libgcc/config/libbid/bid64_next.c

/* Copyright (C) 2007-2017 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/>.  */

#include "bid_internal.h"

/*****************************************************************************
 *  BID64 nextup
 ****************************************************************************/

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_nextup (UINT64 * pres,
	      UINT64 *
	      px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT64 x = *px;
#else
UINT64
bid64_nextup (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
#endif

  UINT64 res;
  UINT64 x_sign;
  UINT64 x_exp;
  BID_UI64DOUBLE tmp1;
  int x_nr_bits;
  int q1, ind;
  UINT64 C1;			// C1 represents x_signif (UINT64)

  // check for NaNs and infinities
  if ((x & MASK_NAN) == MASK_NAN) {	// check for NaN
    if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
      x = x & 0xfe00000000000000ull;	// clear G6-G12 and the payload bits
    else
      x = x & 0xfe03ffffffffffffull;	// clear G6-G12
    if ((x & MASK_SNAN) == MASK_SNAN) {	// SNaN
      // set invalid flag
      *pfpsf |= INVALID_EXCEPTION;
      // return quiet (SNaN)
      res = x & 0xfdffffffffffffffull;
    } else {	// QNaN
      res = x;
    }
    BID_RETURN (res);
  } else if ((x & MASK_INF) == MASK_INF) {	// check for Infinity
    if (!(x & 0x8000000000000000ull)) {	// x is +inf
      res = 0x7800000000000000ull;
    } else {	// x is -inf
      res = 0xf7fb86f26fc0ffffull;	// -MAXFP = -999...99 * 10^emax
    }
    BID_RETURN (res);
  }
  // unpack the argument
  x_sign = x & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    x_exp = (x & MASK_BINARY_EXPONENT2) >> 51;	// biased
    C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (C1 > 9999999999999999ull) {	// non-canonical
      x_exp = 0;
      C1 = 0;
    }
  } else {
    x_exp = (x & MASK_BINARY_EXPONENT1) >> 53;	// biased
    C1 = x & MASK_BINARY_SIG1;
  }

  // check for zeros (possibly from non-canonical values)
  if (C1 == 0x0ull) {
    // x is 0
    res = 0x0000000000000001ull;	// MINFP = 1 * 10^emin
  } else {	// x is not special and is not zero
    if (x == 0x77fb86f26fc0ffffull) {
      // x = +MAXFP = 999...99 * 10^emax
      res = 0x7800000000000000ull;	// +inf
    } else if (x == 0x8000000000000001ull) {
      // x = -MINFP = 1...99 * 10^emin
      res = 0x8000000000000000ull;	// -0
    } else {	// -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
      // can add/subtract 1 ulp to the significand

      // Note: we could check here if x >= 10^16 to speed up the case q1 =16 
      // q1 = nr. of decimal digits in x (1 <= q1 <= 54)
      //  determine first the nr. of bits in x
      if (C1 >= MASK_BINARY_OR2) {	// x >= 2^53
	// split the 64-bit value in two 32-bit halves to avoid rounding errors
	if (C1 >= 0x0000000100000000ull) {	// x >= 2^32
	  tmp1.d = (double) (C1 >> 32);	// exact conversion
	  x_nr_bits =
	    33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	} else {	// x < 2^32
	  tmp1.d = (double) C1;	// exact conversion
	  x_nr_bits =
	    1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	}
      } else {	// if x < 2^53
	tmp1.d = (double) C1;	// exact conversion
	x_nr_bits =
	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
      q1 = nr_digits[x_nr_bits - 1].digits;
      if (q1 == 0) {
	q1 = nr_digits[x_nr_bits - 1].digits1;
	if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
	  q1++;
      }
      // if q1 < P16 then pad the significand with zeros
      if (q1 < P16) {
	if (x_exp > (UINT64) (P16 - q1)) {
	  ind = P16 - q1;	// 1 <= ind <= P16 - 1
	  // pad with P16 - q1 zeros, until exponent = emin
	  // C1 = C1 * 10^ind
	  C1 = C1 * ten2k64[ind];
	  x_exp = x_exp - ind;
	} else {	// pad with zeros until the exponent reaches emin
	  ind = x_exp;
	  C1 = C1 * ten2k64[ind];
	  x_exp = EXP_MIN;
	}
      }
      if (!x_sign) {	// x > 0
	// add 1 ulp (add 1 to the significand)
	C1++;
	if (C1 == 0x002386f26fc10000ull) {	// if  C1 = 10^16
	  C1 = 0x00038d7ea4c68000ull;	// C1 = 10^15
	  x_exp++;
	}
	// Ok, because MAXFP = 999...99 * 10^emax was caught already
      } else {	// x < 0
	// subtract 1 ulp (subtract 1 from the significand)
	C1--;
	if (C1 == 0x00038d7ea4c67fffull && x_exp != 0) {	// if  C1 = 10^15 - 1
	  C1 = 0x002386f26fc0ffffull;	// C1 = 10^16 - 1
	  x_exp--;
	}
      }
      // assemble the result
      // if significand has 54 bits
      if (C1 & MASK_BINARY_OR2) {
	res =
	  x_sign | (x_exp << 51) | MASK_STEERING_BITS | (C1 &
							 MASK_BINARY_SIG2);
      } else {	// significand fits in 53 bits
	res = x_sign | (x_exp << 53) | C1;
      }
    }	// end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
  }	// end x is not special and is not zero
  BID_RETURN (res);
}

