diff -drNu src.orig/c9x-complex/cgamma.c src/c9x-complex/cgamma.c
--- src.orig/c9x-complex/cgamma.c 2010-04-06 11:46:28.000000000 +0200
+++ src/c9x-complex/cgamma.c 2013-01-08 15:07:41.335642544 +0100
@@ -258,7 +258,7 @@
w = clgam(1.0 - x);
c = LOGPI - clog( u ) - w;
/* Adjust for reduced sine arg. */
- cimag(c) += PI * p;
+ (double)(__imag__ c = (cimag(c) + PI * p));
}
goto ldone;
}
diff -drNu src.orig/c9x-complex/cgammaf.c src/c9x-complex/cgammaf.c
--- src.orig/c9x-complex/cgammaf.c 2010-04-06 11:46:28.000000000 +0200
+++ src/c9x-complex/cgammaf.c 2013-01-08 15:07:41.343641844 +0100
@@ -80,7 +80,7 @@
Copyright 1984, 1998 Stephen L. Moshier
*/
-#include <complex.h>
+#include "complex.h"
#include "mconf.h"
#define MAXGAM 171.624376956302725
@@ -101,8 +101,14 @@
static float SQTPI = 2.50662827463100050242f;
extern float MAXLOGF, MAXNUMF, PIF;
-#ifndef ANSIPROT
+#ifdef ANSIPROT
+extern float sinhf ( float x );
+extern float coshf ( float x );
+extern float sinf ( float x );
+extern float cosf ( float x );
+#else
float logf(), sinf(), polevlf(), p1evlf(), floorf(), fabsf();
+float cosf(), sinhf(), coshf();
float complex cpowf(), cexpf(), cabsf();
#endif
@@ -145,6 +151,7 @@
{
float p, q;
float complex c, u;
+int k;
if( fabsf(crealf(x)) > 13.0f )
{
@@ -152,14 +159,25 @@
{
q = crealf(x);
p = floorf(q);
- if( p == q )
+ if((p == q ) && (cimag(x) == 0.0f))
{
cgoverf:
mtherr( "cgammaf", OVERFLOW );
return( MAXNUMF + I * MAXNUMF);
}
- c = csinf( PIF * (x - p) );
- c = PIF/(c * cgammaf(1.0f - x) );
+ /* Compute sin(pi x) */
+ k = q - 2.0f * floorf (0.5f * q);
+ q = PIF * (q - p);
+ p = PIF * cimag(x);
+ c = sinf(q) * coshf(p) + cosf(q) * sinhf(p) * I;
+ if (k & 1)
+ c = -c;
+ /* Reflection formula.
+ ??? The denominator has been observed to overflow,
+ producing a NaN result on a SPARCstation instead of zero.
+ Example:
+ cgammaf(-19.425196335160404f - 18.188121066880587f*I) */
+ c = PIF/(c * cgammaf(1.0f - x));
}
else
{
@@ -173,8 +191,8 @@
u = x;
while( crealf(u) < 13.0f )
{
- if (crealf(u) == 0.0f)
- goto cgoverf;
+ if ((crealf(u) == 0.0f) && (cimagf(u) == 0.0f))
+ goto cgoverf;
c *= u;
p += 1.0f;
u = x + p;
@@ -223,7 +241,7 @@
}
/* Reflection formula -z gamma(-z) gamma(z) = pi / sin(pi z) */
-if( crealf(x) < -7.0f )
+if((crealf(x) < -7.0f) || (cimagf(x) < -7.0f))
{
q = crealf(x);
p = floorf(q);
@@ -247,7 +265,8 @@
w = clgamf(1.0f - x);
c = LOGPI - clogf( u ) - w;
/* Adjust for reduced sine arg. */
- cimagf(c) += PIF * p;
+ //cimagf(c) += PIF * p;
+ (float)(__imag__ c = (cimagf(c) + PIF * p));
}
goto ldone;
}
diff -drNu src.orig/c9x-complex/cgammal.c src/c9x-complex/cgammal.c
--- src.orig/c9x-complex/cgammal.c 2010-04-06 11:46:28.000000000 +0200
+++ src/c9x-complex/cgammal.c 2013-01-08 15:07:41.351641311 +0100
@@ -134,8 +134,14 @@
static long double SQTPIL = 2.50662827463100050241576528481104525L;
extern long double MAXLOGL, MAXNUML, PIL;
-#ifndef ANSIPROT
+#ifdef ANSIPROT
+extern long double sinhl ( long double x );
+extern long double coshl ( long double x );
+extern long double sinl ( long double x );
+extern long double cosl ( long double x );
+#else
long double logl(), sinl(), polevll(), p1evll(), floorl(), fabsl();
+long double sinhl(), coshl(), cosl();
long double complex cpowl(), cexpl(), cabsl();
#endif
@@ -174,7 +180,7 @@
{
long double complex c, u;
long double p, q;
-int cj;
+int cj, k;
cj = 0;
if (cimagl(x) < 0.0L)
@@ -183,34 +189,41 @@
x = conj(x);
}
-q = creall(x);
-if( fabsl(q) > NGITER )
+if( fabsl(creall(x)) > NGITER )
{
- if( q < 0.0L )
+ if( creall(x) < 0.0L )
{
+ q = creall(x);
p = floorl(q);
- if( p == q )
+ if(( p == q ) && (cimagl(x) == 0.0L))
{
mtherr( "cgammal", OVERFLOW );
c = MAXNUML + I * MAXNUML;
goto gamdone;
}
- c = csinl( PIL * (x - p) );
+ /* c = csinl( PIL * x );*/
+ /* Compute sin(pi x) */
+ k = q - 2.0L * floorl (0.5L * q);
+ q = PIL * (q - p);
+ p = PIL * cimagl(x);
+ c = sinl(q) * coshl(p) + cosl(q) * sinhl(p) * I;
+ if (k & 1)
+ c = -c;
c = PIL/(c * cgammal(1.0L - x) );
+ goto gamdone;
}
else
{
- c = cstirfl(x);
+ c = cstirfl(x);
+ goto gamdone;
}
- goto gamdone;
}
-
c = 1.0L;
p = 0.0L;
u = x;
while( creall(u) < NGITER )
{
- if( fabsl (creall(u)) < GSMALL )
+ if((fabsl (creall(u)) < GSMALL) && (fabsl (cimagl(u)) < GSMALL))
goto small;
c *= u;
p += 1.0L;
@@ -222,7 +235,7 @@
small:
-if( creall(x) == 0.0L )
+if((creall(x) == 0.0L) && (cimagl(x) == 0.0L))
{
mtherr( "cgammal", SING );
c = MAXNUML + MAXNUML * I;
@@ -280,7 +293,7 @@
/* -z gamma(-z) gamma(z) = pi / sin(pi z) */
/* log gamma(z) = log pi - log sin(pi z) - log(-z) - log gamma(-z) */
-if( creall(x) < -NLGITER )
+if((creall(x) < -NLGITER) || (cimagl(x) < -NLGITER))
{
q = creall(x);
p = floorl(q);
@@ -304,7 +317,8 @@
w = clgaml(1.0L - x);
c = LOGPIL - clogl( u ) - w;
/* Adjust for reduced sine arg. */
- cimagl(c) += PIL * p;
+ //cimagl(c) += PIL * p;
+ (long double)(__imag__ c = cimagl(c) + PIL * p);
}
goto ldone;
}
diff -drNu src.orig/c9x-complex/complex.h src/c9x-complex/complex.h
--- src.orig/c9x-complex/complex.h 2000-02-06 02:39:53.000000000 +0100
+++ src/c9x-complex/complex.h 2013-01-08 15:07:41.359640920 +0100
@@ -1,126 +1,131 @@
-/* This is a C9X complex.h implementation for the GNU C compiler.
