The standard library function abs() is declared in stdlib.h, while fabs() is in math.h.
Why are they reside in different headers?
math.h first appears in 7th Research Unix. It is hard to tell how it got there. For example, [1] claims that bits of C library were merged from "PWB/Unix" which included troff and C compiler pcc, but I cannot prove it.
Another interesting piece of information is library manual from V7 Unix:
intro.3:
(3) These functions, together with those of section 2 and those marked (3S),
constitute library libc, which is automatically loaded by the C compiler
cc(1) and the Fortran compiler f77(1). The link editor ld(1) searches
this library under the `-lc' option. Declarations for some of these
functions may be obtained from include files indicated on the appropri-
ate pages.
<...>
(3M) These functions constitute the math library, libm. They are automati-
cally loaded as needed by the Fortran compiler f77(1). The link editor
searches this library under the `-lm' option. Declarations for these
functions may be obtained from the include file <math.h>.
If you look into V7 commands makefiles, only few C programs are linked with -lm flag. So my conclusion is speculative:
libm.a (and math.h) was primarily needed for FORTRAN programs mostly, so it was separated into library to reduce binary footprint (note that it was linked statically).
Not many machines had floating point support. For example, you would need to buy an optional FPP for PDP-11 [2], there is also libfpsim simulation library in Unix to mitigate that, so floating point can be hardly used in early C programs.
1. A History of UNIX before Berkeley: UNIX Evolution: 1975-1984
2. PDP-11 architecture
Most operators like + - / * are also math operators yet these are also readily available. When programming you use so much math, that developers have started to differentiate between math that is needed for everyday stuff and math that is more specialized that you only use some of the time. Abs is one of those functions that are just used to often. Like with pointer arithmetic when you just want to know the difference to calculate the size of a memory block. But you are not interested in knowing which is higher in memory and which is lower.
So to sum up: abs is used often because it calculates the difference of two integers. The difference between two pointers for instance is also an integer. And so it is in stdlib.h. fabs how ever is not something you will need much unless you are doing math specific stuff. Thus it is in math.h.
I'd like to know how C Header Files and ABIs relate. The sizes of various types are architecture and even compiler-dependent. Then how can one reliably link to a C library?
For a more specific problem: When using Haskell's FFI, one even only uses Haskell types like CDouble to define (duplicate the definition of) the C library interface. I don't know where the binary type size information is coming from. What is the trick for making the linking work?
Please see this link https://code.google.com/p/tabi
It may help you to avoid difficulties with possible ABI differences between Haskell and C.
The library type information comes from magic macros that are run to insert information grabbed from the C compiler by autoconf.
For example, see the definition of CDoublehere: https://hackage.haskell.org/package/base-4.8.2.0/docs/src/Foreign.C.Types.html#CDouble
and then see where the HTYPE_DOUBLE size comes from in this autoconf input here: https://hackage.haskell.org/package/base-4.8.2.0/src/include/HsBaseConfig.h.in
Since GHH compiles against the compiler/arch it is compiled with (except in the special cross-compiler modes, which are new and different in ways I'm not fully cognizant of) this makes everything tie out with the ABI properly.
I need to track down how exactly is double sin(double x) implemented in eglibc-2.13. I downloaded the source code and the only part that made sense was __sin function, that was platform-specific. Is it the heart of what I have in /usr/lib/i386-linux-gnu/libm.a?
How to track down the macrodefinitions that lead from sin() to __sin()? What I really need is the exact code (filename and the line is enough) and a way in which the build process deduces which implementation to use. The architecture's i386.
The (e)glibc build process is black, black magic. You do not want to try to comprehend it. However, glibc adheres to a one-file-per-public-function coding style, so in general, if you have the source tree and you want to find the implementation(s) of some function, the easiest thing to do is
$ find * -name '*function*' -print
from the top level, replacing function with the name of the function, of course.
Talking specifically about sin: the generic implementations of the math functions are in the math directory: however, it appears that there is no generic definition of sin. So the next place to look is sysdeps. Everything that isn't generic is in sysdeps, and in particular, sysdeps/ieee754 is where all the math functions that have some dependence on the IEEE 754 floating point specification, but no other system dependencies, live. This directory is organized by type: sysdeps/ieee754/dbl-64 contains all the math functions for IEEE double. And here you will find sysdeps/ieee754/dbl-64/s_sin.c, which is the code you are looking for. (The e_, s_, k_, etc prefixes on all these files used to mean something but AFAIK no longer do.)
If there were an implementation of sin in assembly language for a particular processor, it would be in a file named sin.S (or possibly s_sin.S) somewhere else in sysdeps. It does not appear that there is one, though.
Not an answer, but just a bit of a background:
When you use sin() or cos() in your C code, it is almost certainly the compiler that provides the implementation, rather than your C library. As an example, look at the list of builtins GCC provides. The linked page also describes the cases where the built-ins are used rather than the versions the C library provides.
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Why do you have to link the math library in C?
