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-
-	  *********************************
- 	  * Announcing FDLIBM Version 5.3 *
-	  *********************************
-============================================================
-			FDLIBM
-============================================================
-	developed at Sun Microsystems, Inc. 
-
-What's new in FDLIBM 5.3?
-
-CONFIGURE
-	To build FDLIBM, edit the supplied Makefile or create
-	a local Makefile by running "sh configure" 
-	using the supplied configure script contributed by Nelson Beebe
-
-BUGS FIXED
-
-    1. e_pow.c incorrect results when 
-	x is very close to -1.0 and y is very large, e.g.
-  	pow(-1.0000000000000002e+00,4.5035996273704970e+15) = 0
-  	pow(-9.9999999999999978e-01,4.5035996273704970e+15) = 0
-	Correct results are close to -e and -1/e.
-
-    2. k_tan.c error was > 1 ulp target for FDLIBM
-	5.2: Worst error at least 1.45 ulp at
-	tan(1.7765241907548024E+269) = 1.7733884462610958E+16
-	5.3: Worst error 0.96 ulp
-
-NOT FIXED YET
-
-    3. Compiler failure on non-standard code
-	Statements like
-	            *(1+(int*)&t1) = 0;
-	are not standard C and cause some optimizing compilers (e.g. GCC)
-	to generate bad code under optimization.    These cases
-	are to be addressed in the next release.
-	
-FDLIBM (Freely Distributable LIBM) is a C math library 
-for machines that support IEEE 754 floating-point arithmetic. 
-In this release, only double precision is supported.
-
-FDLIBM is intended to provide a reasonably portable (see 
-assumptions below), reference quality (below one ulp for
-major functions like sin,cos,exp,log) math library 
-(libm.a).  For a copy of FDLIBM, please see
-	http://www.netlib.org/fdlibm/
-or
-	http://www.validlab.com/software/
-
---------------
-1. ASSUMPTIONS
---------------
-FDLIBM (double precision version) assumes:
- a.  IEEE 754 style (if not precise compliance) arithmetic;
- b.  32 bit 2's complement integer arithmetic;
- c.  Each double precision floating-point number must be in IEEE 754 
-     double format, and that each number can be retrieved as two 32-bit 
-     integers through the using of pointer bashing as in the example 
-     below:
-
-     Example: let y = 2.0
-	double fp number y: 	2.0
-	IEEE double format:	0x4000000000000000
-
-	Referencing y as two integers:
-	*(int*)&y,*(1+(int*)&y) =	{0x40000000,0x0} (on sparc)
-					{0x0,0x40000000} (on 386)
-
-	Note: Four macros are defined in fdlibm.h to handle this kind of
-	retrieving:
-
-	__HI(x)		the high part of a double x 
-			(sign,exponent,the first 21 significant bits)
-	__LO(x)		the least 32 significant bits of x
-	__HIp(x)	same as __HI except that the argument is a pointer
-			to a double
-	__LOp(x)	same as __LO except that the argument is a pointer
-			to a double
-	
-	To ensure obtaining correct ordering, one must define  __LITTLE_ENDIAN
-	during compilation for little endian machine (like 386,486). The 
-	default is big endian.
-
-	If the behavior of pointer bashing is undefined, one may hack on the 
-	macro in fdlibm.h.
-	
-  d. IEEE exceptions may trigger "signals" as is common in Unix
-     implementations. 
-
--------------------
-2. EXCEPTION CASES
--------------------
-All exception cases in the FDLIBM functions will be mapped
-to one of the following four exceptions:
-
-   +-huge*huge, +-tiny*tiny,    +-1.0/0.0,	+-0.0/0.0
-    (overflow)	(underflow)  (divided-by-zero) 	(invalid)
-
-For example, ieee_log(0) is a singularity and is thus mapped to 
-	-1.0/0.0 = -infinity.
-That is, FDLIBM's log will compute -one/zero and return the
-computed value.  On an IEEE machine, this will trigger the 
-divided-by-zero exception and a negative infinity is returned by 
-default.
-
-Similarly, ieee_exp(-huge) will be mapped to tiny*tiny to generate
-an underflow signal. 
-
-
---------------------------------
-3. STANDARD CONFORMANCE WRAPPER 
---------------------------------
-The default FDLIBM functions (compiled with -D_IEEE_LIBM flag)  
-are in "IEEE spirit" (i.e., return the most reasonable result in 
-floating-point arithmetic). If one wants FDLIBM to comply with
-standards like SVID, X/OPEN, or POSIX/ANSI, then one can 
-create a multi-standard compliant FDLIBM. In this case, each
-function in FDLIBM is actually a standard compliant wrapper
-function.  
