fltcalc.c 40.2 KB
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/* fltcalc.c
 * Authors: Matthias Heil
 */

#include "fltcalc.h"
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#include "strcalc.h"

#include <math.h>    /* need isnan() and isinf() (will be changed)*/
/* undef some reused constants defined by math.h */
#ifdef NAN
#  undef NAN
#endif

#include <inttypes.h>
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#include <string.h>
#include <stdlib.h>
#include <stdio.h>
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#include <assert.h>
#include <alloca.h>
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typedef uint32_t UINT32;
#ifdef WORD_LITTLE_ENDIAN
#undef WORD_LITTLE_ENDIAN
#endif
#ifdef WORD_BIG_ENDIAN
#undef WORD_BIG_ENDIAN
#endif
#define WORD_LITTLE_ENDIAN
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#ifdef HAVE_LONG_DOUBLE
#ifdef WORD_LITTLE_ENDIAN
typedef union {
  struct {
    UINT32 low;
    UINT32 mid;
    UINT32 high;
  } val;
  volatile long double d;
} value_t;
#else
typedef union {
  struct {
    UINT32 high;
    UINT32 mid;
    UINT32 low;
  } val;
  volatile long double d;
} value_t;
#endif
#else
#ifdef WORD_LITTLE_ENDIAN
typedef union {
  struct {
    UINT32 low;
    UINT32 high;
  } val;
  volatile double d;
} value_t;
#else
typedef union {
  struct {
    UINT32 high;
    UINT32 low;
  } val;
  volatile double d;
} value_t;
#endif
#endif
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/********
 * globals
 ********/
typedef enum {
  NORMAL,
  ZERO,
  SUBNORMAL,
  INF,
  NAN,
} value_class_t;

typedef struct {
  char  exponent_size;
  char  mantissa_size;
  value_class_t  class;
} descriptor_t;

#define CLEAR_BUFFER(buffer) memset(buffer, 0, CALC_BUFFER_SIZE)

/* because variable sized structs are impossible, the internal
 * value is represented as a pseudo-struct char array, addressed
 * by macros
 * struct {
 *   char sign;             // 0 for positive, 1 for negative
 *   char exp[VALUE_SIZE];
 *   char mant[VALUE_SIZE];
 *   descriptor_t desc;
 * };
 */
#define _sign(a) (((char*)a)[SIGN_POS])
#define _exp(a) (&((char*)a)[EXPONENT_POS])
#define _mant(a) (&((char*)a)[MANTISSA_POS])
#define _desc(a) (*(descriptor_t *)&((char*)a)[DESCRIPTOR_POS])
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#define _save_result(x) memcpy((x), sc_get_buffer(), VALUE_SIZE)
#define _shift_right(x, y, b) sc_shr((x), (y), VALUE_SIZE*4, 0, (b))
#define _shift_left(x, y, b) sc_shl((x), (y), VALUE_SIZE*4, 0, (b))
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#define FC_DEFINE1(code) char* fc_##code(const void *a, void *result)                          \
                   {                                                                           \
                     return _calc((const char*)a, NULL, FC_##code, (char*)result);             \
                   }
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#define FC_DEFINE2(code) char* fc_##code(const void *a, const void *b, void *result)           \
                   {                                                                           \
                     return _calc((const char*)a, (const char*)b, FC_##code, (char*)result);   \
                   }

#define FUNC_PTR(code) fc_##code

#if FLTCALC_DEBUG
#  define DEBUGPRINTF(x) printf x
#else
#  define DEBUGPRINTF(x) ((void)0)
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#endif

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#if FLTCALC_TRACE_CALC
#  define TRACEPRINTF(x) printf x
#else
#  define TRACEPRINTF(x) ((void)0)
#endif
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static char *calc_buffer = NULL;
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static fc_rounding_mode_t ROUNDING_MODE;

static int CALC_BUFFER_SIZE;
static int VALUE_SIZE;
static int SIGN_POS;
static int EXPONENT_POS;
static int MANTISSA_POS;
static int DESCRIPTOR_POS;
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static int max_precision;
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/********
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 * private functions
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 ********/
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#if 0
static void _fail_char(const char *str, unsigned int len, int pos)
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{
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  if (*(str+pos))
    printf("ERROR: Unexpected character '%c'\n", *(str + pos));
  else
    printf("ERROR: Unexpected end of string\n");
  while (len-- && *str) printf("%c", *str++); printf("\n");
  while (pos--) printf(" "); printf("^\n");
  /* the front end has to to check constant strings */
  exit(-1);
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}
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#endif
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/* pack ieee-like */
static char* _pack(const char *int_float, char *packed)
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{
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  char *shift_val;
  char *temp;
  char *val_buffer;
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  temp = alloca(VALUE_SIZE);
  shift_val = alloca(VALUE_SIZE);

  switch (_desc(int_float).class) {
    case NAN:
      val_buffer = alloca(CALC_BUFFER_SIZE);
      fc_get_qnan(_desc(int_float).exponent_size, _desc(int_float).mantissa_size, val_buffer);
      int_float = val_buffer;
      break;

    case INF:
      val_buffer = alloca(CALC_BUFFER_SIZE);
      fc_get_plusinf(_desc(int_float).exponent_size, _desc(int_float).mantissa_size, val_buffer);
      _sign(val_buffer) = _sign(int_float);
      int_float = val_buffer;
      break;

    default:
      break;
  }
  /* pack sign */
  sc_val_from_ulong(_sign(int_float), temp);

  sc_val_from_ulong(_desc(int_float).exponent_size + _desc(int_float).mantissa_size, NULL);
  _shift_left(temp, sc_get_buffer(), packed);

  /* extract exponent */
  sc_val_from_ulong(_desc(int_float).mantissa_size, shift_val);

  _shift_left(_exp(int_float), shift_val, temp);

  sc_or(temp, packed, packed);

  /* extract mantissa */
  /* remove 2 rounding bits */
  sc_val_from_ulong(2, shift_val);
  _shift_right(_mant(int_float), shift_val, temp);

