Update.

1999-12-29  Ulrich Drepper  <drepper@cygnus.com>

	* soft-fp/*: Tons of new files to implement floating-point arithmetic
	in software.
	Contributed by  Richard Henderson, Jakub Jelinek and others.

1 files changed, 608 insertions, 0 deletions

diff --git a/soft-fp/op-2.h b/soft-fp/op-2.h
new file mode 100644
index 0000000000..ad3fbc538a
--- /dev/null
+++ b/soft-fp/op-2.h
@@ -0,0 +1,608 @@
+/* Software floating-point emulation.
+   Basic two-word fraction declaration and manipulation.
+   Copyright (C) 1997,1998,1999 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Richard Henderson (rth@cygnus.com),
+		  Jakub Jelinek (jj@ultra.linux.cz),
+		  David S. Miller (davem@redhat.com) and
+		  Peter Maydell (pmaydell@chiark.greenend.org.uk).
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Library General Public License as
+   published by the Free Software Foundation; either version 2 of the
+   License, or (at your option) any later version.
+
+   The GNU C Library 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
+   Library General Public License for more details.
+
+   You should have received a copy of the GNU Library General Public
+   License along with the GNU C Library; see the file COPYING.LIB.  If
+   not, write to the Free Software Foundation, Inc.,
+   59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  */
+
+#define _FP_FRAC_DECL_2(X)	_FP_W_TYPE X##_f0, X##_f1
+#define _FP_FRAC_COPY_2(D,S)	(D##_f0 = S##_f0, D##_f1 = S##_f1)
+#define _FP_FRAC_SET_2(X,I)	__FP_FRAC_SET_2(X, I)
+#define _FP_FRAC_HIGH_2(X)	(X##_f1)
+#define _FP_FRAC_LOW_2(X)	(X##_f0)
+#define _FP_FRAC_WORD_2(X,w)	(X##_f##w)
+
+#define _FP_FRAC_SLL_2(X,N)						\
+  do {									\
+    if ((N) < _FP_W_TYPE_SIZE)						\
+      {									\
+	if (__builtin_constant_p(N) && (N) == 1) 			\
+	  {								\
+	    X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0);	\
+	    X##_f0 += X##_f0;						\
+	  }								\
+	else								\
+	  {								\
+	    X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N));	\
+	    X##_f0 <<= (N);						\
+	  }								\
+      }									\
+    else								\
+      {									\
+	X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE);			\
+	X##_f0 = 0;							\
+      }									\
+  } while (0)
+
+#define _FP_FRAC_SRL_2(X,N)						\
+  do {									\
+    if ((N) < _FP_W_TYPE_SIZE)						\
+      {									\
+	X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N));	\
+	X##_f1 >>= (N);							\
+      }									\
+    else								\
+      {									\
+	X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE);			\
+	X##_f1 = 0;							\
+      }									\
+  } while (0)
+
+/* Right shift with sticky-lsb.  */
+#define _FP_FRAC_SRS_2(X,N,sz)						\
+  do {									\
+    if ((N) < _FP_W_TYPE_SIZE)						\
+      {									\
+	X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) |	\
+		  (__builtin_constant_p(N) && (N) == 1			\
+		   ? X##_f0 & 1						\
+		   : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0));	\
+	X##_f1 >>= (N);							\
+      }									\
+    else								\
+      {									\
+	X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) |			\
+		  (((X##_f1 << (sz - (N))) | X##_f0) != 0));		\
