fltcalc.c 42 KB
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/*
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 * Copyright (C) 1995-2010 University of Karlsruhe.  All right reserved.
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 *
 * This file is part of libFirm.
 *
 * This file may be distributed and/or modified under the terms of the
 * GNU General Public License version 2 as published by the Free Software
 * Foundation and appearing in the file LICENSE.GPL included in the
 * packaging of this file.
 *
 * Licensees holding valid libFirm Professional Edition licenses may use
 * this file in accordance with the libFirm Commercial License.
 * Agreement provided with the Software.
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE.
 */

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/**
 * @file
 * @brief    tarval floating point calculations
 * @date     2003
 * @author   Mathias Heil
 * @version  $Id$
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 */
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#include "config.h"
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#include "fltcalc.h"
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#include "strcalc.h"

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#include <math.h>
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/* undef some reused constants defined by math.h */
#ifdef NAN
#  undef NAN
#endif

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#include <inttypes.h>
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#include <string.h>
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#include <stdlib.h>
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#include <stdio.h>
#include <assert.h>
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#include "xmalloc.h"

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#if !defined(HAVE_LONG_DOUBLE) || defined(__CYGWIN__)
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/* No strtold on windows and no replacement yet */
#define strtold(s, e) strtod(s, e)
#endif

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/** The number of extra precision rounding bits */
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#define ROUNDING_BITS 2

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typedef uint32_t UINT32;
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#ifdef HAVE_LONG_DOUBLE
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#ifdef WORDS_BIGENDIAN
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typedef union {
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	struct {
		UINT32 high;
		UINT32 mid;
		UINT32 low;
	} val;
	volatile long double d;
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} value_t;
#else
typedef union {
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	struct {
		UINT32 low;
		UINT32 mid;
		UINT32 high;
	} val;
	volatile long double d;
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} value_t;
#endif
#else
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#ifdef WORDS_BIGENDIAN
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typedef union {
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	struct {
		UINT32 high;
		UINT32 low;
	} val;
	volatile double d;
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} value_t;
#else
typedef union {
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	struct {
		UINT32 low;
		UINT32 high;
	} val;
	volatile double d;
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} value_t;
#endif
#endif
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#define CLEAR_BUFFER(buffer) memset(buffer, 0, calc_buffer_size)
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/* our floating point value */
struct _fp_value {
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	ieee_descriptor_t desc;
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	char sign;
	char value[1];			/* exp[value_size] + mant[value_size] */
};

#define _exp(a)  &((a)->value[0])
#define _mant(a) &((a)->value[value_size])
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#define _save_result(x) memcpy((x), sc_get_buffer(), value_size)
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#define _shift_right(x, y, res) sc_shr((x), (y), value_size*4, 0, (res))
#define _shift_left(x, y, res) sc_shl((x), (y), value_size*4, 0, (res))
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#ifdef FLTCALC_DEBUG
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#  define DEBUGPRINTF(x) printf x
#else
#  define DEBUGPRINTF(x) ((void)0)
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#endif

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#ifdef FLTCALC_TRACE_CALC
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#  define TRACEPRINTF(x) printf x
#else
#  define TRACEPRINTF(x) ((void)0)
#endif
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/** The immediate precision. */
static unsigned immediate_prec = 0;

/** A temporal buffer. */
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static fp_value *calc_buffer = NULL;
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/** Current rounding mode.*/
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static fc_rounding_mode_t rounding_mode;
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static int calc_buffer_size;
static int value_size;
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static int max_precision;
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/** Exact flag. */
static int fc_exact = 1;

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#if 0
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static void fail_char(const char *str, unsigned int len, int pos)
{
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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 machine-like */
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static void *pack(const fp_value *int_float, void *packed)
{
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	char     *shift_val;
	char     *temp;
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	fp_value *val_buffer;
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	int      pos;
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	temp      = alloca(value_size);
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	shift_val = alloca(value_size);

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	switch ((value_class_t)int_float->desc.clss) {
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	case NAN:
		val_buffer = alloca(calc_buffer_size);
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		fc_get_qnan(&int_float->desc, val_buffer);
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		int_float = val_buffer;
		break;

	case INF:
		val_buffer = alloca(calc_buffer_size);
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		fc_get_plusinf(&int_float->desc, val_buffer);
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		val_buffer->sign = int_float->sign;
		int_float = val_buffer;
		break;

	default:
		break;
	}
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	assert(int_float->desc.explicit_one <= 1);

