[thirdparty/glibc.git] / sysdeps / ieee754 / dbl-64 / dla.h

/*
 * IBM Accurate Mathematical Library
 * Written by International Business Machines Corp.
 * Copyright (C) 2001-2016 Free Software Foundation, Inc.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2.1 of the License, or
 * (at your option) any later version.
 *
 * This program 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 Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, see <http://www.gnu.org/licenses/>.
 */

#include <math.h>

/***********************************************************************/
/*MODULE_NAME: dla.h                                                   */
/*                                                                     */
/* This file holds C language macros for 'Double Length Floating Point */
/* Arithmetic'. The macros are based on the paper:                     */
/* T.J.Dekker, "A floating-point Technique for extending the           */
/* Available Precision", Number. Math. 18, 224-242 (1971).              */
/* A Double-Length number is defined by a pair (r,s), of IEEE double    */
/* precision floating point numbers that satisfy,                      */
/*                                                                     */
/*              abs(s) <= abs(r+s)*2**(-53)/(1+2**(-53)).              */
/*                                                                     */
/* The computer arithmetic assumed is IEEE double precision in         */
/* round to nearest mode. All variables in the macros must be of type  */
/* IEEE double.                                                        */
/***********************************************************************/

/* CN = 1+2**27 = '41a0000002000000' IEEE double format.  Use it to split a
   double for better accuracy.  */
#define  CN   134217729.0


/* Exact addition of two single-length floating point numbers, Dekker. */
/* The macro produces a double-length number (z,zz) that satisfies     */
/* z+zz = x+y exactly.                                                 */

#define  EADD(x,y,z,zz)  \
	   z=(x)+(y);  zz=(fabs(x)>fabs(y)) ? (((x)-(z))+(y)) : (((y)-(z))+(x));


/* Exact subtraction of two single-length floating point numbers, Dekker. */
/* The macro produces a double-length number (z,zz) that satisfies        */
/* z+zz = x-y exactly.                                                    */

#define  ESUB(x,y,z,zz)  \
	   z=(x)-(y);  zz=(fabs(x)>fabs(y)) ? (((x)-(z))-(y)) : ((x)-((y)+(z)));


/* Exact multiplication of two single-length floating point numbers,   */
/* Veltkamp. The macro produces a double-length number (z,zz) that     */
/* satisfies z+zz = x*y exactly. p,hx,tx,hy,ty are temporary           */
/* storage variables of type double.                                   */

#ifdef DLA_FMS
# define  EMULV(x, y, z, zz, p, hx, tx, hy, ty)          \
  z = x * y; zz = DLA_FMS (x, y, z);
#else
# define  EMULV(x, y, z, zz, p, hx, tx, hy, ty)          \
  p = CN * (x);  hx = ((x) - p) + p;  tx = (x) - hx; \
  p = CN * (y);  hy = ((y) - p) + p;  ty = (y) - hy; \
  z = (x) * (y); zz = (((hx * hy - z) + hx * ty) + tx * hy) + tx * ty;
#endif


/* Exact multiplication of two single-length floating point numbers, Dekker. */
/* The macro produces a nearly double-length number (z,zz) (see Dekker)      */
/* that satisfies z+zz = x*y exactly. p,hx,tx,hy,ty,q are temporary          */
/* storage variables of type double.                                         */

#ifdef DLA_FMS
# define  MUL12(x,y,z,zz,p,hx,tx,hy,ty,q)        \
	   EMULV(x,y,z,zz,p,hx,tx,hy,ty)
#else
# define  MUL12(x,y,z,zz,p,hx,tx,hy,ty,q)        \
	   p=CN*(x);  hx=((x)-p)+p;  tx=(x)-hx; \
	   p=CN*(y);  hy=((y)-p)+p;  ty=(y)-hy; \
	   p=hx*hy;  q=hx*ty+tx*hy; z=p+q;  zz=((p-z)+q)+tx*ty;
#endif


