3 files changed, 1491 insertions, 42 deletions

diff --git a/math/sage/Makefile b/math/sage/Makefile
index cf6b73afc9b1..5e9515889276 100644
--- a/math/sage/Makefile
+++ b/math/sage/Makefile
@@ -7,7 +7,7 @@
 
 PORTNAME=	sage
 PORTVERSION=	4.8
-PORTREVISION=	1
+PORTREVISION=	2
 CATEGORIES=	math
 MASTER_SITES=	http://modular.math.jmu.edu/src/ \
 		http://boxen.math.washington.edu/sage/src/ \
diff --git a/math/sage/files/spkg-patch-cephes-2.8_-_big-patch b/math/sage/files/spkg-patch-cephes-2.8_-_big-patch
new file mode 100644
index 000000000000..de4dd7f7e3a8
--- /dev/null
+++ b/math/sage/files/spkg-patch-cephes-2.8_-_big-patch
@@ -0,0 +1,1490 @@
+--- cephes-2.8/spkg-install.orig	2010-05-26 11:10:08.000000000 +1000
++++ cephes-2.8/spkg-install	2010-07-26 08:25:54.669312906 +1000
+@@ -1,12 +1,11 @@
+ #!/usr/bin/env bash
+ 
+-if [ "$UNAME" != "CYGWIN" ]; then
+-    echo "We do not install the cephes library on any operating system except Cygwin."
+-    exit 0
+-fi
++# Abort if anything fails unexpectedly
++set -e
+ 
+ CUR=`pwd`
+ 
++# Cygwin patch/build/install functions
+ function patch {
+     cd "$CUR"
+     cp patches/complex.h src/
+@@ -77,5 +76,20 @@
+     make_c9x_complex
+ }
+ 
+-patch
+-build
++# Actually execute the code
++if [ "$UNAME" = "CYGWIN" ]; then
++    patch
++    build
++elif [ "$UNAME" = "FreeBSD" ]; then
++    cp patches/Makefile_bsd src/Makefile
++    cp patches/c9x-complex/makefile src/c9x-complex
++    cp patches/c9x-complex/*.c src/c9x-complex
++    cp patches/double/makefile src/double
++    cp patches/ldouble/makefile patches/ldouble/gammal.c src/ldouble
++    cd src
++    make
++    make install
++else
++    echo "We only install the cephes library on Cygwin and FreeBSD."
++    exit 0
++fi
+--- cephes-2.8/patches/ldouble/makefile.orig	2010-04-06 19:27:43.000000000 +1000
++++ cephes-2.8/patches/ldouble/makefile	2010-07-26 08:25:54.665317219 +1000
+@@ -12,7 +12,7 @@
+ 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
+ 
+--- cephes-2.8/patches/ldouble/gammal.c.patch.orig	2010-07-26 13:41:37.467088450 +1000
++++ cephes-2.8/patches/ldouble/gammal.c.patch	2010-07-26 13:42:52.710029506 +1000
+@@ -0,0 +1,240 @@
++--- ../../src/ldouble/gammal.c	2000-05-29 01:21:01.000000000 +1000
+++++ gammal.c	2010-07-26 13:38:38.030338022 +1000
++@@ -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);
++ }
+--- cephes-2.8/patches/ldouble/gammal.c.orig	2010-07-26 13:12:17.957613369 +1000
++++ cephes-2.8/patches/ldouble/gammal.c	2010-07-26 13:38:38.030338022 +1000
+@@ -0,0 +1,759 @@
++/*							gammal.c
++ *
++ *	Gamma function
++ *
++ *
++ *
++ * SYNOPSIS:
++ *
++ * long double x, y, tgammal();
++ *
++ * y = tgammal( x );
++ *
++ *
++ *
++ * DESCRIPTION:
++ *
++ * Returns gamma function of the argument.  The result is
++ * correctly signed.
++ *
++ * Arguments |x| <= 13 are reduced by recurrence and the function
++ * approximated by a rational function of degree 7/8 in the
++ * interval (2,3).  Large arguments are handled by Stirling's
++ * formula. Large negative arguments are made positive using
++ * a reflection formula.  
