diff libgcc/config/libbid/bid64_add.c @ 0:a06113de4d67

first commit
author kent <kent@cr.ie.u-ryukyu.ac.jp>
date Fri, 17 Jul 2009 14:47:48 +0900
parents
children 04ced10e8804
line wrap: on
line diff
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libgcc/config/libbid/bid64_add.c	Fri Jul 17 14:47:48 2009 +0900
@@ -0,0 +1,595 @@
+/* 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);
+}