Index of /source/vmd/1.7.0/src/lib/libm/
============================================================
FDLIBM
============================================================
(developed at SunPro, a Sun Microsystems, Inc. business.)
Version 5.1, 93/09/24
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 send
e-mail to
fdlibm-comments@sunpro.eng.sun.com
--------------
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;
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: FDLIBM will detect, at run time, the correct ordering of
the high and low part of a floating-point number.
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, 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, 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 y0();
printf("y0(1e300) = %1.20e\n",y0(1e300));
exit(0);
}
% cc example1.c libm.a
% a.out
y0: TLOSS error
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 y0();
_LIB_VERSION = _IEEE_;
printf("IEEE: y0(1e300) = %1.20e\n",y0(1e300));
_LIB_VERSION = _XOPEN_;
printf("XOPEN y0(1e300) = %1.20e\n",y0(1e300));
_LIB_VERSION = _POSIX_;
printf("POSIX y0(1e300) = %1.20e\n",y0(1e300));
_LIB_VERSION = _SVID_;
printf("SVID y0(1e300) = %1.20e\n",y0(1e300));
exit(0);
}
% cc example2.c libm.a
% a.out
IEEE: y0(1e300) = -1.36813604503424810557e-151
XOPEN y0(1e300) = 0.00000000000000000000e+00
POSIX y0(1e300) = 0.00000000000000000000e+00
y0: TLOSS error
SVID 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 scalb(double,double) (1) SVID3 defined
double 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 report to:
fdlibm-comments@sunpro.eng.sun.com
$PchId: README,v 1.2 1996/02/22 19:14:10 philip Exp $
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