This chapter describes some tips and tricks for debugging numerical
programs which use GSL.

@menu
* Using gdb::                   
* Examining floating point registers::  
* Handling floating point exceptions::  
* GCC warning options for numerical programs::  
* Debugging References::        
@end menu

@node Using gdb
@section Using gdb
@cindex gdb
@cindex debugging numerical programs
@cindex breakpoints
Any errors reported by the library are passed to the function
@code{gsl_error}.  By running your programs under gdb and setting a
breakpoint in this function you can automatically catch any library
errors.  You can add a breakpoint for every session by putting

@example
break gsl_error
@end example
@comment 

@noindent
into your @file{.gdbinit} file in the directory where your program is
started.  

If the breakpoint catches an error then you can use a backtrace
(@code{bt}) to see the call-tree, and the arguments which possibly
caused the error.  By moving up into the calling function you can
investigate the values of variables at that point.  Here is an example
from the program @code{fft/test_trap}, which contains the following
line,

@smallexample
status = gsl_fft_complex_wavetable_alloc (0, &complex_wavetable);
@end smallexample

@noindent
The function @code{gsl_fft_complex_wavetable_alloc} takes the length of
an FFT as its first argument.  When this line is executed an error will
be generated because the length of an FFT is not allowed to be zero.

To debug this problem we start @code{gdb}, using the file
@file{.gdbinit} to define a breakpoint in @code{gsl_error},

@smallexample
$ gdb test_trap

GDB is free software and you are welcome to distribute copies
of it under certain conditions; type "show copying" to see
the conditions.  There is absolutely no warranty for GDB;
type "show warranty" for details.  GDB 4.16 (i586-debian-linux), 
Copyright 1996 Free Software Foundation, Inc.

Breakpoint 1 at 0x8050b1e: file error.c, line 14.
@end smallexample

@noindent
When we run the program this breakpoint catches the error and shows the
reason for it. 

@smallexample
(gdb) run
Starting program: test_trap 

Breakpoint 1, gsl_error (reason=0x8052b0d 
    "length n must be positive integer", 
    file=0x8052b04 "c_init.c", line=108, gsl_errno=1) 
    at error.c:14
14        if (gsl_error_handler) 
@end smallexample
@comment 

@noindent
The first argument of @code{gsl_error} is always a string describing the
error.  Now we can look at the backtrace to see what caused the problem,

@smallexample
(gdb) bt
#0  gsl_error (reason=0x8052b0d 
    "length n must be positive integer", 
    file=0x8052b04 "c_init.c", line=108, gsl_errno=1)
    at error.c:14
#1  0x8049376 in gsl_fft_complex_wavetable_alloc (n=0,
    wavetable=0xbffff778) at c_init.c:108
#2  0x8048a00 in main (argc=1, argv=0xbffff9bc) 
    at test_trap.c:94
#3  0x80488be in ___crt_dummy__ ()
@end smallexample
@comment 

@noindent
We can see that the error was generated in the function
@code{gsl_fft_complex_wavetable_alloc} when it was called with an
argument of @var{n=0}.  The original call came from line 94 in the
file @file{test_trap.c}.

By moving up to the level of the original call we can find the line that
caused the error,

@smallexample
(gdb) up
#1  0x8049376 in gsl_fft_complex_wavetable_alloc (n=0,
    wavetable=0xbffff778) at c_init.c:108
108   GSL_ERROR ("length n must be positive integer", GSL_EDOM);
(gdb) up
#2  0x8048a00 in main (argc=1, argv=0xbffff9bc) 
    at test_trap.c:94
94    status = gsl_fft_complex_wavetable_alloc (0,
        &complex_wavetable);
@end smallexample
@comment 

@noindent
Thus we have found the line that caused the problem.  From this point we
could also print out the values of other variables such as
@code{complex_wavetable}.

@node Examining floating point registers
@section Examining floating point registers

The contents of floating point registers can be examined using the
command @code{info float} (on supported platforms).

@smallexample
(gdb) info float
     st0: 0xc4018b895aa17a945000  Valid Normal -7.838871e+308
     st1: 0x3ff9ea3f50e4d7275000  Valid Normal 0.0285946
     st2: 0x3fe790c64ce27dad4800  Valid Normal 6.7415931e-08
     st3: 0x3ffaa3ef0df6607d7800  Spec  Normal 0.0400229
     st4: 0x3c028000000000000000  Valid Normal 4.4501477e-308
     st5: 0x3ffef5412c22219d9000  Zero  Normal 0.9580257
     st6: 0x3fff8000000000000000  Valid Normal 1
     st7: 0xc4028b65a1f6d243c800  Valid Normal -1.566206e+309
   fctrl: 0x0272 53 bit; NEAR; mask DENOR UNDER LOS;
   fstat: 0xb9ba flags 0001; top 7; excep DENOR OVERF UNDER LOS
    ftag: 0x3fff
     fip: 0x08048b5c
     fcs: 0x051a0023
  fopoff: 0x08086820
  fopsel: 0x002b
@end smallexample

@noindent
Individual registers can be examined using the variables @var{$reg},
where @var{reg} is the register name.