  /* remove leading 1 (or 0 if denormalized) */
  sc_max_from_bits(_desc(int_float).mantissa_size, 0, shift_val); /* all mantissa bits are 1's */
  sc_and(temp, shift_val, temp);

  /* save result */
  sc_or(temp, packed, packed);

  return packed;
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}

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char* _normalize(const char *in_val, char *out_val, int sticky)
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{
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  int hsb;
  char lsb, guard, round, round_dir = 0;
  char *temp;

  temp = alloca(VALUE_SIZE);

  /* +2: save two rounding bits at the end */
  hsb = 2 + _desc(in_val).mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1;

  if (in_val != out_val)
  {
    _sign(out_val) = _sign(in_val);
    memcpy(&_desc(out_val), &_desc(in_val), sizeof(descriptor_t));
  }

  _desc(out_val).class = NORMAL;

  /* mantissa all zeroes, so zero exponent (because of explicit one)*/
  if (hsb == 2 + _desc(in_val).mantissa_size)
  {
    sc_val_from_ulong(0, _exp(out_val));
    hsb = -1;
  }

  /* shift the first 1 ito the left of the radix point (i.e. hsb == -1) */
  if (hsb < -1)
  {
    /* shift right */
    sc_val_from_ulong(-hsb-1, temp);

    _shift_right(_mant(in_val), temp, _mant(out_val));

    /* remember if some bits were shifted away */
    if (!sticky) sticky = sc_had_carry();

    sc_add(_exp(in_val), temp, _exp(out_val));
  }
  else if (hsb > -1)
  {
    /* shift left */
    sc_val_from_ulong(hsb+1, temp);

    _shift_left(_mant(in_val), temp, _mant(out_val));

    sc_sub(_exp(in_val), temp, _exp(out_val));
  }

  /* check for exponent underflow */
  if (sc_is_negative(_exp(out_val)) || sc_is_zero(_exp(out_val))) {
    DEBUGPRINTF(("Exponent underflow!\n"));
    /* exponent underflow */
    /* shift the mantissa right to have a zero exponent */
    sc_val_from_ulong(1, temp);
    sc_sub(temp, _exp(out_val), NULL);

    _shift_right(_mant(out_val), sc_get_buffer(), _mant(out_val));
    if (!sticky) sticky = sc_had_carry();
    /* denormalized means exponent of zero */
    sc_val_from_ulong(0, _exp(out_val));

    _desc(out_val).class = SUBNORMAL;
  }

  /* perform rounding by adding a value that clears the guard bit and the round bit
   * and either causes a carry to round up or not */
  /* get the last 3 bits of the value */
  lsb = sc_sub_bits(_mant(out_val), _desc(out_val).mantissa_size + 2, 0) & 0x7;
  guard = (lsb&0x2)>>1;
  round = lsb&0x1;

  switch (ROUNDING_MODE)
  {
    case FC_TONEAREST:
      /* round to nearest representable value, if in doubt choose the version
       * with lsb == 0 */
      round_dir = guard && (sticky || round || lsb>>2);
      break;
    case FC_TOPOSITIVE:
      /* if positive: round to one if the exact value is bigger, else to zero */
      round_dir = (!_sign(out_val) && (guard || round || sticky));
      break;
    case FC_TONEGATIVE:
      /* if negative: round to one if the exact value is bigger, else to zero */
      round_dir = (_sign(out_val) && (guard || round || sticky));
      break;
    case FC_TOZERO:
      /* always round to 0 (chopping mode) */
      round_dir = 0;
      break;
  }
  DEBUGPRINTF(("Rounding (s%d, l%d, g%d, r%d, s%d) %s\n", _sign(out_val), lsb>>2, guard, round, sticky, (round_dir)?"up":"down"));

  if (round_dir == 1)
  {
    guard = (round^guard)<<1;
    lsb = !(round || guard)<<2 | guard | round;
  }
  else
  {
    lsb = -((guard<<1) | round);
  }

  /* add the rounded value */
  if (lsb != 0) {
    sc_val_from_long(lsb, temp);
    sc_add(_mant(out_val), temp, _mant(out_val));
  }

  /* could have rounded down to zero */
  if (sc_is_zero(_mant(out_val)) && (_desc(out_val).class == SUBNORMAL))
    _desc(out_val).class = ZERO;

  /* check for rounding overflow */
  hsb = 2 + _desc(out_val).mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1;
  if ((_desc(out_val).class != SUBNORMAL) && (hsb < -1))
  {
    sc_val_from_ulong(1, temp);
    _shift_right(_mant(out_val), temp, _mant(out_val));

    sc_add(_exp(out_val), temp, _exp(out_val));
  }
  else if ((_desc(out_val).class == SUBNORMAL) && (hsb == -1))
  {
    /* overflow caused the matissa to be normal again,
     * so adapt the exponent accordingly */
    sc_val_from_ulong(1, temp);
    sc_add(_exp(out_val), temp, _exp(out_val));

    _desc(out_val).class = NORMAL;
  }
  /* no further rounding is needed, because rounding overflow means
   * the carry of the original rounding was propagated all the way
   * up to the bit left of the radix point. This implies the bits
   * to the right are all zeros (rounding is +1) */

