Type-generic math
The header <tgmath.h> includes the headers <math.h> and <complex.h> and defines several type-generic macros that determine which real or, when applicable, complex function to call based on the types of the arguments.
For each macro, the parameters whose corresponding real type in the unsuffixed math.h function is double are known as generic parameters (for example, both parameters of MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 26 MINUTES 43 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE are generic parameters, but only the first parameter of MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 26 MINUTES 42 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE is a generic parameter).
When a <tgmath.h> macro is used the types of the arguments passed to the generic parameters determine which function is selected by the macro as described below. If the types of the arguments are not MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 26 MINUTES 40 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE with the parameter types of the selected function, the behavior is undefined (e.g. if a complex argument is passed into a real-only <tgmath.h>'s macro: float MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 26 MINUTES 39 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE fc; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 26 MINUTES 38 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(fc); or double MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 26 MINUTES 37 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE dc; double d; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 26 MINUTES 35 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(dc, d); are examples of undefined behavior).
Note: type-generic macros were implemented in implementation-defined manner in 哋它亢99, but 哋它亢11 keyword MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 26 MINUTES 34 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE makes it possible to implement these macros in portable manner.
Complex/real type-generic macros
For all functions that have both real and complex counterparts, a type-generic macro XXX exists, which calls either of:
- real function:
- float variant
XXXf - double variant
XXX - long double variant
XXXl
- float variant
- complex function:
- float variant
cXXXf - double variant
cXXX - long double variant
cXXXl
- float variant
An exception to the above rule is the fabs macro (see the table below).
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- If any of the arguments for the generic parameters is imaginary, the behavior is specified on each function reference page individually (in particular,
sin,cos,tag,cosh,sinh,tanh,asin,atan,asinh, andatanhcall real functions, the return types ofsin,tan,sinh,tanh,asin,atan,asinh, andatanhare imaginary, and the return types ofcosandcoshare real). - If any of the arguments for the generic parameters is complex, then the complex function is called, otherwise the real function is called.
- If any of the arguments for the generic parameters is long double, then the long double variant is called. Otherwise, if any of the parameters is double or integer, then the double variant is called. Otherwise, float variant is called.
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Real-only functions
For all functions that do not have complex counterparts, with the exception of modf, a type-generic macro XXX exists, which calls either of the variants of a real function:
- float variant
XXXf - double variant
XXX - long double variant
XXXl
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- If any of the arguments for the generic parameters is long double, then the long double variant is called. Otherwise, if any of the arguments for the generic parameters is double, then the double variant is called. Otherwise, float variant is called.
Complex-only functions
For all complex number functions that do not have real counterparts, a type-generic macro cXXX exists, which calls either of the variants of a complex function:
- float MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 22 MINUTES 00 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE variant
cXXXf - double MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 59 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE variant
cXXX - long double MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 58 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE variant
cXXXl
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- If any of the arguments for the generic parameters is real, complex, or imaginary, then the appropriate complex function is called.
Example
#include <stdio.h> #include <tgmath.h> int main(void) { int i = 2; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 37 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("sqrt(2) = %f\n", MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 36 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(i)); // argument type is int, calls sqrt float f = 0.5; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 35 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("sin(0.5f) = %f\n", MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 34 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(f)); // argument type is float, calls sinf float MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 32 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE dc = 1 + 0.5*I; float MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 31 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE z = MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 30 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(dc); // argument type is float complex, calls csqrtf MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 29 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("sqrt(1 + 0.5i) = %f+%fi\n", MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 28 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(z), // argument type is float complex, calls crealf MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 08 HOURS 21 MINUTES 26 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(z)); // argument type is float complex, calls cimagf }
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sqrt(2) = 1.414214 sin(0.5f) = 0.479426 sqrt(1 + 0.5i) = 1.029086+0.242934i
References
- 哋它亢17 standard (ISO/IEC 9899:2018):
- 7.25 Type-generic math <tgmath.h> (p: 272-273)
- 哋它亢11 standard (ISO/IEC 9899:2011):
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
- 哋它亢99 standard (ISO/IEC 9899:1999):
- 7.22 Type-generic math <tgmath.h> (p: 335-337)