gcc/libgcc/config/libbid/bid64_add.c

/* Copyright (C) 2007  Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 2, or (at your option) any later
version.

In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file into combinations with other programs,
and to distribute those combinations without any restriction coming
from the use of this file.  (The General Public License restrictions
do apply in other respects; for example, they cover modification of
the file, and distribution when not linked into a combine
executable.)

GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING.  If not, write to the Free
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.  */

/*****************************************************************************
 *    BID64 add
 *****************************************************************************
 *
 *  Algorithm description:
 *
 *   if(exponent_a < exponent_b)
 *       switch a, b
 *   diff_expon = exponent_a - exponent_b
 *   if(diff_expon > 16)
 *      return normalize(a)
 *   if(coefficient_a*10^diff_expon guaranteed below 2^62)
 *       S = sign_a*coefficient_a*10^diff_expon + sign_b*coefficient_b
 *       if(|S|<10^16)
 *           return get_BID64(sign(S),exponent_b,|S|)
 *       else
 *          determine number of extra digits in S (1, 2, or 3)
 *            return rounded result
 *   else // large exponent difference
 *       if(number_digits(coefficient_a*10^diff_expon) +/- 10^16)
 *          guaranteed the same as
 *          number_digits(coefficient_a*10^diff_expon) )
 *           S = normalize(coefficient_a + (sign_a^sign_b)*10^(16-diff_expon))
 *           corr = 10^16 + (sign_a^sign_b)*coefficient_b
 *           corr*10^exponent_b is rounded so it aligns with S*10^exponent_S
 *           return get_BID64(sign_a,exponent(S),S+rounded(corr))
 *       else
 *         add sign_a*coefficient_a*10^diff_expon, sign_b*coefficient_b
 *             in 128-bit integer arithmetic, then round to 16 decimal digits
 *           
 *
 ****************************************************************************/

#include "bid_internal.h"

#if DECIMAL_CALL_BY_REFERENCE
void bid64_add (UINT64 * pres, UINT64 * px,
		UINT64 *
		py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		_EXC_INFO_PARAM);
#else
UINT64 bid64_add (UINT64 x,
		  UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
		  _EXC_MASKS_PARAM _EXC_INFO_PARAM);
#endif

#if DECIMAL_CALL_BY_REFERENCE

void
bid64_sub (UINT64 * pres, UINT64 * px,
	   UINT64 *
	   py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	   _EXC_INFO_PARAM) {
  UINT64 y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  _IDEC_round rnd_mode = *prnd_mode;
#endif
  // check if y is not NaN
  if (((y & NAN_MASK64) != NAN_MASK64))
    y ^= 0x8000000000000000ull;
  bid64_add (pres, px,
	     &y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	     _EXC_INFO_ARG);
}
#else

UINT64
bid64_sub (UINT64 x,
	   UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
	   _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  // check if y is not NaN
  if (((y & NAN_MASK64) != NAN_MASK64))
    y ^= 0x8000000000000000ull;

  return bid64_add (x,
		    y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		    _EXC_INFO_ARG);
}
#endif



#if DECIMAL_CALL_BY_REFERENCE

void
bid64_add (UINT64 * pres, UINT64 * px,
	   UINT64 *
	   py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	   _EXC_INFO_PARAM) {
  UINT64 x, y;
#else

UINT64
bid64_add (UINT64 x,
	   UINT64 y _RND_MODE_PARAM _EXC_FLAGS_PARAM
	   _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif

  UINT128 CA, CT, CT_new;
  UINT64 sign_x, sign_y, coefficient_x, coefficient_y, C64_new;
  UINT64 valid_x, valid_y;
  UINT64 res;
  UINT64 sign_a, sign_b, coefficient_a, coefficient_b, sign_s, sign_ab,
    rem_a;
  UINT64 saved_ca, saved_cb, C0_64, C64, remainder_h, T1, carry, tmp;
  int_double tempx;
  int exponent_x, exponent_y, exponent_a, exponent_b, diff_dec_expon;
  int bin_expon_ca, extra_digits, amount, scale_k, scale_ca;
  unsigned rmode, status;

#if DECIMAL_CALL_BY_REFERENCE
#if !DECIMAL_GLOBAL_ROUNDING
  _IDEC_round rnd_mode = *prnd_mode;
#endif
  x = *px;
  y = *py;
#endif

  valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
  valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);

  // unpack arguments, check for NaN or Infinity
  if (!valid_x) {
    // x is Inf. or NaN