  /* check for exponent overflow */
  sc_val_from_ulong((1 << _desc(out_val).exponent_size) - 1, temp);
  if (sc_comp(_exp(out_val), temp) != -1) {
    DEBUGPRINTF(("Exponent overflow!\n"));
    /* exponent overflow, reaction depends on rounding method:
     *
     * mode        | sign of value |  result
     *--------------------------------------------------------------
     * TO_NEAREST  |      +        |   +inf
     *             |      -        |   -inf
     *--------------------------------------------------------------
     * TO_POSITIVE |      +        |   +inf
     *             |      -        |   smallest representable value
     *--------------------------------------------------------------
     * TO_NEAGTIVE |      +        |   largest representable value
     *             |      -        |   -inf
     *--------------------------------------------------------------
     * TO_ZERO     |      +        |   largest representable value
     *             |      -        |   smallest representable value
     *--------------------------------------------------------------*/
    if (_sign(out_val) == 0)
    {
      /* value is positive */
      switch (ROUNDING_MODE) {
        case FC_TONEAREST:
        case FC_TOPOSITIVE:
          _desc(out_val).class = INF;
          break;

        case FC_TONEGATIVE:
        case FC_TOZERO:
          fc_get_max(_desc(out_val).exponent_size, _desc(out_val).mantissa_size, out_val);
      }
    } else {
      /* value is negative */
      switch (ROUNDING_MODE) {
        case FC_TONEAREST:
        case FC_TONEGATIVE:
          _desc(out_val).class = INF;
          break;

        case FC_TOPOSITIVE:
        case FC_TOZERO:
          fc_get_min(_desc(out_val).exponent_size, _desc(out_val).mantissa_size, out_val);
      }
    }
  }

  return out_val;
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}

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/*
 * calculate a + b, where a is the value with the bigger exponent
 */
static char* _add(const char* a, const char* b, char* result)
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{
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  char *temp;
  char *exp_diff;

  char sign;
  char sticky;

  if (_desc(a).class == NAN) {
    if (a != result) memcpy(result, a, CALC_BUFFER_SIZE);
    return result;
  }
  if (_desc(b).class == NAN) {
    if (b != result) memcpy(result, b, CALC_BUFFER_SIZE);
    return result;
  }

  /* make sure result has a descriptor */
  if (result != a && result != b)
    memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));

  /* determine if this is an addition or subtraction */
  sign = _sign(a) ^ _sign(b);
  DEBUGPRINTF(("sign a: %d, sign b: %d -> %s\n", _sign(a), _sign(b), sign?"sub":"add"));

  /* produce nan on inf - inf */
  if (sign && (_desc(a).class == INF) && (_desc(b).class == INF))
    return fc_get_qnan(_desc(a).exponent_size, _desc(b).mantissa_size, result);

  temp = alloca(VALUE_SIZE);
  exp_diff = alloca(VALUE_SIZE);

  /* get exponent difference */
  sc_sub(_exp(a), _exp(b), exp_diff);

  /* initially set sign to be the sign of a, special treatment of subtraction
   * when exponents are equal is required though.
   * Also special care about the sign is needed when the mantissas are equal
   * (+/- 0 ?) */
  if (sign && sc_val_to_long(exp_diff) == 0) {
    switch (sc_comp(_mant(a), _mant(b))) {
      case 1:  /* a > b */
        if (_sign(a)) _sign(result) = 1;  /* abs(a) is bigger and a is negative */
        else _sign(result) = 0;
        break;
      case 0:  /* a == b */
        if (ROUNDING_MODE == FC_TONEGATIVE)
          _sign(result) = 1;
        else
          _sign(result) = 0;
        break;
      case -1: /* a < b */
        if (_sign(b)) _sign(result) = 1; /* abs(b) is bigger and b is negative */
        else _sign(result) = 0;
        break;
      default:
        /* can't be reached */
        break;
    }
  } else {
    _sign(result) = _sign(a);
  }

  /* sign has been taken care of, check for special cases */
  if (_desc(a).class == ZERO) {
    if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, CALC_BUFFER_SIZE-SIGN_POS-1);
    return result;
  }
  if (_desc(b).class == ZERO) {
    if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, CALC_BUFFER_SIZE-SIGN_POS-1);
    return result;
  }

  if (_desc(a).class == INF) {
    if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, CALC_BUFFER_SIZE-SIGN_POS-1);
    return result;
  }
  if (_desc(b).class == INF) {
    if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, CALC_BUFFER_SIZE-SIGN_POS-1);
    return result;
  }

  /* shift the smaller value to the right to align the radix point */
  /* subnormals have their radix point shifted to the right,
   * take care of this first */
  if ((_desc(b).class == SUBNORMAL) && (_desc(a).class != SUBNORMAL))
  {
    sc_val_from_ulong(1, temp);
    sc_sub(exp_diff, temp, exp_diff);
  }

  _shift_right(_mant(b), exp_diff, temp);
  sticky = sc_had_carry();

  if (sticky && sign)
  {
    /* if subtracting a little more than the represented value or adding a little
     * more than the represented value to a negative value this, in addition to the
     * still set sticky bit, takes account of the 'little more' */
    char *temp1 = alloca(CALC_BUFFER_SIZE);
    sc_val_from_ulong(1, temp1);
    sc_add(temp, temp1, temp);
  }

  if (sign) {
    if (sc_comp(_mant(a), temp) == -1)
      sc_sub(temp, _mant(a), _mant(result));
    else
      sc_sub(_mant(a), temp, _mant(result));
  } else {
    sc_add(_mant(a), temp, _mant(result));
  }

  /* _normalize expects a 'normal' radix point, adding two subnormals
   * results in a subnormal radix point -> shifting before normalizing */
  if ((_desc(a).class == SUBNORMAL) && (_desc(b).class == SUBNORMAL))
  {
    sc_val_from_ulong(1, NULL);
    _shift_left(_mant(result), sc_get_buffer(), _mant(result));
  }

  /* resulting exponent is the bigger one */
  memmove(_exp(result), _exp(a), VALUE_SIZE);

  return _normalize(result, result, sticky);
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}

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static char* _mul(const char* a, const char* b, char* result)
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{
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  char *temp;
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  if (_desc(a).class == NAN) {
    if (a != result) memcpy(result, a, CALC_BUFFER_SIZE);
    return result;
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  }
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  if (_desc(b).class == NAN) {
    if (b != result) memcpy(result, b, CALC_BUFFER_SIZE);
    return result;
  }

  temp = alloca(VALUE_SIZE);

  if (result != a && result != b)
    memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));

  _sign(result) = _sign(a) ^ _sign(b);