/* Double-length addition, Dekker. The macro produces a double-length   */
/* number (z,zz) which satisfies approximately   z+zz = x+xx + y+yy.    */
/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy)       */
/* are assumed to be double-length numbers. r,s are temporary           */
/* storage variables of type double.                                    */

#define  ADD2(x, xx, y, yy, z, zz, r, s)                   \
  r = (x) + (y);  s = (fabs (x) > fabs (y)) ?                \
		      (((((x) - r) + (y)) + (yy)) + (xx)) : \
		      (((((y) - r) + (x)) + (xx)) + (yy));  \
  z = r + s;  zz = (r - z) + s;


/* Double-length subtraction, Dekker. The macro produces a double-length  */
/* number (z,zz) which satisfies approximately   z+zz = x+xx - (y+yy).    */
/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy)         */
/* are assumed to be double-length numbers. r,s are temporary             */
/* storage variables of type double.                                      */

#define  SUB2(x, xx, y, yy, z, zz, r, s)                   \
  r = (x) - (y);  s = (fabs (x) > fabs (y)) ?                \
		      (((((x) - r) - (y)) - (yy)) + (xx)) : \
		      ((((x) - ((y) + r)) + (xx)) - (yy));  \
  z = r + s;  zz = (r - z) + s;


/* Double-length multiplication, Dekker. The macro produces a double-length  */
/* number (z,zz) which satisfies approximately   z+zz = (x+xx)*(y+yy).       */
/* An error bound: abs((x+xx)*(y+yy))*1.24e-31. (x,xx), (y,yy)               */
/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc are         */
/* temporary storage variables of type double.                               */

#define  MUL2(x, xx, y, yy, z, zz, p, hx, tx, hy, ty, q, c, cc)  \
  MUL12 (x, y, c, cc, p, hx, tx, hy, ty, q)                      \
  cc = ((x) * (yy) + (xx) * (y)) + cc;   z = c + cc;   zz = (c - z) + cc;


/* Double-length division, Dekker. The macro produces a double-length        */
/* number (z,zz) which satisfies approximately   z+zz = (x+xx)/(y+yy).       */
/* An error bound: abs((x+xx)/(y+yy))*1.50e-31. (x,xx), (y,yy)               */
/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc,u,uu        */
/* are temporary storage variables of type double.                           */

#define  DIV2(x,xx,y,yy,z,zz,p,hx,tx,hy,ty,q,c,cc,u,uu)  \
	   c=(x)/(y);   MUL12(c,y,u,uu,p,hx,tx,hy,ty,q)  \
	   cc=(((((x)-u)-uu)+(xx))-c*(yy))/(y);   z=c+cc;   zz=(c-z)+cc;


/* Double-length addition, slower but more accurate than ADD2.               */
/* The macro produces a double-length                                        */
/* number (z,zz) which satisfies approximately   z+zz = (x+xx)+(y+yy).       */
/* An error bound: abs(x+xx + y+yy)*1.50e-31. (x,xx), (y,yy)                 */
/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w                 */
/* are temporary storage variables of type double.                           */

#define  ADD2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w)                 \
  r = (x) + (y);                                                            \
  if (fabs (x) > fabs (y)) { rr = ((x) - r) + (y);  s = (rr + (yy)) + (xx); } \
  else               { rr = ((y) - r) + (x);  s = (rr + (xx)) + (yy); }     \
  if (rr != 0.0) {                                                          \
      z = r + s;  zz = (r - z) + s; }                                       \
  else {                                                                    \
      ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) + (yy)) : (((yy) - s) + (xx));\
      u = r + s;                                                            \
      uu = (fabs (r) > fabs (s))   ? ((r - u) + s)   : ((s - u) + r);         \
      w = uu + ss;  z = u + w;                                              \
      zz = (fabs (u) > fabs (w))   ? ((u - z) + w)   : ((w - z) + u); }


/* Double-length subtraction, slower but more accurate than SUB2.            */
/* The macro produces a double-length                                        */
/* number (z,zz) which satisfies approximately   z+zz = (x+xx)-(y+yy).       */
/* An error bound: abs(x+xx - (y+yy))*1.50e-31. (x,xx), (y,yy)               */
/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w                 */
/* are temporary storage variables of type double.                           */

