd2->exponent) {
    diff = epd1->exponent - epd2->exponent;
    if (diff <= EPD_MAX_BIN) {
      value = epd1->type.value -
        epd2->type.value / pow((double)2.0, (double)diff);
    } else
      value = epd1->type.value;
    exponent = epd1->exponent;
  } else if (epd1->exponent < epd2->exponent) {
    diff = epd2->exponent - epd1->exponent;
    if (diff <= EPD_MAX_BIN) {
      value = epd1->type.value / pow((double)2.0, (double)diff) -
        epd2->type.value;
    } else
      value = epd2->type.value * (double)(-1.0);
    exponent = epd2->exponent;
  } else {
    value = epd1->type.value - epd2->type.value;
    exponent = epd1->exponent;
  }
  epd1->type.value = value;
  epd1->exponent = exponent;
  EpdNormalize(epd1);
}


/**Function********************************************************************

  Synopsis    [Subtracts two arbitrary precision double values.]

  Description [Subtracts two arbitrary precision double values.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdSubtract3(EpDouble *epd1, EpDouble *epd2, EpDouble *epd3)
{
  double    value;
  int        exponent, diff;

  if (EpdIsNan(epd1) || EpdIsNan(epd2)) {
    EpdMakeNan(epd3);
    return;
  } else if (EpdIsInf(epd1) || EpdIsInf(epd2)) {
    int    sign;

    if (EpdIsInf(epd1) && EpdIsInf(epd2)) {
      sign = epd1->type.bits.sign ^ epd2->type.bits.sign;
      if (sign == 0)
    EpdCopy(epd1, epd3);
      else
    EpdMakeNan(epd3);
    } else if (EpdIsInf(epd1)) {
      EpdCopy(epd1, epd1);
    } else {
      sign = epd2->type.bits.sign ^ 0x1;
      EpdMakeInf(epd3, sign);
    }
    return;
  }

  assert(epd1->type.bits.exponent == EPD_MAX_BIN);
  assert(epd2->type.bits.exponent == EPD_MAX_BIN);

  if (epd1->exponent > epd2->exponent) {
    diff = epd1->exponent - epd2->exponent;
    if (diff <= EPD_MAX_BIN) {
      value = epd1->type.value -
        epd2->type.value / pow((double)2.0, (double)diff);
    } else
      value = epd1->type.value;
    exponent = epd1->exponent;
  } else if (epd1->exponent < epd2->exponent) {
    diff = epd2->exponent - epd1->exponent;
    if (diff <= EPD_MAX_BIN) {
      value = epd1->type.value / pow((double)2.0, (double)diff) -
        epd2->type.value;
    } else
      value = epd2->type.value * (double)(-1.0);
    exponent = epd2->exponent;
  } else {
    value = epd1->type.value - epd2->type.value;
    exponent = epd1->exponent;
  }
  epd3->type.value = value;
  epd3->exponent = exponent;
  EpdNormalize(epd3);
}


/**Function********************************************************************

  Synopsis    [Computes arbitrary precision pow of base 2.]

  Description [Computes arbitrary precision pow of base 2.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdPow2(int n, EpDouble *epd)
{
  if (n <= EPD_MAX_BIN) {
    EpdConvert(pow((double)2.0, (double)n), epd);
  } else {
    EpDouble    epd1, epd2;
    int        n1, n2;

    n1 = n / 2;
    n2 = n - n1;
    EpdPow2(n1, &epd1);
    EpdPow2(n2, &epd2);
    EpdMultiply3(&epd1, &epd2, epd);
  }
}


/**Function********************************************************************

  Synopsis    [Computes arbitrary precision pow of base 2.]

  Description [Computes arbitrary precision pow of base 2.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdPow2Decimal(int n, EpDouble *epd)
{
  if (n <= EPD_MAX_BIN) {
    epd->type.value = pow((double)2.0, (double)n);
    epd->exponent = 0;
    EpdNormalizeDecimal(epd);
  } else {
    EpDouble    epd1, epd2;
    int        n1, n2;

    n1 = n / 2;
    n2 = n - n1;
    EpdPow2Decimal(n1, &epd1);
    EpdPow2Decimal(n2, &epd2);
    EpdMultiply3Decimal(&epd1, &epd2, epd);
  }
}


/**Function********************************************************************

  Synopsis    [Normalize an arbitrary precision double value.]

  Description [Normalize an arbitrary precision double value.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdNormalize(EpDouble *epd)
{
  int        exponent;

  if (IsNanOrInfDouble(epd->type.value)) {
    epd->exponent = 0;
    return;
  }

  exponent = EpdGetExponent(epd->type.value);
  if (exponent == EPD_MAX_BIN)
    return;
  exponent -= EPD_MAX_BIN;
  epd->type.bits.exponent = EPD_MAX_BIN;
  epd->exponent += exponent;
}


/**Function********************************************************************

  Synopsis    [Normalize an arbitrary precision double value.]

  Description [Normalize an arbitrary precision double value.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdNormalizeDecimal(EpDouble *epd)
{
  int        exponent;

  if (IsNanOrInfDouble(epd->type.value)) {
    epd->exponent = 0;
    return;
  }

  exponent = EpdGetExponentDecimal(epd->type.value);
  epd->type.value /= pow((double)10.0, (double)exponent);
  epd->exponent += exponent;
}


/**Function********************************************************************

  Synopsis    [Returns value and decimal exponent of EpDouble.]