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	/* pack sign: move it to the left after exponent AND mantissa */
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	sc_val_from_ulong(int_float->sign, temp);

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	pos = int_float->desc.exponent_size + int_float->desc.mantissa_size + int_float->desc.explicit_one;
	sc_val_from_ulong(pos, NULL);
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	_shift_left(temp, sc_get_buffer(), packed);

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	/* pack exponent: move it to the left after mantissa */
	pos = int_float->desc.mantissa_size + int_float->desc.explicit_one;
	sc_val_from_ulong(pos, shift_val);
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	_shift_left(_exp(int_float), shift_val, temp);

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	/* combine sign|exponent */
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	sc_or(temp, packed, packed);

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

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

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	/* combine sign|exponent|mantissa */
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	sc_or(temp, packed, packed);

	return packed;
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}

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/**
 * Normalize a fp_value.
 *
 * @return non-zero if result is exact
 */
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static int normalize(const fp_value *in_val, fp_value *out_val, int sticky)
{
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	int exact = 1;
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	int hsb;
	char lsb, guard, round, round_dir = 0;
	char *temp = alloca(value_size);

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	/* save rounding bits at the end */
	hsb = ROUNDING_BITS + in_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(in_val)) - 1;
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	if (in_val != out_val)   {
		out_val->sign = in_val->sign;
		memcpy(&out_val->desc, &in_val->desc, sizeof(out_val->desc));
	}

	out_val->desc.clss = NORMAL;

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

	/* shift the first 1 into 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 */
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		if (sc_had_carry()) {
			exact = 0;
			sticky = 1;
		}
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		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));
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		if (sc_had_carry()) {
			exact  = 0;
			sticky = 1;
		}
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		/* denormalized means exponent of zero */
		sc_val_from_ulong(0, _exp(out_val));

		out_val->desc.clss = 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 */
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	lsb = sc_sub_bits(_mant(out_val), out_val->desc.mantissa_size + ROUNDING_BITS, 0) & 0x7;
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	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 = (!out_val->sign && (guard || round || sticky));
		break;
	case FC_TONEGATIVE:
		/* if negative: round to one if the exact value is bigger, else to zero */
		round_dir = (out_val->sign && (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", out_val->sign, 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));
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		exact = 0;
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	}

	/* could have rounded down to zero */
	if (sc_is_zero(_mant(out_val)) && (out_val->desc.clss == SUBNORMAL))
		out_val->desc.clss = ZERO;

	/* check for rounding overflow */
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	hsb = ROUNDING_BITS + out_val->desc.mantissa_size - sc_get_highest_set_bit(_mant(out_val)) - 1;
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	if ((out_val->desc.clss != SUBNORMAL) && (hsb < -1)) {
		sc_val_from_ulong(1, temp);
		_shift_right(_mant(out_val), temp, _mant(out_val));
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		if (exact && sc_had_carry())
			exact = 0;
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		sc_add(_exp(out_val), temp, _exp(out_val));
	} else if ((out_val->desc.clss == SUBNORMAL) && (hsb == -1)) {
		/* overflow caused the mantissa to be normal again,
		 * so adapt the exponent accordingly */
		sc_val_from_ulong(1, temp);
		sc_add(_exp(out_val), temp, _exp(out_val));

		out_val->desc.clss = 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 << out_val->desc.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 (out_val->sign == 0) {
			/* value is positive */
			switch (rounding_mode) {
			case FC_TONEAREST:
			case FC_TOPOSITIVE:
				out_val->desc.clss = INF;
				break;

			case FC_TONEGATIVE:
			case FC_TOZERO:
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				fc_get_max(&out_val->desc, out_val);
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			}
		} else {
			/* value is negative */
			switch (rounding_mode) {
			case FC_TONEAREST:
			case FC_TONEGATIVE:
				out_val->desc.clss = INF;
				break;

			case FC_TOPOSITIVE:
			case FC_TOZERO:
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				fc_get_min(&out_val->desc, out_val);
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			}
		}
	}
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	return exact;
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}

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/**
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 * Operations involving NaN's must return NaN.
 * They are NOT exact.
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 */
#define handle_NAN(a, b, result) \
do {                                                      \
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  if (a->desc.clss == NAN) {                              \
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    if (a != result) memcpy(result, a, calc_buffer_size); \
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    fc_exact = 0;                                         \
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    return;                                               \
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  }                                                       \
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  if (b->desc.clss == NAN) {                              \
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    if (b != result) memcpy(result, b, calc_buffer_size); \
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    fc_exact = 0;                                         \
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    return;                                               \
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  }                                                       \
}while (0)


