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/*****************************************************************************
 *    BID64 remainder
 *****************************************************************************
 *
 *  Algorithm description:
 *
 *  if(exponent_x < exponent_y)
 *    scale coefficient_y so exponents are aligned
 *    perform coefficient divide (64-bit integer divide), unless
 *            coefficient_y is longer than 64 bits (clearly larger 
 *                                               than coefficient_x) 
 *  else  // exponent_x > exponent_y
 *     use a loop to scale coefficient_x to 18_digits, divide by 
 *         coefficient_y (64-bit integer divide), calculate remainder
 *         as new_coefficient_x and repeat until final remainder is obtained 
 *         (when new_exponent_x < exponent_y)
 *
 ****************************************************************************/

#define BID_FUNCTION_SETS_BINARY_FLAGS

#include "bid_internal.h"

#define MAX_FORMAT_DIGITS     16
#define DECIMAL_EXPONENT_BIAS 398
#define MASK_BINARY_EXPONENT  0x7ff0000000000000ull
#define BINARY_EXPONENT_BIAS  0x3ff
#define UPPER_EXPON_LIMIT     51


BID_TYPE0_FUNCTION_ARGTYPE1_ARGTYPE2_NORND(BID_UINT64, bid64_rem, BID_UINT64, x, BID_UINT64, y)

  BID_UINT128 CY;
  BID_UINT64 sign_x, sign_y, coefficient_x, coefficient_y, res;
  BID_UINT64 Q, R, R2, T, valid_y, valid_x;
  int_float tempx;
  int exponent_x, exponent_y, bin_expon, e_scale;
  int digits_x, diff_expon;

  BID_OPT_SAVE_BINARY_FLAGS()

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

  // unpack arguments, check for NaN or Infinity
  if (!valid_x) {
    // x is Inf. or NaN or 0
#ifdef BID_SET_STATUS_FLAGS
    if ((y & SNAN_MASK64) == SNAN_MASK64)	// y is sNaN
      __set_status_flags (pfpsf, BID_INVALID_EXCEPTION);
#endif

    // test if x is NaN
    if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef BID_SET_STATUS_FLAGS
      if (((x & SNAN_MASK64) == SNAN_MASK64))
	__set_status_flags (pfpsf, BID_INVALID_EXCEPTION);
#endif
      res = coefficient_x & QUIET_MASK64;;
      BID_RETURN (res);
    }
    // x is Infinity?
    if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
      if (((y & NAN_MASK64) != NAN_MASK64)) {
#ifdef BID_SET_STATUS_FLAGS
	__set_status_flags (pfpsf, BID_INVALID_EXCEPTION);
#endif
	// return NaN
	res = 0x7c00000000000000ull;
	BID_RETURN (res);
      }
    }
    // x is 0
    // return x if y != 0
    if (((y & 0x7800000000000000ull) < 0x7800000000000000ull) &&
	coefficient_y) {
      if ((y & 0x6000000000000000ull) == 0x6000000000000000ull)
	exponent_y = (y >> 51) & 0x3ff;
      else
	exponent_y = (y >> 53) & 0x3ff;

      if (exponent_y < exponent_x)
	exponent_x = exponent_y;

      x = exponent_x;
      x <<= 53;

      res = x | sign_x;
      BID_RETURN (res);
    }

  }
  if (!valid_y) {
    // y is Inf. or NaN

    // test if y is NaN
    if ((y & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
#ifdef BID_SET_STATUS_FLAGS
      if (((y & SNAN_MASK64) == SNAN_MASK64))
	__set_status_flags (pfpsf, BID_INVALID_EXCEPTION);
#endif
      res = coefficient_y & QUIET_MASK64;;
      BID_RETURN (res);
    }
    // y is Infinity?
    if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) {
      res = very_fast_get_BID64 (sign_x, exponent_x, coefficient_x);
      BID_RETURN (res);
    }
    // y is 0, return NaN
    {
#ifdef BID_SET_STATUS_FLAGS
      __set_status_flags (pfpsf, BID_INVALID_EXCEPTION);
#endif
      res = 0x7c00000000000000ull;
      BID_RETURN (res);
    }
  }


  diff_expon = exponent_x - exponent_y;
  if (diff_expon <= 0) {
    diff_expon = -diff_expon;

    if (diff_expon > 16) {
      // |x|<|y| in this case
      res = x;
      BID_RETURN (res);
    }
    // set exponent of y to exponent_x, scale coefficient_y
    T = bid_power10_table_128[diff_expon].w[0];
    __mul_64x64_to_128 (CY, coefficient_y, T);

    if (CY.w[1] || CY.w[0] > (coefficient_x << 1)) {
      res = x;
      BID_RETURN (res);
    }

    Q = coefficient_x / CY.w[0];
    R = coefficient_x - Q * CY.w[0];

    R2 = R + R;
    if (R2 > CY.w[0] || (R2 == CY.w[0] && (Q & 1))) {
      R = CY.w[0] - R;
      sign_x ^= 0x8000000000000000ull;
    }

    res = very_fast_get_BID64 (sign_x, exponent_x, R);
    BID_RETURN (res);
  }


  while (diff_expon > 0) {
    // get number of digits in coeff_x
    tempx.d = (float) coefficient_x;
    bin_expon = ((tempx.i >> 23) & 0xff) - 0x7f;
    digits_x = bid_estimate_decimal_digits[bin_expon];
    // will not use this test, dividend will have 18 or 19 digits
    //if(coefficient_x >= bid_power10_table_128[digits_x].w[0])
    //      digits_x++;

    e_scale = 18 - digits_x;
    if (diff_expon >= e_scale) {
      diff_expon -= e_scale;
    } else {
      e_scale = diff_expon;
      diff_expon = 0;
    }

    // scale dividend to 18 or 19 digits
    coefficient_x *= bid_power10_table_128[e_scale].w[0];

    // quotient
    Q = coefficient_x / coefficient_y;
    // remainder
    coefficient_x -= Q * coefficient_y;

    // check for remainder == 0
    if (!coefficient_x) {
      res = very_fast_get_BID64_small_mantissa (sign_x, exponent_y, 0);
      BID_RETURN (res);
    }
  }

  R2 = coefficient_x + coefficient_x;
  if (R2 > coefficient_y || (R2 == coefficient_y && (Q & 1))) {
    coefficient_x = coefficient_y - coefficient_x;
    sign_x ^= 0x8000000000000000ull;
  }

  res = very_fast_get_BID64 (sign_x, exponent_y, coefficient_x);
  BID_RETURN (res);

}
