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

/*
 * IBM Accurate Mathematical Library
 * Written by International Business Machines Corp.
 * Copyright (C) 2001 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, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */

/***********************************************************************/
/*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 */
#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=(ABS(x)>ABS(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=(ABS(x)>ABS(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.                                   */

#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;


/* 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.                                         */

#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;


/* 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=(ABS(x)>ABS(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=(ABS(x)>ABS(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 (ABS(x)>ABS(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=(ABS(xx)>ABS(yy)) ? (((xx)-s)+(yy)) : (((yy)-s)+(xx)); \
             u=r+s;                                                    \
             uu=(ABS(r)>ABS(s))   ? ((r-u)+s)   : ((s-u)+r)  ;         \
             w=uu+ss;  z=u+w;                                          \
             zz=(ABS(u)>ABS(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 (ABS(x)>ABS(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=(ABS(xx)>ABS(yy)) ? (((xx)-s)-(yy)) : ((xx)-((yy)+s)); \
             u=r+s;                                                    \
             uu=(ABS(r)>ABS(s))   ? ((r-u)+s)   : ((s-u)+r)  ;         \
             w=uu+ss;  z=u+w;                                          \
             zz=(ABS(u)>ABS(w))   ? ((u-z)+w)   : ((w-z)+u)  ; }
Commit	Line	Data
e4d82761 UD	1	/*
e4d82761 UD	2	* IBM Accurate Mathematical Library
c6c6dd48 RM	3	* Written by International Business Machines Corp.
c6c6dd48 RM	4	* Copyright (C) 2001 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	*
	16	* You should have received a copy of the GNU Lesser General Public License
	17	* along with this program; if not, write to the Free Software
c6c6dd48	18	* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
e4d82761	19	*/
c6c6dd48	20
e4d82761 UD	21	/***********************************************************************/
	22	/MODULE_NAME: dla.h /
	23	/* */
	24	/* This file holds C language macros for 'Double Length Floating Point */
	25	/* Arithmetic'. The macros are based on the paper: */
	26	/* T.J.Dekker, "A floating-point Technique for extending the */
	27	/* Available Precision", Number. Math. 18, 224-242 (1971). */
	28	/* A Double-Length number is defined by a pair (r,s), of IEEE double */
	29	/* precision floating point numbers that satisfy, */
	30	/* */
	31	/* abs(s) <= abs(r+s)2(-53)/(1+2(-53)). /
	32	/* */
	33	/* The computer arithmetic assumed is IEEE double precision in */
	34	/* round to nearest mode. All variables in the macros must be of type */
	35	/* IEEE double. */
	36	/***********************************************************************/
	37
	38	/* CN = 1+2*27 = '41a0000002000000' IEEE double format /
	39	#define CN 134217729.0
	40
	41
	42	/* Exact addition of two single-length floating point numbers, Dekker. */
	43	/* The macro produces a double-length number (z,zz) that satisfies */
	44	/* z+zz = x+y exactly. */
	45
	46	#define EADD(x,y,z,zz) \
	47	z=(x)+(y); zz=(ABS(x)>ABS(y)) ? (((x)-(z))+(y)) : (((y)-(z))+(x));
	48
	49
	50	/* Exact subtraction of two single-length floating point numbers, Dekker. */
	51	/* The macro produces a double-length number (z,zz) that satisfies */
	52	/* z+zz = x-y exactly. */
	53
	54	#define ESUB(x,y,z,zz) \
	55	z=(x)-(y); zz=(ABS(x)>ABS(y)) ? (((x)-(z))-(y)) : ((x)-((y)+(z)));
	56
	57
	58	/* Exact multiplication of two single-length floating point numbers, */
	59	/* Veltkamp. The macro produces a double-length number (z,zz) that */
	60	/* satisfies z+zz = xy exactly. p,hx,tx,hy,ty are temporary /
	61	/* storage variables of type double. */
	62
	63	#define EMULV(x,y,z,zz,p,hx,tx,hy,ty) \