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

	char sign, res_sign;
	char sticky;

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	fc_exact = 1;

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	handle_NAN(a, b, result);

	/* make sure result has a descriptor */
	if (result != a && result != b)
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		result->desc = a->desc;
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	/* determine if this is an addition or subtraction */
	sign = a->sign ^ b->sign;

	/* produce NaN on inf - inf */
	if (sign && (a->desc.clss == INF) && (b->desc.clss == INF)) {
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		fc_exact = 0;
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		fc_get_qnan(&a->desc, result);
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		return;
	}

	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 */
			res_sign = a->sign;  /* abs(a) is bigger and a is negative */
			break;
		case 0:  /* a == b */
			res_sign = (rounding_mode == FC_TONEGATIVE);
			break;
		case -1: /* a < b */
			res_sign = b->sign; /* abs(b) is bigger and b is negative */
			break;
		default:
			/* can't be reached */
			res_sign = 0;
			break;
		}
	}
	else
		res_sign = a->sign;
	result->sign = res_sign;

	/* sign has been taken care of, check for special cases */
	if (a->desc.clss == ZERO || b->desc.clss == INF) {
		if (b != result)
			memcpy(result, b, calc_buffer_size);
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		fc_exact = b->desc.clss == NORMAL;
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		result->sign = res_sign;
		return;
	}
	if (b->desc.clss == ZERO || a->desc.clss == INF) {
		if (a != result)
			memcpy(result, a, calc_buffer_size);
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		fc_exact = a->desc.clss == NORMAL;
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		result->sign = res_sign;
		return;
	}

	/* 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 ((b->desc.clss == SUBNORMAL) && (a->desc.clss != 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();
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	fc_exact &= !sticky;
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	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 ((a->desc.clss == SUBNORMAL) && (b->desc.clss == 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);

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	fc_exact &= normalize(result, result, sticky);
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}

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/**
 * calculate a * b
 */
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static void _fmul(const fp_value *a, const fp_value *b, fp_value *result)
{
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	int sticky;
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	char *temp;
	char res_sign;

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	fc_exact = 1;

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	handle_NAN(a, b, result);

	temp = alloca(value_size);

	if (result != a && result != b)
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		result->desc = a->desc;
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	result->sign = res_sign = a->sign ^ b->sign;

	/* produce NaN on 0 * inf */
	if (a->desc.clss == ZERO) {
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		if (b->desc.clss == INF) {
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			fc_get_qnan(&a->desc, result);
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			fc_exact = 0;
		} else {
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			if (a != result)
				memcpy(result, a, calc_buffer_size);
			result->sign = res_sign;
		}
		return;
	}
	if (b->desc.clss == ZERO) {
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		if (a->desc.clss == INF) {
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			fc_get_qnan(&a->desc, result);
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			fc_exact = 0;
		} else {
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			if (b != result)
				memcpy(result, b, calc_buffer_size);
			result->sign = res_sign;
		}
		return;
	}

	if (a->desc.clss == INF) {
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		fc_exact = 0;
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		if (a != result)
			memcpy(result, a, calc_buffer_size);
		result->sign = res_sign;
		return;
	}
	if (b->desc.clss == INF) {
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		fc_exact = 0;
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		if (b != result)
			memcpy(result, b, calc_buffer_size);
		result->sign = res_sign;
		return;
	}

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

	sc_val_from_ulong((1 << (a->desc.exponent_size - 1)) - 1, temp);
	sc_sub(_exp(result), temp, _exp(result));

	/* mixed normal, subnormal values introduce an error of 1, correct it */
	if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == 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
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	 * because of the rounding bits */
	sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
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	_shift_right(_mant(result), temp, _mant(result));
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	sticky = sc_had_carry();
	fc_exact &= !sticky;
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	fc_exact &= normalize(result, result, sticky);
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}

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/**
 * calculate a / b
 */
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static void _fdiv(const fp_value *a, const fp_value *b, fp_value *result)
{
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	int sticky;
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	char *temp, *dividend;
	char res_sign;

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	fc_exact = 1;

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	handle_NAN(a, b, result);

	temp = alloca(value_size);
	dividend = alloca(value_size);

	if (result != a && result != b)
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		result->desc = a->desc;
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	result->sign = res_sign = a->sign ^ b->sign;

