| /* |
| * 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) ; } |
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