++ *
++ *
++ * ACCURACY:
++ *
++ *                      Relative error:
++ * arithmetic   domain     # trials      peak         rms
++ *    IEEE     -40,+40      10000       3.6e-19     7.9e-20
++ *    IEEE    -1755,+1755   10000       4.8e-18     6.5e-19
++ *
++ * Accuracy for large arguments is dominated by error in powl().
++ *
++ */
++/*							lgammal()
++ *
++ *	Natural logarithm of gamma function
++ *
++ *
++ *
++ * SYNOPSIS:
++ *
++ * long double x, y, lgammal();
++ * extern int signgam;
++ *
++ * y = lgammal( x );
++ *
++ *
++ *
++ * DESCRIPTION:
++ *
++ * 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 signgam.
++ *
++ * For arguments greater than 33, the logarithm of the gamma
++ * function is approximated by the logarithmic version of
++ * Stirling's formula using a polynomial approximation of
++ * degree 4. Arguments between -33 and +33 are reduced by
++ * recurrence to the interval [2,3] of a rational approximation.
++ * The cosecant reflection formula is employed for arguments
++ * less than -33.
++ *
++ * Arguments greater than MAXLGML (10^4928) return MAXNUML.
++ *
++ *
++ *
++ * ACCURACY:
++ *
++ *
++ * arithmetic      domain        # trials     peak         rms
++ *    IEEE         -40, 40        100000     2.2e-19     4.6e-20
++ *    IEEE    10^-2000,10^+2000    20000     1.6e-19     3.3e-20
++ * The error criterion was relative when the function magnitude
++ * was greater than one but absolute when it was less than one.
++ *
++ */
++
++/*							gamma.c	*/
++/*	gamma function	*/
++
++/*
++Copyright 1994 by Stephen L. Moshier
++*/
++
++#include "mconf.h"
++/*
++gamma(x+2)  = gamma(x+2) P(x)/Q(x)
++0 <= x <= 1
++Relative error
++n=7, d=8
++Peak error =  1.83e-20
++Relative error spread =  8.4e-23
++*/
++#if UNK
++static long double P[8] = {
++ 4.212760487471622013093E-5L,
++ 4.542931960608009155600E-4L,
++ 4.092666828394035500949E-3L,
++ 2.385363243461108252554E-2L,
++ 1.113062816019361559013E-1L,
++ 3.629515436640239168939E-1L,
++ 8.378004301573126728826E-1L,
++ 1.000000000000000000009E0L,
++};
++static long double Q[9] = {
++-1.397148517476170440917E-5L,
++ 2.346584059160635244282E-4L,
++-1.237799246653152231188E-3L,
++-7.955933682494738320586E-4L,
++ 2.773706565840072979165E-2L,
++-4.633887671244534213831E-2L,
++-2.243510905670329164562E-1L,
++ 4.150160950588455434583E-1L,
++ 9.999999999999999999908E-1L,
++};
++#endif
++#if IBMPC
++static short P[] = {
++0x434a,0x3f22,0x2bda,0xb0b2,0x3ff0, XPD
++0xf5aa,0xe82f,0x335b,0xee2e,0x3ff3, XPD
++0xbe6c,0x3757,0xc717,0x861b,0x3ff7, XPD
++0x7f43,0x5196,0xb166,0xc368,0x3ff9, XPD
++0x9549,0x8eb5,0x8c3a,0xe3f4,0x3ffb, XPD
++0x8d75,0x23af,0xc8e4,0xb9d4,0x3ffd, XPD
++0x29cf,0x19b3,0x16c8,0xd67a,0x3ffe, XPD
++0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
++};
++static short Q[] = {
++0x5473,0x2de8,0x1268,0xea67,0xbfee, XPD