  /* produce nan on 0 * inf */
  if (_desc(a).class == ZERO) {
    if (_desc(b).class == INF)
      fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
    else
      if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, CALC_BUFFER_SIZE-1);
    return result;
  }
  if (_desc(b).class == ZERO) {
    if (_desc(a).class == INF)
      fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
    else
      if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, CALC_BUFFER_SIZE-1);
    return result;
  }

  if (_desc(a).class == INF) {
    if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, CALC_BUFFER_SIZE-1);
    return result;
  }
  if (_desc(b).class == INF) {
    if (b != result) memcpy(result+SIGN_POS+1, b+SIGN_POS+1, CALC_BUFFER_SIZE-1);
    return result;
  }

  /* exp = exp(a) + exp(b) - excess */
  sc_add(_exp(a), _exp(b), _exp(result));

  sc_val_from_ulong((1<<_desc(a).exponent_size)/2-1, temp);
  sc_sub(_exp(result), temp, _exp(result));

  /* mixed normal, subnormal values introduce an error of 1, correct it */
  if ((_desc(a).class == SUBNORMAL) ^ (_desc(b).class == SUBNORMAL))
  {
    sc_val_from_ulong(1, temp);
    sc_add(_exp(result), temp, _exp(result));
  }

  sc_mul(_mant(a), _mant(b), _mant(result));

  /* realign result: after a multiplication the digits right of the radix
   * point are the sum of the factors' digits after the radix point. As all
   * values are normalized they both have the same amount of these digits,
   * which has to be restored by proper shifting
   * +2 because of the two rounding bits */
  sc_val_from_ulong(2 + _desc(result).mantissa_size, temp);

  _shift_right(_mant(result), temp, _mant(result));

  return _normalize(result, result, sc_had_carry());
605
606
}

607
static char* _div(const char* a, const char* b, char* result)
608
{
609
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611
612
613
614
615
616
617
618
619
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621
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623
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625
626
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657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
  char *temp, *dividend;

  if (_desc(a).class == NAN) {
    if (a != result) memcpy(result, a, CALC_BUFFER_SIZE);
    return result;
  }
  if (_desc(b).class == NAN) {
    if (b != result) memcpy(result, b, CALC_BUFFER_SIZE);
    return result;
  }

  temp = alloca(VALUE_SIZE);
  dividend = alloca(VALUE_SIZE);

  if (result != a && result != b)
    memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));

  _sign(result) = _sign(a) ^ _sign(b);

  /* produce nan on 0/0 and inf/inf */
  if (_desc(a).class == ZERO) {
    if (_desc(b).class == ZERO)
      /* 0/0 -> nan */
      fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
    else
      /* 0/x -> a */
      if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, CALC_BUFFER_SIZE-1);
    return result;
  }

  if (_desc(b).class == INF) {
    if (_desc(a).class == INF)
      /* inf/inf -> nan */
      fc_get_qnan(_desc(a).exponent_size, _desc(a).mantissa_size, result);
    else {
      /* x/inf -> 0 */
      sc_val_from_ulong(0, NULL);
      _save_result(_exp(result));
      _save_result(_mant(result));
      _desc(result).class = ZERO;
    }
    return result;
  }

  if (_desc(a).class == INF) {
    /* inf/x -> inf */
    if (a != result) memcpy(result+SIGN_POS+1, a+SIGN_POS+1, CALC_BUFFER_SIZE-1);
    return result;
  }
  if (_desc(b).class == ZERO) {
    /* division by zero */
    if (_sign(result))
      fc_get_minusinf(_desc(a).exponent_size, _desc(a).mantissa_size, result);
    else
      fc_get_plusinf(_desc(a).exponent_size, _desc(a).mantissa_size, result);
    return result;
  }

  /* exp = exp(a) - exp(b) + excess - 1*/
  sc_sub(_exp(a), _exp(b), _exp(result));
  sc_val_from_ulong((1 << _desc(a).exponent_size)/2-2, temp);
  sc_add(_exp(result), temp, _exp(result));

  /* mixed normal, subnormal values introduce an error of 1, correct it */
  if ((_desc(a).class == SUBNORMAL) ^ (_desc(b).class == SUBNORMAL))
674
  {
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
    sc_val_from_ulong(1, temp);
    sc_add(_exp(result), temp, _exp(result));
  }

  /* mant(res) = mant(a) / 1/2mant(b) */
  /* to gain more bits of precision in the result the dividend could be
   * shifted left, as this operation does not loose bits. This would not
   * fit into the integer precision, but due to the rounding bits (which
   * are always zero because the values are all normalized) the divisor
   * can be shifted right instead to achieve the same result */
  sc_val_from_ulong(2 + _desc(result).mantissa_size, temp);

  _shift_left(_mant(a), temp, dividend);

  {
    char *divisor = alloca(CALC_BUFFER_SIZE);
    sc_val_from_ulong(1, divisor);
    _shift_right(_mant(b), divisor, divisor);
    sc_div(dividend, divisor, _mant(result));
694
  }
695
696

  return _normalize(result, result, sc_had_carry());
697
698
}

699
void _power_of_ten(int exp, descriptor_t *desc, char *result)
700
{
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
  char *build;
  char *temp;

  /* positive sign */
  _sign(result) = 0;

  /* set new descriptor (else result is supposed to already have one) */
  if (desc != NULL)
    memcpy(&_desc(result), desc, sizeof(descriptor_t));

  build = alloca(VALUE_SIZE);
  temp = alloca(VALUE_SIZE);

  sc_val_from_ulong((1 << _desc(result).exponent_size)/2-1, _exp(result));

  if (exp > 0)
  {
    /* temp is value of ten now */
    sc_val_from_ulong(10, NULL);
    _save_result(temp);

    for (exp--; exp > 0; exp--) {
      _save_result(build);
      sc_mul(build, temp, NULL);
    }
    _save_result(build);

    /* temp is amount of leftshift needed to put the value left of the radix point */
    sc_val_from_ulong(_desc(result).mantissa_size + 2, temp);
730

731
732
733
734
    _shift_left(build, temp, _mant(result));