#define  SUB2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w)                   \
  r = (x) - (y);                                                              \
  if (fabs (x) > fabs (y)) { rr = ((x) - r) - (y);  s = (rr - (yy)) + (xx); }   \
  else               { rr = (x) - ((y) + r);  s = (rr + (xx)) - (yy); }       \
  if (rr != 0.0) {                                                            \
      z = r + s;  zz = (r - z) + s; }                                         \
  else {                                                                      \
      ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) - (yy)) : ((xx) - ((yy) + s)); \
      u = r + s;                                                              \
      uu = (fabs (r) > fabs (s))   ? ((r - u) + s)   : ((s - u) + r);           \
      w = uu + ss;  z = u + w;                                                \
      zz = (fabs (u) > fabs (w))   ? ((u - z) + w)   : ((w - z) + u); }
Commit	Line	Data
e4d82761 UD	1	/*
e4d82761 UD	2	* IBM Accurate Mathematical Library
c6c6dd48	3	* Written by International Business Machines Corp.
f7a9f785	4	* Copyright (C) 2001-2016 Free Software Foundation, Inc.
e4d82761 UD	5	*
	6	* This program is free software; you can redistribute it and/or modify
	7	* it under the terms of the GNU Lesser General Public License as published by
cc7375ce	8	* the Free Software Foundation; either version 2.1 of the License, or
e4d82761	9	* (at your option) any later version.
c6c6dd48	10	*
e4d82761 UD	11	* This program is distributed in the hope that it will be useful,
	12	* but WITHOUT ANY WARRANTY; without even the implied warranty of
	13	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
c6c6dd48	14	* GNU Lesser General Public License for more details.
e4d82761 UD	15	*
e4d82761 UD	16	* You should have received a copy of the GNU Lesser General Public License
59ba27a6	17	* along with this program; if not, see <http://www.gnu.org/licenses/>.
e4d82761	18	*/
c6c6dd48	19
0e9be4db WD	20	#include <math.h>
0e9be4db WD	21
e4d82761 UD	22	/***********************************************************************/
	23	/MODULE_NAME: dla.h /
	24	/* */
	25	/* This file holds C language macros for 'Double Length Floating Point */
	26	/* Arithmetic'. The macros are based on the paper: */
	27	/* T.J.Dekker, "A floating-point Technique for extending the */
	28	/* Available Precision", Number. Math. 18, 224-242 (1971). */
	29	/* A Double-Length number is defined by a pair (r,s), of IEEE double */
	30	/* precision floating point numbers that satisfy, */
	31	/* */
	32	/* abs(s) <= abs(r+s)2(-53)/(1+2(-53)). /
	33	/* */
	34	/* The computer arithmetic assumed is IEEE double precision in */
	35	/* round to nearest mode. All variables in the macros must be of type */
	36	/* IEEE double. */
	37	/***********************************************************************/
	38
085ec079 SP	39	/* CN = 1+2**27 = '41a0000002000000' IEEE double format. Use it to split a
085ec079 SP	40	double for better accuracy. */
e4d82761 UD	41	#define CN 134217729.0
	42
	43
	44	/* Exact addition of two single-length floating point numbers, Dekker. */
	45	/* The macro produces a double-length number (z,zz) that satisfies */