++0x334b,0xc2f0,0xa2dd,0xf60e,0x3ff2, XPD
++0xbeed,0x1853,0xa691,0xa23d,0xbff5, XPD
++0x296e,0x7cb1,0x5dfd,0xd08f,0xbff4, XPD
++0x0417,0x7989,0xd7bc,0xe338,0x3ff9, XPD
++0x3295,0x3698,0xd580,0xbdcd,0xbffa, XPD
++0x75ef,0x3ab7,0x4ad3,0xe5bc,0xbffc, XPD
++0xe458,0x2ec7,0xfd57,0xd47c,0x3ffd, XPD
++0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
++};
++#endif
++#if MIEEE
++static long P[24] = {
++0x3ff00000,0xb0b22bda,0x3f22434a,
++0x3ff30000,0xee2e335b,0xe82ff5aa,
++0x3ff70000,0x861bc717,0x3757be6c,
++0x3ff90000,0xc368b166,0x51967f43,
++0x3ffb0000,0xe3f48c3a,0x8eb59549,
++0x3ffd0000,0xb9d4c8e4,0x23af8d75,
++0x3ffe0000,0xd67a16c8,0x19b329cf,
++0x3fff0000,0x80000000,0x00000000,
++};
++static long Q[27] = {
++0xbfee0000,0xea671268,0x2de85473,
++0x3ff20000,0xf60ea2dd,0xc2f0334b,
++0xbff50000,0xa23da691,0x1853beed,
++0xbff40000,0xd08f5dfd,0x7cb1296e,
++0x3ff90000,0xe338d7bc,0x79890417,
++0xbffa0000,0xbdcdd580,0x36983295,
++0xbffc0000,0xe5bc4ad3,0x3ab775ef,
++0x3ffd0000,0xd47cfd57,0x2ec7e458,
++0x3fff0000,0x80000000,0x00000000,
++};
++#endif
++/*
++static long double P[] = {
++-3.01525602666895735709e0L,
++-3.25157411956062339893e1L,
++-2.92929976820724030353e2L,
++-1.70730828800510297666e3L,
++-7.96667499622741999770e3L,
++-2.59780216007146401957e4L,
++-5.99650230220855581642e4L,
++-7.15743521530849602425e4L
++};
++static long double Q[] = {
++ 1.00000000000000000000e0L,
++-1.67955233807178858919e1L,
++ 8.85946791747759881659e1L,
++ 5.69440799097468430177e1L,
++-1.98526250512761318471e3L,
++ 3.31667508019495079814e3L,
++ 1.60577839621734713377e4L,
++-2.97045081369399940529e4L,
++-7.15743521530849602412e4L
++};
++*/
++#define MAXGAML 1755.455L
++/*static long double LOGPI = 1.14472988584940017414L;*/
++
++/* Stirling's formula for the gamma function
++gamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x))
++z(x) = x
++13 <= x <= 1024
++Relative error
++n=8, d=0
++Peak error =  9.44e-21
++Relative error spread =  8.8e-4
++*/
++#if UNK
++static long double STIR[9] = {
++ 7.147391378143610789273E-4L,
++-2.363848809501759061727E-5L,
++-5.950237554056330156018E-4L,
++ 6.989332260623193171870E-5L,
++ 7.840334842744753003862E-4L,
++-2.294719747873185405699E-4L,
++-2.681327161876304418288E-3L,
++ 3.472222222230075327854E-3L,
++ 8.333333333333331800504E-2L,
++};
++#endif
++#if IBMPC
++static short STIR[] = {
++0x6ede,0x69f7,0x54e3,0xbb5d,0x3ff4, XPD
++0xc395,0x0295,0x4443,0xc64b,0xbfef, XPD
++0xba6f,0x7c59,0x5e47,0x9bfb,0xbff4, XPD
++0x5704,0x1a39,0xb11d,0x9293,0x3ff1, XPD
++0x30b7,0x1a21,0x98b2,0xcd87,0x3ff4, XPD
++0xbef3,0x7023,0x6a08,0xf09e,0xbff2, XPD
++0x3a1c,0x5ac8,0x3478,0xafb9,0xbff6, XPD
++0xc3c9,0x906e,0x38e3,0xe38e,0x3ff6, XPD
++0xa1d5,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD
++};
++#endif
++#if MIEEE
++static long STIR[27] = {
++0x3ff40000,0xbb5d54e3,0x69f76ede,
