What is "minmax.h" in C++?

The C++ programming language is accompanied by the C++ Standard Library. There is no <minmax.h> header in the C++ Standard Library. No header in the standard-library has the .h extension. Furthermore, the header is not part of the ported C standard library either, as those headers have the c prefix, like <cmath> (which replaces the C standard-library <math.h> header), <ctime>(which replaces the <time.h> header) when used from the C++ Standard Library.

The std::min and std::max functions are declared inside the <algorithm> header.

^{That being said, there indeed appears to be some MS header called <minmax.h> inside the C:\Program Files (x86)\Windows Kits\10\Include\10.0.18362.0\ucrt folder which defines min and max macros, not functions. But, that is some implementation specific header, and you should be using the standard <algorithm> header instead.}

why aren't I?

People do all sort of odd things that they heard about somewhere once, be it in school or that came up as some "solution" that fixed their immediate need (usually under timeline pressure). They then keep doing things the same way because they "work". But I'm glad you stopped for a minute to ask. Hopefully we'll steer you back onto the portable C++ route :)

No, there's no need to use the non-standard minmax.h header. On Windows you need to define the NOMINMAX macro before you include any headers whatsoever, and include <algorithm> right after this macro definition. This is just to free the min and max symbols from being taken over by ill-conceived WINAPI macros. In C++, std::min etc. are in the <algorithm> header and that's what you ought to be using. Thus, the following is portable:

#define NOMINMAX
#include <algorithm>
// other includes
#undef NOMINMAX

// your code here

See this answer for details for Windows.

An ancient reference w.r.t. C++, using ancient compilers, supplying examples using non-standard C++ (e.g. headers such as minmax.h)

Note that the book you are mentioning, C++ Design Patterns and Derivatives Pricing (M.S. Joshi), was first released in 2004, with a subsequent second edition released in 2008. As can be seen in the extract below, the examples in the book relied on successful compilation on ancient compiler versions (not so ancient back in 2004, but still far from recent versions).

Appendix D of the book even specifically mentions that the code examples covered by the book may not be standard-compliant, followed by the pragmatic advice that "[...] fixing the problems should not be hard" [emphasis mine]:

The code has been tested under three compilers: MingW 2.95, Borland 5.5, and Visual C++ 6.0. The first two of these are available for free so you should have no trouble finding a compiler that the code works for. In addition, MingW is the Windows port of the GNU compiler, gcc, so the code should work with that compiler too. Visual C++ is not free but is popular in the City and the introductory version is not very expensive. In addition, I have strived to use only ANSI/ISO code so the code should work under any compiler. In any case, it does not use any cutting-edge language features so if it is not compatible with your compiler, fixing the problems should not be hard.

The compiler releases listed above are very old:

• Borland 5.5 was released in 2000,
• Visual C++ 6.0 was released in 1998,
• GCC 2.95 was released in 1999.

Much like any other ancient compiler it is not surprising that these compilers supplied non-standard headers such as minmax.h, particularly as it seems to have been a somewhat common non-standard convention, based on e.g. the following references.

• Gnulib Module List - Extra functions based on ANSI C 89: minmax.h, possibly accessible in GCC 2.95,
• Known problems in using the Microsoft Visual C++ compiler, version 6.0:

  The MS library does not define the min and max algorithms, which should be found in The workaround we use is to define a new header file, say minmax.h, which we include in any file that uses these functions: [...]

• What is the worst real-world macros/pre-processor abuse you've ever come across?:

  Real-world? MSVC has macros in minmax.h, called max and min, which cause a compiler error every time I intend to use the standard std::numeric_limits::max() function.

Alternative references for the C++ language

Based on the passage above, the book should most likely be considered primarily a reference for its main domain, quant finance, and not such much for C++, other than the latter being a tool used to cover the former.

For references that are focusing on the C++ language and not its application in a particular applied domain (with emphasis on the latter), consider having a look at:

• StackOverfow C++ FAQ: The Definitive C++ Book Guide and List.