When I write a program that uses functions from the math.h library, why is it that I have to explicitly link to libm even though they are part of the C standard library?
For instance, when I want to use the sin() function I need to #include <math.h> but I also need to pass -lm to GCC. But for any other library from the standard library, I don't have to do that. Why the difference?
In the old days, linkers were slow and separating the mostly unused math code from the rest made the compilation process go faster. The difference is not so great today, so you can add the -lm option to your default compiler configuration.
Note that the header <math.h> (or any other header) does not contain code. It contains information about the code, specifically how to call functions. The code itself is in a library. I mean, your program does not use the "<math.h> library", it uses the math library and uses the prototypes declared in the <math.h> header.
It's the same reason you have to explicitly link to libpthread on most implementations. When something new and scary is added to the standard library, it usually first gets implemented as a separate add-on library that overrides some of the symbols in the old standard library implementation with versions that conform to the new requirements, while also adding lots of new interfaces. I wouldn't be surprised if some historical implementations had separate versions of printf in libm for floating point printing, with a "light" version in the main libc lacking floating point. This kind of implementation is actually mentioned and encouraged for tiny systems in the ISO C rationale document, if I remember correctly.
Of course in the long-term, separating the standard library out like this leads to a lot more problems than benefits. The worst part is probably the increased load time and memory usage for dynamic-linked programs.
Actually, the reason you normally don't need to link against libm for most math functions is that these are inlined by your compiler. Your program would fail to link on a platform where this is not the case.
If I include <stdlib.h> or <stdio.h> in a C program, I don't have to link these when compiling, but I do have to link to <math.h>, using -lm with GCC, for example:
gcc test.c -o test -lm
What is the reason for this? Why do I have to explicitly link the math library, but not the other libraries?
The functions in stdlib.h and stdio.h have implementations in libc.so (or libc.a for static linking), which is linked into your executable by default (as if -lc were specified). GCC can be instructed to avoid this automatic link with the -nostdlib or -nodefaultlibs options.
The math functions in math.h have implementations in libm.so (or libm.a for static linking), and libm is not linked in by default. There are historical reasons for this libm/libc split, none of them very convincing.
Interestingly, the C++ runtime libstdc++ requires libm, so if you compile a C++ program with GCC (g++), you will automatically get libm linked in.
Remember that C is an old language and that FPUs are a relatively recent phenomenon. I first saw C on 8-bit processors where it was a lot of work to do even 32-bit integer arithmetic. Many of these implementations didn't even have a floating point math library available!
Even on the first 68000 machines (Mac, Atari ST, Amiga), floating point coprocessors were often expensive add-ons.
To do all that floating point math, you needed a pretty sizable library. And the math was going to be slow. So you rarely used floats. You tried to do everything with integers or scaled integers. When you had to include math.h, you gritted your teeth. Often, you'd write your own approximations and lookup tables to avoid it.
Trade-offs existed for a long time. Sometimes there were competing math packages called "fastmath" or such. What's the best solution for math? Really accurate but slow stuff? Inaccurate but fast? Big tables for trig functions? It wasn't until coprocessors were guaranteed to be in the computer that most implementations became obvious. I imagine that there's some programmer out there somewhere right now, working on an embedded chip, trying to decide whether to bring in the math library to handle some math problem.
That's why math wasn't standard. Many or maybe most programs didn't use a single float. If FPUs had always been around and floats and doubles were always cheap to operate on, no doubt there would have been a "stdmath".
Because of ridiculous historical practice that nobody is willing to fix. Consolidating all of the functions required by C and POSIX into a single library file would not only avoid this question getting asked over and over, but would also save a significant amount of time and memory when dynamic linking, since each .so file linked requires the filesystem operations to locate and find it, and a few pages for its static variables, relocations, etc.
An implementation where all functions are in one library and the -lm, -lpthread, -lrt, etc. options are all no-ops (or link to empty .a files) is perfectly POSIX conformant and certainly preferable.
Note: I'm talking about POSIX because C itself does not specify anything about how the compiler is invoked. Thus you can just treat gcc -std=c99 -lm as the implementation-specific way the compiler must be invoked for conformant behavior.
Because time() and some other functions are builtin defined in the C library (libc) itself and GCC always links to libc unless you use the -ffreestanding compile option. However math functions live in libm which is not implicitly linked by gcc.
An explanation is given here:
So if your program is using math functions and including math.h, then you need to explicitly link the math library by passing the -lm flag. The reason for this particular separation is that mathematicians are very picky about the way their math is being computed and they may want to use their own implementation of the math functions instead of the standard implementation. If the math functions were lumped into libc.a it wouldn't be possible to do that.
[Edit]
I'm not sure I agree with this, though. If you have a library which provides, say, sqrt(), and you pass it before the standard library, a Unix linker will take your version, right?
There's a thorough discussion of linking to external libraries in An Introduction to GCC - Linking with external libraries. If a library is a member of the standard libraries (like stdio), then you don't need to specify to the compiler (really the linker) to link them.