+	X##_f1 = 0;							\
+      }									\
+  } while (0)
+
+#define _FP_FRAC_ADDI_2(X,I)	\
+  __FP_FRAC_ADDI_2(X##_f1, X##_f0, I)
+
+#define _FP_FRAC_ADD_2(R,X,Y)	\
+  __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
+
+#define _FP_FRAC_SUB_2(R,X,Y)	\
+  __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
+
+#define _FP_FRAC_DEC_2(X,Y)	\
+  __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0)
+
+#define _FP_FRAC_CLZ_2(R,X)	\
+  do {				\
+    if (X##_f1)			\
+      __FP_CLZ(R,X##_f1);	\
+    else 			\
+    {				\
+      __FP_CLZ(R,X##_f0);	\
+      R += _FP_W_TYPE_SIZE;	\
+    }				\
+  } while(0)
+
+/* Predicates */
+#define _FP_FRAC_NEGP_2(X)	((_FP_WS_TYPE)X##_f1 < 0)
+#define _FP_FRAC_ZEROP_2(X)	((X##_f1 | X##_f0) == 0)
+#define _FP_FRAC_OVERP_2(fs,X)	(_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
+#define _FP_FRAC_EQ_2(X, Y)	(X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
+#define _FP_FRAC_GT_2(X, Y)	\
+  (X##_f1 > Y##_f1 || X##_f1 == Y##_f1 && X##_f0 > Y##_f0)
+#define _FP_FRAC_GE_2(X, Y)	\
+  (X##_f1 > Y##_f1 || X##_f1 == Y##_f1 && X##_f0 >= Y##_f0)
+
+#define _FP_ZEROFRAC_2		0, 0
+#define _FP_MINFRAC_2		0, 1
+#define _FP_MAXFRAC_2		(~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
+
+/*
+ * Internals 
+ */
+
+#define __FP_FRAC_SET_2(X,I1,I0)	(X##_f0 = I0, X##_f1 = I1)
+
+#define __FP_CLZ_2(R, xh, xl)	\
+  do {				\
+    if (xh)			\
+      __FP_CLZ(R,xh);		\
+    else 			\
+    {				\
+      __FP_CLZ(R,xl);		\
+      R += _FP_W_TYPE_SIZE;	\
+    }				\
+  } while(0)
+
+#if 0
+
+#ifndef __FP_FRAC_ADDI_2
+#define __FP_FRAC_ADDI_2(xh, xl, i)	\
+  (xh += ((xl += i) < i))
+#endif
+#ifndef __FP_FRAC_ADD_2
+#define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl)	\
+  (rh = xh + yh + ((rl = xl + yl) < xl))
+#endif
+#ifndef __FP_FRAC_SUB_2
+#define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl)	\
+  (rh = xh - yh - ((rl = xl - yl) > xl))
+#endif
+#ifndef __FP_FRAC_DEC_2
+#define __FP_FRAC_DEC_2(xh, xl, yh, yl)	\
+  do {					\
+    UWtype _t = xl;			\
+    xh -= yh + ((xl -= yl) > _t);	\
+  } while (0)
+#endif
+
+#else
+
+#undef __FP_FRAC_ADDI_2
+#define __FP_FRAC_ADDI_2(xh, xl, i)	add_ssaaaa(xh, xl, xh, xl, 0, i)
+#undef __FP_FRAC_ADD_2
+#define __FP_FRAC_ADD_2			add_ssaaaa
+#undef __FP_FRAC_SUB_2
+#define __FP_FRAC_SUB_2			sub_ddmmss
+#undef __FP_FRAC_DEC_2
+#define __FP_FRAC_DEC_2(xh, xl, yh, yl)	sub_ddmmss(xh, xl, xh, xl, yh, yl)
+
+#endif
+
+/*
+ * Unpack the raw bits of a native fp value.  Do not classify or
+ * normalize the data.
+ */
+
+#define _FP_UNPACK_RAW_2(fs, X, val)			\
+  do {							\
+    union _FP_UNION_##fs _flo; _flo.flt = (val);	\
+							\
+    X##_f0 = _flo.bits.frac0;				\
+    X##_f1 = _flo.bits.frac1;				\
+    X##_e  = _flo.bits.exp;				\
+    X##_s  = _flo.bits.sign;				\
+  } while (0)
+
+#define _FP_UNPACK_RAW_2_P(fs, X, val)			\
+  do {							\
+    union _FP_UNION_##fs *_flo =			\
+      (union _FP_UNION_##fs *)(val);			\
+							\
+    X##_f0 = _flo->bits.frac0;				\
+    X##_f1 = _flo->bits.frac1;				\
+    X##_e  = _flo->bits.exp;				\
+    X##_s  = _flo->bits.sign;				\
+  } while (0)
+
+
+/*
+ * Repack the raw bits of a native fp value.