    _normalize(result, result, 0);
  }
735
736
}

737
static char* _trunc(const char *a, char *result)
738
{
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
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759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
  /* when exponent == 0 all bits left of the radix point
   * are the integral part of the value. For 15bit exp_size
   * this would require a leftshift of max. 16383 bits which
   * is too much.
   * But it is enough to ensure that no bit right of the radix
   * point remains set. This restricts the interesting
   * exponents to the interval [0, mant_size-1].
   * Outside this interval the truncated value is either 0 or
   * it is are already truncated */

  int exp_bias, exp_val;
  char *temp;

  temp = alloca(VALUE_SIZE);

  if (a != result)
    memcpy(&_desc(result), &_desc(a), sizeof(descriptor_t));

  exp_bias = (1<<_desc(a).exponent_size)/2-1;
  exp_val = sc_val_to_long(_exp(a)) - exp_bias;

  if (exp_val < 0) {
    sc_val_from_ulong(0, NULL);
    _save_result(_exp(result));
    _save_result(_mant(result));
    _desc(result).class = ZERO;

    return result;
  }

  if (exp_val > _desc(a).mantissa_size) {
    if (a != result)
      memcpy(result, a, CALC_BUFFER_SIZE);

    return result;
  }

  /* set up a proper mask to delete all bits right of the
   * radix point if the mantissa had been shifted until exp == 0 */
  sc_max_from_bits(1 + exp_val, 0, temp);
  sc_val_from_long(_desc(a).mantissa_size - exp_val + 2, NULL);
  _shift_left(temp, sc_get_buffer(), temp);

  /* and the mask and return the result */
  sc_and(_mant(a), temp, _mant(result));

  if (a != result) memcpy(_exp(result), _exp(a), VALUE_SIZE);

  return result;
788
789
}

790
791
792
793
794
/*
 * This does value sanity checking(or should do it), sets up any prerequisites,
 * calls the proper internal functions, clears up and returns
 * the result */
char* _calc(const char *a, const char *b, int opcode, char *result)
795
{
796
797
798
799
800
801
802
803
804
805
  char *temp;
#ifdef FLTCALC_TRACE_CALC
  char *buffer;

  buffer = alloca(100);
#endif

  if (result == NULL) result = calc_buffer;

  TRACEPRINTF(("%s ", fc_print(a, buffer, 100, FC_HEX)));
806
807
  switch (opcode)
  {
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
    case FC_add:
      /* make the value with the bigger exponent the first one */
      TRACEPRINTF(("+ %s ", fc_print(b, buffer, 100, FC_HEX)));
      if (sc_comp(_exp(a), _exp(b)) == -1)
        _add(b, a, result);
      else
        _add(a, b, result);
      break;
    case FC_sub:
      TRACEPRINTF(("- %s ", fc_print(b, buffer, 100, FC_HEX)));
      temp = alloca(CALC_BUFFER_SIZE);
      memcpy(temp, b, CALC_BUFFER_SIZE);
      _sign(temp) = !_sign(b);
      if (sc_comp(_exp(a), _exp(temp)) == -1)
        _add(temp, a, result);
      else
        _add(a, temp, result);
825
      break;
826
827
828
    case FC_mul:
      TRACEPRINTF(("* %s ", fc_print(b, buffer, 100, FC_HEX)));
      _mul(a, b, result);
829
      break;
830
831
832
    case FC_div:
      TRACEPRINTF(("/ %s ", fc_print(b, buffer, 100, FC_HEX)));
      _div(a, b, result);
833
      break;
834
835
836
837
    case FC_neg:
      TRACEPRINTF(("negated "));
      if (a != result) memcpy(result, a, CALC_BUFFER_SIZE);
      _sign(result) = !_sign(a);
838
      break;
839
840
841
842
    case FC_int:
      _trunc(a, result);
      break;
    case FC_rnd:
843
      break;
844
  }
845
846
847

  TRACEPRINTF(("= %s\n", fc_print(result, buffer, 100, FC_HEX)));
  return result;
848
849
}

850
851
852
853
/********
 * functions defined in fltcalc.h
 ********/
const void *fc_get_buffer(void)
854
{
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
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897
898
899
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901
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905
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931
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991
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999
1000
1001
1002
1003
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1005
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1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
  return calc_buffer;
}

const int fc_get_buffer_length(void)
{
  return CALC_BUFFER_SIZE;
}

char* fc_val_from_str(const char *str, unsigned int len, char exp_size, char mant_size, char *result)
{
#if 0
  enum {
    START,
    LEFT_OF_DOT,
    RIGHT_OF_DOT,
    EXP_START,
    EXPONENT,
    END
  };

  char exp_sign;
  int exp_int, hsb, state;

  const char *old_str;

  int pos;
  char *mant_str, *exp_val, *power_val;

  if (result == NULL) result = calc_buffer;

  exp_val = alloca(VALUE_SIZE);
  power_val = alloca(CALC_BUFFER_SIZE);
  mant_str = alloca((len)?(len):(strlen(str)));

  _desc(result).exponent_size = exp_size;
  _desc(result).mantissa_size = mant_size;
  _desc(result).class = NORMAL;

  old_str = str;
  pos = 0;
  exp_int = 0;
  state = START;

  while (len == 0 || str-old_str < len)
  {
    switch (state) {
      case START:
        switch (*str) {
          case '+':
            _sign(result) = 0;
            state = LEFT_OF_DOT;
            str++;
            break;

          case '-':
            _sign(result) = 1;
            state = LEFT_OF_DOT;
            str++;
            break;

          case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
            _sign(result) = 0;
            state = LEFT_OF_DOT;
            break;

          case '.':
            _sign(result) = 0;
            state = RIGHT_OF_DOT;
            str++;
            break;

          case 'n':
          case 'N':
          case 'i':
          case 'I':
            break;

          default:
            _fail_char(old_str, len, str - old_str);
        }
        break;

      case LEFT_OF_DOT:
        switch (*str) {
          case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
            mant_str[pos++] = *(str++);
            break;

