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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
+