- It uses GNU extensions such as __complex__, but defines them
- so the syntax specified by C9X works.
+/*
+** Replacement <complex.h> merging host version with cephes functions
+*/
- S. L. Moshier
- February, 1997 */
+/* Start by using host complex file.
+ * This has to come before the following protective #ifdef so that
+ * #include "complex.h" is correctly handled. */
+#include_next <complex.h>
+#ifndef __CEPHES_COMPLEX_H
+#define __CEPHES_COMPLEX_H
-/* This may look like something else, but it is really C9X. */
+#if defined(__cplusplus)
+extern "C" {
+#endif
-/* Use `I' as the imaginary unit.
- Initialize complex constants like this:
- double complex c = 1.0 + 2.0 * I; */
-#define _Imaginary_I (1.0fi)
-#define I _Imaginary_I
+/* The following content is derived from
+ * http://www.opengroup.org/onlinepubs/9699919799/basedefs/complex.h.html
+ */
+extern double (cabs)(double complex);
+extern float (cabsf)(float complex);
+extern long double (cabsl)(long double complex);
+extern double complex (cacos)(double complex);
+extern float complex (cacosf)(float complex);
+extern double complex (cacosh)(double complex);
+extern float complex (cacoshf)(float complex);
+extern long double complex (cacoshl)(long double complex);
+extern long double complex (cacosl)(long double complex);
+extern double complex (cadd)(double complex a, double complex b); /*ceph*/
+extern double (carg)(double complex);
+extern float (cargf)(float complex);
+extern long double (cargl)(long double complex);
+extern double complex (casin)(double complex);
+extern float complex (casinf)(float complex);
+extern double complex (casinh)(double complex);
+extern float complex (casinhf)(float complex);
+extern long double complex (casinhl)(long double complex);
+extern long double complex (casinl)(long double complex);
+extern double complex (catan)(double complex);
+extern float complex (catanf)(float complex);
+extern double complex (catanh)(double complex);
+extern float complex (catanhf)(float complex);
+extern long double complex (catanhl)(long double complex);
+extern long double complex (catanl)(long double complex);
+extern double complex (ccos)(double complex);
+extern float complex (ccosf)(float complex);
+extern double complex (ccosh)(double complex);
+extern float complex (ccoshf)(float complex);
+extern long double complex (ccoshl)(long double complex);
+extern long double complex (ccosl)(long double complex);
+extern double complex (ccot)(double complex z); /*ceph*/
+extern float complex (ccotf)(float complex z); /*ceph*/
+extern long double complex (ccotl)(long double complex z); /*ceph*/
+extern double complex (cdiv)(double complex a, double complex b); /*ceph*/
+extern double complex (cexp)(double complex);
+extern float complex (cexpf)(float complex);
+extern long double complex (cexpl)(long double complex);
+extern double complex (cgamma)(double complex z); /*ceph*/
+extern float complex (cgammaf)(float complex z); /*ceph*/
+extern long double complex (cgammal)(long double complex z); /*ceph*/
+extern double (cimag)(double complex);
+extern float (cimagf)(float complex);
+extern long double (cimagl)(long double complex);
+extern double complex (clgam)(double complex z); /*ceph*/
+extern float complex (clgamf)(float complex z); /*ceph*/
+extern long double complex (clgaml)(long double complex z); /*ceph*/
+extern double complex (clog)(double complex);
+extern float complex (clogf)(float complex);
+extern long double complex (clogl)(long double complex);
+extern double complex (cmul)(double complex a, double complex b); /*ceph*/
+extern double complex (conj)(double complex);
+extern float complex (conjf)(float complex);
+extern long double complex (conjl)(long double complex);
+extern double complex (cpow)(double complex, double complex);
+extern float complex (cpowf)(float complex, float complex);
+extern long double complex (cpowl)(long double complex, long double complex);
+extern double complex (cproj)(double complex);
+extern float complex (cprojf)(float complex);
+extern long double complex (cprojl)(long double complex);
+extern double (creal)(double complex);
+extern float (crealf)(float complex);
+extern long double (creall)(long double complex);
+extern double complex (csin)(double complex);
+extern float complex (csinf)(float complex);
+extern double complex (csinh)(double complex);
+extern float complex (csinhf)(float complex);
+extern long double complex (csinhl)(long double complex);
+extern long double complex (csinl)(long double complex);
+extern double complex (csqrt)(double complex);
+extern float complex (csqrtf)(float complex);
+extern long double complex (csqrtl)(long double complex);
+extern double complex (csub)(double complex a, double complex b); /*ceph*/
+extern double complex (ctan)(double complex);
+extern float complex (ctanf)(float complex);
+extern double complex (ctanh)(double complex);
+extern float complex (ctanhf)(float complex);
+extern long double complex (ctanhl)(long double complex);
+extern long double complex (ctanl)(long double complex);
+/* macro versions of some of the above functions, from the cephes complex.h */
/* These are not typed in gcc. They preseve the type of the argument. */
/* Complex conjugate function. */
#define conj(x) (~(x))
/* Function to get imaginary part. */
-#define cimag(x) (__imag__ (x))
+#define cimag(x) (__imag__(x))
/* Function to get real part. */
-#define creal(x) (__real__ (x))
+#define creal(x) (__real__(x))
-extern double atan2 (double, double);
-#define carg(z) (atan2 ((double) cimag (z), (double) creal (z)))
+extern double (atan2)(double, double);
+#define carg(z) (atan2((double)cimag(z), (double)creal(z)))
-/* This is the new C language key word.