          case '.':
            state = RIGHT_OF_DOT;
            str++;
            break;

          case 'e':
          case 'E':
            state = EXP_START;
            str++;
            break;

          case '\0':
            mant_str[pos] = '\0';
            goto done;

          default:
            _fail_char(old_str, len, str - old_str);
        }
        break;

      case RIGHT_OF_DOT:
        switch (*str) {
          case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
            mant_str[pos++] = *(str++);
            exp_int++;
            break;

          case 'e':
          case 'E':
            state = EXP_START;
            str++;
            break;

          case '\0':
            mant_str[pos] = '\0';
            goto done;

          default:
            _fail_char(old_str, len, str - old_str);
        }
        break;

      case EXP_START:
        switch (*str) {
          case '-':
            exp_sign = 1;
            /* fall through */
          case '+':
            if (*(str-1) != 'e' && *(str-1) != 'E') _fail_char(old_str, len, str - old_str);
            str++;
            break;

          case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
            mant_str[pos] = '\0';
            pos = 1;
            str++;
            state = EXPONENT;
            break;

          default:
            _fail_char(old_str, len, str - old_str);
        }
        break;

      case EXPONENT:
        switch (*str) {
          case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9':
            pos++;
            str++;
            break;

          case '\0': goto done;

          default:
            _fail_char(old_str, len, str - old_str);
        }
    }
  } // switch(state)

done:
  sc_val_from_str(mant_str, strlen(mant_str), _mant(result));
1024

1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
  /* shift to put value left of radix point */
  sc_val_from_ulong(mant_size + 2, exp_val);

  _shift_left(_mant(result), exp_val, _mant(result));

  sc_val_from_ulong((1 << exp_size)/2-1, _exp(result));

  _normalize(result, result, 0);

  if (state == EXPONENT) {
    exp_int -= atoi(str-pos);
  }

  _power_of_ten(exp_int, &_desc(result), power_val);

  _div(result, power_val, result);

  return result;
#else

  /* XXX excuse of an implementation to make things work */
  LLDBL val;
#ifdef HAVE_LONG_DOUBLE
  val = strtold(str, NULL);
#else
  val = strtod(str, NULL);
#endif

  DEBUGPRINTF(("val_from_str(%s)\n", str));
  return fc_val_from_float(val, exp_size, mant_size, result);
#endif
}

char* fc_val_from_float(LLDBL l, char exp_size, char mant_size, char* result)
{
  char *temp;
  int bias_res = ((1<<exp_size)/2-1);
  int bias_val;
  char mant_val;
  value_t srcval;

  srcval.d = l;

#ifdef HAVE_LONG_DOUBLE
  mant_val = 64;
  bias_val = 0x3fff;
  UINT32 sign = (srcval.val.high & 0x80000000) != 0;
  UINT32 exponent = (srcval.val.high & 0x7FFF0000) >> 16;
  UINT32 mantissa1 = srcval.val.mid;
  UINT32 mantissa0 = srcval.val.low;
#else /* no long double */
  mant_val = 52;
  bias_val = 0x3ff;
  UINT32 sign = (srcval.val.high & 0x80000000) != 0;
  UINT32 exponent = (srcval.val.high & 0x7FF00000) >> 20;
  UINT32 mantissa0 = srcval.val.high & 0x000FFFFF;
  UINT32 mantissa1 = srcval.val.low;
#endif

#ifdef HAVE_LONG_DOUBLE
  TRACEPRINTF(("val_from_float(%.8X%.8X%.8X)\n", ((int*)&l)[2], ((int*)&l)[1], ((int*)&l)[0]));
  DEBUGPRINTF(("(%d-%.4X-%.8X%.8X)\n", sign, exponent, mantissa0, mantissa1));
#else
  TRACEPRINTF(("val_from_float(%.8X%.8X)\n", ((int*)&l)[1], ((int*)&l)[0]));
  DEBUGPRINTF(("(%d-%.3X-%.5X%.8X)\n", sign, exponent, mantissa0, mantissa1));
#endif

  if (result == NULL) result = calc_buffer;
  temp = alloca(VALUE_SIZE);

  _desc(result).exponent_size = exp_size;
  _desc(result).mantissa_size = mant_size;

  /* extract sign */
  _sign(result) = sign;

  /* sign and flag suffice to identify nan or inf, no exponent/mantissa
   * encoding is needed. the function can return immediately in these cases */
  if (isnan(l)) {
    _desc(result).class = NAN;
    TRACEPRINTF(("val_from_float resulted in NAN\n"));
    return result;
1107
  }
1108
1109
1110
1111
  else if (isinf(l)) {
    _desc(result).class = INF;
    TRACEPRINTF(("val_from_float resulted in %sINF\n", (_sign(result)==1)?"-":""));
    return result;
1112
  }
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123

  /* extract exponent */
  sc_val_from_long((exponent-bias_val+bias_res)-(mant_val-mant_size), _exp(result));

  /* extract mantissa */
  if (exponent != 0)
  {
    /* insert the hidden bit */
    sc_val_from_ulong(1, temp);
    sc_val_from_ulong(mant_val + 2, NULL);
    _shift_left(temp, sc_get_buffer(), NULL);
1124
  }
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
  else
  {
    sc_val_from_ulong(0, NULL);
  }

  _save_result(_mant(result));

  /* bits from the upper word */
  sc_val_from_ulong(mantissa0, temp);
  sc_val_from_ulong(34, NULL);
  _shift_left(temp, sc_get_buffer(), temp);
  sc_or(_mant(result), temp, _mant(result));

  /* bits from the lower word */
  sc_val_from_ulong(mantissa1, temp);
  sc_val_from_ulong(2, NULL);
  _shift_left(temp, sc_get_buffer(), temp);
  sc_or(_mant(result), temp, _mant(result));

  /* _normalize expects the radix point to be normal, so shift mantissa of subnormal
   * origin one to the left */
  if (exponent == 0)
  {
    sc_val_from_ulong(1, NULL);
    _shift_left(_mant(result), sc_get_buffer(), _mant(result));
  }

