ibphoenix/tomsfastmath
6
0
Fork 1
Code Issues Pull Requests Packages Releases Wiki Activity

added tomsfastmath-0.07

Browse Source
This commit is contained in:
Tom St Denis 2005-11-18 05:16:25 +00:00 committed by Steffen Jaeckel
parent 091b337fe8
commit 9ce1fe4656
15 changed files with 190 additions and 174 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

5
changes.txt
View File

@ -1,3 +1,8 @@
November 18th, 2005
0.07 -- Fixes to fp_mul and fp_sqr to clean up the handling of the defines, fix to tfm.h to also clear up the prototypes.
-- Updates to build and run on a IBM PPC 405 [using GCC 3.4.4]
-- Made the "make" command renamable in the build system
October 31st, 2005
0.06 -- fixed fp_mul() and fp_sqr() to trim digits when overflows would occur. Produces numerically inprecise results
(e.g. the lower FP_SIZE digits) but shouldn't segfault at least ;-)

8
demo/test.c
View File

@ -23,7 +23,7 @@ static ulong64 TIMFUNC (void)
{
#if defined __GNUC__
#if defined(INTEL_CC)
ulong64 a;
ulong64 a;
asm ("rdtsc":"=A"(a));
return a;
#elif defined(__i386__) || defined(__x86_64__)
@ -31,9 +31,9 @@ static ulong64 TIMFUNC (void)
__asm__ __volatile__ ("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::"m"(a):"%eax","%edx");
return a;
#elif defined(TFM_PPC32)
unsigned long a;
__asm__ __volatile__ ("mftb %0":"=r"(a));
return a;
unsigned long a, b;
__asm__ __volatile__ ("mftbu %1 \nmftb %0\n":"=r"(a), "=r"(b));
return (((ulong64)b) << 32ULL) | ((ulong64)a);
#else /* gcc-IA64 version */
unsigned long result;
__asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");

BIN
doc/tfm.pdf
View File

Binary file not shown.

30
fp_montgomery_reduce.c
View File

@ -259,24 +259,24 @@ asm( \
#define INNERMUL \
asm( \
" mullw r16,%3,%4 \n\t" \
" mulhwu r17,%3,%4 \n\t" \
" addc r16,r16,%0 \n\t" \
" addze r17,r17 \n\t" \
" lwz r18,%1 \n\t" \
" addc r16,r16,r18 \n\t" \
" addze %0,r17 \n\t" \
" stw r16,%1 \n\t" \
:"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(*tmpm++),"1"(_c[0]):"r16", "r17", "r18","%cc");
" mullw 16,%3,%4 \n\t" \
" mulhwu 17,%3,%4 \n\t" \
" addc 16,16,%0 \n\t" \
" addze 17,17 \n\t" \
" lwz 18,%1 \n\t" \
" addc 16,16,18 \n\t" \
" addze %0,17 \n\t" \
" stw 16,%1 \n\t" \
:"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(tmpm[0]),"1"(_c[0]):"16", "17", "18","%cc"); ++tmpm;
#define PROPCARRY \
asm( \
" lwz r16,%1 \n\t" \
" addc r16,r16,%0 \n\t" \
" stw r16,%1 \n\t" \
" xor %0,%0,%0 \n\t" \
" addze %0,%0 \n\t" \
:"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"r16","%cc");
" lwz 16,%1 \n\t" \
" addc 16,16,%0 \n\t" \
" stw 16,%1 \n\t" \
" xor %0,%0,%0 \n\t" \
" addze %0,%0 \n\t" \
:"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"16","%cc");
/******************************************************************/
#else

32
fp_mul.c
View File

@ -34,28 +34,28 @@ void fp_mul(fp_int *A, fp_int *B, fp_int *C)
#ifdef TFM_SMALL_SET
if (y <= 16) {
fp_mul_comba_small(A,B,C);
#elif defined(TFM_HUGE)
if (0) { 1;
#endif
return;
}
#endif
#if defined(TFM_MUL32)
} else if (y <= 32) {
if (yy >= 24 && y <= 32) {
fp_mul_comba32(A,B,C);
return;
}
#endif
#if defined(TFM_MUL48)
} else if (y <= 48) {
if (yy >= 40 && y <= 48) {
fp_mul_comba48(A,B,C);
#endif
#if defined(TFM_MUL64)
} else if (y <= 64) {
fp_mul_comba64(A,B,C);
#endif
#if !defined(TFM_HUGE) && !defined(TFM_SMALL_SET)
{
#else
} else {
#endif
fp_mul_comba(A,B,C);
return;
}
#endif
#if defined(TFM_MUL64)
if (yy >= 56 && y <= 64) {
fp_mul_comba64(A,B,C);
return;
}
#endif
fp_mul_comba(A,B,C);
} else {
/* do the karatsuba action

