libgcc/config/libbid/bid64_fma.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/>.  */

/*****************************************************************************
 *    BID64 fma
 *****************************************************************************
 *
 *  Algorithm description:
 *
 *  if multiplication is guranteed exact (short coefficients)
 *     call the unpacked arg. equivalent of bid64_add(x*y, z)
 *  else 
 *     get full coefficient_x*coefficient_y product
 *     call subroutine to perform addition of 64-bit argument 
 *                                         to 128-bit product
 *
 ****************************************************************************/

#include "bid_inline_add.h"

#if DECIMAL_CALL_BY_REFERENCE
extern void bid64_mul (UINT64 * pres, UINT64 * px,
		       UINT64 *
		       py _RND_MODE_PARAM _EXC_FLAGS_PARAM
		       _EXC_MASKS_PARAM _EXC_INFO_PARAM);
#else

extern UINT64 bid64_mul (UINT64 x,
			 UINT64 y _RND_MODE_PARAM
			 _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			 _EXC_INFO_PARAM);
#endif

#if DECIMAL_CALL_BY_REFERENCE

void
bid64_fma (UINT64 * pres, UINT64 * px, UINT64 * py,
	   UINT64 *
	   pz _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	   _EXC_INFO_PARAM) {
  UINT64 x, y, z;
#else

UINT64
bid64_fma (UINT64 x, UINT64 y,
	   UINT64 z _RND_MODE_PARAM _EXC_FLAGS_PARAM
	   _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  UINT128 P, PU, CT, CZ;
  UINT64 sign_x, sign_y, coefficient_x, coefficient_y, sign_z,
    coefficient_z;
  UINT64 C64, remainder_y, res;
  UINT64 CYh, CY0L, T, valid_x, valid_y, valid_z;
  int_double tempx, tempy;
  int extra_digits, exponent_x, exponent_y, bin_expon_cx, bin_expon_cy,
    bin_expon_product, rmode;
  int digits_p, bp, final_exponent, exponent_z, digits_z, ez, ey,
    scale_z, uf_status;

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

  valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x);
  valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y);
  valid_z = unpack_BID64 (&sign_z, &exponent_z, &coefficient_z, z);

  // unpack arguments, check for NaN, Infinity, or 0
  if (!valid_x || !valid_y || !valid_z) {

    if ((y & MASK_NAN) == MASK_NAN) {	// y is NAN
      // if x = {0, f, inf, NaN}, y = NaN, z = {0, f, inf, NaN} then res = Q (y)
      // check first for non-canonical NaN payload
      y = y & 0xfe03ffffffffffffull;	// clear G6-G12
      if ((y & 0x0003ffffffffffffull) > 999999999999999ull) {
	y = y & 0xfe00000000000000ull;	// clear G6-G12 and the payload bits
      }
      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;
	// if z = SNaN or x = SNaN signal invalid exception
	if ((z & MASK_SNAN) == MASK_SNAN
	    || (x & MASK_SNAN) == MASK_SNAN) {
	  // set invalid flag
	  *pfpsf |= INVALID_EXCEPTION;
	}
      }
      BID_RETURN (res)
    } else if ((z & MASK_NAN) == MASK_NAN) {	// z is NAN
      // if x = {0, f, inf, NaN}, y = {0, f, inf}, z = NaN then res = Q (z)
      // check first for non-canonical NaN payload
      z = z & 0xfe03ffffffffffffull;	// clear G6-G12
      if ((z & 0x0003ffffffffffffull) > 999999999999999ull) {
	z = z & 0xfe00000000000000ull;	// clear G6-G12 and the payload bits
      }
      if ((z & MASK_SNAN) == MASK_SNAN) {	// z is SNAN
	// set invalid flag
	*pfpsf |= INVALID_EXCEPTION;
	// return quiet (z)
	res = z & 0xfdffffffffffffffull;
      } else {	// z is QNaN
	// return z
	res = z;
	// if x = SNaN signal invalid exception
	if ((x & MASK_SNAN) == MASK_SNAN) {
	  // set invalid flag
	  *pfpsf |= INVALID_EXCEPTION;
	}
      }
      BID_RETURN (res)
    } else if ((x & MASK_NAN) == MASK_NAN) {	// x is NAN
      // if x = NaN, y = {0, f, inf}, z = {0, f, inf} then res = Q (x)
      // check first for non-canonical NaN payload
      x = x & 0xfe03ffffffffffffull;	// clear G6-G12
      if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {
	x = x & 0xfe00000000000000ull;	// clear G6-G12 and the payload bits
      }
      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
	// return x
	res = x;	// clear out G[6]-G[16]
      }
      BID_RETURN (res)
    }