  _normalize(result, result, 0);

  TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, CALC_BUFFER_SIZE, FC_HEX)));

  return result;
1157
1158
}

1159
LLDBL fc_val_to_float(const void *val)
1160
{
1161
1162
1163
1164
1165
  const char *value;
  char *temp = NULL;
  char *pack = NULL;

  int byte_offset;
1166

1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
  UINT32 sign;
  UINT32 exponent;
  UINT32 mantissa0;
  UINT32 mantissa1;

  value_t buildval;

#ifdef HAVE_LONG_DOUBLE
  char result_mantissa = 64;
  char result_exponent = 15;
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#else
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  char result_mantissa = 52;
  char result_exponent = 11;
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#endif
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  temp = alloca(CALC_BUFFER_SIZE);
  pack = alloca(VALUE_SIZE);
  value = fc_cast(val, result_exponent, result_mantissa, temp);

  sign = _sign(value);
  /* long double exponent is 15bit, so the use of sc_val_to_long should not
   * lead to wrong results */
  exponent = sc_val_to_long(_exp(value)) ;

  _pack(value, pack);

  mantissa0 = 0;
  mantissa1 = 0;

  for (byte_offset = 0; byte_offset < 4; byte_offset++)
    mantissa1 |= sc_sub_bits(pack, result_mantissa, byte_offset) << (byte_offset<<3);

  for (; (byte_offset<<3) < result_mantissa; byte_offset++)
    mantissa0 |= sc_sub_bits(pack, result_mantissa, byte_offset) << ((byte_offset-4)<<3);

#ifndef HAVE_LONG_DOUBLE
  mantissa0 &= 0x000FFFFF;
#endif

#ifdef HAVE_LONG_DOUBLE
  buildval.val.high = sign << 31;
  buildval.val.high |= exponent << 16;
  buildval.val.mid = mantissa1;
  buildval.val.low = mantissa0;
#else /* no long double */
  buildval.val.high = sign << 31;
  buildval.val.high |= exponent << 20;
  buildval.val.high |= mantissa0;
  buildval.val.low = mantissa1;
#endif

  TRACEPRINTF(("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1));
  //printf("val_to_float: %d-%x-%x%x\n", sign, exponent, mantissa0, mantissa1);
  return buildval.d;
}

char* fc_cast(const void *val, char exp_size, char mant_size, char *result)
{
  const char *value = (const char*) val;
  char *temp;
  int exp_offset, val_bias, res_bias;

  if (result == NULL) result = calc_buffer;
  temp = alloca(CALC_BUFFER_SIZE);

  if (_desc(value).exponent_size == exp_size && _desc(value).mantissa_size == mant_size)
  {
    if (value != result) memcpy(result, value, CALC_BUFFER_SIZE);
    return result;
  }

  /* set the descriptor of the new value */
  _desc(result).exponent_size = exp_size;
  _desc(result).mantissa_size = mant_size;
  _desc(result).class = _desc(value).class;

  _sign(result) = _sign(value);

  /* when the mantissa sizes differ normalizing has to shift to align it.
   * this would change the exponent, which is unwanted. So calculate this
   * offset and add it */
  val_bias = (1<<_desc(value).exponent_size)/2-1;
  res_bias = (1<<exp_size)/2-1;
  exp_offset = (res_bias - val_bias) - (_desc(value).mantissa_size - mant_size);

  sc_val_from_long(exp_offset, temp);
  sc_add(_exp(value), temp, _exp(result));

  if (value != result) memcpy(_mant(result), _mant(value), VALUE_SIZE);
  else memmove(_mant(result), _mant(value), VALUE_SIZE);

  return _normalize(result, result, 0);
}

char* fc_get_max(unsigned int exponent_size, unsigned int mantissa_size, char* result)
{
  if (result == NULL) result = calc_buffer;

  _desc(result).exponent_size = exponent_size;
  _desc(result).mantissa_size = mantissa_size;
  _desc(result).class = NORMAL;

  _sign(result) = 0;

  sc_val_from_ulong((1<<exponent_size) - 2, _exp(result));

  sc_max_from_bits(mantissa_size + 1, 0, _mant(result));
  sc_val_from_ulong(2, NULL);
  _shift_left(_mant(result), sc_get_buffer(), _mant(result));

  return result;
}

char* fc_get_min(unsigned int exponent_size, unsigned int mantissa_size, char *result)
{
  if (result == NULL) result = calc_buffer;

  fc_get_max(exponent_size, mantissa_size, result);
  _sign(result) = 1;

  return result;
}

char* fc_get_snan(unsigned int exponent_size, unsigned int mantissa_size, char *result)
{
  if (result == NULL) result = calc_buffer;

  _desc(result).exponent_size = exponent_size;
  _desc(result).mantissa_size = mantissa_size;
  _desc(result).class = NAN;

  _sign(result) = 0;

  sc_val_from_ulong((1<<exponent_size)-1, _exp(result));

  /* signalling nan has non-zero mantissa with msb not set */
  sc_val_from_ulong(1, _mant(result));

  return result;
}

char* fc_get_qnan(unsigned int exponent_size, unsigned int mantissa_size, char *result)
{
  if (result == NULL) result = calc_buffer;

  _desc(result).exponent_size = exponent_size;
  _desc(result).mantissa_size = mantissa_size;
  _desc(result).class = NAN;

  _sign(result) = 0;

  sc_val_from_ulong((1<<exponent_size)-1, _exp(result));

  /* quiet nan has the msb of the mantissa set, so shift one there */
  sc_val_from_ulong(1, _mant(result));
  /* mantissa_size >+< 1 because of two extra rounding bits */
  sc_val_from_ulong(mantissa_size + 1, NULL);
  _shift_left(_mant(result), sc_get_buffer(), _mant(result));

  return result;
}

char* fc_get_plusinf(unsigned int exponent_size, unsigned int mantissa_size, char *result)
{
  if (result == NULL) result = calc_buffer;