  Description [Returns value and decimal exponent of EpDouble.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdGetValueAndDecimalExponent(EpDouble *epd, double *value, int *exponent)
{
  EpDouble    epd1, epd2;

  if (EpdIsNanOrInf(epd))
    return;

  if (EpdIsZero(epd)) {
    *value = 0.0;
    *exponent = 0;
    return;
  }

  epd1.type.value = epd->type.value;
  epd1.exponent = 0;
  EpdPow2Decimal(epd->exponent, &epd2);
  EpdMultiply2Decimal(&epd1, &epd2);

  *value = epd1.type.value;
  *exponent = epd1.exponent;
}

/**Function********************************************************************

  Synopsis    [Returns the exponent value of a double.]

  Description [Returns the exponent value of a double.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
EpdGetExponent(double value)
{
  int        exponent;
  EpDouble    epd;

  epd.type.value = value;
  exponent = epd.type.bits.exponent;
  return(exponent);
}


/**Function********************************************************************

  Synopsis    [Returns the decimal exponent value of a double.]

  Description [Returns the decimal exponent value of a double.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
EpdGetExponentDecimal(double value)
{
  char    *pos, str[24];
  int    exponent;

  sprintf(str, "%E", value);
  pos = strstr(str, "E");
  sscanf(pos, "E%d", &exponent);
  return(exponent);
}


/**Function********************************************************************

  Synopsis    [Makes EpDouble Inf.]

  Description [Makes EpDouble Inf.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdMakeInf(EpDouble *epd, int sign)
{
  epd->type.bits.mantissa1 = 0;
  epd->type.bits.mantissa0 = 0;
  epd->type.bits.exponent = EPD_EXP_INF;
  epd->type.bits.sign = sign;
  epd->exponent = 0;
}


/**Function********************************************************************

  Synopsis    [Makes EpDouble Zero.]

  Description [Makes EpDouble Zero.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdMakeZero(EpDouble *epd, int sign)
{
  epd->type.bits.mantissa1 = 0;
  epd->type.bits.mantissa0 = 0;
  epd->type.bits.exponent = 0;
  epd->type.bits.sign = sign;
  epd->exponent = 0;
}


/**Function********************************************************************

  Synopsis    [Makes EpDouble NaN.]

  Description [Makes EpDouble NaN.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdMakeNan(EpDouble *epd)
{
  epd->type.nan.mantissa1 = 0;
  epd->type.nan.mantissa0 = 0;
  epd->type.nan.quiet_bit = 1;
  epd->type.nan.exponent = EPD_EXP_INF;
  epd->type.nan.sign = 1;
  epd->exponent = 0;
}


/**Function********************************************************************

  Synopsis    [Copies a EpDouble struct.]

  Description [Copies a EpDouble struct.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
EpdCopy(EpDouble *from, EpDouble *to)
{
  to->type.value = from->type.value;
  to->exponent = from->exponent;
}


/**Function********************************************************************

  Synopsis    [Checks whether the value is Inf.]

  Description [Checks whether the value is Inf.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
EpdIsInf(EpDouble *epd)
{
  return(IsInfDouble(epd->type.value));
}


/**Function********************************************************************

  Synopsis    [Checks whether the value is Zero.]

  Description [Checks whether the value is Zero.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
EpdIsZero(EpDouble *epd)
{
  if (epd->type.value == 0.0)
    return(1);
  else
    return(0);
}


/**Function********************************************************************

  Synopsis    [Checks whether the value is NaN.]

  Description [Checks whether the value is NaN.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
EpdIsNan(EpDouble *epd)
{
  return(IsNanDouble(epd->type.value));
}


/**Function********************************************************************

  Synopsis    [Checks whether the value is NaN or Inf.]

  Description [Checks whether the value is NaN or Inf.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
EpdIsNanOrInf(EpDouble *epd)
{
  return(IsNanOrInfDouble(epd->type.value));
}


/**Function********************************************************************

  Synopsis    [Checks whether the value is Inf.]

  Description [Checks whether the value is Inf.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
IsInfDouble(double value)
{
  IeeeDouble    *ptr = (IeeeDouble *)(&value);

  if (ptr->exponent == EPD_EXP_INF &&
      ptr->mantissa0 == 0 &&
      ptr->mantissa1 == 0) {
    if (ptr->sign == 0)
      return(1);
    else
      return(-1);
  }
  return(0);
}


/**Function********************************************************************

  Synopsis    [Checks whether the value is NaN.]

  Description [Checks whether the value is NaN.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
IsNanDouble(double value)
{
  IeeeNan    *ptr = (IeeeNan *)(&value);

  if (ptr->exponent == EPD_EXP_INF &&
      ptr->sign == 1 &&
      ptr->quiet_bit == 1 &&
      ptr->mantissa0 == 0 &&
      ptr->mantissa1 == 0) {
    return(1);
  }
  return(0);
}


/**Function********************************************************************

  Synopsis    [Checks whether the value is NaN or Inf.]

  Description [Checks whether the value is NaN or Inf.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
IsNanOrInfDouble(double value)
{
  IeeeNan    *ptr = (IeeeNan *)(&value);

  if (ptr->exponent == EPD_EXP_INF &&
      ptr->mantissa0 == 0 &&
      ptr->mantissa1 == 0 &&
      (ptr->sign == 1 || ptr->quiet_bit == 0)) {
    return(1);
  }
  return(0);
}