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/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001-2013 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/>.
*/
/***********************************************************************/
/*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=(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. */
#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=(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) ; }
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