  _desc(result).exponent_size = exponent_size;
  _desc(result).mantissa_size = mantissa_size;
  _desc(result).class = NORMAL;

  _sign(result) = 0;

  sc_val_from_ulong((1<<exponent_size)-1, _exp(result));

  sc_val_from_ulong(0, _mant(result));

  return result;
}

char* fc_get_minusinf(unsigned int exponent_size, unsigned int mantissa_size, char *result)
{
  if (result == NULL) result = calc_buffer;

  fc_get_plusinf(exponent_size, mantissa_size, result);
  _sign(result) = 1;

  return result;
}

int fc_comp(const void *a, const void *b)
{
  const char *val_a = (const char*)a;
  const char *val_b = (const char*)b;

  /* unordered */
  if (_desc(val_a).class == NAN || _desc(val_b).class == NAN) return 2;
  /* zero is equal independent of sign */
  if ((_desc(val_a).class == ZERO) && (_desc(val_b).class == ZERO)) return 0;
  /* different signs make compare easy */
  if (_sign(val_a) != _sign(val_b)) return (_sign(val_a)==0)?(1):(-1);
  /* both infinity means equality */
  if ((_desc(val_a).class == INF) && (_desc(val_b).class == INF)) return 0;
  /* infinity is bigger than the rest */
  if (_desc(val_a).class == INF) return _sign(val_a)?(-1):(1);
  if (_desc(val_b).class == INF) return _sign(val_b)?(1):(-1);

  switch (sc_comp(_exp(val_a), _exp(val_b))) {
    case -1:
      return -1;
    case  1:
      return  1;
    case  0:
      return sc_comp(_mant(val_a), _mant(val_b));
    default:
      return 2;
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  }
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}

int fc_is_zero(const void *a)
{
  return _desc((const char*)a).class == ZERO;
}

int fc_is_negative(const void *a)
{
  return _sign((const char*)a);
}

int fc_is_inf(const void *a)
{
  return _desc(a).class == INF;
}

int fc_is_nan(const void *a)
{
  return _desc(a).class == NAN;
}
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int fc_is_subnormal(const void *a)
{
  return _desc(a).class == SUBNORMAL;
}

char *fc_print(const void *a, char *buf, int buflen, unsigned base)
{
  const char *val;
  char *mul_1;

  val = (const char*)a;

  mul_1 = alloca(CALC_BUFFER_SIZE);

  switch (base) {
    case FC_DEC:
      switch (_desc(val).class) {
        case INF:
          if (buflen >= 8+_sign(val)) sprintf(buf, "%sINFINITY", _sign(val)?"-":"");
          else snprintf(buf, buflen, "%sINF", _sign(val)?"-":NULL);
          break;
        case NAN:
          snprintf(buf, buflen, "NAN");
          break;
        case ZERO:
          snprintf(buf, buflen, "0.0");
          break;
        default:
          /* XXX to be implemented */
#ifdef HAVE_LONG_DOUBLE
          /* XXX 30 is arbitrary */
          snprintf(buf, buflen, "%.30LE", fc_val_to_float(val));
#else
          snprintf(buf, buflen, "%.18E", fc_val_to_float(val));
#endif
      }
      break;
    case FC_HEX:
      snprintf(buf, buflen, "%s", sc_print(_pack(val, mul_1), 0, SC_HEX));
      break;
  }
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  return buf;
}
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unsigned char fc_sub_bits(const void *value, unsigned num_bits, unsigned byte_ofs)
{
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  /* this is used to cache the packed version of the value */
  static char *pack = NULL;

  if (pack == NULL) pack = malloc(VALUE_SIZE);

  if (value != NULL)
    _pack((const char*)value, pack);

  return sc_sub_bits(pack, num_bits, byte_ofs);
}

fc_rounding_mode_t fc_set_rounding_mode(fc_rounding_mode_t mode)
{
  if (mode == FC_TONEAREST || mode == FC_TOPOSITIVE || mode == FC_TONEGATIVE || mode == FC_TOZERO)
      ROUNDING_MODE = mode;
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  return ROUNDING_MODE;
}
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fc_rounding_mode_t fc_get_rounding_mode(void)
{
  return ROUNDING_MODE;
}
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void init_fltcalc(int precision)
{
  if (calc_buffer == NULL) {
    /* does nothing if already init */
    if (precision == 0) precision = FC_DEFAULT_PRECISION;
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    init_strcalc(precision + 4);
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    /* needs additionally two bits to round, a bit as explicit 1., and one for
     * addition overflow */
    max_precision = sc_get_precision() - 4;
    if (max_precision < precision)
      printf("WARING: not enough precision available, using %d\n", max_precision);
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    ROUNDING_MODE = FC_TONEAREST;
    VALUE_SIZE = sc_get_buffer_length();
    SIGN_POS = 0;
    EXPONENT_POS = SIGN_POS + sizeof(char);
    MANTISSA_POS = EXPONENT_POS + VALUE_SIZE;
    DESCRIPTOR_POS = MANTISSA_POS + VALUE_SIZE;
    CALC_BUFFER_SIZE = DESCRIPTOR_POS + sizeof(descriptor_t);

    calc_buffer = malloc(CALC_BUFFER_SIZE);
    DEBUGPRINTF(("init fltcalc:\n\tVALUE_SIZE = %d\n\tSIGN_POS = %d\n\tEXPONENT_POS = %d\n\tMANTISSA_POS = %d\n\tDESCRIPTOR_POS = %d\n\tCALC_BUFFER_SIZE = %d\n\tcalc_buffer = %p\n\n", VALUE_SIZE, SIGN_POS, EXPONENT_POS, MANTISSA_POS, DESCRIPTOR_POS, CALC_BUFFER_SIZE, calc_buffer));
  }
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}
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/* definition of interface functions */
FC_DEFINE2(add)
FC_DEFINE2(sub)
FC_DEFINE2(mul)
FC_DEFINE2(div)
FC_DEFINE1(neg)
FC_DEFINE1(int)
FC_DEFINE1(rnd)