	64	p=CN*(x); hx=((x)-p)+p; tx=(x)-hx; \
	65	p=CN*(y); hy=((y)-p)+p; ty=(y)-hy; \
	66	z=(x)(y); zz=(((hxhy-z)+hxty)+txhy)+tx*ty;
	67
	68
	69	/* Exact multiplication of two single-length floating point numbers, Dekker. */
	70	/* The macro produces a nearly double-length number (z,zz) (see Dekker) */
	71	/* that satisfies z+zz = xy exactly. p,hx,tx,hy,ty,q are temporary /
	72	/* storage variables of type double. */
	73
	74	#define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \
	75	p=CN*(x); hx=((x)-p)+p; tx=(x)-hx; \
	76	p=CN*(y); hy=((y)-p)+p; ty=(y)-hy; \
	77	p=hxhy; q=hxty+txhy; z=p+q; zz=((p-z)+q)+txty;
	78
	79
	80	/* Double-length addition, Dekker. The macro produces a double-length */
	81	/* number (z,zz) which satisfies approximately z+zz = x+xx + y+yy. */
	82	/* An error bound: (abs(x+xx)+abs(y+yy))4.94e-32. (x,xx), (y,yy) /
	83	/* are assumed to be double-length numbers. r,s are temporary */
	84	/* storage variables of type double. */
85
86	#define ADD2(x,xx,y,yy,z,zz,r,s) \
87	r=(x)+(y); s=(ABS(x)>ABS(y)) ? \
88	(((((x)-r)+(y))+(yy))+(xx)) : \
89	(((((y)-r)+(x))+(xx))+(yy)); \
90	z=r+s; zz=(r-z)+s;
91
92
93	/* Double-length subtraction, Dekker. The macro produces a double-length */
94	/* number (z,zz) which satisfies approximately z+zz = x+xx - (y+yy). */
95	/* An error bound: (abs(x+xx)+abs(y+yy))4.94e-32. (x,xx), (y,yy) /
96	/* are assumed to be double-length numbers. r,s are temporary */
97	/* storage variables of type double. */
98
99	#define SUB2(x,xx,y,yy,z,zz,r,s) \
100	r=(x)-(y); s=(ABS(x)>ABS(y)) ? \
101	(((((x)-r)-(y))-(yy))+(xx)) : \
102	((((x)-((y)+r))+(xx))-(yy)); \
103	z=r+s; zz=(r-z)+s;
104
105
106	/* Double-length multiplication, Dekker. The macro produces a double-length */
107	/* number (z,zz) which satisfies approximately z+zz = (x+xx)(y+yy). /
108	/* An error bound: abs((x+xx)(y+yy))1.24e-31. (x,xx), (y,yy) */
109	/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc are */
110	/* temporary storage variables of type double. */
111
112	#define MUL2(x,xx,y,yy,z,zz,p,hx,tx,hy,ty,q,c,cc) \
113	MUL12(x,y,c,cc,p,hx,tx,hy,ty,q) \
114	cc=((x)(yy)+(xx)(y))+cc; z=c+cc; zz=(c-z)+cc;
115
116
117	/* Double-length division, Dekker. The macro produces a double-length */
118	/* number (z,zz) which satisfies approximately z+zz = (x+xx)/(y+yy). */
119	/* An error bound: abs((x+xx)/(y+yy))1.50e-31. (x,xx), (y,yy) /
120	/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc,u,uu */
121	/* are temporary storage variables of type double. */
122
123	#define DIV2(x,xx,y,yy,z,zz,p,hx,tx,hy,ty,q,c,cc,u,uu) \
124	c=(x)/(y); MUL12(c,y,u,uu,p,hx,tx,hy,ty,q) \
125	cc=(((((x)-u)-uu)+(xx))-c*(yy))/(y); z=c+cc; zz=(c-z)+cc;
126
127
128	/* Double-length addition, slower but more accurate than ADD2. */
129	/* 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. r,rr,s,ss,u,uu,w */
133	/* are temporary storage variables of type double. */
134
135	#define ADD2A(x,xx,y,yy,z,zz,r,rr,s,ss,u,uu,w) \
136	r=(x)+(y); \
137	if (ABS(x)>ABS(y)) { rr=((x)-r)+(y); s=(rr+(yy))+(xx); } \
138	else { rr=((y)-r)+(x); s=(rr+(xx))+(yy); } \
139	if (rr!=0.0) { \
140	z=r+s; zz=(r-z)+s; } \
141	else { \
142	ss=(ABS(xx)>ABS(yy)) ? (((xx)-s)+(yy)) : (((yy)-s)+(xx)); \
143	u=r+s; \
144	uu=(ABS(r)>ABS(s)) ? ((r-u)+s) : ((s-u)+r) ; \
145	w=uu+ss; z=u+w; \
146	zz=(ABS(u)>ABS(w)) ? ((u-z)+w) : ((w-z)+u) ; }
147
148
149	/* Double-length subtraction, slower but more accurate than SUB2. */
150	/* The macro produces a double-length */
151	/* number (z,zz) which satisfies approximately z+zz = (x+xx)-(y+yy). */
152	/* An error bound: abs(x+xx - (y+yy))1.50e-31. (x,xx), (y,yy) /
153	/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */
154	/* are temporary storage variables of type double. */
155
156	#define SUB2A(x,xx,y,yy,z,zz,r,rr,s,ss,u,uu,w) \
157	r=(x)-(y); \
158	if (ABS(x)>ABS(y)) { rr=((x)-r)-(y); s=(rr-(yy))+(xx); } \
159	else { rr=(x)-((y)+r); s=(rr+(xx))-(yy); } \
160	if (rr!=0.0) { \
161	z=r+s; zz=(r-z)+s; } \
162	else { \
163	ss=(ABS(xx)>ABS(yy)) ? (((xx)-s)-(yy)) : ((xx)-((yy)+s)); \
164	u=r+s; \
165	uu=(ABS(r)>ABS(s)) ? ((r-u)+s) : ((s-u)+r) ; \
166	w=uu+ss; z=u+w; \
167	zz=(ABS(u)>ABS(w)) ? ((u-z)+w) : ((w-z)+u) ; }
168
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