After reading some of the other answers and comments, I think the libc.a reference and the libm reference that it links to both have a lot to say about why the two are separate.
Note that many of the functions in 'libm.a' (the math library) are defined in 'math.h' but are not present in libc.a. Some are, which may get confusing, but the rule of thumb is this--the C library contains those functions that ANSI dictates must exist, so that you don't need the -lm if you only use ANSI functions. In contrast, `libm.a' contains more functions and supports additional functionality such as the matherr call-back and compliance to several alternative standards of behavior in case of FP errors. See section libm, for more details.
As ephemient said, the C library libc is linked by default and this library contains the implementations of stdlib.h, stdio.h and several other standard header files. Just to add to it, according to "An Introduction to GCC" the linker command for a basic "Hello World" program in C is as below:
ld -dynamic-linker /lib/ld-linux.so.2 /usr/lib/crt1.o
/usr/lib/crti.o /usr/libgcc-lib /i686/3.3.1/crtbegin.o
-L/usr/lib/gcc-lib/i686/3.3.1 hello.o -lgcc -lgcc_eh -lc
-lgcc -lgcc_eh /usr/lib/gcc-lib/i686/3.3.1/crtend.o /usr/lib/crtn.o
Notice the option -lc in the third line that links the C library.
If I put stdlib.h or stdio.h, I don't have to link those but I have to link when I compile:
stdlib.h, stdio.h are the header files. You include them for your convenience. They only forecast what symbols will become available if you link in the proper library. The implementations are in the library files, that's where the functions really live.
Including math.h is only the first step to gaining access to all the math functions.
Also, you don't have to link against libm if you don't use it's functions, even if you do a #include <math.h> which is only an informational step for you, for the compiler about the symbols.
stdlib.h, stdio.h refer to functions available in libc, which happens to be always linked in so that the user doesn't have to do it himself.
It's a bug. You shouldn't have to explicitly specify -lm any more. Perhaps if enough people complain about it, it will be fixed. (I don't seriously believe this, as the maintainers who are perpetuating the distinction are evidently very stubborn, but I can hope.)
I think it's kind of arbitrary. You have to draw a line somewhere (which libraries are default and which need to be specified).
It gives you the opportunity to replace it with a different one that has the same functions, but I don't think it's very common to do so.
I think GCC does this to maintain backwards compatibility with the original cc executable. My guess for why cc does this is because of build time -- cc was written for machines with far less power than we have now. A lot of programs don't have any floating-point math, and they probably took every library that wasn't commonly used out of the default. I'm guessing that the build time of the Unix OS and the tools that go along with it were the driving force.
I would guess that it is a way to make applications which don't use it at all perform slightly better. Here's my thinking on this.
x86 OSes (and I imagine others) need to store FPU state on context switch. However, most OSes only bother to save/restore this state after the app attempts to use the FPU for the first time.
In addition to this, there is probably some basic code in the math library which will set the FPU to a sane base state when the library is loaded.
So, if you don't link in any math code at all, none of this will happen, therefore the OS doesn't have to save/restore any FPU state at all, making context switches slightly more efficient.
Just a guess though.
The same base premise still applies to non-FPU cases (the premise being that it was to make apps which didn't make use libm perform slightly better).
For example, if there is a soft-FPU which was likely in the early days of C. Then having libm separate could prevent a lot of large (and slow if it was used) code from unnecessarily being linked in.
In addition, if there is only static linking available, then a similar argument applies that it would keep executable sizes and compile times down.
stdio is part of the standard C library which, by default, GCC will link against.
The math function implementations are in a separate libm file that is not linked to by default, so you have to specify it -lm. By the way, there is no relation between those header files and library files.
All libraries like stdio.h and stdlib.h have their implementation in libc.so or libc.a and get linked by the linker by default. The libraries for libc.so are automatically linked while compiling and is included in the executable file.
But math.h has its implementations in libm.so or libm.a which is separate from libc.so. It does not get linked by default and you have to manually link it while compiling your program in GCC by using the -lm flag.
The GNU GCC team designed it to be separate from the other header files, while the other header files get linked by default, but math.h file doesn't.
Here read the item number 14.3, you could read it all if you wish:
Reason why math.h is needs to be linked
Look at this article: Why do we have to link math.h in GCC?
Have a look at the usage:
Using the library
Note that -lm may not always need to be specified even if you use some C math functions.
For example, the following simple program:
#include <stdio.h>
#include <math.h>
int main() {
printf("output: %f\n", sqrt(2.0));
return 0;
}
can be compiled and run successfully with the following command:
gcc test.c -o test
It was tested on GCC 7.5.0 (on Ubuntu 16.04) and GCC 4.8.0 (on CentOS 7).
The post here gives some explanations:
The math functions you call are implemented by compiler built-in functions
See also:
Other Built-in Functions Provided by GCC
How to get the gcc compiler to not optimize a standard library function call like printf?