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	/* produce NAN on 0/0 and inf/inf */
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	if (a->desc.clss == ZERO) {
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		if (b->desc.clss == ZERO) {
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			/* 0/0 -> NaN */
			fc_get_qnan(&a->desc, result);
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			fc_exact = 0;
		} else {
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			/* 0/x -> a */
			if (a != result)
				memcpy(result, a, calc_buffer_size);
			result->sign = res_sign;
		}
		return;
	}

	if (b->desc.clss == INF) {
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		fc_exact = 0;
		if (a->desc.clss == INF) {
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			/* inf/inf -> NaN */
			fc_get_qnan(&a->desc, result);
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		} else {
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			/* x/inf -> 0 */
			sc_val_from_ulong(0, NULL);
			_save_result(_exp(result));
			_save_result(_mant(result));
			result->desc.clss = ZERO;
		}
		return;
	}

	if (a->desc.clss == INF) {
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		fc_exact = 0;
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		/* inf/x -> inf */
		if (a != result)
			memcpy(result, a, calc_buffer_size);
		result->sign = res_sign;
		return;
	}
	if (b->desc.clss == ZERO) {
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		fc_exact = 0;
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		/* division by zero */
		if (result->sign)
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			fc_get_minusinf(&a->desc, result);
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		else
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			fc_get_plusinf(&a->desc, result);
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		return;
	}

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

	/* mixed normal, subnormal values introduce an error of 1, correct it */
	if ((a->desc.clss == SUBNORMAL) ^ (b->desc.clss == SUBNORMAL)) {
		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 */
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	sc_val_from_ulong(ROUNDING_BITS + result->desc.mantissa_size, temp);
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	_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));
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		sticky = sc_had_carry();
		fc_exact &= !sticky;
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	}

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	fc_exact &= normalize(result, result, sticky);
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}

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#if 0
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static void _power_of_ten(int exp, ieee_descriptor_t *desc, char *result)
{
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	char *build;
	char *temp;
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	/* positive sign */
	result->sign = 0;
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	/* set new descriptor (else result is supposed to already have one) */
	if (desc != NULL)
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		result->desc = *desc;
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	build = alloca(value_size);
	temp = alloca(value_size);
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	sc_val_from_ulong((1 << (result->desc.exponent_size - 1)) - 1, _exp(result));
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	if (exp > 0) {
		/* temp is value of ten now */
		sc_val_from_ulong(10, NULL);
		_save_result(temp);
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		for (exp--; exp > 0; exp--) {
			_save_result(build);
			sc_mul(build, temp, NULL);
		}
		_save_result(build);
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		/* temp is amount of left shift needed to put the value left of the radix point */
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		sc_val_from_ulong(result->desc.mantissa_size + ROUNDING_BITS, temp);
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		_shift_left(build, temp, _mant(result));
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		_normalize(result, result, 0);
	}
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}
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#endif
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/**
 * Truncate the fractional part away.
 *
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 * This does not clip to any integer range.
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 */
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static void _trunc(const fp_value *a, fp_value *result)
{
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	/*
	 * 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 left shift 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 does not have fractional parts.
	 */

	int exp_bias, exp_val;
	char *temp;

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	/* fixme: can be exact */
	fc_exact = 0;

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	temp = alloca(value_size);

	if (a != result)
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		result->desc = a->desc;
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	exp_bias = (1 << (a->desc.exponent_size - 1)) - 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));
		result->desc.clss = ZERO;

		return;
	}

	if (exp_val > a->desc.mantissa_size) {
		if (a != result)
			memcpy(result, a, calc_buffer_size);

		return;
	}

	/* 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(a->desc.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));

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	if (a != result) {
		memcpy(_exp(result), _exp(a), value_size);
		result->sign = a->sign;
	}
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}

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/********
 * functions defined in fltcalc.h
 ********/
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const void *fc_get_buffer(void)
{
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	return calc_buffer;
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}

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int fc_get_buffer_length(void)
{
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	return calc_buffer_size;
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}

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void *fc_val_from_str(const char *str, unsigned int len, const ieee_descriptor_t *desc, void *result)
{
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	char *buffer;
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	/* XXX excuse of an implementation to make things work */
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	LLDBL             val;
	fp_value          *tmp = alloca(calc_buffer_size);
	ieee_descriptor_t tmp_desc;
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	buffer = alloca(len+1);
	memcpy(buffer, str, len);
	buffer[len] = '\0';
	val = strtold(buffer, NULL);