10
fp_mul_comba.c
View File

@ -179,12 +179,12 @@ asm( \
/* untested: will mulhwu change the flags? Docs say no */
#define MULADD(i, j) \
asm( \
" mullw r16,%6,%7 \n\t" \
" addc %0,%0,r16 \n\t" \
" mulhwu r16,%6,%7 \n\t" \
" adde %1,%1,r16 \n\t" \
" mullw 16,%6,%7 \n\t" \
" addc %0,%0,16 \n\t" \
" mulhwu 16,%6,%7 \n\t" \
" adde %1,%1,16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i), "r"(j):"r16");
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i), "r"(j):"16");
#else
/* ISO C code */

25
fp_sqr.c
View File

@ -27,29 +27,28 @@ void fp_sqr(fp_int *A, fp_int *B)
#if defined(TFM_SMALL_SET)
if (y <= 16) {
fp_sqr_comba_small(A,B);
#elif defined(TFM_HUGE)
if (0) { 1;
return;
}
#endif
#if defined(TFM_SQR32)
} else if (y <= 32) {
if (y <= 32) {
fp_sqr_comba32(A,B);
return;
}
#endif
#if defined(TFM_SQR48)
} else if (y <= 48) {
if (y <= 48) {
fp_sqr_comba48(A,B);
return;
}
#endif
#if defined(TFM_SQR64)
} else if (y <= 64) {
if (y <= 64) {
fp_sqr_comba64(A,B);
#endif
#if !defined(TFM_SMALL_SET) && !defined(TFM_HUGE)
{
#else
} else {
#endif
fp_sqr_comba(A, B);
return;
}
#endif
fp_sqr_comba(A, B);
} else {
/* do the karatsuba action

58
fp_sqr_comba.c
View File

@ -303,7 +303,7 @@ asm( \
/* PPC32 */
#define COMBA_START \
#define COMBA_START
#define CLEAR_CARRY \
c0 = c1 = c2 = 0;
@ -317,30 +317,30 @@ asm( \
#define CARRY_FORWARD \
do { c0 = c1; c1 = c2; c2 = 0; } while (0);
#define COMBA_FINI \
#define COMBA_FINI
/* multiplies point i and j, updates carry "c1" and digit c2 */
#define SQRADD(i, j) \
asm( \
" mullw r16,%6,%6 \n\t" \
" addc %0,%0,r16 \n\t" \
" mulhwu r16,%6,%6 \n\t" \
" adde %1,%1,r16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i):"r16","%cc");
#define SQRADD(i, j) \
asm( \
" mullw 16,%6,%6 \n\t" \
" addc %0,%0,16 \n\t" \
" mulhwu 16,%6,%6 \n\t" \
" adde %1,%1,16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i):"16","%cc");
/* for squaring some of the terms are doubled... */
#define SQRADD2(i, j) \
asm( \
" mullw r16,%6,%7 \n\t" \
" mulhwu r17,%6,%7 \n\t" \
" addc %0,%0,r16 \n\t" \
" adde %1,%1,r17 \n\t" \
" addze %2,%2 \n\t" \
" addc %0,%0,r16 \n\t" \
" adde %1,%1,r17 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i), "r"(j):"r16", "r17","%cc");
#define SQRADD2(i, j) \
asm( \
" mullw 16,%6,%7 \n\t" \
" mulhwu 17,%6,%7 \n\t" \
" addc %0,%0,16 \n\t" \
" adde %1,%1,17 \n\t" \
" addze %2,%2 \n\t" \
" addc %0,%0,16 \n\t" \
" adde %1,%1,17 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i), "r"(j):"16", "17","%cc");
#define SQRADDSC(i, j) \
asm( \
@ -349,14 +349,14 @@ asm( \
" xor %2,%2,%2 \n\t" \
:"=r"(sc0), "=r"(sc1), "=r"(sc2):"0"(sc0), "1"(sc1), "2"(sc2), "r"(i),"r"(j) : "%cc");
#define SQRADDAC(i, j) \
asm( \
" mullw r16,%6,%7 \n\t" \
" addc %0,%0,r16 \n\t" \
" mulhwu r16,%6,%7 \n\t" \
" adde %1,%1,r16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(sc0), "=r"(sc1), "=r"(sc2):"0"(sc0), "1"(sc1), "2"(sc2), "r"(i), "r"(j):"r16", "%cc");
#define SQRADDAC(i, j) \
asm( \
" mullw 16,%6,%7 \n\t" \
" addc %0,%0,16 \n\t" \
" mulhwu 16,%6,%7 \n\t" \
" adde %1,%1,16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(sc0), "=r"(sc1), "=r"(sc2):"0"(sc0), "1"(sc1), "2"(sc2), "r"(i), "r"(j):"16", "%cc");
#define SQRADDDB \
asm( \