+ */
+
+#define _FP_PACK_RAW_2(fs, val, X)			\
+  do {							\
+    union _FP_UNION_##fs _flo;				\
+							\
+    _flo.bits.frac0 = X##_f0;				\
+    _flo.bits.frac1 = X##_f1;				\
+    _flo.bits.exp   = X##_e;				\
+    _flo.bits.sign  = X##_s;				\
+							\
+    (val) = _flo.flt;					\
+  } while (0)
+
+#define _FP_PACK_RAW_2_P(fs, val, X)			\
+  do {							\
+    union _FP_UNION_##fs *_flo =			\
+      (union _FP_UNION_##fs *)(val);			\
+							\
+    _flo->bits.frac0 = X##_f0;				\
+    _flo->bits.frac1 = X##_f1;				\
+    _flo->bits.exp   = X##_e;				\
+    _flo->bits.sign  = X##_s;				\
+  } while (0)
+
+
+/*
+ * Multiplication algorithms:
+ */
+
+/* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
+
+#define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit)			\
+  do {									\
+    _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);	\
+									\
+    doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0);	\
+    doit(_b_f1, _b_f0, X##_f0, Y##_f1);					\
+    doit(_c_f1, _c_f0, X##_f1, Y##_f0);					\
+    doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1);	\
+									\
+    __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
+		    _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0,		\
+		    _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
+		    _FP_FRAC_WORD_4(_z,1));				\
+    __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
+		    _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0,		\
+		    _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
+		    _FP_FRAC_WORD_4(_z,1));				\
+									\
+    /* Normalize since we know where the msb of the multiplicands	\
+       were (bit B), we know that the msb of the of the product is	\
+       at either 2B or 2B-1.  */					\
+    _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits);			\
+    R##_f0 = _FP_FRAC_WORD_4(_z,0);					\
+    R##_f1 = _FP_FRAC_WORD_4(_z,1);					\
+  } while (0)
+
+/* Given a 1W * 1W => 2W primitive, do the extended multiplication.
+   Do only 3 multiplications instead of four. This one is for machines
+   where multiplication is much more expensive than subtraction.  */
+
+#define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit)		\
+  do {									\
+    _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c);	\
+    _FP_W_TYPE _d;							\
+    int _c1, _c2;							\
+									\
+    _b_f0 = X##_f0 + X##_f1;						\
+    _c1 = _b_f0 < X##_f0;						\
+    _b_f1 = Y##_f0 + Y##_f1;						\
+    _c2 = _b_f1 < Y##_f0;						\
+    doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0);			\
+    doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1);	\
+    doit(_c_f1, _c_f0, X##_f1, Y##_f1);					\
+									\
+    _b_f0 &= -_c2;							\
+    _b_f1 &= -_c1;							\
+    __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
+		    _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d,		\
+		    0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1));	\
+    __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
+		     _b_f0);						\
+    __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
+		     _b_f1);						\
+    __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
+		    _FP_FRAC_WORD_4(_z,1),				\
+		    0, _d, _FP_FRAC_WORD_4(_z,0));			\
+    __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2),	\
+		    _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0);		\
+    __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2),	\
+		    _c_f1, _c_f0,					\
+		    _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2));	\
+									\
+    /* Normalize since we know where the msb of the multiplicands	\
+       were (bit B), we know that the msb of the of the product is	\
+       at either 2B or 2B-1.  */					\
+    _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits);			\
+    R##_f0 = _FP_FRAC_WORD_4(_z,0);					\
+    R##_f1 = _FP_FRAC_WORD_4(_z,1);					\
+  } while (0)
+
+#define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y)				\
+  do {									\
+    _FP_FRAC_DECL_4(_z);						\
+    _FP_W_TYPE _x[2], _y[2];						\
+    _x[0] = X##_f0; _x[1] = X##_f1;					\
+    _y[0] = Y##_f0; _y[1] = Y##_f1;					\
+									\
+    mpn_mul_n(_z_f, _x, _y, 2);						\
+									\
+    /* Normalize since we know where the msb of the multiplicands	\
+       were (bit B), we know that the msb of the of the product is	\
+       at either 2B or 2B-1.  */					\
+    _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits);			\
+    R##_f0 = _z_f[0];							\
+    R##_f1 = _z_f[1];							\
+  } while (0)
+
+/* Do at most 120x120=240 bits multiplication using double floating
+   point multiplication.  This is useful if floating point
+   multiplication has much bigger throughput than integer multiply.