++0xbfef0000,0xc64b4443,0x0295c395,
++0xbff40000,0x9bfb5e47,0x7c59ba6f,
++0x3ff10000,0x9293b11d,0x1a395704,
++0x3ff40000,0xcd8798b2,0x1a2130b7,
++0xbff20000,0xf09e6a08,0x7023bef3,
++0xbff60000,0xafb93478,0x5ac83a1c,
++0x3ff60000,0xe38e38e3,0x906ec3c9,
++0x3ffb0000,0xaaaaaaaa,0xaaaaa1d5,
++};
++#endif
++#define MAXSTIR 1024.0L
++static long double SQTPI = 2.50662827463100050242E0L;
++
++/* 1/gamma(x) = z P(z)
++ * z(x) = 1/x
++ * 0 < x < 0.03125
++ * Peak relative error 4.2e-23
++ */
++#if UNK
++static long double S[9] = {
++-1.193945051381510095614E-3L,
++ 7.220599478036909672331E-3L,
++-9.622023360406271645744E-3L,
++-4.219773360705915470089E-2L,
++ 1.665386113720805206758E-1L,
++-4.200263503403344054473E-2L,
++-6.558780715202540684668E-1L,
++ 5.772156649015328608253E-1L,
++ 1.000000000000000000000E0L,
++};
++#endif
++#if IBMPC
++static short S[] = {
++0xbaeb,0xd6d3,0x25e5,0x9c7e,0xbff5, XPD
++0xfe9a,0xceb4,0xc74e,0xec9a,0x3ff7, XPD
++0x9225,0xdfef,0xb0e9,0x9da5,0xbff8, XPD
++0x10b0,0xec17,0x87dc,0xacd7,0xbffa, XPD
++0x6b8d,0x7515,0x1905,0xaa89,0x3ffc, XPD
++0xf183,0x126b,0xf47d,0xac0a,0xbffa, XPD
++0x7bf6,0x57d1,0xa013,0xa7e7,0xbffe, XPD
++0xc7a9,0x7db0,0x67e3,0x93c4,0x3ffe, XPD
++0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
++};
++#endif
++#if MIEEE
++static long S[27] = {
++0xbff50000,0x9c7e25e5,0xd6d3baeb,
++0x3ff70000,0xec9ac74e,0xceb4fe9a,
++0xbff80000,0x9da5b0e9,0xdfef9225,
++0xbffa0000,0xacd787dc,0xec1710b0,
++0x3ffc0000,0xaa891905,0x75156b8d,
++0xbffa0000,0xac0af47d,0x126bf183,
++0xbffe0000,0xa7e7a013,0x57d17bf6,
++0x3ffe0000,0x93c467e3,0x7db0c7a9,
++0x3fff0000,0x80000000,0x00000000,
++};
++#endif
++/* 1/gamma(-x) = z P(z)
++ * z(x) = 1/x
++ * 0 < x < 0.03125
++ * Peak relative error 5.16e-23
++ * Relative error spread =  2.5e-24
++ */
++#if UNK
++static long double SN[9] = {
++ 1.133374167243894382010E-3L,
++ 7.220837261893170325704E-3L,
++ 9.621911155035976733706E-3L,
++-4.219773343731191721664E-2L,
++-1.665386113944413519335E-1L,
++-4.200263503402112910504E-2L,
++ 6.558780715202536547116E-1L,
++ 5.772156649015328608727E-1L,
++-1.000000000000000000000E0L,
++};
++#endif
++#if IBMPC
++static short SN[] = {
++0x5dd1,0x02de,0xb9f7,0x948d,0x3ff5, XPD
++0x989b,0xdd68,0xc5f1,0xec9c,0x3ff7, XPD
++0x2ca1,0x18f0,0x386f,0x9da5,0x3ff8, XPD
++0x783f,0x41dd,0x87d1,0xacd7,0xbffa, XPD
++0x7a5b,0xd76d,0x1905,0xaa89,0xbffc, XPD
++0x7f64,0x1234,0xf47d,0xac0a,0xbffa, XPD
++0x5e26,0x57d1,0xa013,0xa7e7,0x3ffe, XPD
++0xc7aa,0x7db0,0x67e3,0x93c4,0x3ffe, XPD
++0x0000,0x0000,0x0000,0x8000,0xbfff, XPD
++};
++#endif
++#if MIEEE
++static long SN[27] = {
++0x3ff50000,0x948db9f7,0x02de5dd1,
++0x3ff70000,0xec9cc5f1,0xdd68989b,
++0x3ff80000,0x9da5386f,0x18f02ca1,
++0xbffa0000,0xacd787d1,0x41dd783f,
++0xbffc0000,0xaa891905,0xd76d7a5b,
++0xbffa0000,0xac0af47d,0x12347f64,
++0x3ffe0000,0xa7e7a013,0x57d15e26,