@smallexample
(gdb) p $st1 
$1 = 0.02859464454261210347719
@end smallexample

@node Handling floating point exceptions
@section Handling floating point exceptions

It is possible to stop the program whenever a @code{SIGFPE} floating
point exception occurs.  This can be useful for finding the cause of an
unexpected infinity or @code{NaN}.  The current handler settings can be
shown with the command @code{info signal SIGFPE}.

@smallexample
(gdb) info signal SIGFPE
Signal  Stop  Print  Pass to program Description
SIGFPE  Yes   Yes    Yes             Arithmetic exception
@end smallexample

@noindent
Unless the program uses a signal handler the default setting should be
changed so that SIGFPE is not passed to the program, as this would cause
it to exit.  The command @code{handle SIGFPE stop nopass} prevents this.

@smallexample
(gdb) handle SIGFPE stop nopass
Signal  Stop  Print  Pass to program Description
SIGFPE  Yes   Yes    No              Arithmetic exception
@end smallexample

@noindent
Depending on the platform it may be necessary to instruct the kernel to
generate signals for floating point exceptions.  For programs using GSL
this can be achieved using the @code{GSL_IEEE_MODE} environment variable
in conjunction with the function @code{gsl_ieee_env_setup} as described
in @pxref{IEEE floating-point arithmetic}.

@example
(gdb) set env GSL_IEEE_MODE=double-precision
@end example


@node GCC warning options for numerical programs
@section GCC warning options for numerical programs
@cindex warning options
@cindex gcc warning options

Writing reliable numerical programs in C requires great care.  The
following GCC warning options are recommended when compiling numerical
programs:

@comment Uninitialized variables, conversions to and from integers or from
@comment signed to unsigned integers can all cause hard-to-find problems.  For
@comment many non-numerical programs compiling with @code{gcc}'s warning option
@comment @code{-Wall} provides a good check against common errors.  However, for
@comment numerical programs @code{-Wall} is not enough. 

@comment If you are unconvinced take a look at this program which contains an
@comment error that can occur in numerical code,

@comment @example
@comment #include <math.h>
@comment #include <stdio.h>

@comment double f (int x);

@comment int main ()
@comment @{
@comment   double a = 1.5;
@comment   double y = f(a);
@comment   printf("a = %g, sqrt(a) = %g\n", a, y);  
@comment   return 0;
@comment @}

@comment double f(x) @{
@comment   return sqrt(x);
@comment @}
@comment @end example

@comment @noindent
@comment This code compiles cleanly with @code{-Wall} but produces some strange
@comment output,

@comment @example
@comment bash$ gcc -Wall tmp.c -lm
@comment bash$ ./a.out 
@comment a = 1.5, sqrt(a) = 1
@comment @end example

@comment @noindent
@comment Note that adding @code{-ansi} does not help here, since the program does
@comment not contain any invalid constructs.  What is happening is that the
@comment prototype for the function @code{f(int x)} is not consistent with the
@comment function call @code{f(y)}, where @code{y} is a floating point
@comment number.  This results in the argument being silently converted to an
@comment integer.  This is valid C, but in a numerical program it also likely to
@comment be a programming error so we would like to be warned about it. (If we
@comment genuinely wanted to convert @code{y} to an integer then we could use an
@comment explicit cast, @code{(int)y}).  

@comment Fortunately GCC provides many additional warnings which can alert you to
@comment problems such as this.  You just have to remember to use them.  Here is a
@comment set of recommended warning options for numerical programs.

@example
gcc -ansi -pedantic -Werror -Wall -W 
  -Wmissing-prototypes -Wstrict-prototypes 
  -Wtraditional -Wconversion -Wshadow
  -Wpointer-arith -Wcast-qual -Wcast-align 
  -Wwrite-strings -Wnested-externs 
  -fshort-enums -fno-common -Dinline= -g -O2
@end example

@noindent
For details of each option consult the manual @cite{Using and Porting
GCC}.  The following table gives a brief explanation of what types of
errors these options catch.