/*****************************************************************************
 *  BID64 nextdown
 ****************************************************************************/

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_nextdown (UINT64 * pres,
		UINT64 *
		px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT64 x = *px;
#else
UINT64
bid64_nextdown (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		_EXC_INFO_PARAM) {
#endif

  UINT64 res;
  UINT64 x_sign;
  UINT64 x_exp;
  BID_UI64DOUBLE tmp1;
  int x_nr_bits;
  int q1, ind;
  UINT64 C1;			// C1 represents x_signif (UINT64)

  // check for NaNs and infinities
  if ((x & MASK_NAN) == MASK_NAN) {	// check for NaN 
    if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
      x = x & 0xfe00000000000000ull;	// clear G6-G12 and the payload bits 
    else
      x = x & 0xfe03ffffffffffffull;	// clear G6-G12 
    if ((x & MASK_SNAN) == MASK_SNAN) {	// SNaN 
      // set invalid flag
      *pfpsf |= INVALID_EXCEPTION;
      // return quiet (SNaN)
      res = x & 0xfdffffffffffffffull;
    } else {	// QNaN 
      res = x;
    }
    BID_RETURN (res);
  } else if ((x & MASK_INF) == MASK_INF) {	// check for Infinity
    if (x & 0x8000000000000000ull) {	// x is -inf
      res = 0xf800000000000000ull;
    } else {	// x is +inf
      res = 0x77fb86f26fc0ffffull;	// +MAXFP = +999...99 * 10^emax
    }
    BID_RETURN (res);
  }
  // unpack the argument
  x_sign = x & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    x_exp = (x & MASK_BINARY_EXPONENT2) >> 51;	// biased
    C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (C1 > 9999999999999999ull) {	// non-canonical
      x_exp = 0;
      C1 = 0;
    }
  } else {
    x_exp = (x & MASK_BINARY_EXPONENT1) >> 53;	// biased
    C1 = x & MASK_BINARY_SIG1;
  }

  // check for zeros (possibly from non-canonical values)
  if (C1 == 0x0ull) {
    // x is 0
    res = 0x8000000000000001ull;	// -MINFP = -1 * 10^emin
  } else {	// x is not special and is not zero
    if (x == 0xf7fb86f26fc0ffffull) {
      // x = -MAXFP = -999...99 * 10^emax
      res = 0xf800000000000000ull;	// -inf
    } else if (x == 0x0000000000000001ull) {
      // x = +MINFP = 1...99 * 10^emin
      res = 0x0000000000000000ull;	// -0
    } else {	// -MAXFP + 1ulp <= x <= -MINFP OR MINFP + 1 ulp <= x <= MAXFP
      // can add/subtract 1 ulp to the significand