++0x3ffe0000,0x93c467e3,0x7db0c7aa,
++0xbfff0000,0x80000000,0x00000000,
++};
++#endif
++
++/*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 lgammal ( long double );
++extern long double logl ( long double );
++extern long double expl ( 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 );
++extern long double polevll ( long double, void *, int );
++extern long double p1evll ( long double, void *, int );
++extern int isnanl ( long double );
++extern int isfinitel ( long double );
++static long double stirf ( long double );
++#else
++long double fabsl(), lgammal(), logl(), expl(), tgammal(), sinl();
++long double floorl(), powl(), polevll(), p1evll(), isnanl(), isfinitel();
++static long double stirf();
++#endif
++#ifdef INFINITIES
++extern long double INFINITYL;
++#endif
++#ifdef NANS
++extern long double NANL;
++#endif
++
++/* Gamma function computed by Stirling's formula.
++ */
++static long double stirf(x)
++long double x;
++{
++long double y, w, v;
++
++w = 1.0L/x;
++/* For large x, use rational coefficients from the analytical expansion.  */
++if( x > 1024.0L )
++	w = (((((6.97281375836585777429E-5L * w
++		+ 7.84039221720066627474E-4L) * w
++		- 2.29472093621399176955E-4L) * w
++		- 2.68132716049382716049E-3L) * w
++		+ 3.47222222222222222222E-3L) * w
++		+ 8.33333333333333333333E-2L) * w
++		+ 1.0L;
++else
++	w = 1.0L + w * polevll( w, STIR, 8 );
++y = expl(x);
++if( x > MAXSTIR )
++	{ /* Avoid overflow in pow() */
++	v = powl( x, 0.5L * x - 0.25L );
++	y = v * (v / y);
++	}
++else
++	{
++	y = powl( x, x - 0.5L ) / y;
++	}
++y = SQTPI * y * w;
++return( y );
++}
++
++
++
++long double tgammal(x)
++long double x;
++{
++long double p, q, z;
++int i;
++int signgam = 1;
++
++#ifdef NANS
++if( isnanl(x) )
++	return(NANL);
++#endif
++#ifdef INFINITIES
++if(x == INFINITYL)
++	return(INFINITYL);
++#ifdef NANS
++if(x == -INFINITYL)
++	goto gamnan;
++#endif
++#endif
++q = fabsl(x);
++
++if( q > 13.0L )
++	{
++	if( q > MAXGAML )
++		goto goverf;
++	if( x < 0.0L )
++		{
++		p = floorl(q);
++		if( p == q )
++			{
++gamnan:
++#ifdef NANS
++			mtherr( "tgammal", DOMAIN );
++			return (NANL);
++#else
++			goto goverf;
++#endif
++			}
++		i = p;
++		if( (i & 1) == 0 )
++			signgam = -1;
++		z = q - p;
++		if( z > 0.5L )
++			{
++			p += 1.0L;
++			z = q - p;
++			}
++		z = q * sinl( PIL * z );
++		z = fabsl(z) * stirf(q);
++		if( z <= PIL/MAXNUML )
++			{
++goverf:
++#ifdef INFINITIES
++			return( signgam * INFINITYL);
++#else
++			mtherr( "tgammal", OVERFLOW );
++			return( signgam * MAXNUML);
++#endif
++			}
++		z = PIL/z;
++		}
++	else
++		{
++		z = stirf(x);
++		}
++	return( signgam * z );
++	}
++
++z = 1.0L;
++while( x >= 3.0L )
++	{
++	x -= 1.0L;
++	z *= x;
++	}
++
++while( x < -0.03125L )
++	{
++	z /= x;
++	x += 1.0L;
++	}
++
++if( x <= 0.03125L )
++	goto small;
++