@table @code
@item -ansi -pedantic 
Use ANSI C, and reject any non-ANSI extensions.  These flags help in
writing portable programs that will compile on other systems.
@item -Werror 
Consider warnings to be errors, so that compilation stops.  This prevents
warnings from scrolling off the top of the screen and being lost.  You
won't be able to compile the program until it is completely
warning-free.
@item -Wall 
This turns on a set of warnings for common programming problems.  You
need @code{-Wall}, but it is not enough on its own.
@item -O2
Turn on optimization.  The warnings for uninitialized variables in
@code{-Wall} rely on the optimizer to analyze the code.  If there is no
optimization then these warnings aren't generated.
@item -W 
This turns on some extra warnings not included in @code{-Wall}, such as
missing return values and comparisons between signed and unsigned
integers.
@item -Wmissing-prototypes -Wstrict-prototypes 
Warn if there are any missing or inconsistent prototypes.  Without
prototypes it is harder to detect problems with incorrect arguments. 
@item -Wtraditional 
This warns about certain constructs that behave differently in
traditional and ANSI C. Whether the traditional or ANSI interpretation
is used might be unpredictable on other compilers. 
@item -Wconversion 
The main use of this option is to warn about conversions from signed to
unsigned integers.  For example, @code{unsigned int x = -1}.  If you need
to perform such a conversion you can use an explicit cast.
@item -Wshadow
This warns whenever a local variable shadows another local variable.  If
two variables have the same name then it is a potential source of
confusion.
@item -Wpointer-arith -Wcast-qual -Wcast-align 
These options warn if you try to do pointer arithmetic for types which
don't have a size, such as @code{void}, if you remove a @code{const}
cast from a pointer, or if you cast a pointer to a type which has a
different size, causing an invalid alignment.
@item -Wwrite-strings
This option gives string constants a @code{const} qualifier so that it
will be a compile-time error to attempt to overwrite them.
@item -fshort-enums 
This option makes the type of @code{enum} as short as possible.  Normally
this makes an @code{enum} different from an @code{int}.  Consequently any
attempts to assign a pointer-to-int to a pointer-to-enum will generate a
cast-alignment warning.
@item -fno-common
This option prevents global variables being simultaneously defined in
different object files (you get an error at link time).  Such a variable
should be defined in one file and referred to in other files with an
@code{extern} declaration.
@item -Wnested-externs 
This warns if an @code{extern} declaration is encountered within a
function.
@item -Dinline= 
The @code{inline} keyword is not part of ANSI C. Thus if you want to use
@code{-ansi} with a program which uses inline functions you can use this
preprocessor definition to remove the @code{inline} keywords.
@item -g 
It always makes sense to put debugging symbols in the executable so that
you can debug it using @code{gdb}.  The only effect of debugging symbols
is to increase the size of the file, and you can use the @code{strip}
command to remove them later if necessary.
@end table

@comment For comparison, this is what happens when the test program above is
@comment compiled with these options.

@comment @example
@comment bash$ gcc -ansi -pedantic -Werror -W -Wall -Wtraditional 
@comment -Wconversion -Wshadow -Wpointer-arith -Wcast-qual -Wcast-align 
@comment -Wwrite-strings -Waggregate-return -Wstrict-prototypes -fshort-enums 
@comment -fno-common -Wmissing-prototypes -Wnested-externs -Dinline= 
@comment -g -O4 tmp.c 
@comment cc1: warnings being treated as errors
@comment tmp.c:7: warning: function declaration isn't a prototype
@comment tmp.c: In function `main':
@comment tmp.c:9: warning: passing arg 1 of `f' as integer rather than floating 
@comment due to prototype
@comment tmp.c: In function `f':
@comment tmp.c:14: warning: type of `x' defaults to `int'
@comment tmp.c:15: warning: passing arg 1 of `sqrt' as floating rather than integer 
@comment due to prototype
@comment make: *** [tmp] Error 1
@comment @end example

@comment @noindent
@comment The error in the prototype is flagged, plus the fact that we should have
@comment defined main as @code{int main (void)} in ANSI C. Clearly there is some
@comment work to do before this program is ready to run.

@node Debugging References
@section References and Further Reading

The following books are essential reading for anyone writing and
debugging numerical programs with @sc{gcc} and @sc{gdb}.

@itemize @asis
@item
R.M. Stallman, @cite{Using and Porting GNU CC}, Free Software
Foundation, ISBN 1882114388

@item
R.M. Stallman, R.H. Pesch, @cite{Debugging with GDB: The GNU
Source-Level Debugger}, Free Software Foundation, ISBN 1882114779
@end itemize

@noindent
For a tutorial introduction to the GNU C Compiler and related programs,
see 

@itemize @asis
@item
B.J. Gough, @cite{An Introduction to GCC}, Network Theory Ltd, ISBN
0954161793
@end itemize