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	DEBUGPRINTF(("val_from_str(%s)\n", str));
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	tmp_desc.exponent_size = 15;
	tmp_desc.mantissa_size = 63;
	tmp_desc.explicit_one  = 1;
	tmp_desc.clss          = NORMAL;
	fc_val_from_ieee754(val, &tmp_desc, tmp);
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	return fc_cast(tmp, desc, result);
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}

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fp_value *fc_val_from_ieee754(LLDBL l, const ieee_descriptor_t *desc, fp_value *result)
{
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	char    *temp;
	int     bias_res, bias_val, mant_val;
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	value_t srcval;
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	char    sign;
	UINT32  exponent, mantissa0, mantissa1;
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	srcval.d = l;
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	bias_res = ((1 << (desc->exponent_size - 1)) - 1);
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#ifdef HAVE_LONG_DOUBLE
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	mant_val  = 63;
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	bias_val  = 0x3fff;
	sign      = (srcval.val.high & 0x00008000) != 0;
	exponent  = (srcval.val.high & 0x00007FFF) ;
	mantissa0 = srcval.val.mid;
	mantissa1 = srcval.val.low;
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#else /* no long double */
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	mant_val  = 52;
	bias_val  = 0x3ff;
	sign      = (srcval.val.high & 0x80000000) != 0;
	exponent  = (srcval.val.high & 0x7FF00000) >> 20;
	mantissa0 = srcval.val.high & 0x000FFFFF;
	mantissa1 = srcval.val.low;
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#endif

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

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

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	/* CLEAR the buffer, else some bits might be uninitialized */
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	memset(result, 0, fc_get_buffer_length());
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	result->desc.exponent_size = desc->exponent_size;
	result->desc.mantissa_size = desc->mantissa_size;
	result->desc.explicit_one  = desc->explicit_one;
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	/* extract sign */
	result->sign = sign;

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	/* sign and flag suffice to identify NaN or inf, no exponent/mantissa
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	 * encoding is needed. the function can return immediately in these cases */
	if (isnan(l)) {
		result->desc.clss = NAN;
		TRACEPRINTF(("val_from_float resulted in NAN\n"));
		return result;
	}
	else if (isinf(l)) {
		result->desc.clss = INF;
		TRACEPRINTF(("val_from_float resulted in %sINF\n", (result->sign == 1) ? "-" : ""));
		return result;
	}

	/* build exponent, because input and output exponent and mantissa sizes may differ
	 * this looks more complicated than it is: unbiased input exponent + output bias,
	 * minus the mantissa difference which is added again later when the output float
	 * becomes normalized */
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	sc_val_from_long((exponent - bias_val + bias_res) - (mant_val - desc->mantissa_size), _exp(result));
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	/* build mantissa representation */
	if (exponent != 0) {
		/* insert the hidden bit */
		sc_val_from_ulong(1, temp);
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		sc_val_from_ulong(mant_val + ROUNDING_BITS, NULL);
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		_shift_left(temp, sc_get_buffer(), NULL);
	}
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	else {
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		sc_val_from_ulong(0, NULL);
	}
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	_save_result(_mant(result));
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	/* 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));
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	/* bits from the lower word */
	sc_val_from_ulong(mantissa1, temp);
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	sc_val_from_ulong(ROUNDING_BITS, NULL);
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	_shift_left(temp, sc_get_buffer(), temp);
	sc_or(_mant(result), temp, _mant(result));
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	/* _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));
	}
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	normalize(result, result, 0);
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	TRACEPRINTF(("val_from_float results in %s\n", fc_print(result, temp, calc_buffer_size, FC_PACKED)));
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	return result;
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}