++while( x < 2.0L )
++	{
++	z /= x;
++	x += 1.0L;
++	}
++
++if( x == 2.0L )
++	return(z);
++
++x -= 2.0L;
++p = polevll( x, P, 7 );
++q = polevll( x, Q, 8 );
++return( z * p / q );
++
++small:
++if( x == 0.0L )
++	{
++	  goto gamnan;
++	}
++else
++	{
++	if( x < 0.0L )
++		{
++		x = -x;
++		q = z / (x * polevll( x, SN, 8 ));
++		}
++	else
++		q = z / (x * polevll( x, S, 8 ));
++	}
++return q;
++}
++
++
++
++/* A[]: Stirling's formula expansion of log gamma
++ * B[], C[]: log gamma function between 2 and 3
++ */
++
++
++/* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x A(1/x^2)
++ * x >= 8
++ * Peak relative error 1.51e-21
++ * Relative spread of error peaks 5.67e-21
++ */
++#if UNK
++static long double A[7] = {
++ 4.885026142432270781165E-3L,
++-1.880801938119376907179E-3L,
++ 8.412723297322498080632E-4L,
++-5.952345851765688514613E-4L,
++ 7.936507795855070755671E-4L,
++-2.777777777750349603440E-3L,
++ 8.333333333333331447505E-2L,
++};
++#endif
++#if IBMPC
++static short A[] = {
++0xd984,0xcc08,0x91c2,0xa012,0x3ff7, XPD
++0x3d91,0x0304,0x3da1,0xf685,0xbff5, XPD
++0x3bdc,0xaad1,0xd492,0xdc88,0x3ff4, XPD
++0x8b20,0x9fce,0x844e,0x9c09,0xbff4, XPD
++0xf8f2,0x30e5,0x0092,0xd00d,0x3ff4, XPD
++0x4d88,0x03a8,0x60b6,0xb60b,0xbff6, XPD
++0x9fcc,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD
++};
++#endif
++#if MIEEE
++static long A[21] = {
++0x3ff70000,0xa01291c2,0xcc08d984,
++0xbff50000,0xf6853da1,0x03043d91,
++0x3ff40000,0xdc88d492,0xaad13bdc,
++0xbff40000,0x9c09844e,0x9fce8b20,
++0x3ff40000,0xd00d0092,0x30e5f8f2,
++0xbff60000,0xb60b60b6,0x03a84d88,
++0x3ffb0000,0xaaaaaaaa,0xaaaa9fcc,
++};
++#endif
++
++/* log gamma(x+2) = x B(x)/C(x)
++ * 0 <= x <= 1
++ * Peak relative error 7.16e-22
++ * Relative spread of error peaks 4.78e-20
++ */
++#if UNK
++static long double B[7] = {
++-2.163690827643812857640E3L,
++-8.723871522843511459790E4L,
++-1.104326814691464261197E6L,
++-6.111225012005214299996E6L,
++-1.625568062543700591014E7L,
++-2.003937418103815175475E7L,
++-8.875666783650703802159E6L,
++};
++static long double C[7] = {
++/* 1.000000000000000000000E0L,*/
++-5.139481484435370143617E2L,
++-3.403570840534304670537E4L,
++-6.227441164066219501697E5L,
++-4.814940379411882186630E6L,
++-1.785433287045078156959E7L,
++-3.138646407656182662088E7L,
++-2.099336717757895876142E7L,
++};
++#endif
++#if IBMPC
++static short B[] = {
++0x9557,0x4995,0x0da1,0x873b,0xc00a, XPD
++0xfe44,0x9af8,0x5b8c,0xaa63,0xc00f, XPD
++0x5aa8,0x7cf5,0x3684,0x86ce,0xc013, XPD
++0x259a,0x258c,0xf206,0xba7f,0xc015, XPD
++0xbe18,0x1ca3,0xc0a0,0xf80a,0xc016, XPD
++0x168f,0x2c42,0x6717,0x98e3,0xc017, XPD
++0x2051,0x9d55,0x92c8,0x876e,0xc016, XPD
++};
++static short C[] = {
++/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
++0xaa77,0xcf2f,0xae76,0x807c,0xc008, XPD
++0xb280,0x0d74,0xb55a,0x84f3,0xc00e, XPD