+   It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits
+   between 106 and 120 only.  
+   Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set.
+   SETFETZ is a macro which will disable all FPU exceptions and set rounding
+   towards zero,  RESETFE should optionally reset it back.  */
+
+#define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe)	\
+  do {										\
+    static const double _const[] = {						\
+      /* 2^-24 */ 5.9604644775390625e-08,					\
+      /* 2^-48 */ 3.5527136788005009e-15,					\
+      /* 2^-72 */ 2.1175823681357508e-22,					\
+      /* 2^-96 */ 1.2621774483536189e-29,					\
+      /* 2^28 */ 2.68435456e+08,						\
+      /* 2^4 */ 1.600000e+01,							\
+      /* 2^-20 */ 9.5367431640625e-07,						\
+      /* 2^-44 */ 5.6843418860808015e-14,					\
+      /* 2^-68 */ 3.3881317890172014e-21,					\
+      /* 2^-92 */ 2.0194839173657902e-28,					\
+      /* 2^-116 */ 1.2037062152420224e-35};					\
+    double _a240, _b240, _c240, _d240, _e240, _f240, 				\
+	   _g240, _h240, _i240, _j240, _k240;					\
+    union { double d; UDItype i; } _l240, _m240, _n240, _o240,			\
+				   _p240, _q240, _r240, _s240;			\
+    UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0;			\
+										\
+    if (wfracbits < 106 || wfracbits > 120)					\
+      abort();									\
+										\
+    setfetz;									\
+										\
+    _e240 = (double)(long)(X##_f0 & 0xffffff);					\
+    _j240 = (double)(long)(Y##_f0 & 0xffffff);					\
+    _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff);				\
+    _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff);				\
+    _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48));	\
+    _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48));	\
+    _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff);				\
+    _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff);				\
+    _a240 = (double)(long)(X##_f1 >> 32);					\
+    _f240 = (double)(long)(Y##_f1 >> 32);					\
+    _e240 *= _const[3];								\
+    _j240 *= _const[3];								\
+    _d240 *= _const[2];								\
+    _i240 *= _const[2];								\
+    _c240 *= _const[1];								\
+    _h240 *= _const[1];								\
+    _b240 *= _const[0];								\
+    _g240 *= _const[0];								\
+    _s240.d =							      _e240*_j240;\
+    _r240.d =						_d240*_j240 + _e240*_i240;\
+    _q240.d =				  _c240*_j240 + _d240*_i240 + _e240*_h240;\
+    _p240.d =		    _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\
+    _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\
+    _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240;		\
+    _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240;				\
+    _l240.d = _a240*_g240 + _b240*_f240;					\
+    _k240 =   _a240*_f240;							\
+    _r240.d += _s240.d;								\
+    _q240.d += _r240.d;								\
+    _p240.d += _q240.d;								\
+    _o240.d += _p240.d;								\
+    _n240.d += _o240.d;								\
+    _m240.d += _n240.d;								\
+    _l240.d += _m240.d;								\
+    _k240 += _l240.d;								\
+    _s240.d -= ((_const[10]+_s240.d)-_const[10]);				\
+    _r240.d -= ((_const[9]+_r240.d)-_const[9]);					\
+    _q240.d -= ((_const[8]+_q240.d)-_const[8]);					\
+    _p240.d -= ((_const[7]+_p240.d)-_const[7]);					\
+    _o240.d += _const[7];							\
+    _n240.d += _const[6];							\
+    _m240.d += _const[5];							\
+    _l240.d += _const[4];							\
+    if (_s240.d != 0.0) _y240 = 1;						\
+    if (_r240.d != 0.0) _y240 = 1;						\
+    if (_q240.d != 0.0) _y240 = 1;						\
+    if (_p240.d != 0.0) _y240 = 1;						\
+    _t240 = (DItype)_k240;							\
+    _u240 = _l240.i;								\
+    _v240 = _m240.i;								\
+    _w240 = _n240.i;								\
+    _x240 = _o240.i;								\
+    R##_f1 = (_t240 << (128 - (wfracbits - 1)))					\
+	     | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104));			\