- ... Actually, the key word that the compiler is supposed to reserve
- and understand as part of the language is spelled "_Complex" but
- gcc understands "__complex__." The macro "complex" is supposed to
- exist and expand to _Complex in complex.h. But "_Complex" will seldom
- if ever appear in user programs. */
-#define complex __complex__
-/* Remove this whenever gcc implements _Complex as a key word. */
-#define _Complex __complex__
+/* There are float and long double sizes, too. */
+#define cimagf(x) ((float)__imag__(x))
+#define crealf(x) ((float)__real__(x))
+extern float (atan2f)(float, float);
+#define cargf(z) (atan2f((float)cimag(z), (float)creal(z)))
+
+#define cimagl(x) ((long double)__imag__(x))
+#define creall(x) ((long double)__real__(x))
+extern long double (atan2l)(long double, long double);
+#define cargl(z) (atan2l((long double)cimag(z), (long double)creal(z)))
/* These pragmas can't work without a compiler modification. */
#define CX_LIMITED_RANGE_ON
#define CX_LIMITED_RANGE_OFF
#define CX_LIMITED_RANGE_DEFAULT CX_LIMITED_RANGE_ON
-/* The builtin complex absolute value in gcc currently is unreachable
- due to overzealous type checking. */
-extern double cabs ( double complex z );
-extern double hypot ( double x, double y );
-
-/* Prototypes for clog.c.
- This is how you declare complex things in the new C language. */
-extern double complex clog ( double complex z );
-extern double complex cexp ( double complex z );
-extern double complex csqrt ( double complex z );
-extern double complex csin ( double complex z );
-extern double complex ccos ( double complex z );
-extern double complex ctan ( double complex z );
-extern double complex ccot ( double complex z );
-extern double complex casin ( double complex z );
-extern double complex cacos ( double complex z );
-extern double complex catan ( double complex z );
-extern double complex csinh ( double complex z );
-extern double complex casinh ( double complex z );
-extern double complex ccosh ( double complex z );
-extern double complex cacosh ( double complex z );
-extern double complex ctanh ( double complex z );
-extern double complex catanh ( double complex z );
-extern double complex cpow (double complex a, double complex z);
-
-/* These functions might be used if the compiler were to generate
- subroutine calls. But their names would be spelled some other way. */
-extern double complex cadd ( double complex a, double complex b );
-extern double complex csub ( double complex a, double complex b );
-extern double complex cmul ( double complex a, double complex b );
-extern double complex cdiv ( double complex a, double complex b );
-
-/* There are float and long double sizes, too. */
-#define cimagf(x) ((float) __imag__ (x))
-#define crealf(x) ((float) __real__ (x))
-extern float atan2f (float, float);
-#define cargf(z) (atan2f ((float) cimag (z), (float) creal (z)))
-extern float cabsf ( float complex z );
-extern float complex clogf ( float complex z );
-extern float complex cexpf ( float complex z );
-extern float complex csqrtf ( float complex z );
-extern float complex csinf ( float complex z );
-extern float complex ccosf ( float complex z );
-extern float complex ctanf ( float complex z );
-extern float complex ccotf ( float complex z );
-extern float complex casinf ( float complex z );
-extern float complex cacosf ( float complex z );
-extern float complex catanf ( float complex z );
-extern float complex csinhf ( float complex z );
-extern float complex casinhf ( float complex z );
-extern float complex ccoshf ( float complex z );
-extern float complex cacoshf ( float complex z );
-extern float complex ctanhf ( float complex z );
-extern float complex catanhf ( float complex z );
-extern float complex cpowf (float complex a, float complex z);
-
-#define cimagl(x) ((long double) __imag__ (x))
-#define creall(x) ((long double) __real__ (x))
-extern long double atan2l (long double, long double);
-#define cargl(z) (atan2l ((long double) cimag (z), (long double) creal (z)))
-extern long double cabsl ( long double complex z );
-extern long double complex clogl ( long double complex z );
-extern long double complex cexpl ( long double complex z );
-extern long double complex csqrtl ( long double complex z );
-extern long double complex csinl ( long double complex z );
-extern long double complex ccosl ( long double complex z );
-extern long double complex ctanl ( long double complex z );
-extern long double complex ccotl ( long double complex z );
-extern long double complex casinl ( long double complex z );
-extern long double complex cacosl ( long double complex z );
-extern long double complex catanl ( long double complex z );
-extern long double complex csinhl ( long double complex z );
-extern long double complex casinhl ( long double complex z );
-extern long double complex ccoshl ( long double complex z );
-extern long double complex cacoshl ( long double complex z );
-extern long double complex ctanhl ( long double complex z );
-extern long double complex catanhl ( long double complex z );
-extern long double complex cpowl (long double complex a, long double complex z);
-extern float complex clgamf ( float complex z );
-extern double complex clgam ( double complex z );
-extern long double complex clgaml ( long double complex z );
-extern float complex cgammaf ( float complex z );
-extern double complex cgamma ( double complex z );
-extern long double complex cgammal ( long double complex z );
+#if defined(__cplusplus)
+}
+#endif
+#endif
diff -drNu src.orig/c9x-complex/makefile src/c9x-complex/makefile
--- src.orig/c9x-complex/makefile 2010-04-06 11:46:28.000000000 +0200
+++ src/c9x-complex/makefile 2013-01-08 15:07:41.367640529 +0100
@@ -1,17 +1,25 @@
# Makefile for C9X complex variables library
# Edit endian-ness and computer type properly in mconf.h before compiling.
+# For additional test programs see also celefunt.mak.
-#CC = gcc
-CC=/b/gnu/linux/gcc/xgcc -B/b/gnu/linux/gcc/ -I/b/gnu/linux/include
+# Caution: the tests contain some references to the cephes math library
+# or references to standard float or long double functions that might
+# not be available.
+# This should be enough to run at least the double precision functions:
+LIBS = stubs.o -lm
+# These are intended to get the cephes libraries:
+#LIBS = -lml -lmd -lmf
+#LIBS = ../libml.a ../libmd.a ../libmf.a
+
+CC = gcc
+#CC = /b/gnu/gcc-build/gcc/xgcc -B/b/gnu/gcc-build/gcc/ -I/b/gnu/gcc-build/gcc
# For 128-bit wide long double
#PRECFLAGS = -DLD128BITS
PRECFLAGS =
-CFLAGS = $(PRECFLAGS) -g -O2 -Wall
-# This should be enough to run at least the double precision functions
-#LIBS = stubs.o -lm
-# These are intended to get the cephes libraries
-LIBS = -lml -lmd -lmf
-#LIBS = ../libml.a ../libmd.a ../libmf.a
+CFLAGS = $(PRECFLAGS) -I. -g -O2 -Wall
+#CFLAGS = $(PRECFLAGS) -I. -g -O1 -Wall
+#CFLAGS = $(PRECFLAGS) -I. -g -O0 -Wall
+
# float precision
SFILES = cmplxf.o clogf.o cgammaf.o
# double precision
@@ -22,7 +30,7 @@
LIBMCFILES = $(SFILES) $(DFILES) $(LFILES)