      // Note: we could check here if x >= 10^16 to speed up the case q1 =16 
      // q1 = nr. of decimal digits in x (1 <= q1 <= 16)
      //  determine first the nr. of bits in x
      if (C1 >= 0x0020000000000000ull) {	// x >= 2^53
	// split the 64-bit value in two 32-bit halves to avoid 
	// rounding errors
	if (C1 >= 0x0000000100000000ull) {	// x >= 2^32
	  tmp1.d = (double) (C1 >> 32);	// exact conversion
	  x_nr_bits =
	    33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	} else {	// x < 2^32
	  tmp1.d = (double) C1;	// exact conversion
	  x_nr_bits =
	    1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	}
      } else {	// if x < 2^53
	tmp1.d = (double) C1;	// exact conversion
	x_nr_bits =
	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
      q1 = nr_digits[x_nr_bits - 1].digits;
      if (q1 == 0) {
	q1 = nr_digits[x_nr_bits - 1].digits1;
	if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
	  q1++;
      }
      // if q1 < P16 then pad the significand with zeros
      if (q1 < P16) {
	if (x_exp > (UINT64) (P16 - q1)) {
	  ind = P16 - q1;	// 1 <= ind <= P16 - 1
	  // pad with P16 - q1 zeros, until exponent = emin
	  // C1 = C1 * 10^ind
	  C1 = C1 * ten2k64[ind];
	  x_exp = x_exp - ind;
	} else {	// pad with zeros until the exponent reaches emin
	  ind = x_exp;
	  C1 = C1 * ten2k64[ind];
	  x_exp = EXP_MIN;
	}
      }
      if (x_sign) {	// x < 0
	// add 1 ulp (add 1 to the significand)
	C1++;
	if (C1 == 0x002386f26fc10000ull) {	// if  C1 = 10^16
	  C1 = 0x00038d7ea4c68000ull;	// C1 = 10^15
	  x_exp++;
	  // Ok, because -MAXFP = -999...99 * 10^emax was caught already
	}
      } else {	// x > 0
	// subtract 1 ulp (subtract 1 from the significand)
	C1--;
	if (C1 == 0x00038d7ea4c67fffull && x_exp != 0) {	// if  C1 = 10^15 - 1
	  C1 = 0x002386f26fc0ffffull;	// C1 = 10^16 - 1
	  x_exp--;
	}
      }
      // assemble the result
      // if significand has 54 bits
      if (C1 & MASK_BINARY_OR2) {
	res =
	  x_sign | (x_exp << 51) | MASK_STEERING_BITS | (C1 &
							 MASK_BINARY_SIG2);
      } else {	// significand fits in 53 bits
	res = x_sign | (x_exp << 53) | C1;
      }
    }	// end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
  }	// end x is not special and is not zero
  BID_RETURN (res);
}

/*****************************************************************************
 *  BID64 nextafter
 ****************************************************************************/

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_nextafter (UINT64 * pres, UINT64 * px,
		 UINT64 *
		 py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
UINT64
bid64_nextafter (UINT64 x,
		 UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		 _EXC_INFO_PARAM) {
#endif

  UINT64 res;
  UINT64 tmp1, tmp2;
  FPSC tmp_fpsf = 0;		// dummy fpsf for calls to comparison functions
  int res1, res2;

  // check for NaNs or infinities
  if (((x & MASK_SPECIAL) == MASK_SPECIAL) ||
      ((y & MASK_SPECIAL) == MASK_SPECIAL)) {
    // x is NaN or infinity or y is NaN or infinity

    if ((x & MASK_NAN) == MASK_NAN) {	// x is NAN
      if ((x & 0x0003ffffffffffffull) > 999999999999999ull)
	x = x & 0xfe00000000000000ull;	// clear G6-G12 and the payload bits
      else
	x = x & 0xfe03ffffffffffffull;	// clear G6-G12
      if ((x & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
	// set invalid flag
	*pfpsf |= INVALID_EXCEPTION;
	// return quiet (x)
	res = x & 0xfdffffffffffffffull;
      } else {	// x is QNaN
	if ((y & MASK_SNAN) == MASK_SNAN) {	// y is SNAN
	  // set invalid flag
	  *pfpsf |= INVALID_EXCEPTION;
	}
	// return x
	res = x;
      }
      BID_RETURN (res);
    } else if ((y & MASK_NAN) == MASK_NAN) {	// y is NAN
      if ((y & 0x0003ffffffffffffull) > 999999999999999ull)
	y = y & 0xfe00000000000000ull;	// clear G6-G12 and the payload bits
      else
	y = y & 0xfe03ffffffffffffull;	// clear G6-G12
      if ((y & MASK_SNAN) == MASK_SNAN) {	// y is SNAN
	// set invalid flag
	*pfpsf |= INVALID_EXCEPTION;
	// return quiet (y)
	res = y & 0xfdffffffffffffffull;
      } else {	// y is QNaN
	// return y
	res = y;
      }
      BID_RETURN (res);
    } else {	// at least one is infinity
      if ((x & MASK_ANY_INF) == MASK_INF) {	// x = inf
	x = x & (MASK_SIGN | MASK_INF);
      }
      if ((y & MASK_ANY_INF) == MASK_INF) {	// y = inf
	y = y & (MASK_SIGN | MASK_INF);
      }
    }
  }
  // neither x nor y is NaN