    // test if x is NaN
    if ((x & NAN_MASK64) == NAN_MASK64) {
#ifdef SET_STATUS_FLAGS
      if (((x & SNAN_MASK64) == SNAN_MASK64)	// sNaN
	  || ((y & SNAN_MASK64) == SNAN_MASK64))
	__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
      res = coefficient_x & QUIET_MASK64;
      BID_RETURN (res);
    }
    // x is Infinity?
    if ((x & INFINITY_MASK64) == INFINITY_MASK64) {
      // check if y is Inf
      if (((y & NAN_MASK64) == INFINITY_MASK64)) {
	if (sign_x == (y & 0x8000000000000000ull)) {
	  res = coefficient_x;
	  BID_RETURN (res);
	}
	// return NaN
	{
#ifdef SET_STATUS_FLAGS
	  __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
	  res = NAN_MASK64;
	  BID_RETURN (res);
	}
      }
      // check if y is NaN
      if (((y & NAN_MASK64) == NAN_MASK64)) {
	res = coefficient_y & QUIET_MASK64;
#ifdef SET_STATUS_FLAGS
	if (((y & SNAN_MASK64) == SNAN_MASK64))
	  __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
	BID_RETURN (res);
      }
      // otherwise return +/-Inf
      {
	res = coefficient_x;
	BID_RETURN (res);
      }
    }
    // x is 0
    {
      if (((y & INFINITY_MASK64) != INFINITY_MASK64) && coefficient_y) {
	if (exponent_y <= exponent_x) {
	  res = y;
	  BID_RETURN (res);
	}
      }
    }

  }
  if (!valid_y) {
    // y is Inf. or NaN?
    if (((y & INFINITY_MASK64) == INFINITY_MASK64)) {
#ifdef SET_STATUS_FLAGS
      if ((y & SNAN_MASK64) == SNAN_MASK64)	// sNaN
	__set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
      res = coefficient_y & QUIET_MASK64;
      BID_RETURN (res);
    }
    // y is 0
    if (!coefficient_x) {	// x==0
      if (exponent_x <= exponent_y)
	res = ((UINT64) exponent_x) << 53;
      else
	res = ((UINT64) exponent_y) << 53;
      if (sign_x == sign_y)
	res |= sign_x;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (rnd_mode == ROUNDING_DOWN && sign_x != sign_y)
	res |= 0x8000000000000000ull;
#endif
#endif
      BID_RETURN (res);
    } else if (exponent_y >= exponent_x) {
      res = x;
      BID_RETURN (res);
    }
  }
  // sort arguments by exponent
  if (exponent_x < exponent_y) {
    sign_a = sign_y;
    exponent_a = exponent_y;
    coefficient_a = coefficient_y;
    sign_b = sign_x;
    exponent_b = exponent_x;
    coefficient_b = coefficient_x;
  } else {
    sign_a = sign_x;
    exponent_a = exponent_x;
    coefficient_a = coefficient_x;
    sign_b = sign_y;
    exponent_b = exponent_y;
    coefficient_b = coefficient_y;
  }

  // exponent difference
  diff_dec_expon = exponent_a - exponent_b;

  /* get binary coefficients of x and y */

  //--- get number of bits in the coefficients of x and y ---

  // version 2 (original)
  tempx.d = (double) coefficient_a;
  bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;

  if (diff_dec_expon > MAX_FORMAT_DIGITS) {
    // normalize a to a 16-digit coefficient

    scale_ca = estimate_decimal_digits[bin_expon_ca];
    if (coefficient_a >= power10_table_128[scale_ca].w[0])
      scale_ca++;

    scale_k = 16 - scale_ca;

    coefficient_a *= power10_table_128[scale_k].w[0];

    diff_dec_expon -= scale_k;
    exponent_a -= scale_k;

    /* get binary coefficients of x and y */

    //--- get number of bits in the coefficients of x and y ---
    tempx.d = (double) coefficient_a;
    bin_expon_ca = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;

    if (diff_dec_expon > MAX_FORMAT_DIGITS) {
#ifdef SET_STATUS_FLAGS
      if (coefficient_b) {
	__set_status_flags (pfpsf, INEXACT_EXCEPTION);
      }
#endif