++0xa505,0xcd30,0x81dc,0x9809,0xc012, XPD
++0x3369,0x4246,0xb8c2,0x92f0,0xc015, XPD
++0x63cf,0x6aee,0xbe6f,0x8837,0xc017, XPD
++0x26bb,0xccc7,0xb009,0xef75,0xc017, XPD
++0x462b,0xbae8,0xab96,0xa02a,0xc017, XPD
++};
++#endif
++#if MIEEE
++static long B[21] = {
++0xc00a0000,0x873b0da1,0x49959557,
++0xc00f0000,0xaa635b8c,0x9af8fe44,
++0xc0130000,0x86ce3684,0x7cf55aa8,
++0xc0150000,0xba7ff206,0x258c259a,
++0xc0160000,0xf80ac0a0,0x1ca3be18,
++0xc0170000,0x98e36717,0x2c42168f,
++0xc0160000,0x876e92c8,0x9d552051,
++};
++static long C[21] = {
++/*0x3fff0000,0x80000000,0x00000000,*/
++0xc0080000,0x807cae76,0xcf2faa77,
++0xc00e0000,0x84f3b55a,0x0d74b280,
++0xc0120000,0x980981dc,0xcd30a505,
++0xc0150000,0x92f0b8c2,0x42463369,
++0xc0170000,0x8837be6f,0x6aee63cf,
++0xc0170000,0xef75b009,0xccc726bb,
++0xc0170000,0xa02aab96,0xbae8462b,
++};
++#endif
++
++/* log( sqrt( 2*pi ) ) */
++static long double LS2PI  =  0.91893853320467274178L;
++#define MAXLGM 1.04848146839019521116e+4928L
++
++
++/* Logarithm of gamma function */
++
++
++long double lgammal(x)
++long double x;
++{
++long double p, q, w, z, f, nx;
++int i;
++
++signgam = 1;
++#ifdef NANS
++if( isnanl(x) )
++	return(NANL);
++#endif
++#ifdef INFINITIES
++if( !isfinitel(x) )
++	return(INFINITYL);
++#endif
++if( x < -34.0L )
++	{
++	q = -x;
++	w = lgammal(q); /* note this modifies signgam! */
++	p = floorl(q);
++	if( p == q )
++		{
++#ifdef INFINITIES
++		mtherr( "lgammal", SING );
++		return (INFINITYL);
++#else
++		goto loverf;
++#endif
++		}
++	i = p;
++	if( (i & 1) == 0 )
++		signgam = -1;
++	else
++		signgam = 1;
++	z = q - p;
++	if( z > 0.5L )
++		{
++		p += 1.0L;
++		z = p - q;
++		}
++	z = q * sinl( PIL * z );
++	if( z == 0.0L )
++		goto loverf;
++/*	z = LOGPI - logl( z ) - w; */
++	z = logl( PIL/z ) - w;
++	return( z );
++	}
++
++if( x < 13.0L )
++	{
++	z = 1.0L;
++	nx = floorl( x +  0.5L );
++	f = x - nx;
++	while( x >= 3.0L )
++		{
++		nx -= 1.0L;
++		x = nx + f;
++		z *= x;
++		}
++	while( x < 2.0L )
++		{
++		if( fabsl(x) <= 0.03125 )
++			goto lsmall;
++		z /= nx +  f;
++		nx += 1.0L;
++		x = nx + f;
++		}
++	if( z < 0.0L )
++		{
++		signgam = -1;
++		z = -z;
++		}
++	else
++		signgam = 1;
++	if( x == 2.0L )
++		return( logl(z) );
++	x = (nx - 2.0L) + f;
++	p = x * polevll( x, B, 6 ) / p1evll( x, C, 7);
++	return( logl(z) + p );
++	}
++
++if( x > MAXLGM )
++	{
++loverf:
++#ifdef INFINITIES
++	return( signgam * INFINITYL );
++#else
++	mtherr( "lgammal", OVERFLOW );
++	return( signgam * MAXNUML );
++#endif
++	}
++
++q = ( x - 0.5L ) * logl(x) - x + LS2PI;
++if( x > 1.0e10L )
++	return(q);
++p = 1.0L/(x*x);
++q += polevll( p, A, 6 ) / x;
++return( q );
++
++
++lsmall:
++if( x == 0.0L )
++	goto loverf;
++if( x < 0.0L )
++	{
++	x = -x;
++	q = z / (x * polevll( x, SN, 8 ));
++	}
++else
++	q = z / (x * polevll( x, S, 8 ));
++if( q < 0.0L )
++	{
