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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