    if (!valid_x) {
      // x is Inf. or 0

      // x is Infinity?
      if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
	// check if y is 0
	if (!coefficient_y) {
	  // y==0, return NaN
#ifdef SET_STATUS_FLAGS
	  if ((z & 0x7e00000000000000ull) != 0x7c00000000000000ull)
	    __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
	  BID_RETURN (0x7c00000000000000ull);
	}
	// test if z is Inf of oposite sign
	if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull)
	    && (((x ^ y) ^ z) & 0x8000000000000000ull)) {
	  // return NaN 
#ifdef SET_STATUS_FLAGS
	  __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
	  BID_RETURN (0x7c00000000000000ull);
	}
	// otherwise return +/-Inf
	BID_RETURN (((x ^ y) & 0x8000000000000000ull) |
		    0x7800000000000000ull);
      }
      // x is 0
      if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)
	  && ((z & 0x7800000000000000ull) != 0x7800000000000000ull)) {

	if (coefficient_z) {
	  exponent_y = exponent_x - DECIMAL_EXPONENT_BIAS + exponent_y;

	  sign_z = z & 0x8000000000000000ull;

	  if (exponent_y >= exponent_z)
	    BID_RETURN (z);
	  res =
	    add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z,
			&rnd_mode, pfpsf);
	  BID_RETURN (res);
	}
      }
    }
    if (!valid_y) {
      // y is Inf. or 0

      // y is Infinity?
      if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) {
	// check if x is 0
	if (!coefficient_x) {
	  // y==0, return NaN
#ifdef SET_STATUS_FLAGS
	  __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
	  BID_RETURN (0x7c00000000000000ull);
	}
	// test if z is Inf of oposite sign
	if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull)
	    && (((x ^ y) ^ z) & 0x8000000000000000ull)) {
#ifdef SET_STATUS_FLAGS
	  __set_status_flags (pfpsf, INVALID_EXCEPTION);
#endif
	  // return NaN
	  BID_RETURN (0x7c00000000000000ull);
	}
	// otherwise return +/-Inf
	BID_RETURN (((x ^ y) & 0x8000000000000000ull) |
		    0x7800000000000000ull);
      }
      // y is 0 
      if (((z & 0x7800000000000000ull) != 0x7800000000000000ull)) {

	if (coefficient_z) {
	  exponent_y += exponent_x - DECIMAL_EXPONENT_BIAS;

	  sign_z = z & 0x8000000000000000ull;

	  if (exponent_y >= exponent_z)
	    BID_RETURN (z);
	  res =
	    add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z,
			&rnd_mode, pfpsf);
	  BID_RETURN (res);
	}
      }
    }

    if (!valid_z) {
      // y is Inf. or 0

      // test if y is NaN/Inf
      if ((z & 0x7800000000000000ull) == 0x7800000000000000ull) {
	BID_RETURN (coefficient_z & QUIET_MASK64);
      }
      // z is 0, return x*y
      if ((!coefficient_x) || (!coefficient_y)) {
	//0+/-0
	exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS;
	if (exponent_x > DECIMAL_MAX_EXPON_64)
	  exponent_x = DECIMAL_MAX_EXPON_64;
	else if (exponent_x < 0)
	  exponent_x = 0;
	if (exponent_x <= exponent_z)
	  res = ((UINT64) exponent_x) << 53;
	else
	  res = ((UINT64) exponent_z) << 53;
	if ((sign_x ^ sign_y) == sign_z)
	  res |= sign_z;
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
#ifndef IEEE_ROUND_NEAREST
	else if (rnd_mode == ROUNDING_DOWN)
	  res |= 0x8000000000000000ull;
#endif
#endif
	BID_RETURN (res);
      }
    }
  }