++	signgam = -1;
++	q = -q;
++	}
++else
++	signgam = 1;
++q = logl( q );
++return(q);
++}
+--- cephes-2.8/patches/math_bsd.h.orig	2010-07-26 08:25:54.647311343 +1000
++++ cephes-2.8/patches/math_bsd.h	2010-07-26 08:25:54.652310772 +1000
+@@ -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
+--- cephes-2.8/patches/Makefile_bsd.orig	2010-07-26 08:25:54.660310527 +1000
++++ cephes-2.8/patches/Makefile_bsd	2010-07-26 08:25:54.662310466 +1000
+@@ -0,0 +1,77 @@
++# 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 > $@
++
++math.h: ../patches/math_bsd.h
++	${CP} $^ $@
++
++complex.h: ../patches/complex_bsd.h
++	${CP} $^ $@
++
++c9x-complex/complex.h: ../patches/complex_bsd.h
++	${CP} $^ $@
++
++# 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
+--- cephes-2.8/patches/complex_bsd.h.orig	2010-07-26 08:25:54.654310990 +1000
++++ cephes-2.8/patches/complex_bsd.h	2010-07-26 08:25:54.658310309 +1000
+@@ -0,0 +1,131 @@
++/*
++** Replacement <complex.h> merging host version with cephes functions
++*/
++
++/* 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
++
++#if defined(__cplusplus)
++extern "C" {
++#endif
++
++/* 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))
++/* Function to get real part.  */
++#define creal(x) (__real__(x))
++
++extern double (atan2)(double, double);
++#define carg(z) (atan2((double)cimag(z), (double)creal(z)))
++
++/* 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
++
++#if defined(__cplusplus)
++}
++#endif
++#endif
+--- cephes-2.8/patches/double/makefile.orig	2010-04-06 19:30:28.000000000 +1000
++++ cephes-2.8/patches/double/makefile	2010-07-26 08:25:54.645313081 +1000
+@@ -24,6 +24,12 @@
+ 
+ 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"
+ 	touch stamp-timing
diff --git a/math/sage/files/spkg-patch-sage-4.8_-_sage_symbolic_pynac_cc.h b/math/sage/files/spkg-patch-sage-4.8_-_sage_symbolic_pynac_cc.h
deleted file mode 100644
index fd4c26c6d695..000000000000
--- a/math/sage/files/spkg-patch-sage-4.8_-_sage_symbolic_pynac_cc.h
+++ /dev/null
@@ -1,41 +0,0 @@
---- sage-4.8/sage/symbolic/pynac_cc.h.orig	2010-06-28 16:37:01.000000000 +0000
-+++ sage-4.8/sage/symbolic/pynac_cc.h	2012-01-21 22:48:22.000000000 +0000
-@@ -1,37 +1,21 @@
--#include <math.h>
-+#include <cmath>
- 
- inline long double sage_logl(long double x) 
- {
--#if defined(__CYGWIN__)
-   return log(x);
--#else
--  return logl(x);
--#endif 
- }
- 
- inline long double sage_sqrtl(long double x) 
- {
--#if defined(__CYGWIN__)
-   return sqrt(x);
--#else
--  return sqrtl(x);
--#endif 
- } 
- 
- inline long double sage_tgammal(long double x) 
- {
--#if defined(__CYGWIN__)
-   return tgamma(x);
--#else
--  return tgammal(x);
--#endif 
- }
- 
- inline long double sage_lgammal(long double x)
- {
--#if defined(__CYGWIN__)
-   return lgamma(x);
--#else
--  return lgammal(x);
--#endif 
- }