-
-File organization:
-    1. For FDLIBM's kernel (internal) function,
-		File name	Entry point
-		---------------------------
-		k_sin.c		__kernel_sin
-		k_tan.c		__kernel_tan
-		---------------------------
-    2. For functions that have no standards conflict 
-		File name	Entry point
-		---------------------------
-		s_sin.c		sin
-		s_erf.c		erf
-		---------------------------
-    3. Ieee754 core functions
-		File name	Entry point
-		---------------------------
-		e_exp.c		__ieee754_exp
-		e_sinh.c	__ieee754_sinh
-		---------------------------
-    4. Wrapper functions
-		File name	Entry point
-		---------------------------
-		w_exp.c		exp
-		w_sinh.c	sinh
-		---------------------------
-
-Wrapper functions will twist the result of the ieee754 
-function to comply to the standard specified by the value 
-of _LIB_VERSION 
-    if _LIB_VERSION = _IEEE_, return the ieee754 result;
-    if _LIB_VERSION = _SVID_, return SVID result;
-    if _LIB_VERSION = _XOPEN_, return XOPEN result;
-    if _LIB_VERSION = _POSIX_, return POSIX/ANSI result.
-(These are macros, see fdlibm.h for their definition.)
-
-
---------------------------------
-4. HOW TO CREATE FDLIBM's libm.a
---------------------------------
-There are two types of libm.a. One is IEEE only, and the other is
-multi-standard compliant (supports IEEE,XOPEN,POSIX/ANSI,SVID).
-
-To create the IEEE only libm.a, use 
-	    make "CFLAGS = -D_IEEE_LIBM"	 
-This will create an IEEE libm.a, which is smaller in size, and 
-somewhat faster.
-
-To create a multi-standard compliant libm, use
-    make "CFLAGS = -D_IEEE_MODE"   --- multi-standard fdlibm: default
-					 to IEEE
-    make "CFLAGS = -D_XOPEN_MODE"  --- multi-standard fdlibm: default
-					 to X/OPEN
-    make "CFLAGS = -D_POSIX_MODE"  --- multi-standard fdlibm: default
-					 to POSIX/ANSI
-    make "CFLAGS = -D_SVID3_MODE"  --- multi-standard fdlibm: default
-					 to SVID
-
-
-Here is how one makes a SVID compliant libm.
-    Make the library by
-		make "CFLAGS = -D_SVID3_MODE".
-    The libm.a of FDLIBM will be multi-standard compliant and 
-    _LIB_VERSION is initialized to the value _SVID_ . 
-
-    example1:
-    ---------
-	    main()
-	    {
-		double ieee_y0();
-		printf("y0(1e300) = %1.20e\n",y0(1e300));
-		exit(0);
-	    }
-
-    % cc example1.c libm.a
-    % a.out
-    y0: TLOSS error
-    ieee_y0(1e300) = 0.00000000000000000000e+00
-
-
-It is possible to change the default standard in multi-standard 
-fdlibm. Here is an example of how to do it:
-    example2:
-    ---------
-	#include "fdlibm.h"	/* must include FDLIBM's fdlibm.h */
-	main()
-	{
-		double ieee_y0();
-		_LIB_VERSION =  _IEEE_;
-		printf("IEEE: ieee_y0(1e300) = %1.20e\n",y0(1e300));
-		_LIB_VERSION = _XOPEN_;
-		printf("XOPEN ieee_y0(1e300) = %1.20e\n",y0(1e300));
-		_LIB_VERSION = _POSIX_;
-		printf("POSIX ieee_y0(1e300) = %1.20e\n",y0(1e300));
-		_LIB_VERSION = _SVID_;
-		printf("SVID  ieee_y0(1e300) = %1.20e\n",y0(1e300));
-		exit(0);
-	}
-
-    % cc example2.c libm.a
-    % a.out
-      IEEE: ieee_y0(1e300) = -1.36813604503424810557e-151
-      XOPEN ieee_y0(1e300) = 0.00000000000000000000e+00
-      POSIX ieee_y0(1e300) = 0.00000000000000000000e+00
-      y0: TLOSS error
-      SVID  ieee_y0(1e300) = 0.00000000000000000000e+00
-
-Note:	Here _LIB_VERSION is a global variable. If global variables 
-	are forbidden, then one should modify fdlibm.h to change
-	_LIB_VERSION to be a global constant. In this case, one
-	may not change the value of _LIB_VERSION as in example2.
-
----------------------------
-5. NOTES ON PORTING FDLIBM
----------------------------
-	Care must be taken when installing FDLIBM over existing
-	libm.a.
-	All co-existing function prototypes must agree, otherwise
-	users will encounter mysterious failures.
-
-	So far, the only known likely conflict is the declaration 
-	of the IEEE recommended function scalb:
-
-		double ieee_scalb(double,double)	(1)	SVID3 defined
-		double ieee_scalb(double,int)	(2)	IBM,DEC,...
-
-	FDLIBM follows Sun definition and use (1) as default. 
-	If one's existing libm.a uses (2), then one may raise
-	the flags _SCALB_INT during the compilation of FDLIBM
-	to get the correct function prototype.
-	(E.g., make "CFLAGS = -D_IEEE_LIBM -D_SCALB_INT".)
-	NOTE that if -D_SCALB_INT is raised, it won't be SVID3
-	conformant.
-
---------------
-6. PROBLEMS ?
---------------
-Please send comments and bug reports to the electronic mail address
-suggested by: 
-		fdlibm-comments AT sun.com
-