	46	/* z+zz = x+y exactly. */
	47
	48	#define EADD(x,y,z,zz) \
0e9be4db	49	z=(x)+(y); zz=(fabs(x)>fabs(y)) ? (((x)-(z))+(y)) : (((y)-(z))+(x));
e4d82761 UD	50
	51
	52	/* Exact subtraction of two single-length floating point numbers, Dekker. */
	53	/* The macro produces a double-length number (z,zz) that satisfies */
	54	/* z+zz = x-y exactly. */
	55
	56	#define ESUB(x,y,z,zz) \
0e9be4db	57	z=(x)-(y); zz=(fabs(x)>fabs(y)) ? (((x)-(z))-(y)) : ((x)-((y)+(z)));
e4d82761 UD	58
	59
	60	/* Exact multiplication of two single-length floating point numbers, */
	61	/* Veltkamp. The macro produces a double-length number (z,zz) that */
	62	/* satisfies z+zz = xy exactly. p,hx,tx,hy,ty are temporary /
	63	/* storage variables of type double. */
	64
774a2669	65	#ifdef DLA_FMS
c5d5d574 OB	66	# define EMULV(x, y, z, zz, p, hx, tx, hy, ty) \
c5d5d574 OB	67	z = x * y; zz = DLA_FMS (x, y, z);
a1a87169	68	#else
c5d5d574 OB	69	# define EMULV(x, y, z, zz, p, hx, tx, hy, ty) \
	70	p = CN * (x); hx = ((x) - p) + p; tx = (x) - hx; \
	71	p = CN * (y); hy = ((y) - p) + p; ty = (y) - hy; \
	72	z = (x) * (y); zz = (((hx * hy - z) + hx * ty) + tx * hy) + tx * ty;
a1a87169	73	#endif
e4d82761 UD	74
	75
	76	/* Exact multiplication of two single-length floating point numbers, Dekker. */
	77	/* The macro produces a nearly double-length number (z,zz) (see Dekker) */
	78	/* that satisfies z+zz = xy exactly. p,hx,tx,hy,ty,q are temporary /
	79	/* storage variables of type double. */
	80
774a2669	81	#ifdef DLA_FMS
a1a87169 UD	82	# define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \
	83	EMULV(x,y,z,zz,p,hx,tx,hy,ty)
	84	#else
	85	# define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \
	86	p=CN*(x); hx=((x)-p)+p; tx=(x)-hx; \
	87	p=CN*(y); hy=((y)-p)+p; ty=(y)-hy; \
	88	p=hxhy; q=hxty+txhy; z=p+q; zz=((p-z)+q)+txty;
	89	#endif
e4d82761 UD	90
	91
	92	/* Double-length addition, Dekker. The macro produces a double-length */
	93	/* number (z,zz) which satisfies approximately z+zz = x+xx + y+yy. */
	94	/* An error bound: (abs(x+xx)+abs(y+yy))4.94e-32. (x,xx), (y,yy) /
	95	/* are assumed to be double-length numbers. r,s are temporary */
	96	/* storage variables of type double. */
	97
c5d5d574	98	#define ADD2(x, xx, y, yy, z, zz, r, s) \
0e9be4db	99	r = (x) + (y); s = (fabs (x) > fabs (y)) ? \
c5d5d574 OB	100	(((((x) - r) + (y)) + (yy)) + (xx)) : \
	101	(((((y) - r) + (x)) + (xx)) + (yy)); \
	102	z = r + s; zz = (r - z) + s;
e4d82761 UD	103
	104
	105	/* Double-length subtraction, Dekker. The macro produces a double-length */
	106	/* number (z,zz) which satisfies approximately z+zz = x+xx - (y+yy). */
	107	/* An error bound: (abs(x+xx)+abs(y+yy))4.94e-32. (x,xx), (y,yy) /
	108	/* are assumed to be double-length numbers. r,s are temporary */
	109	/* storage variables of type double. */
	110
c5d5d574	111	#define SUB2(x, xx, y, yy, z, zz, r, s) \
0e9be4db	112	r = (x) - (y); s = (fabs (x) > fabs (y)) ? \
c5d5d574 OB	113	(((((x) - r) - (y)) - (yy)) + (xx)) : \
	114	((((x) - ((y) + r)) + (xx)) - (yy)); \
	115	z = r + s; zz = (r - z) + s;
e4d82761 UD	116
	117
	118	/* Double-length multiplication, Dekker. The macro produces a double-length */