# mtstf and mtstl test the float and long double functions.
-all: libmc.a mtst cvect dccalc mtstf mtstl
+all: libmc.a mtst cvect dccalc mtstf whitebxf whitebx
mtst: mtst.o $(DFILES) stubs.o
$(CC) -v -o mtst mtst.o $(DFILES) $(LIBS)
@@ -36,8 +44,19 @@
cvect: cvect.o clog.o cmplx.o stubs.o
$(CC) -o cvect cvect.o clog.o cmplx.o $(LIBS)
-cvect-nans: cvect-nans.o clog-nans.o cmplx-nans.o
- $(CC) -o cvect-nans cvect-nans.o clog-nans.o cmplx-nans.o $(LIBS)
+#cvect-nans: cvect-nans.o clog-nans.o cmplx-nans.o
+# $(CC) -o cvect-nans cvect-nans.o clog-nans.o cmplx-nans.o $(LIBS)
+
+whitebxf: whitebxf.o libmc.a
+ $(CC) $(CFLAGS) -o whitebxf whitebxf.o libmc.a $(LIBS)
+
+whitebxf.o: whitebxf.c complex.h
+
+whitebx: whitebx.o libmc.a
+ $(CC) $(CFLAGS) -o whitebx whitebx.o libmc.a $(LIBS)
+
+whitebx.o: whitebx.c complex.h
+
libmc.a: $(LIBMCFILES)
rm -f libmc.a
@@ -66,11 +85,13 @@
#clog-nans.o: clog-nans.c complex.h protos.h
#cmplx-nans.o: cmplx-nans.c complex.h protos.h
-check: mtst cvect mtstf
- -mtstf
- -cvect
- -mtst
- -mtstl
+check: mtst cvect mtstf whitebxf whitebx
+ -./mtstf
+ -./cvect
+ -./mtst
+ -./whitebxf
+ -./whitebx
+ echo For additional tests, make -f celefunt.mak
clean:
rm -f *.o
@@ -93,11 +114,13 @@
rm -f tcsinf
rm -f tcsqrt
rm -f tcsqrtf
+ rm -f whitebxf
+ rm -f whitebx
-zip:
- rm -f c9x-complex.zip
- rm -f c9x-complex.shar
- rm -f c9x-complex.shar.gz
- zip c9x-complex.zip *.c *.h *.pat *.doc *.mak makefile read.me
- shar *.c *.h *.pat *.doc *.mak makefile read.me > c9x-complex.shar
- gzip c9x-complex.shar
+#zip:
+# rm -f c9x-complex.zip
+# rm -f c9x-complex.shar
+# rm -f c9x-complex.shar.gz
+# zip c9x-complex.zip *.c *.h *.pat *.doc *.mak makefile read.me
+# shar *.c *.h *.pat *.doc *.mak makefile read.me > c9x-complex.shar
+# gzip c9x-complex.shar
diff -drNu src.orig/complex.h src/complex.h
--- src.orig/complex.h 2000-02-06 02:39:53.000000000 +0100
+++ src/complex.h 2013-01-08 15:07:41.375640150 +0100
@@ -1,126 +1,131 @@
-/* This is a C9X complex.h implementation for the GNU C compiler.
- It uses GNU extensions such as __complex__, but defines them
- so the syntax specified by C9X works.
+/*
+** Replacement <complex.h> merging host version with cephes functions
+*/
- S. L. Moshier
- February, 1997 */
+/* Start by using host complex file.
+ * This has to come before the following protective #ifdef so that
+ * #include "complex.h" is correctly handled. */
+#include_next <complex.h>
+#ifndef __CEPHES_COMPLEX_H
+#define __CEPHES_COMPLEX_H
-/* This may look like something else, but it is really C9X. */
+#if defined(__cplusplus)
+extern "C" {
+#endif
-/* Use `I' as the imaginary unit.
- Initialize complex constants like this:
- double complex c = 1.0 + 2.0 * I; */
-#define _Imaginary_I (1.0fi)
-#define I _Imaginary_I
+/* The following content is derived from
+ * http://www.opengroup.org/onlinepubs/9699919799/basedefs/complex.h.html
+ */
+extern double (cabs)(double complex);
+extern float (cabsf)(float complex);
+extern long double (cabsl)(long double complex);
+extern double complex (cacos)(double complex);
+extern float complex (cacosf)(float complex);
+extern double complex (cacosh)(double complex);
+extern float complex (cacoshf)(float complex);
+extern long double complex (cacoshl)(long double complex);
+extern long double complex (cacosl)(long double complex);
+extern double complex (cadd)(double complex a, double complex b); /*ceph*/
+extern double (carg)(double complex);
+extern float (cargf)(float complex);
+extern long double (cargl)(long double complex);
+extern double complex (casin)(double complex);
+extern float complex (casinf)(float complex);
+extern double complex (casinh)(double complex);
+extern float complex (casinhf)(float complex);
+extern long double complex (casinhl)(long double complex);
+extern long double complex (casinl)(long double complex);
+extern double complex (catan)(double complex);
+extern float complex (catanf)(float complex);
+extern double complex (catanh)(double complex);
+extern float complex (catanhf)(float complex);
+extern long double complex (catanhl)(long double complex);
+extern long double complex (catanl)(long double complex);
+extern double complex (ccos)(double complex);
+extern float complex (ccosf)(float complex);
+extern double complex (ccosh)(double complex);
+extern float complex (ccoshf)(float complex);
+extern long double complex (ccoshl)(long double complex);
+extern long double complex (ccosl)(long double complex);
+extern double complex (ccot)(double complex z); /*ceph*/
+extern float complex (ccotf)(float complex z); /*ceph*/
+extern long double complex (ccotl)(long double complex z); /*ceph*/
+extern double complex (cdiv)(double complex a, double complex b); /*ceph*/
+extern double complex (cexp)(double complex);
+extern float complex (cexpf)(float complex);
+extern long double complex (cexpl)(long double complex);
+extern double complex (cgamma)(double complex z); /*ceph*/
+extern float complex (cgammaf)(float complex z); /*ceph*/
+extern long double complex (cgammal)(long double complex z); /*ceph*/
+extern double (cimag)(double complex);
+extern float (cimagf)(float complex);
+extern long double (cimagl)(long double complex);
+extern double complex (clgam)(double complex z); /*ceph*/
+extern float complex (clgamf)(float complex z); /*ceph*/
+extern long double complex (clgaml)(long double complex z); /*ceph*/
+extern double complex (clog)(double complex);
+extern float complex (clogf)(float complex);
+extern long double complex (clogl)(long double complex);
+extern double complex (cmul)(double complex a, double complex b); /*ceph*/
+extern double complex (conj)(double complex);
+extern float complex (conjf)(float complex);
+extern long double complex (conjl)(long double complex);
+extern double complex (cpow)(double complex, double complex);
+extern float complex (cpowf)(float complex, float complex);
+extern long double complex (cpowl)(long double complex, long double complex);
+extern double complex (cproj)(double complex);
+extern float complex (cprojf)(float complex);
+extern long double complex (cprojl)(long double complex);
+extern double (creal)(double complex);
+extern float (crealf)(float complex);
+extern long double (creall)(long double complex);
+extern double complex (csin)(double complex);
+extern float complex (csinf)(float complex);
+extern double complex (csinh)(double complex);
+extern float complex (csinhf)(float complex);
+extern long double complex (csinhl)(long double complex);
+extern long double complex (csinl)(long double complex);
+extern double complex (csqrt)(double complex);
+extern float complex (csqrtf)(float complex);
+extern long double complex (csqrtl)(long double complex);
+extern double complex (csub)(double complex a, double complex b); /*ceph*/
+extern double complex (ctan)(double complex);
+extern float complex (ctanf)(float complex);
+extern double complex (ctanh)(double complex);
+extern float complex (ctanhf)(float complex);
+extern long double complex (ctanhl)(long double complex);
+extern long double complex (ctanl)(long double complex);
+/* macro versions of some of the above functions, from the cephes complex.h */
/* These are not typed in gcc. They preseve the type of the argument. */
/* Complex conjugate function. */
#define conj(x) (~(x))
/* Function to get imaginary part. */
-#define cimag(x) (__imag__ (x))
+#define cimag(x) (__imag__(x))
/* Function to get real part. */
-#define creal(x) (__real__ (x))
+#define creal(x) (__real__(x))
-extern double atan2 (double, double);
-#define carg(z) (atan2 ((double) cimag (z), (double) creal (z)))
+extern double (atan2)(double, double);
+#define carg(z) (atan2((double)cimag(z), (double)creal(z)))
-/* This is the new C language key word.