17
makefile
View File

@ -1,10 +1,14 @@
#makefile for TomsFastMath
#
#
VERSION=0.06
VERSION=0.07
CFLAGS += -Wall -W -Wshadow -I./
ifndef MAKE
MAKE=make
endif
ifndef IGNORE_SPEED
CFLAGS += -O3 -funroll-all-loops
@ -85,7 +89,7 @@ install: $(LIBNAME)
install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)
mtest/mtest: mtest/mtest.c
cd mtest ; CFLAGS="$(CFLAGS) -I../" make mtest
cd mtest ; CFLAGS="$(CFLAGS) -I../" MAKE=${MAKE} ${MAKE} mtest
test: $(LIBNAME) demo/test.o mtest/mtest
$(CC) $(CFLAGS) demo/test.o $(LIBNAME) $(PROF) -o test
@ -128,7 +132,7 @@ clean:
rm -f `find . -type f | grep "[.]dpi" | xargs`
rm -rf `find . -type d | grep "[.]libs" | xargs`
rm -f tfm.aux tfm.dvi tfm.idx tfm.ilg tfm.ind tfm.lof tfm.log tfm.toc
cd mtest ; make clean
cd mtest ; MAKE=${MAKE} ${MAKE} clean
no_oops: clean
cd .. ; cvs commit
@ -140,8 +144,9 @@ zipup: no_oops docs clean
cd .. ; rm -rf tfm* tomsfastmath-$(VERSION) ; mkdir tomsfastmath-$(VERSION) ; \
cp -R ./tomsfastmath/* ./tomsfastmath-$(VERSION)/ ; \
tar -c tomsfastmath-$(VERSION)/* | bzip2 -9vvc > tfm-$(VERSION).tar.bz2 ; \
zip -9r tfm-$(VERSION).zip tomsfastmath-$(VERSION)/*
zip -9r tfm-$(VERSION).zip tomsfastmath-$(VERSION)/* ; \
mv -f tfm* ~ ; rm -rf tomsfastmath-$(VERSION)
# $Source: /cvs/libtom/tomsfastmath/makefile,v $
# $Revision: 1.19 $
# $Date: 2005/08/25 23:53:40 $
# $Revision: 1.23 $
# $Date: 2005/11/18 06:13:57 $

6
makefile.shared
View File

@ -1,7 +1,7 @@
#makefile for TomsFastMath
#
#
VERSION=0:6
VERSION=0:7
CC=libtool --mode=compile gcc
@ -104,6 +104,6 @@ stest: $(LIBNAME) demo/stest.o
$(CC) $(CFLAGS) demo/stest.o $(LIBNAME_S) -o stest
# $Source: /cvs/libtom/tomsfastmath/makefile.shared,v $
# $Revision: 1.7 $
# $Date: 2005/10/06 23:31:17 $
# $Revision: 1.8 $
# $Date: 2005/10/31 17:26:00 $

