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30891f35fa
We stopped adding "Contributed by" or similar lines in sources in 2012 in favour of git logs and keeping the Contributors section of the glibc manual up to date. Removing these lines makes the license header a bit more consistent across files and also removes the possibility of error in attribution when license blocks or files are copied across since the contributed-by lines don't actually reflect reality in those cases. Move all "Contributed by" and similar lines (Written by, Test by, etc.) into a new file CONTRIBUTED-BY to retain record of these contributions. These contributors are also mentioned in manual/contrib.texi, so we just maintain this additional record as a courtesy to the earlier developers. The following scripts were used to filter a list of files to edit in place and to clean up the CONTRIBUTED-BY file respectively. These were not added to the glibc sources because they're not expected to be of any use in future given that this is a one time task: https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02 Reviewed-by: Carlos O'Donell <carlos@redhat.com>
187 lines
9.3 KiB
C
187 lines
9.3 KiB
C
/*
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* IBM Accurate Mathematical Library
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* Copyright (C) 2001-2021 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <https://www.gnu.org/licenses/>.
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*/
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#include <math.h>
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/***********************************************************************/
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/*MODULE_NAME: dla.h */
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/* */
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/* This file holds C language macros for 'Double Length Floating Point */
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/* Arithmetic'. The macros are based on the paper: */
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/* T.J.Dekker, "A floating-point Technique for extending the */
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/* Available Precision", Number. Math. 18, 224-242 (1971). */
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/* A Double-Length number is defined by a pair (r,s), of IEEE double */
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/* precision floating point numbers that satisfy, */
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/* */
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/* abs(s) <= abs(r+s)*2**(-53)/(1+2**(-53)). */
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/* */
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/* The computer arithmetic assumed is IEEE double precision in */
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/* round to nearest mode. All variables in the macros must be of type */
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/* IEEE double. */
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/***********************************************************************/
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/* CN = 1+2**27 = '41a0000002000000' IEEE double format. Use it to split a
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double for better accuracy. */
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#define CN 134217729.0
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/* Exact addition of two single-length floating point numbers, Dekker. */
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/* The macro produces a double-length number (z,zz) that satisfies */
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/* z+zz = x+y exactly. */
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#define EADD(x,y,z,zz) \
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z=(x)+(y); zz=(fabs(x)>fabs(y)) ? (((x)-(z))+(y)) : (((y)-(z))+(x));
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/* Exact subtraction of two single-length floating point numbers, Dekker. */
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/* The macro produces a double-length number (z,zz) that satisfies */
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/* z+zz = x-y exactly. */
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#define ESUB(x,y,z,zz) \
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z=(x)-(y); zz=(fabs(x)>fabs(y)) ? (((x)-(z))-(y)) : ((x)-((y)+(z)));
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#ifdef __FP_FAST_FMA
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# define DLA_FMS(x, y, z) __builtin_fma (x, y, -(z))
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#endif
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/* Exact multiplication of two single-length floating point numbers, */
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/* Veltkamp. The macro produces a double-length number (z,zz) that */
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/* satisfies z+zz = x*y exactly. p,hx,tx,hy,ty are temporary */
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/* storage variables of type double. */
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#ifdef DLA_FMS
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# define EMULV(x, y, z, zz) \
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z = x * y; zz = DLA_FMS (x, y, z);
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#else
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# define EMULV(x, y, z, zz) \
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({ __typeof__ (x) __p, hx, tx, hy, ty; \
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__p = CN * (x); hx = ((x) - __p) + __p; tx = (x) - hx; \
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__p = CN * (y); hy = ((y) - __p) + __p; ty = (y) - hy; \
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z = (x) * (y); zz = (((hx * hy - z) + hx * ty) + tx * hy) + tx * ty; \
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})
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#endif
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/* Exact multiplication of two single-length floating point numbers, Dekker. */
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/* The macro produces a nearly double-length number (z,zz) (see Dekker) */
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/* that satisfies z+zz = x*y exactly. p,hx,tx,hy,ty,q are temporary */
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/* storage variables of type double. */
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#ifdef DLA_FMS
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# define MUL12(x, y, z, zz) \
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EMULV(x, y, z, zz)
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#else
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# define MUL12(x, y, z, zz) \
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({ __typeof__ (x) __p, hx, tx, hy, ty, __q; \
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__p=CN*(x); hx=((x)-__p)+__p; tx=(x)-hx; \
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__p=CN*(y); hy=((y)-__p)+__p; ty=(y)-hy; \
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__p=hx*hy; __q=hx*ty+tx*hy; z=__p+__q; zz=((__p-z)+__q)+tx*ty; \
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})
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#endif