+    R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1)))			\
+    	     | ((_v240 & 0xffffff) << (144 - (wfracbits - 1)))			\
+    	     | ((_w240 & 0xffffff) << (120 - (wfracbits - 1)))			\
+    	     | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96))			\
+    	     | _y240;								\
+    resetfe;									\
+  } while (0)
+
+/*
+ * Division algorithms:
+ */
+
+#define _FP_DIV_MEAT_2_udiv(fs, R, X, Y)				\
+  do {									\
+    _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0;		\
+    if (_FP_FRAC_GT_2(X, Y))						\
+      {									\
+	_n_f2 = X##_f1 >> 1;						\
+	_n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1;		\
+	_n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1);			\
+      }									\
+    else								\
+      {									\
+	R##_e--;							\
+	_n_f2 = X##_f1;							\
+	_n_f1 = X##_f0;							\
+	_n_f0 = 0;							\
+      }									\
+									\
+    /* Normalize, i.e. make the most significant bit of the 		\
+       denominator set. */						\
+    _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs);				\
+									\
+    udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1);			\
+    umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0);				\
+    _r_f0 = _n_f0;							\
+    if (_FP_FRAC_GT_2(_m, _r))						\
+      {									\
+	R##_f1--;							\
+	_FP_FRAC_ADD_2(_r, Y, _r);					\
+	if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r))		\
+	  {								\
+	    R##_f1--;							\
+	    _FP_FRAC_ADD_2(_r, Y, _r);					\
+	  }								\
+      }									\
+    _FP_FRAC_DEC_2(_r, _m);						\
+									\
+    if (_r_f1 == Y##_f1)						\
+      {									\
+	/* This is a special case, not an optimization			\
+	   (_r/Y##_f1 would not fit into UWtype).			\
+	   As _r is guaranteed to be < Y,  R##_f0 can be either		\
+	   (UWtype)-1 or (UWtype)-2.  But as we know what kind		\
+	   of bits it is (sticky, guard, round),  we don't care.	\
+	   We also don't care what the reminder is,  because the	\
+	   guard bit will be set anyway.  -jj */			\
+	R##_f0 = -1;							\
+      }									\
+    else								\
+      {									\
+	udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1);		\
+	umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0);			\
+	_r_f0 = 0;							\
+	if (_FP_FRAC_GT_2(_m, _r))					\
+	  {								\
+	    R##_f0--;							\
+	    _FP_FRAC_ADD_2(_r, Y, _r);					\
+	    if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r))		\
+	      {								\
+		R##_f0--;						\
+		_FP_FRAC_ADD_2(_r, Y, _r);				\
+	      }								\
+	  }								\
+	if (!_FP_FRAC_EQ_2(_r, _m))					\
+	  R##_f0 |= _FP_WORK_STICKY;					\
+      }									\
+  } while (0)
+
+
+#define _FP_DIV_MEAT_2_gmp(fs, R, X, Y)					\
+  do {									\
+    _FP_W_TYPE _x[4], _y[2], _z[4];					\
+    _y[0] = Y##_f0; _y[1] = Y##_f1;					\
+    _x[0] = _x[3] = 0;							\
+    if (_FP_FRAC_GT_2(X, Y))						\
+      {									\
+	R##_e++;							\
+	_x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) |	\
+		 X##_f1 >> (_FP_W_TYPE_SIZE -				\
+			    (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE)));	\
+	_x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE);	\
+      }									\
+    else								\
+      {									\
+	_x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) |	\
+		 X##_f1 >> (_FP_W_TYPE_SIZE -				\
+			    (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE)));	\
+	_x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE);	\
+      }									\
+									\
+    (void) mpn_divrem (_z, 0, _x, 4, _y, 2);				\
+    R##_f1 = _z[1];							\
+    R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0);				\
+  } while (0)
+
+
+/*
+ * Square root algorithms:
+ * We have just one right now, maybe Newton approximation
+ * should be added for those machines where division is fast.