155
pre_gen/mpi.c
View File

@ -1951,24 +1951,24 @@ asm( \
#define INNERMUL \
asm( \
" mullw r16,%3,%4 \n\t" \
" mulhwu r17,%3,%4 \n\t" \
" addc r16,r16,%0 \n\t" \
" addze r17,r17 \n\t" \
" lwz r18,%1 \n\t" \
" addc r16,r16,r18 \n\t" \
" addze %0,r17 \n\t" \
" stw r16,%1 \n\t" \
:"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(*tmpm++),"1"(_c[0]):"r16", "r17", "r18","%cc");
" mullw 16,%3,%4 \n\t" \
" mulhwu 17,%3,%4 \n\t" \
" addc 16,16,%0 \n\t" \
" addze 17,17 \n\t" \
" lwz 18,%1 \n\t" \
" addc 16,16,18 \n\t" \
" addze %0,17 \n\t" \
" stw 16,%1 \n\t" \
:"=r"(cy),"=m"(_c[0]):"0"(cy),"r"(mu),"r"(tmpm[0]),"1"(_c[0]):"16", "17", "18","%cc"); ++tmpm;
#define PROPCARRY \
asm( \
" lwz r16,%1 \n\t" \
" addc r16,r16,%0 \n\t" \
" stw r16,%1 \n\t" \
" xor %0,%0,%0 \n\t" \
" addze %0,%0 \n\t" \
:"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"r16","%cc");
" lwz 16,%1 \n\t" \
" addc 16,16,%0 \n\t" \
" stw 16,%1 \n\t" \
" xor %0,%0,%0 \n\t" \
" addze %0,%0 \n\t" \
:"=r"(cy),"=m"(_c[0]):"0"(cy),"1"(_c[0]):"16","%cc");
/******************************************************************/
#else
@ -2169,28 +2169,28 @@ void fp_mul(fp_int *A, fp_int *B, fp_int *C)
#ifdef TFM_SMALL_SET
if (y <= 16) {
fp_mul_comba_small(A,B,C);
#elif defined(TFM_HUGE)
if (0) { 1;
#endif
return;
}
#endif
#if defined(TFM_MUL32)
} else if (y <= 32) {
if (yy >= 24 && y <= 32) {
fp_mul_comba32(A,B,C);
return;
}
#endif
#if defined(TFM_MUL48)
} else if (y <= 48) {
if (yy >= 40 && y <= 48) {
fp_mul_comba48(A,B,C);
#endif
#if defined(TFM_MUL64)
} else if (y <= 64) {
fp_mul_comba64(A,B,C);
#endif
#if !defined(TFM_HUGE) && !defined(TFM_SMALL_SET)
{
#else
} else {
#endif
fp_mul_comba(A,B,C);
return;
}
#endif
#if defined(TFM_MUL64)
if (yy >= 56 && y <= 64) {
fp_mul_comba64(A,B,C);
return;
}
#endif
fp_mul_comba(A,B,C);
} else {
/* do the karatsuba action
@ -2596,12 +2596,12 @@ asm( \
/* untested: will mulhwu change the flags? Docs say no */
#define MULADD(i, j) \
asm( \
" mullw r16,%6,%7 \n\t" \
" addc %0,%0,r16 \n\t" \
" mulhwu r16,%6,%7 \n\t" \
" adde %1,%1,r16 \n\t" \
" mullw 16,%6,%7 \n\t" \
" addc %0,%0,16 \n\t" \
" mulhwu 16,%6,%7 \n\t" \
" adde %1,%1,16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i), "r"(j):"r16");
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i), "r"(j):"16");
#else
/* ISO C code */
@ -5740,29 +5740,28 @@ void fp_sqr(fp_int *A, fp_int *B)
#if defined(TFM_SMALL_SET)
if (y <= 16) {
fp_sqr_comba_small(A,B);
#elif defined(TFM_HUGE)
if (0) { 1;
return;
}
#endif
#if defined(TFM_SQR32)
} else if (y <= 32) {
if (y <= 32) {
fp_sqr_comba32(A,B);
return;
}
#endif
#if defined(TFM_SQR48)
} else if (y <= 48) {
if (y <= 48) {
fp_sqr_comba48(A,B);
return;
}
#endif
#if defined(TFM_SQR64)
} else if (y <= 64) {
if (y <= 64) {
fp_sqr_comba64(A,B);
#endif
#if !defined(TFM_SMALL_SET) && !defined(TFM_HUGE)
{
#else
} else {
#endif
fp_sqr_comba(A, B);
return;
}
#endif
fp_sqr_comba(A, B);
} else {
/* do the karatsuba action
@ -6150,7 +6149,7 @@ asm( \
/* PPC32 */
#define COMBA_START \
#define COMBA_START
#define CLEAR_CARRY \
c0 = c1 = c2 = 0;
@ -6164,30 +6163,30 @@ asm( \
#define CARRY_FORWARD \
do { c0 = c1; c1 = c2; c2 = 0; } while (0);
#define COMBA_FINI \
#define COMBA_FINI
/* multiplies point i and j, updates carry "c1" and digit c2 */
#define SQRADD(i, j) \
asm( \
" mullw r16,%6,%6 \n\t" \
" addc %0,%0,r16 \n\t" \
" mulhwu r16,%6,%6 \n\t" \
" adde %1,%1,r16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i):"r16","%cc");
#define SQRADD(i, j) \
asm( \
" mullw 16,%6,%6 \n\t" \
" addc %0,%0,16 \n\t" \
" mulhwu 16,%6,%6 \n\t" \
" adde %1,%1,16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i):"16","%cc");
/* for squaring some of the terms are doubled... */
#define SQRADD2(i, j) \
asm( \
" mullw r16,%6,%7 \n\t" \
" mulhwu r17,%6,%7 \n\t" \
" addc %0,%0,r16 \n\t" \
" adde %1,%1,r17 \n\t" \
" addze %2,%2 \n\t" \
" addc %0,%0,r16 \n\t" \
" adde %1,%1,r17 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i), "r"(j):"r16", "r17","%cc");
#define SQRADD2(i, j) \
asm( \
" mullw 16,%6,%7 \n\t" \
" mulhwu 17,%6,%7 \n\t" \
" addc %0,%0,16 \n\t" \
" adde %1,%1,17 \n\t" \
" addze %2,%2 \n\t" \
" addc %0,%0,16 \n\t" \
" adde %1,%1,17 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(c0), "=r"(c1), "=r"(c2):"0"(c0), "1"(c1), "2"(c2), "r"(i), "r"(j):"16", "17","%cc");
#define SQRADDSC(i, j) \
asm( \
@ -6196,14 +6195,14 @@ asm( \
" xor %2,%2,%2 \n\t" \
:"=r"(sc0), "=r"(sc1), "=r"(sc2):"0"(sc0), "1"(sc1), "2"(sc2), "r"(i),"r"(j) : "%cc");
#define SQRADDAC(i, j) \
asm( \
" mullw r16,%6,%7 \n\t" \
" addc %0,%0,r16 \n\t" \
" mulhwu r16,%6,%7 \n\t" \
" adde %1,%1,r16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(sc0), "=r"(sc1), "=r"(sc2):"0"(sc0), "1"(sc1), "2"(sc2), "r"(i), "r"(j):"r16", "%cc");
#define SQRADDAC(i, j) \
asm( \
" mullw 16,%6,%7 \n\t" \
" addc %0,%0,16 \n\t" \
" mulhwu 16,%6,%7 \n\t" \
" adde %1,%1,16 \n\t" \
" addze %2,%2 \n\t" \
:"=r"(sc0), "=r"(sc1), "=r"(sc2):"0"(sc0), "1"(sc1), "2"(sc2), "r"(i), "r"(j):"16", "%cc");
#define SQRADDDB \
asm( \