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/* Double-length addition, Dekker. The macro produces a double-length */
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/* number (z,zz) which satisfies approximately z+zz = x+xx + y+yy. */
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/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy) */
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/* are assumed to be double-length numbers. r,s are temporary */
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/* storage variables of type double. */
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#define ADD2(x, xx, y, yy, z, zz, r, s) \
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r = (x) + (y); s = (fabs (x) > fabs (y)) ? \
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(((((x) - r) + (y)) + (yy)) + (xx)) : \
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(((((y) - r) + (x)) + (xx)) + (yy)); \
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z = r + s; zz = (r - z) + s;
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/* Double-length subtraction, Dekker. The macro produces a double-length */
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/* number (z,zz) which satisfies approximately z+zz = x+xx - (y+yy). */
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/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy) */
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/* are assumed to be double-length numbers. r,s are temporary */
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/* storage variables of type double. */
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#define SUB2(x, xx, y, yy, z, zz, r, s) \
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r = (x) - (y); s = (fabs (x) > fabs (y)) ? \
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(((((x) - r) - (y)) - (yy)) + (xx)) : \
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((((x) - ((y) + r)) + (xx)) - (yy)); \
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z = r + s; zz = (r - z) + s;
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/* Double-length multiplication, Dekker. The macro produces a double-length */
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/* number (z,zz) which satisfies approximately z+zz = (x+xx)*(y+yy). */
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/* An error bound: abs((x+xx)*(y+yy))*1.24e-31. (x,xx), (y,yy) */
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/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc are */
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/* temporary storage variables of type double. */
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#define MUL2(x, xx, y, yy, z, zz, c, cc) \
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MUL12 (x, y, c, cc); \
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cc = ((x) * (yy) + (xx) * (y)) + cc; z = c + cc; zz = (c - z) + cc;
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/* Double-length division, Dekker. The macro produces a double-length */
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/* number (z,zz) which satisfies approximately z+zz = (x+xx)/(y+yy). */
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/* An error bound: abs((x+xx)/(y+yy))*1.50e-31. (x,xx), (y,yy) */
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/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc,u,uu */
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/* are temporary storage variables of type double. */
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#define DIV2(x, xx, y, yy, z, zz, c, cc, u, uu) \
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c=(x)/(y); MUL12(c,y,u,uu); \
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cc=(((((x)-u)-uu)+(xx))-c*(yy))/(y); z=c+cc; zz=(c-z)+cc;
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/* Double-length addition, slower but more accurate than ADD2. */
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/* The macro produces a double-length */
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/* number (z,zz) which satisfies approximately z+zz = (x+xx)+(y+yy). */
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/* An error bound: abs(x+xx + y+yy)*1.50e-31. (x,xx), (y,yy) */
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/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */
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/* are temporary storage variables of type double. */
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#define ADD2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w) \
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r = (x) + (y); \
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if (fabs (x) > fabs (y)) { rr = ((x) - r) + (y); s = (rr + (yy)) + (xx); } \
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else { rr = ((y) - r) + (x); s = (rr + (xx)) + (yy); } \
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if (rr != 0.0) { \
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z = r + s; zz = (r - z) + s; } \
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else { \
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ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) + (yy)) : (((yy) - s) + (xx));\
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u = r + s; \
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uu = (fabs (r) > fabs (s)) ? ((r - u) + s) : ((s - u) + r); \
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w = uu + ss; z = u + w; \
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zz = (fabs (u) > fabs (w)) ? ((u - z) + w) : ((w - z) + u); }
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/* Double-length subtraction, slower but more accurate than SUB2. */
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/* The macro produces a double-length */
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/* number (z,zz) which satisfies approximately z+zz = (x+xx)-(y+yy). */
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/* An error bound: abs(x+xx - (y+yy))*1.50e-31. (x,xx), (y,yy) */
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/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */
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/* are temporary storage variables of type double. */
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#define SUB2A(x, xx, y, yy, z, zz, r, rr, s, ss, u, uu, w) \
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r = (x) - (y); \
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if (fabs (x) > fabs (y)) { rr = ((x) - r) - (y); s = (rr - (yy)) + (xx); } \
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else { rr = (x) - ((y) + r); s = (rr + (xx)) - (yy); } \
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if (rr != 0.0) { \
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z = r + s; zz = (r - z) + s; } \
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else { \
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ss = (fabs (xx) > fabs (yy)) ? (((xx) - s) - (yy)) : ((xx) - ((yy) + s)); \
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u = r + s; \
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uu = (fabs (r) > fabs (s)) ? ((r - u) + s) : ((s - u) + r); \
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w = uu + ss; z = u + w; \
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zz = (fabs (u) > fabs (w)) ? ((u - z) + w) : ((w - z) + u); }
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