- ... Actually, the key word that the compiler is supposed to reserve
- and understand as part of the language is spelled "_Complex" but
- gcc understands "__complex__." The macro "complex" is supposed to
- exist and expand to _Complex in complex.h. But "_Complex" will seldom
- if ever appear in user programs. */
-#define complex __complex__
-/* Remove this whenever gcc implements _Complex as a key word. */
-#define _Complex __complex__
+/* There are float and long double sizes, too. */
+#define cimagf(x) ((float)__imag__(x))
+#define crealf(x) ((float)__real__(x))
+extern float (atan2f)(float, float);
+#define cargf(z) (atan2f((float)cimag(z), (float)creal(z)))
+
+#define cimagl(x) ((long double)__imag__(x))
+#define creall(x) ((long double)__real__(x))
+extern long double (atan2l)(long double, long double);
+#define cargl(z) (atan2l((long double)cimag(z), (long double)creal(z)))
/* These pragmas can't work without a compiler modification. */
#define CX_LIMITED_RANGE_ON
#define CX_LIMITED_RANGE_OFF
#define CX_LIMITED_RANGE_DEFAULT CX_LIMITED_RANGE_ON
-/* The builtin complex absolute value in gcc currently is unreachable
- due to overzealous type checking. */
-extern double cabs ( double complex z );
-extern double hypot ( double x, double y );
-
-/* Prototypes for clog.c.
- This is how you declare complex things in the new C language. */
-extern double complex clog ( double complex z );
-extern double complex cexp ( double complex z );
-extern double complex csqrt ( double complex z );
-extern double complex csin ( double complex z );
-extern double complex ccos ( double complex z );
-extern double complex ctan ( double complex z );
-extern double complex ccot ( double complex z );
-extern double complex casin ( double complex z );
-extern double complex cacos ( double complex z );
-extern double complex catan ( double complex z );
-extern double complex csinh ( double complex z );
-extern double complex casinh ( double complex z );
-extern double complex ccosh ( double complex z );
-extern double complex cacosh ( double complex z );
-extern double complex ctanh ( double complex z );
-extern double complex catanh ( double complex z );
-extern double complex cpow (double complex a, double complex z);
-
-/* These functions might be used if the compiler were to generate
- subroutine calls. But their names would be spelled some other way. */
-extern double complex cadd ( double complex a, double complex b );
-extern double complex csub ( double complex a, double complex b );
-extern double complex cmul ( double complex a, double complex b );
-extern double complex cdiv ( double complex a, double complex b );
-
-/* There are float and long double sizes, too. */
-#define cimagf(x) ((float) __imag__ (x))
-#define crealf(x) ((float) __real__ (x))
-extern float atan2f (float, float);
-#define cargf(z) (atan2f ((float) cimag (z), (float) creal (z)))
-extern float cabsf ( float complex z );
-extern float complex clogf ( float complex z );
-extern float complex cexpf ( float complex z );
-extern float complex csqrtf ( float complex z );
-extern float complex csinf ( float complex z );
-extern float complex ccosf ( float complex z );
-extern float complex ctanf ( float complex z );
-extern float complex ccotf ( float complex z );
-extern float complex casinf ( float complex z );
-extern float complex cacosf ( float complex z );
-extern float complex catanf ( float complex z );
-extern float complex csinhf ( float complex z );
-extern float complex casinhf ( float complex z );
-extern float complex ccoshf ( float complex z );
-extern float complex cacoshf ( float complex z );
-extern float complex ctanhf ( float complex z );
-extern float complex catanhf ( float complex z );
-extern float complex cpowf (float complex a, float complex z);
-
-#define cimagl(x) ((long double) __imag__ (x))
-#define creall(x) ((long double) __real__ (x))
-extern long double atan2l (long double, long double);
-#define cargl(z) (atan2l ((long double) cimag (z), (long double) creal (z)))
-extern long double cabsl ( long double complex z );
-extern long double complex clogl ( long double complex z );
-extern long double complex cexpl ( long double complex z );
-extern long double complex csqrtl ( long double complex z );
-extern long double complex csinl ( long double complex z );
-extern long double complex ccosl ( long double complex z );
-extern long double complex ctanl ( long double complex z );
-extern long double complex ccotl ( long double complex z );
-extern long double complex casinl ( long double complex z );
-extern long double complex cacosl ( long double complex z );
-extern long double complex catanl ( long double complex z );
-extern long double complex csinhl ( long double complex z );
-extern long double complex casinhl ( long double complex z );
-extern long double complex ccoshl ( long double complex z );
-extern long double complex cacoshl ( long double complex z );
-extern long double complex ctanhl ( long double complex z );
-extern long double complex catanhl ( long double complex z );
-extern long double complex cpowl (long double complex a, long double complex z);
-extern float complex clgamf ( float complex z );
-extern double complex clgam ( double complex z );
-extern long double complex clgaml ( long double complex z );
-extern float complex cgammaf ( float complex z );
-extern double complex cgamma ( double complex z );
-extern long double complex cgammal ( long double complex z );
+#if defined(__cplusplus)
+}
+#endif
+#endif
diff -drNu src.orig/double/makefile src/double/makefile
--- src.orig/double/makefile 2010-04-06 11:46:28.000000000 +0200
+++ src/double/makefile 2013-01-08 15:07:41.383639902 +0100
@@ -22,7 +22,13 @@
tan.o tandg.o tanh.o unity.o yn.o zeta.o zetac.o \
sqrt.o floor.o setprec.o mtherr.o
-all: libmd.a mtst dtestvec monot dcalc paranoia # stamp-timing
+all: libmd.a mtst dtestvec monot dcalc # stamp-timing
+
+check: mtst dtestvec monot dcalc
+ ./mtst
+ ./dtestvec
+ ./monot
+ ./dcalc
stamp-timing: libmd.a mtst time-it
time-it "mtst > /dev/null"