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LLDBL fc_val_to_ieee754(const fp_value *val)
{
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	fp_value *value;
	fp_value *temp = NULL;
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	int byte_offset;
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	UINT32 sign;
	UINT32 exponent;
	UINT32 mantissa0;
	UINT32 mantissa1;
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	value_t           buildval;
	ieee_descriptor_t desc;
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	unsigned          mantissa_size;
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#ifdef HAVE_LONG_DOUBLE
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	desc.exponent_size = 15;
	desc.mantissa_size = 63;
	desc.explicit_one  = 1;
	desc.clss          = NORMAL;
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#else
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	desc.exponent_size = 11;
	desc.mantissa_size = 52;
	desc.explicit_one  = 0;
	desc.clss          = NORMAL;
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#endif
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	mantissa_size = desc.mantissa_size + desc.explicit_one;
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	temp = alloca(calc_buffer_size);
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	value = fc_cast(val, &desc, temp);
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	sign = value->sign;
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	/* @@@ 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)) ;
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	sc_val_from_ulong(ROUNDING_BITS, NULL);
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	_shift_right(_mant(value), sc_get_buffer(), _mant(value));
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	mantissa0 = 0;
	mantissa1 = 0;
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	for (byte_offset = 0; byte_offset < 4; byte_offset++)
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		mantissa1 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << (byte_offset << 3);
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	for (; (byte_offset<<3) < desc.mantissa_size; byte_offset++)
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		mantissa0 |= sc_sub_bits(_mant(value), mantissa_size, byte_offset) << ((byte_offset - 4) << 3);
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#ifdef HAVE_LONG_DOUBLE
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	buildval.val.high = sign << 15;
	buildval.val.high |= exponent;
	buildval.val.mid = mantissa0;
	buildval.val.low = mantissa1;
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#else /* no long double */
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	mantissa0 &= 0x000FFFFF;  /* get rid of garbage */
	buildval.val.high = sign << 31;
	buildval.val.high |= exponent << 20;
	buildval.val.high |= mantissa0;
	buildval.val.low = mantissa1;
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#endif

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

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fp_value *fc_cast(const fp_value *value, const ieee_descriptor_t *desc, fp_value *result)
{
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	char *temp;
	int exp_offset, val_bias, res_bias;

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

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	if (value->desc.exponent_size == desc->exponent_size &&
		value->desc.mantissa_size == desc->mantissa_size &&
		value->desc.explicit_one  == desc->explicit_one) {
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		if (value != result)
			memcpy(result, value, calc_buffer_size);
		return result;
	}

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	if (value->desc.clss == NAN) {
		if (sc_get_highest_set_bit(_mant(value)) == value->desc.mantissa_size + 1)
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			return fc_get_qnan(desc, result);
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		else
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			return fc_get_snan(desc, result);
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	}
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	else if (value->desc.clss == INF) {
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		if (value->sign == 0)
			return fc_get_plusinf(desc, result);
		else
			return fc_get_minusinf(desc, result);
	}
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	/* set the descriptor of the new value */
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	result->desc.exponent_size = desc->exponent_size;
	result->desc.mantissa_size = desc->mantissa_size;
	result->desc.explicit_one  = desc->explicit_one;
	result->desc.clss          = value->desc.clss;
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	result->sign = value->sign;

	/* 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 << (value->desc.exponent_size - 1)) - 1;
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	res_bias = (1 << (desc->exponent_size - 1)) - 1;
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	exp_offset = (res_bias - val_bias) - (value->desc.mantissa_size - desc->mantissa_size);
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	sc_val_from_long(exp_offset, temp);
	sc_add(_exp(value), temp, _exp(result));

	/* _normalize expects normalized radix point */
	if (value->desc.clss == SUBNORMAL) {
		sc_val_from_ulong(1, NULL);
		_shift_left(_mant(value), sc_get_buffer(), _mant(result));
	} else if (value != result) {
		memcpy(_mant(result), _mant(value), value_size);
	} else {
		memmove(_mant(result), _mant(value), value_size);
	}

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	normalize(result, result, 0);
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	TRACEPRINTF(("Cast results in %s\n", fc_print(result, temp, value_size, FC_PACKED)));
	return result;
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}

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fp_value *fc_get_max(const ieee_descriptor_t *desc, fp_value *result)
{
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	if (result == NULL) result = calc_buffer;
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	result->desc.exponent_size = desc->exponent_size;
	result->desc.mantissa_size = desc->mantissa_size;
	result->desc.explicit_one  = desc->explicit_one;
	result->desc.clss          = NORMAL;
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	result->sign = 0;
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	sc_val_from_ulong((1 << desc->exponent_size) - 2, _exp(result));
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	sc_max_from_bits(desc->mantissa_size + 1, 0, _mant(result));
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	sc_val_from_ulong(ROUNDING_BITS, NULL);
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	_shift_left(_mant(result), sc_get_buffer(), _mant(result));
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	return result;
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}

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fp_value *fc_get_min(const ieee_descriptor_t *desc, fp_value *result)
{
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	if (result == NULL) result = calc_buffer;
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	fc_get_max(desc, result);
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	result->sign = 1;
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	return result;
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}

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fp_value *fc_get_snan(const ieee_descriptor_t *desc, fp_value *result)
{
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	if (result == NULL) result = calc_buffer;