  // if not infinity, check for non-canonical values x (treated as zero)
  if ((x & MASK_ANY_INF) != MASK_INF) {	// x != inf
    // unpack x
    if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
      // if the steering bits are 11 (condition will be 0), then
      // the exponent is G[0:w+1]
      if (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >
	  9999999999999999ull) {
	// non-canonical
	x = (x & MASK_SIGN) | ((x & MASK_BINARY_EXPONENT2) << 2);
      }
    } else {	// if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) x is unch.
      ;	// canonical
    }
  }
  // no need to check for non-canonical y

  // neither x nor y is NaN
  tmp_fpsf = *pfpsf;	// save fpsf
#if DECIMAL_CALL_BY_REFERENCE
  bid64_quiet_equal (&res1, px,
		     py _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_quiet_greater (&res2, px,
		       py _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
#else
  res1 =
    bid64_quiet_equal (x,
		       y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res2 =
    bid64_quiet_greater (x,
			 y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
#endif
  *pfpsf = tmp_fpsf;	// restore fpsf
  if (res1) {	// x = y
    // return x with the sign of y
    res = (y & 0x8000000000000000ull) | (x & 0x7fffffffffffffffull);
  } else if (res2) {	// x > y
#if DECIMAL_CALL_BY_REFERENCE
    bid64_nextdown (&res,
		    px _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
#else
    res =
      bid64_nextdown (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
#endif
  } else {	// x < y
#if DECIMAL_CALL_BY_REFERENCE
    bid64_nextup (&res, px _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
#else
    res = bid64_nextup (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
#endif
  }
  // if the operand x is finite but the result is infinite, signal
  // overflow and inexact
  if (((x & MASK_INF) != MASK_INF) && ((res & MASK_INF) == MASK_INF)) {
    // set the inexact flag
    *pfpsf |= INEXACT_EXCEPTION;
    // set the overflow flag
    *pfpsf |= OVERFLOW_EXCEPTION;
  }
  // if the result is in (-10^emin, 10^emin), and is different from the
  // operand x, signal underflow and inexact 
  tmp1 = 0x00038d7ea4c68000ull;	// +100...0[16] * 10^emin
  tmp2 = res & 0x7fffffffffffffffull;
  tmp_fpsf = *pfpsf;	// save fpsf
#if DECIMAL_CALL_BY_REFERENCE
  bid64_quiet_greater (&res1, &tmp1,
		       &tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
		       _EXC_INFO_ARG);
  bid64_quiet_not_equal (&res2, &x,
			 &res _EXC_FLAGS_ARG _EXC_MASKS_ARG
			 _EXC_INFO_ARG);
#else
  res1 =
    bid64_quiet_greater (tmp1,
			 tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
			 _EXC_INFO_ARG);
  res2 =
    bid64_quiet_not_equal (x,
			   res _EXC_FLAGS_ARG _EXC_MASKS_ARG
			   _EXC_INFO_ARG);
#endif
  *pfpsf = tmp_fpsf;	// restore fpsf
  if (res1 && res2) {
    // if (bid64_quiet_greater (tmp1, tmp2, &tmp_fpsf) &&
    // bid64_quiet_not_equal (x, res, &tmp_fpsf)) {
    // set the inexact flag
    *pfpsf |= INEXACT_EXCEPTION;
    // set the underflow flag
    *pfpsf |= UNDERFLOW_EXCEPTION;
  }
  BID_RETURN (res);
}