@@ -86,14 +92,14 @@
# $(AS) -o setprec.o setprec.387
# ELF versions for linux (no underscores)
-sqrt.o: sqrtelf.387
- $(AS) -o sqrt.o sqrtelf.387
+#sqrt.o: sqrtelf.387
+# $(AS) -o sqrt.o sqrtelf.387
#floor.o: floorelf.387
# $(AS) -o floor.o floorelf.387
-setprec.o: setprelf.387
- $(AS) -o setprec.o setprelf.387
+#setprec.o: setprelf.387
+# $(AS) -o setprec.o setprelf.387
# Motorola 68881. Caution, subroutine return conventions vary.
#sqrt.o: sqrt.688
diff -drNu src.orig/ldouble/gammal.c src/ldouble/gammal.c
--- src.orig/ldouble/gammal.c 2000-05-28 17:21:01.000000000 +0200
+++ src/ldouble/gammal.c 2013-01-08 15:07:41.391639726 +0100
@@ -6,20 +6,16 @@
*
* SYNOPSIS:
*
- * long double x, y, gammal();
- * extern int sgngam;
+ * long double x, y, tgammal();
*
- * y = gammal( x );
+ * y = tgammal( x );
*
*
*
* DESCRIPTION:
*
* Returns gamma function of the argument. The result is
- * correctly signed, and the sign (+1 or -1) is also
- * returned in a global (extern) variable named sgngam.
- * This variable is also filled in by the logarithmic gamma
- * function lgam().
+ * correctly signed.
*
* Arguments |x| <= 13 are reduced by recurrence and the function
* approximated by a rational function of degree 7/8 in the
@@ -38,7 +34,7 @@
* Accuracy for large arguments is dominated by error in powl().
*
*/
-/* lgaml()
+/* lgammal()
*
* Natural logarithm of gamma function
*
@@ -46,10 +42,10 @@
*
* SYNOPSIS:
*
- * long double x, y, lgaml();
- * extern int sgngam;
+ * long double x, y, lgammal();
+ * extern int signgam;
*
- * y = lgaml( x );
+ * y = lgammal( x );
*
*
*
@@ -58,7 +54,7 @@
* Returns the base e (2.718...) logarithm of the absolute
* value of the gamma function of the argument.
* The sign (+1 or -1) of the gamma function is returned in a
- * global (extern) variable named sgngam.
+ * global (extern) variable named signgam.
*
* For arguments greater than 33, the logarithm of the gamma
* function is approximated by the logarithmic version of
@@ -90,7 +86,6 @@
Copyright 1994 by Stephen L. Moshier
*/
-
#include "mconf.h"
/*
gamma(x+2) = gamma(x+2) P(x)/Q(x)
@@ -336,18 +331,18 @@
};
#endif
-int sgngaml = 0;
-extern int sgngaml;
+/*int signgam = 0;*/
+extern int signgam;
extern long double MAXLOGL, MAXNUML, PIL;
/* #define PIL 3.14159265358979323846L */
/* #define MAXNUML 1.189731495357231765021263853E4932L */
#ifdef ANSIPROT
extern long double fabsl ( long double );
-extern long double lgaml ( long double );
+extern long double lgammal ( long double );
extern long double logl ( long double );
extern long double expl ( long double );
-extern long double gammal ( long double );
+extern long double tgammal ( long double );
extern long double sinl ( long double );
extern long double floorl ( long double );
extern long double powl ( long double, long double );
@@ -357,7 +352,7 @@
extern int isfinitel ( long double );
static long double stirf ( long double );
#else
-long double fabsl(), lgaml(), logl(), expl(), gammal(), sinl();
+long double fabsl(), lgammal(), logl(), expl(), tgammal(), sinl();
long double floorl(), powl(), polevll(), p1evll(), isnanl(), isfinitel();
static long double stirf();
#endif
@@ -403,13 +398,13 @@
-long double gammal(x)
+long double tgammal(x)
long double x;
{
long double p, q, z;
int i;
+int signgam = 1;
-sgngaml = 1;
#ifdef NANS
if( isnanl(x) )
return(NANL);
@@ -435,7 +430,7 @@
{
gamnan:
#ifdef NANS
- mtherr( "gammal", DOMAIN );
+ mtherr( "tgammal", DOMAIN );
return (NANL);
#else
goto goverf;
@@ -443,7 +438,7 @@
}
i = p;
if( (i & 1) == 0 )
- sgngaml = -1;
+ signgam = -1;
z = q - p;
if( z > 0.5L )
{
@@ -456,10 +451,10 @@
{
goverf:
#ifdef INFINITIES
- return( sgngaml * INFINITYL);
+ return( signgam * INFINITYL);
#else
- mtherr( "gammal", OVERFLOW );
- return( sgngaml * MAXNUML);
+ mtherr( "tgammal", OVERFLOW );
+ return( signgam * MAXNUML);
#endif
}
z = PIL/z;
@@ -468,7 +463,7 @@
{
z = stirf(x);
}
- return( sgngaml * z );
+ return( signgam * z );
}
z = 1.0L;
@@ -642,13 +637,13 @@
/* Logarithm of gamma function */
-long double lgaml(x)
+long double lgammal(x)
long double x;
{
long double p, q, w, z, f, nx;
int i;
-sgngaml = 1;
+signgam = 1;
#ifdef NANS
if( isnanl(x) )
return(NANL);
@@ -660,12 +655,12 @@
if( x < -34.0L )
{
q = -x;
- w = lgaml(q); /* note this modifies sgngam! */
+ w = lgammal(q); /* note this modifies signgam! */
p = floorl(q);
if( p == q )
{
#ifdef INFINITIES
- mtherr( "lgaml", SING );
+ mtherr( "lgammal", SING );
return (INFINITYL);
#else
goto loverf;
@@ -673,9 +668,9 @@
}
i = p;
if( (i & 1) == 0 )
- sgngaml = -1;
+ signgam = -1;