  /* 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_x;
  bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52);

  tempy.d = (double) coefficient_y;
  bin_expon_cy = ((tempy.i & MASK_BINARY_EXPONENT) >> 52);

  // magnitude estimate for coefficient_x*coefficient_y is 
  //        2^(unbiased_bin_expon_cx + unbiased_bin_expon_cx)
  bin_expon_product = bin_expon_cx + bin_expon_cy;

  // check if coefficient_x*coefficient_y<2^(10*k+3)
  // equivalent to unbiased_bin_expon_cx + unbiased_bin_expon_cx < 10*k+1
  if (bin_expon_product < UPPER_EXPON_LIMIT + 2 * BINARY_EXPONENT_BIAS) {
    //  easy multiply
    C64 = coefficient_x * coefficient_y;
    final_exponent = exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS;
    if ((final_exponent > 0) || (!coefficient_z)) {
      res =
	get_add64 (sign_x ^ sign_y,
		   final_exponent, C64, sign_z, exponent_z, coefficient_z, rnd_mode, pfpsf);
      BID_RETURN (res);
    } else {
      P.w[0] = C64;
      P.w[1] = 0;
      extra_digits = 0;
    }
  } else {
    if (!coefficient_z) {
#if DECIMAL_CALL_BY_REFERENCE
      bid64_mul (&res, px,
		 py _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		 _EXC_INFO_ARG);
#else
      res =
	bid64_mul (x,
		   y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		   _EXC_INFO_ARG);
#endif
      BID_RETURN (res);
    }
    // get 128-bit product: coefficient_x*coefficient_y
    __mul_64x64_to_128 (P, coefficient_x, coefficient_y);

    // tighten binary range of P:  leading bit is 2^bp
    // unbiased_bin_expon_product <= bp <= unbiased_bin_expon_product+1
    bin_expon_product -= 2 * BINARY_EXPONENT_BIAS;
    __tight_bin_range_128 (bp, P, bin_expon_product);

    // get number of decimal digits in the product
    digits_p = estimate_decimal_digits[bp];
    if (!(__unsigned_compare_gt_128 (power10_table_128[digits_p], P)))
      digits_p++;	// if power10_table_128[digits_p] <= P

    // determine number of decimal digits to be rounded out
    extra_digits = digits_p - MAX_FORMAT_DIGITS;
    final_exponent =
      exponent_x + exponent_y + extra_digits - DECIMAL_EXPONENT_BIAS;
  }

  if (((unsigned) final_exponent) >= 3 * 256) {
    if (final_exponent < 0) {
      //--- get number of bits in the coefficients of z  ---
      tempx.d = (double) coefficient_z;
      bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff;
      // get number of decimal digits in the coeff_x
      digits_z = estimate_decimal_digits[bin_expon_cx];
      if (coefficient_z >= power10_table_128[digits_z].w[0])
	digits_z++;
      // underflow
      if ((final_exponent + 16 < 0)
	  || (exponent_z + digits_z > 33 + final_exponent)) {
	res =
	  BID_normalize (sign_z, exponent_z, coefficient_z,
			 sign_x ^ sign_y, 1, rnd_mode, pfpsf);
	BID_RETURN (res);
      }

      ez = exponent_z + digits_z - 16;
      if (ez < 0)
	ez = 0;
      scale_z = exponent_z - ez;
      coefficient_z *= power10_table_128[scale_z].w[0];
      ey = final_exponent - extra_digits;
      extra_digits = ez - ey;
      if (extra_digits > 33) {
	res =
	  BID_normalize (sign_z, exponent_z, coefficient_z,
			 sign_x ^ sign_y, 1, rnd_mode, pfpsf);
	BID_RETURN (res);
      }
      //else  // extra_digits<=32

      if (extra_digits > 17) {
	CYh = __truncate (P, 16);
	// get remainder
	T = power10_table_128[16].w[0];
	__mul_64x64_to_64 (CY0L, CYh, T);
	remainder_y = P.w[0] - CY0L;

	extra_digits -= 16;
	P.w[0] = CYh;
	P.w[1] = 0;
      } else
	remainder_y = 0;

