diff libgcc/config/libbid/bid64_fma.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_fma.c	Fri Jul 17 14:47:48 2009 +0900
@@ -0,0 +1,506 @@
+/* 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 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);
+  }
+}