else
- sgngaml = 1;
+ signgam = 1;
z = q - p;
if( z > 0.5L )
{
@@ -711,11 +706,11 @@
}
if( z < 0.0L )
{
- sgngaml = -1;
+ signgam = -1;
z = -z;
}
else
- sgngaml = 1;
+ signgam = 1;
if( x == 2.0L )
return( logl(z) );
x = (nx - 2.0L) + f;
@@ -727,10 +722,10 @@
{
loverf:
#ifdef INFINITIES
- return( sgngaml * INFINITYL );
+ return( signgam * INFINITYL );
#else
- mtherr( "lgaml", OVERFLOW );
- return( sgngaml * MAXNUML );
+ mtherr( "lgammal", OVERFLOW );
+ return( signgam * MAXNUML );
#endif
}
@@ -754,11 +749,11 @@
q = z / (x * polevll( x, S, 8 ));
if( q < 0.0L )
{
- sgngaml = -1;
+ signgam = -1;
q = -q;
}
else
- sgngaml = 1;
+ signgam = 1;
q = logl( q );
return(q);
}
diff -drNu src.orig/ldouble/makefile src/ldouble/makefile
--- src.orig/ldouble/makefile 2010-04-06 11:46:28.000000000 +0200
+++ src/ldouble/makefile 2013-01-08 15:07:41.399639696 +0100
@@ -12,11 +12,11 @@
exp10l.o exp2l.o expl.o fdtrl.o gammal.o gdtrl.o igamil.o igaml.o \
incbetl.o incbil.o isnanl.o j0l.o j1l.o jnl.o ldrand.o log10l.o log2l.o \
logl.o nbdtrl.o ndtril.o ndtrl.o pdtrl.o powl.o powil.o sinhl.o sinl.o \
-sqrtl.o stdtrl.o tanhl.o tanl.o unityl.o ynl.o \
+sqrtl.o stdtrl.o tanhl.o tanl.o ynl.o \
floorl.o polevll.o unityl.o mtherr.o
# cmplxl.o clogl.o
-all: mtstl lparanoi lcalc fltestl nantst testvect monotl libml.a
+all: mtstl lcalc fltestl nantst testvect monotl libml.a
mtstl: libml.a mtstl.o $(OBJS)
$(CC) $(CFLAGS) -o mtstl mtstl.o libml.a $(LIBS)
@@ -59,10 +59,10 @@
# ELF versions for linux
#floorl.o: floorlelf.387
# as -o floorl.o floorlelf.387
-sqrtl.o: sqrtlelf.387
- as -o sqrtl.o sqrtlelf.387
-setprec.o: setprelf.387
- as -o setprec.o setprelf.387
+#sqrtl.o: sqrtlelf.387
+# as -o sqrtl.o sqrtlelf.387
+#setprec.o: setprelf.387
+# as -o setprec.o setprelf.387
# 68K routines
# For Sun 3
diff -drNu src.orig/Makefile src/Makefile
--- src.orig/Makefile 1970-01-01 01:00:00.000000000 +0100
+++ src/Makefile 2013-01-08 15:08:01.743638992 +0100
@@ -0,0 +1,68 @@
+# FreeBSD makefile for cephes.
+
+# Build tools
+CC ?= gcc
+LD ?= ld
+CP ?= cp
+INSTALL ?= install
+
+# Intermediate (ar) libraries
+LIBS=c9x-complex/libmc.a double/libmd.a ldouble/libml.a single/libmf.a
+
+all: libm.so
+
+install: libm.so complex.h math.h
+ ${INSTALL} -C -m 644 complex.h math.h "${SAGE_LOCAL}/include"
+ ${INSTALL} -C -m 755 libm.so "${SAGE_LOCAL}/lib"
+
+check:
+ cd c9x-complex && ${MAKE} "CC=${CC}" check
+ cd double && ${MAKE} "CC=${CC}" check
+ cd ldouble && ${MAKE} "CC=${CC}" check
+ cd single && ${MAKE} "CC=${CC}" check
+# cd c9x-complex && ${MAKE} "LIBS=-L.. -rpath .. -lm" "CC=${CC}" check
+# cd double && ${MAKE} "LIBS=-L.. -rpath .. -lm" "CC=${CC}" check
+# cd ldouble && ${MAKE} "LIBS=-L.. -rpath .. -lm" "CC=${CC}" check
+# cd single && ${MAKE} "LIBS=-L.. -rpath .. -lm" "CC=${CC}" check
+# TBD
+
+clean:
+ rm -f libm.so syms.c99 syms.libm syms.wanted
+ cd c9x-complex && ${MAKE} clean
+ cd double && ${MAKE} clean
+ cd ldouble && ${MAKE} clean
+ cd single && ${MAKE} clean
+
+# FreeBSD includes some but not all of the C99 maths functions. Build
+# a "new" libm.so that uses cephes functions to replace the missing ones
+# (listed in syms.wanted) and then fallback to the base libm.so
+libm.so: ${LIBS} syms.wanted
+ ${LD} -shared -o $@ $$(sed 's/^/-u /' syms.wanted) -L/usr/lib -lc -lm \
+ ${LIBS} -lgcc
+
+# List of symbols defined in the FreeBSD base libc.so and libm.so
+# libc.so is included because some math-related functions are in libc.so
+syms.libm: /usr/lib/libc.so /usr/lib/libm.so
+ nm -Dgp $^ | sed 's/^.* //' | sort -uo $@
+
+# List of symbols defined in C99 math.h and complex.h
+# Doing it this way saves having to maintain a second list
+syms.c99: math.h complex.h
+ sed -ne 's/)(.*//' -e '/^extern/s/^.* (//p' $^ | sort -uo $@
+
+# List of symbols in C99 not defined in FreeBSD
+syms.wanted: syms.libm syms.c99
+ comm -23 syms.c99 syms.libm > $@
+
+# Force compilation in PIC mode to allow creation of a shared library
+c9x-complex/libmc.a: c9x-complex/complex.h
+ cd c9x-complex && ${MAKE} "CC=${CC} -DPIC -fpic" libmc.a
+
+double/libmd.a:
+ cd double && ${MAKE} "CC=${CC} -DPIC -fpic" libmd.a
+
+ldouble/libml.a:
+ cd ldouble && ${MAKE} "CC=${CC} -DPIC -fpic" libml.a
+
+single/libmf.a:
+ cd single && ${MAKE} "CC=${CC} -DPIC -fpic" libmf.a
diff -drNu src.orig/math.h src/math.h
--- src.orig/math.h 1970-01-01 01:00:00.000000000 +0100
+++ src/math.h 2013-01-08 15:07:41.407639759 +0100
@@ -0,0 +1,201 @@
+/*
+** Replacement <math.h> merging host version with cephes functions
+*/
+
+/* Start by using host math file.