      // align coeff_x, CYh
      __mul_64x64_to_128 (CZ, coefficient_z,
			  power10_table_128[extra_digits].w[0]);

      if (sign_z == (sign_y ^ sign_x)) {
	__add_128_128 (CT, CZ, P);
	if (__unsigned_compare_ge_128
	    (CT, power10_table_128[16 + extra_digits])) {
	  extra_digits++;
	  ez++;
	}
      } else {
	if (remainder_y && (__unsigned_compare_ge_128 (CZ, P))) {
	  P.w[0]++;
	  if (!P.w[0])
	    P.w[1]++;
	}
	__sub_128_128 (CT, CZ, P);
	if (((SINT64) CT.w[1]) < 0) {
	  sign_z = sign_y ^ sign_x;
	  CT.w[0] = 0 - CT.w[0];
	  CT.w[1] = 0 - CT.w[1];
	  if (CT.w[0])
	    CT.w[1]--;
	} else if(!(CT.w[1]|CT.w[0]))
		sign_z = (rnd_mode!=ROUNDING_DOWN)? 0: 0x8000000000000000ull;
	if (ez
	    &&
	    (__unsigned_compare_gt_128
	     (power10_table_128[15 + extra_digits], CT))) {
	  extra_digits--;
	  ez--;
	}
      }

#ifdef SET_STATUS_FLAGS
      uf_status = 0;
      if ((!ez)
	  &&
	  __unsigned_compare_gt_128 (power10_table_128
				     [extra_digits + 15], CT)) {
	rmode = rnd_mode;
	if (sign_z && (unsigned) (rmode - 1) < 2)
	  rmode = 3 - rmode;
	//__add_128_64(PU, CT, round_const_table[rmode][extra_digits]);
	PU = power10_table_128[extra_digits + 15];
	PU.w[0]--;
	if (__unsigned_compare_gt_128 (PU, CT)
	    || (rmode == ROUNDING_DOWN)
	    || (rmode == ROUNDING_TO_ZERO))
	  uf_status = UNDERFLOW_EXCEPTION;
	else if (extra_digits < 2) {
	  if ((rmode == ROUNDING_UP)) {
	    if (!extra_digits)
	      uf_status = UNDERFLOW_EXCEPTION;
	    else {
	      if (remainder_y && (sign_z != (sign_y ^ sign_x)))
		remainder_y = power10_table_128[16].w[0] - remainder_y;

	      if (power10_table_128[15].w[0] > remainder_y)
		uf_status = UNDERFLOW_EXCEPTION;
	    }
	  } else	// RN or RN_away
	  {
	    if (remainder_y && (sign_z != (sign_y ^ sign_x)))
	      remainder_y = power10_table_128[16].w[0] - remainder_y;

	    if (!extra_digits) {
	      remainder_y += round_const_table[rmode][15];
	      if (remainder_y < power10_table_128[16].w[0])
		uf_status = UNDERFLOW_EXCEPTION;
	    } else {
	      if (remainder_y < round_const_table[rmode][16])
		uf_status = UNDERFLOW_EXCEPTION;
	    }
	  }
	  //__set_status_flags (pfpsf, uf_status);
	}
      }
#endif
      res =
	__bid_full_round64_remainder (sign_z, ez - extra_digits, CT,
				      extra_digits, remainder_y,
				      rnd_mode, pfpsf, uf_status);
      BID_RETURN (res);

    } else {
      if ((sign_z == (sign_x ^ sign_y))
	  || (final_exponent > 3 * 256 + 15)) {
	res =
	  fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent,
				   1000000000000000ull, rnd_mode,
				   pfpsf);
	BID_RETURN (res);
      }
    }
  }


  if (extra_digits > 0) {
    res =
      get_add128 (sign_z, exponent_z, coefficient_z, sign_x ^ sign_y,
		  final_exponent, P, extra_digits, rnd_mode, pfpsf);
    BID_RETURN (res);
  }
  // go to convert_format and exit
  else {
    C64 = __low_64 (P);

    res =
      get_add64 (sign_x ^ sign_y,
		 exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS, C64, 
		 sign_z, exponent_z, coefficient_z, 
		 rnd_mode, pfpsf);
    BID_RETURN (res);
  }
}