	119	/* number (z,zz) which satisfies approximately z+zz = (x+xx)(y+yy). /
	120	/* An error bound: abs((x+xx)(y+yy))1.24e-31. (x,xx), (y,yy) */
	121	/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc are */
	122	/* temporary storage variables of type double. */
	123
c5d5d574 OB	124	#define MUL2(x, xx, y, yy, z, zz, p, hx, tx, hy, ty, q, c, cc) \
	125	MUL12 (x, y, c, cc, p, hx, tx, hy, ty, q) \
	126	cc = ((x) * (yy) + (xx) * (y)) + cc; z = c + cc; zz = (c - z) + cc;
e4d82761 UD	127
	128
	129	/* Double-length division, Dekker. The macro produces a double-length */
	130	/* number (z,zz) which satisfies approximately z+zz = (x+xx)/(y+yy). */
	131	/* An error bound: abs((x+xx)/(y+yy))1.50e-31. (x,xx), (y,yy) /
	132	/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc,u,uu */
	133	/* are temporary storage variables of type double. */
	134
	135	#define DIV2(x,xx,y,yy,z,zz,p,hx,tx,hy,ty,q,c,cc,u,uu) \
a1a87169 UD	136	c=(x)/(y); MUL12(c,y,u,uu,p,hx,tx,hy,ty,q) \
a1a87169 UD	137	cc=(((((x)-u)-uu)+(xx))-c*(yy))/(y); z=c+cc; zz=(c-z)+cc;
e4d82761 UD	138
	139
	140	/* Double-length addition, slower but more accurate than ADD2. */
	141	/* The macro produces a double-length */
	142	/* number (z,zz) which satisfies approximately z+zz = (x+xx)+(y+yy). */
	143	/* An error bound: abs(x+xx + y+yy)1.50e-31. (x,xx), (y,yy) /
	144	/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */
	145	/* are temporary storage variables of type double. */
	146
c5d5d574 OB	147	#define ADD2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w) \
c5d5d574 OB	148	r = (x) + (y); \
0e9be4db	149	if (fabs (x) > fabs (y)) { rr = ((x) - r) + (y); s = (rr + (yy)) + (xx); } \
c5d5d574 OB	150	else { rr = ((y) - r) + (x); s = (rr + (xx)) + (yy); } \
	151	if (rr != 0.0) { \
	152	z = r + s; zz = (r - z) + s; } \
	153	else { \
0e9be4db	154	ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) + (yy)) : (((yy) - s) + (xx));\
c5d5d574	155	u = r + s; \
0e9be4db	156	uu = (fabs (r) > fabs (s)) ? ((r - u) + s) : ((s - u) + r); \
c5d5d574	157	w = uu + ss; z = u + w; \
0e9be4db	158	zz = (fabs (u) > fabs (w)) ? ((u - z) + w) : ((w - z) + u); }
e4d82761 UD	159
	160
	161	/* Double-length subtraction, slower but more accurate than SUB2. */
	162	/* The macro produces a double-length */
	163	/* number (z,zz) which satisfies approximately z+zz = (x+xx)-(y+yy). */
	164	/* An error bound: abs(x+xx - (y+yy))1.50e-31. (x,xx), (y,yy) /
	165	/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */
	166	/* are temporary storage variables of type double. */
	167
c5d5d574 OB	168	#define SUB2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w) \
c5d5d574 OB	169	r = (x) - (y); \
0e9be4db	170	if (fabs (x) > fabs (y)) { rr = ((x) - r) - (y); s = (rr - (yy)) + (xx); } \
c5d5d574 OB	171	else { rr = (x) - ((y) + r); s = (rr + (xx)) - (yy); } \
	172	if (rr != 0.0) { \
	173	z = r + s; zz = (r - z) + s; } \
	174	else { \
0e9be4db	175	ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) - (yy)) : ((xx) - ((yy) + s)); \
c5d5d574	176	u = r + s; \
0e9be4db	177	uu = (fabs (r) > fabs (s)) ? ((r - u) + s) : ((s - u) + r); \
c5d5d574	178	w = uu + ss; z = u + w; \
0e9be4db	179	zz = (fabs (u) > fabs (w)) ? ((u - z) + w) : ((w - z) + u); }