+ * This has to come before the following protective #ifdef so that
+ * #include "math.h" is correctly handled. */
+#include_next <math.h>
+
+#ifndef __CEPHES_MATH_H
+#define __CEPHES_MATH_H
+
+#if defined(__cplusplus)
+extern "C" {
+#endif
+
+/* The following content is derived from
+ * http://www.opengroup.org/onlinepubs/9699919799/basedefs/math.h.html
+ */
+extern double (acos)(double);
+extern float (acosf)(float);
+extern double (acosh)(double);
+extern float (acoshf)(float);
+extern long double (acoshl)(long double);
+extern long double (acosl)(long double);
+extern double (asin)(double);
+extern float (asinf)(float);
+extern double (asinh)(double);
+extern float (asinhf)(float);
+extern long double (asinhl)(long double);
+extern long double (asinl)(long double);
+extern double (atan)(double);
+extern double (atan2)(double, double);
+extern float (atan2f)(float, float);
+extern long double (atan2l)(long double, long double);
+extern float (atanf)(float);
+extern double (atanh)(double);
+extern float (atanhf)(float);
+extern long double (atanhl)(long double);
+extern long double (atanl)(long double);
+extern double (cbrt)(double);
+extern float (cbrtf)(float);
+extern long double (cbrtl)(long double);
+extern double (ceil)(double);
+extern float (ceilf)(float);
+extern long double (ceill)(long double);
+extern double (copysign)(double, double);
+extern float (copysignf)(float, float);
+extern long double (copysignl)(long double, long double);
+extern double (cos)(double);
+extern float (cosf)(float);
+extern double (cosh)(double);
+extern float (coshf)(float);
+extern long double (coshl)(long double);
+extern long double (cosl)(long double);
+extern double (erf)(double);
+extern double (erfc)(double);
+extern float (erfcf)(float);
+extern long double (erfcl)(long double);
+extern float (erff)(float);
+extern long double (erfl)(long double);
+extern double (exp)(double);
+extern double (exp2)(double);
+extern float (exp2f)(float);
+extern long double (exp2l)(long double);
+extern float (expf)(float);
+extern long double (expl)(long double);
+extern double (expm1)(double);
+extern float (expm1f)(float);
+extern long double (expm1l)(long double);
+extern double (fabs)(double);
+extern float (fabsf)(float);
+extern long double (fabsl)(long double);
+extern double (fdim)(double, double);
+extern float (fdimf)(float, float);
+extern long double (fdiml)(long double, long double);
+extern double (floor)(double);
+extern float (floorf)(float);
+extern long double (floorl)(long double);
+extern double (fma)(double, double, double);
+extern float (fmaf)(float, float, float);
+extern long double (fmal)(long double, long double, long double);
+extern double (fmax)(double, double);
+extern float (fmaxf)(float, float);
+extern long double (fmaxl)(long double, long double);
+extern double (fmin)(double, double);
+extern float (fminf)(float, float);
+extern long double (fminl)(long double, long double);
+extern double (fmod)(double, double);
+extern float (fmodf)(float, float);
+extern long double (fmodl)(long double, long double);
+extern double (frexp)(double, int *);
+extern float (frexpf)(float, int *);
+extern long double (frexpl)(long double, int *);
+extern double (hypot)(double, double);
+extern float (hypotf)(float, float);
+extern long double (hypotl)(long double, long double);
+extern int (ilogb)(double);
+extern int (ilogbf)(float);
+extern int (ilogbl)(long double);
+extern double (j0)(double); /* XSI extension */
+extern double (j1)(double); /* XSI extension */
+extern double (jn)(int, double); /* XSI extension */
+extern double (ldexp)(double, int);
+extern float (ldexpf)(float, int);
+extern long double (ldexpl)(long double, int);
+extern double (lgamma)(double);
+extern float (lgammaf)(float);
+extern long double (lgammal)(long double);
+extern long long (llrint)(double);
+extern long long (llrintf)(float);
+extern long long (llrintl)(long double);
+extern long long (llround)(double);
+extern long long (llroundf)(float);
+extern long long (llroundl)(long double);
+extern double (log)(double);
+extern double (log10)(double);
+extern float (log10f)(float);
+extern long double (log10l)(long double);
+extern double (log1p)(double);
+extern float (log1pf)(float);
+extern long double (log1pl)(long double);
+extern double (log2)(double);
+extern float (log2f)(float);
+extern long double (log2l)(long double);
+extern double (logb)(double);
+extern float (logbf)(float);
+extern long double (logbl)(long double);
+extern float (logf)(float);
+extern long double (logl)(long double);
+extern long (lrint)(double);
+extern long (lrintf)(float);
+extern long (lrintl)(long double);
+extern long (lround)(double);
+extern long (lroundf)(float);
+extern long (lroundl)(long double);
+extern double (modf)(double, double *);
+extern float (modff)(float, float *);
+extern long double (modfl)(long double, long double *);
+extern double (nan)(const char *);
+extern float (nanf)(const char *);
+extern long double (nanl)(const char *);
+extern double (nearbyint)(double);
+extern float (nearbyintf)(float);
+extern long double (nearbyintl)(long double);
+extern double (nextafter)(double, double);
+extern float (nextafterf)(float, float);
+extern long double (nextafterl)(long double, long double);
+extern double (nexttoward)(double, long double);
+extern float (nexttowardf)(float, long double);
+extern long double (nexttowardl)(long double, long double);
+extern double (pow)(double, double);
+extern float (powf)(float, float);
+extern long double (powl)(long double, long double);
+extern double (remainder)(double, double);
+extern float (remainderf)(float, float);
+extern long double (remainderl)(long double, long double);
+extern double (remquo)(double, double, int *);
+extern float (remquof)(float, float, int *);
+extern long double (remquol)(long double, long double, int *);
+extern double (rint)(double);
+extern float (rintf)(float);
+extern long double (rintl)(long double);
+extern double (round)(double);
+extern float (roundf)(float);
+extern long double (roundl)(long double);
+extern double (scalbln)(double, long);
+extern float (scalblnf)(float, long);
+extern long double (scalblnl)(long double, long);
+extern double (scalbn)(double, int);
+extern float (scalbnf)(float, int);
+extern long double (scalbnl)(long double, int);
+extern double (sin)(double);
+extern float (sinf)(float);
+extern double (sinh)(double);
+extern float (sinhf)(float);
+extern long double (sinhl)(long double);
+extern long double (sinl)(long double);
+extern double (sqrt)(double);
+extern float (sqrtf)(float);
+extern long double (sqrtl)(long double);
+extern double (tan)(double);
+extern float (tanf)(float);
+extern double (tanh)(double);
+extern float (tanhf)(float);
+extern long double (tanhl)(long double);
+extern long double (tanl)(long double);
+extern double (tgamma)(double);
+extern float (tgammaf)(float);
+extern long double (tgammal)(long double);
+extern double (trunc)(double);
+extern float (truncf)(float);
+extern long double (truncl)(long double);
+extern double (y0)(double); /* XSI extension */
+extern double (y1)(double); /* XSI extension */
+extern double (yn)(int, double); /* XSI extension */
+
+#if defined(__cplusplus)
+}
+#endif
+#endif
