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Diffstat (limited to 'sysdeps/ieee754/dbl-64/dla.h')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/dla.h | 183 |
1 files changed, 0 insertions, 183 deletions
diff --git a/sysdeps/ieee754/dbl-64/dla.h b/sysdeps/ieee754/dbl-64/dla.h deleted file mode 100644 index 88e8ffb1ca..0000000000 --- a/sysdeps/ieee754/dbl-64/dla.h +++ /dev/null @@ -1,183 +0,0 @@ -/* - * IBM Accurate Mathematical Library - * Written by International Business Machines Corp. - * Copyright (C) 2001-2017 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))); - - -#ifdef __FP_FAST_FMA -# define DLA_FMS(x, y, z) __builtin_fma (x, y, -(z)) -#endif - -/* 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); } |