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/* Copyright (C) 2007, 2009  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 3, or (at your option) any later

version.

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.

Under Section 7 of GPL version 3, you are granted additional

permissions described in the GCC Runtime Library Exception, version

3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and

a copy of the GCC Runtime Library Exception along with this program;

see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see

<http://www.gnu.org/licenses/>.  */

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

 *    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);

}