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (((rnd_mode) & 3) && coefficient_b)	// not ROUNDING_TO_NEAREST
      {
	switch (rnd_mode) {
	case ROUNDING_DOWN:
	  if (sign_b) {
	    coefficient_a -= ((((SINT64) sign_a) >> 63) | 1);
	    if (coefficient_a < 1000000000000000ull) {
	      exponent_a--;
	      coefficient_a = 9999999999999999ull;
	    } else if (coefficient_a >= 10000000000000000ull) {
	      exponent_a++;
	      coefficient_a = 1000000000000000ull;
	    }
	  }
	  break;
	case ROUNDING_UP:
	  if (!sign_b) {
	    coefficient_a += ((((SINT64) sign_a) >> 63) | 1);
	    if (coefficient_a < 1000000000000000ull) {
	      exponent_a--;
	      coefficient_a = 9999999999999999ull;
	    } else if (coefficient_a >= 10000000000000000ull) {
	      exponent_a++;
	      coefficient_a = 1000000000000000ull;
	    }
	  }
	  break;
	default:	// RZ
	  if (sign_a != sign_b) {
	    coefficient_a--;
	    if (coefficient_a < 1000000000000000ull) {
	      exponent_a--;
	      coefficient_a = 9999999999999999ull;
	    }
	  }
	  break;
	}
      } else
#endif
#endif
	// check special case here
	if ((coefficient_a == 1000000000000000ull)
	    && (diff_dec_expon == MAX_FORMAT_DIGITS + 1)
	    && (sign_a ^ sign_b)
	    && (coefficient_b > 5000000000000000ull)) {
	coefficient_a = 9999999999999999ull;
	exponent_a--;
      }

      res =
	fast_get_BID64_check_OF (sign_a, exponent_a, coefficient_a,
				 rnd_mode, pfpsf);
      BID_RETURN (res);
    }
  }
  // test whether coefficient_a*10^(exponent_a-exponent_b)  may exceed 2^62
  if (bin_expon_ca + estimate_bin_expon[diff_dec_expon] < 60) {
    // coefficient_a*10^(exponent_a-exponent_b)<2^63

    // multiply by 10^(exponent_a-exponent_b)
    coefficient_a *= power10_table_128[diff_dec_expon].w[0];

    // sign mask
    sign_b = ((SINT64) sign_b) >> 63;
    // apply sign to coeff. of b
    coefficient_b = (coefficient_b + sign_b) ^ sign_b;

    // apply sign to coefficient a
    sign_a = ((SINT64) sign_a) >> 63;
    coefficient_a = (coefficient_a + sign_a) ^ sign_a;

    coefficient_a += coefficient_b;
    // get sign
    sign_s = ((SINT64) coefficient_a) >> 63;
    coefficient_a = (coefficient_a + sign_s) ^ sign_s;
    sign_s &= 0x8000000000000000ull;

    // coefficient_a < 10^16 ?
    if (coefficient_a < power10_table_128[MAX_FORMAT_DIGITS].w[0]) {
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
      if (rnd_mode == ROUNDING_DOWN && (!coefficient_a)
	  && sign_a != sign_b)
	sign_s = 0x8000000000000000ull;
#endif
#endif
      res = very_fast_get_BID64 (sign_s, exponent_b, coefficient_a);
      BID_RETURN (res);
    }
    // otherwise rounding is necessary

    // already know coefficient_a<10^19
    // coefficient_a < 10^17 ?
    if (coefficient_a < power10_table_128[17].w[0])
      extra_digits = 1;
    else if (coefficient_a < power10_table_128[18].w[0])
      extra_digits = 2;
    else
      extra_digits = 3;

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
    rmode = rnd_mode;
    if (sign_s && (unsigned) (rmode - 1) < 2)
      rmode = 3 - rmode;
#else
    rmode = 0;
#endif
#else
    rmode = 0;
#endif
    coefficient_a += round_const_table[rmode][extra_digits];

    // get P*(2^M[extra_digits])/10^extra_digits
    __mul_64x64_to_128 (CT, coefficient_a,
			reciprocals10_64[extra_digits]);

    // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
    amount = short_recip_scale[extra_digits];
    C64 = CT.w[1] >> amount;

  } else {
    // coefficient_a*10^(exponent_a-exponent_b) is large
    sign_s = sign_a;

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
    rmode = rnd_mode;
    if (sign_s && (unsigned) (rmode - 1) < 2)
      rmode = 3 - rmode;
#else
    rmode = 0;
#endif
#else
    rmode = 0;
#endif

    // check whether we can take faster path
    scale_ca = estimate_decimal_digits[bin_expon_ca];

    sign_ab = sign_a ^ sign_b;
    sign_ab = ((SINT64) sign_ab) >> 63;

    // T1 = 10^(16-diff_dec_expon)
    T1 = power10_table_128[16 - diff_dec_expon].w[0];

    // get number of digits in coefficient_a
    if (coefficient_a >= power10_table_128[scale_ca].w[0]) {
      scale_ca++;
    }

    scale_k = 16 - scale_ca;

    // addition
    saved_ca = coefficient_a - T1;
    coefficient_a =
      (SINT64) saved_ca *(SINT64) power10_table_128[scale_k].w[0];
    extra_digits = diff_dec_expon - scale_k;

    // apply sign
    saved_cb = (coefficient_b + sign_ab) ^ sign_ab;
    // add 10^16 and rounding constant
    coefficient_b =
      saved_cb + 10000000000000000ull +
      round_const_table[rmode][extra_digits];