BIN
tfm.dvi
View File

Binary file not shown.

12
tfm.h
View File

@ -372,9 +372,13 @@ void fp_mul_comba(fp_int *A, fp_int *B, fp_int *C);
void fp_mul_comba_small(fp_int *A, fp_int *B, fp_int *C);
#endif
#ifdef TFM_HUGE
#ifdef TFM_MUL32
void fp_mul_comba32(fp_int *A, fp_int *B, fp_int *C);
#endif
#ifdef TFM_MUL48
void fp_mul_comba48(fp_int *A, fp_int *B, fp_int *C);
#endif
#ifdef TFM_MUL64
void fp_mul_comba64(fp_int *A, fp_int *B, fp_int *C);
#endif
@ -384,9 +388,13 @@ void fp_sqr_comba(fp_int *A, fp_int *B);
void fp_sqr_comba_small(fp_int *A, fp_int *B);
#endif
#ifdef TFM_HUGE
#ifdef TFM_SQR32
void fp_sqr_comba32(fp_int *A, fp_int *B);
#endif
#ifdef TFM_SQR48
void fp_sqr_comba48(fp_int *A, fp_int *B);
#endif
#ifdef TFM_SQR64
void fp_sqr_comba64(fp_int *A, fp_int *B);
#endif
extern const char *fp_s_rmap;

4
tfm.log
View File

@ -1,4 +1,4 @@
This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=latex 2005.9.20) 31 OCT 2005 11:30
This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=latex 2005.11.6) 18 NOV 2005 06:14
entering extended mode
**tfm
(./tfm.tex
@ -329,4 +329,4 @@ Here is how much of TeX's memory you used:
580 hyphenation exceptions out of 1000
25i,9n,25p,195b,321s stack positions out of 1500i,500n,1500p,200000b,5000s
Output written on tfm.dvi (25 pages, 51616 bytes).
Output written on tfm.dvi (25 pages, 51624 bytes).

2
tfm.tex
View File

@ -49,7 +49,7 @@
\begin{document}
\frontmatter
\pagestyle{empty}
\title{TomsFastMath User Manual \\ v0.06}
\title{TomsFastMath User Manual \\ v0.07}
\author{Tom St Denis \\ tomstdenis@gmail.com}
\maketitle
This text and library are all hereby placed in the public domain. This book has been formatted for B5