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| Nearest integer floating point operations | |||||||||||||||||||||||||||||||||||||||||
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Defined in header <cmath> | ||
| (1) | ||
float expm1(float num); double expm1(double num); | (until C++23) | |
/*floating-point-type*/ expm1(/*floating-point-type*/ num); | (since C++23) (constexpr since C++26) | |
float expm1f(float num); | (2) | (since C++11) (constexpr since C++26) |
longdouble expm1l(longdouble num); | (3) | (since C++11) (constexpr since C++26) |
SIMD overload(since C++26) | ||
Defined in header <simd> | ||
template</*math-floating-point*/ V> constexpr/*deduced-simd-t*/<V> | (S) | (since C++26) |
Additional overloads(since C++11) | ||
Defined in header <cmath> | ||
template<class Integer> double expm1( Integer num); | (A) | (constexpr since C++26) |
std::expm1 for all cv-unqualified floating-point types as the type of the parameter.(since C++23)S) The SIMD overload performs an element-wise std::expm1 onv_num.
| (since C++26) |
A) Additional overloads are provided for all integer types, which are treated asdouble. | (since C++11) |
Contents |
| num | - | floating-point or integer value |
If no errors occurenum
-1 is returned.
If a range error due to overflow occurs,+HUGE_VAL,+HUGE_VALF, or+HUGE_VALL is returned.
If a range error occurs due to underflow, the correct result (after rounding) is returned.
Errors are reported as specified inmath_errhandling.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
The functionsstd::expm1 andstd::log1p are useful for financial calculations, for example, when calculating small daily interest rates:(1+x)n
-1 can be expressed asstd::expm1(n*std::log1p(x)). These functions also simplify writing accurate inverse hyperbolic functions.
For IEEE-compatible typedouble, overflow is guaranteed if709.8 < num.
The additional overloads are not required to be provided exactly as(A). They only need to be sufficient to ensure that for their argumentnum of integer type,std::expm1(num) has the same effect asstd::expm1(static_cast<double>(num)).
#include <cerrno>#include <cfenv>#include <cmath>#include <cstring>#include <iostream>// #pragma STDC FENV_ACCESS ON int main(){std::cout<<"expm1(1) = "<< std::expm1(1)<<'\n'<<"Interest earned in 2 days on $100, compounded daily at 1%\n"<<" on a 30/360 calendar = "<<100* std::expm1(2*std::log1p(0.01/360))<<'\n'<<"exp(1e-16)-1 = "<<std::exp(1e-16)-1<<", but expm1(1e-16) = "<< std::expm1(1e-16)<<'\n'; // special valuesstd::cout<<"expm1(-0) = "<< std::expm1(-0.0)<<'\n'<<"expm1(-Inf) = "<< std::expm1(-INFINITY)<<'\n'; // error handlingerrno=0;std::feclearexcept(FE_ALL_EXCEPT); std::cout<<"expm1(710) = "<< std::expm1(710)<<'\n'; if(errno==ERANGE)std::cout<<" errno == ERANGE: "<<std::strerror(errno)<<'\n';if(std::fetestexcept(FE_OVERFLOW))std::cout<<" FE_OVERFLOW raised\n";}
Possible output:
expm1(1) = 1.71828Interest earned in 2 days on $100, compounded daily at 1% on a 30/360 calendar = 0.00555563exp(1e-16)-1 = 0, but expm1(1e-16) = 1e-16expm1(-0) = -0expm1(-Inf) = -1expm1(710) = inf errno == ERANGE: Result too large FE_OVERFLOW raised
(C++11)(C++11) | returnse raised to the given power (\({\small e^x}\)ex) (function)[edit] |
(C++11)(C++11)(C++11) | returns2 raised to the given power (\({\small 2^x}\)2x) (function)[edit] |
(C++11)(C++11)(C++11) | natural logarithm (to basee) of1 plus the given number (\({\small\ln{(1+x)}}\)ln(1+x)) (function)[edit] |
C documentation forexpm1 | |