    // get P*(2^M[extra_digits])/10^extra_digits
    __mul_64x64_to_128 (CT, coefficient_b,
			reciprocals10_64[extra_digits]);

    // now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
    amount = short_recip_scale[extra_digits];
    C0_64 = CT.w[1] >> amount;

    // result coefficient 
    C64 = C0_64 + coefficient_a;
    // filter out difficult (corner) cases
    // this test ensures the number of digits in coefficient_a does not change 
    // after adding (the appropriately scaled and rounded) coefficient_b
    if ((UINT64) (C64 - 1000000000000000ull - 1) >
	9000000000000000ull - 2) {
      if (C64 >= 10000000000000000ull) {
	// result has more than 16 digits
	if (!scale_k) {
	  // must divide coeff_a by 10
	  saved_ca = saved_ca + T1;
	  __mul_64x64_to_128 (CA, saved_ca, 0x3333333333333334ull);
	  //reciprocals10_64[1]);
	  coefficient_a = CA.w[1] >> 1;
	  rem_a =
	    saved_ca - (coefficient_a << 3) - (coefficient_a << 1);
	  coefficient_a = coefficient_a - T1;

	  saved_cb += rem_a * power10_table_128[diff_dec_expon].w[0];
	} else
	  coefficient_a =
	    (SINT64) (saved_ca - T1 -
		      (T1 << 3)) * (SINT64) power10_table_128[scale_k -
							      1].w[0];

	extra_digits++;
	coefficient_b =
	  saved_cb + 100000000000000000ull +
	  round_const_table[rmode][extra_digits];

	// get P*(2^M[extra_digits])/10^extra_digits
	__mul_64x64_to_128 (CT, coefficient_b,
			    reciprocals10_64[extra_digits]);

	// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
	amount = short_recip_scale[extra_digits];
	C0_64 = CT.w[1] >> amount;

	// result coefficient 
	C64 = C0_64 + coefficient_a;
      } else if (C64 <= 1000000000000000ull) {
	// less than 16 digits in result
	coefficient_a =
	  (SINT64) saved_ca *(SINT64) power10_table_128[scale_k +
							1].w[0];
	//extra_digits --;
	exponent_b--;
	coefficient_b =
	  (saved_cb << 3) + (saved_cb << 1) + 100000000000000000ull +
	  round_const_table[rmode][extra_digits];

	// get P*(2^M[extra_digits])/10^extra_digits
	__mul_64x64_to_128 (CT_new, coefficient_b,
			    reciprocals10_64[extra_digits]);

	// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128
	amount = short_recip_scale[extra_digits];
	C0_64 = CT_new.w[1] >> amount;

	// result coefficient 
	C64_new = C0_64 + coefficient_a;
	if (C64_new < 10000000000000000ull) {
	  C64 = C64_new;
#ifdef SET_STATUS_FLAGS
	  CT = CT_new;
#endif
	} else
	  exponent_b++;
      }

    }

  }

#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
  if (rmode == 0)	//ROUNDING_TO_NEAREST
#endif
    if (C64 & 1) {
      // check whether fractional part of initial_P/10^extra_digits is 
      // exactly .5
      // this is the same as fractional part of 
      //      (initial_P + 0.5*10^extra_digits)/10^extra_digits is exactly zero

      // get remainder
      remainder_h = CT.w[1] << (64 - amount);

      // test whether fractional part is 0
      if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits])) {
	C64--;
      }
    }
#endif

#ifdef SET_STATUS_FLAGS
  status = INEXACT_EXCEPTION;

  // get remainder
  remainder_h = CT.w[1] << (64 - amount);

  switch (rmode) {
  case ROUNDING_TO_NEAREST:
  case ROUNDING_TIES_AWAY:
    // test whether fractional part is 0
    if ((remainder_h == 0x8000000000000000ull)
	&& (CT.w[0] < reciprocals10_64[extra_digits]))
      status = EXACT_STATUS;
    break;
  case ROUNDING_DOWN:
  case ROUNDING_TO_ZERO:
    if (!remainder_h && (CT.w[0] < reciprocals10_64[extra_digits]))
      status = EXACT_STATUS;
    //if(!C64 && rmode==ROUNDING_DOWN) sign_s=sign_y;
    break;
  default:
    // round up
    __add_carry_out (tmp, carry, CT.w[0],
		     reciprocals10_64[extra_digits]);
    if ((remainder_h >> (64 - amount)) + carry >=
	(((UINT64) 1) << amount))
      status = EXACT_STATUS;
    break;
  }
  __set_status_flags (pfpsf, status);

#endif

  res =
    fast_get_BID64_check_OF (sign_s, exponent_b + extra_digits, C64,
			     rnd_mode, pfpsf);
  BID_RETURN (res);
}