+ */
+ 
+#define _FP_SQRT_MEAT_2(R, S, T, X, q)			\
+  do {							\
+    while (q)						\
+      {							\
+	T##_f1 = S##_f1 + q;				\
+	if (T##_f1 <= X##_f1)				\
+	  {						\
+	    S##_f1 = T##_f1 + q;			\
+	    X##_f1 -= T##_f1;				\
+	    R##_f1 += q;				\
+	  }						\
+	_FP_FRAC_SLL_2(X, 1);				\
+	q >>= 1;					\
+      }							\
+    q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1);		\
+    while (q != _FP_WORK_ROUND)				\
+      {							\
+	T##_f0 = S##_f0 + q;				\
+	T##_f1 = S##_f1;				\
+	if (T##_f1 < X##_f1 || 				\
+	    (T##_f1 == X##_f1 && T##_f0 <= X##_f0))	\
+	  {						\
+	    S##_f0 = T##_f0 + q;			\
+	    S##_f1 += (T##_f0 > S##_f0);		\
+	    _FP_FRAC_DEC_2(X, T);			\
+	    R##_f0 += q;				\
+	  }						\
+	_FP_FRAC_SLL_2(X, 1);				\
+	q >>= 1;					\
+      }							\
+    if (X##_f0 | X##_f1)				\
+      {							\
+	if (S##_f1 < X##_f1 || 				\
+	    (S##_f1 == X##_f1 && S##_f0 < X##_f0))	\
+	  R##_f0 |= _FP_WORK_ROUND;			\
+	R##_f0 |= _FP_WORK_STICKY;			\
+      }							\
+  } while (0)
+
+
+/*
+ * Assembly/disassembly for converting to/from integral types.  
+ * No shifting or overflow handled here.
+ */
+
+#define _FP_FRAC_ASSEMBLE_2(r, X, rsize)	\
+  do {						\
+    if (rsize <= _FP_W_TYPE_SIZE)		\
+      r = X##_f0;				\
+    else					\
+      {						\
+	r = X##_f1;				\
+	r <<= _FP_W_TYPE_SIZE;			\
+	r += X##_f0;				\
+      }						\
+  } while (0)
+
+#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize)				\
+  do {									\
+    X##_f0 = r;								\
+    X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE);	\
+  } while (0)
+
+/*
+ * Convert FP values between word sizes
+ */
+
+#define _FP_FRAC_CONV_1_2(dfs, sfs, D, S)				\
+  do {									\
+    if (S##_c != FP_CLS_NAN)						\
+      _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs),	\
+		     _FP_WFRACBITS_##sfs);				\
+    else								\
+      _FP_FRAC_SRL_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs));	\
+    D##_f = S##_f0;							\
+  } while (0)
+
+#define _FP_FRAC_CONV_2_1(dfs, sfs, D, S)				\
+  do {									\
+    D##_f0 = S##_f;							\
+    D##_f1 = 0;								\
+    _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs));	\
+  } while (0)
+