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Difference between revisions of "cpp/numeric/math/expm1"

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< cpp‎ | numeric‎ | math
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float      expm1 ( float num );
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double      expm1 ( double num );
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|desc=Computes the ''e'' ({{enwiki|E (mathematical_constant)|Euler's number}}, {{c/core|2.7182818...}}) raised to the given power {{c|num}}, minus {{c|1.0}}. This function is more accurate than the expression {{c|std::exp(num) - 1.0}} if {{c|num}} is close to zero.
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long double expm1 ( long double num );
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/* floating-point-type */ expm1( /* floating-point-type */ num );
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float      expm1f( float num );
 
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long double expm1l( long double num );
 
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{{dcl h|[[#Notes|Additional overloads]]}}
 
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{{dcl header|cmath}}
 
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template< class Integer >
 
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double      expm1 ( Integer num );
 
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@1-3@ Computes the ''e'' ({{enwiki|E (mathematical_constant)|Euler's number}}, {{c/core|2.7182818...}}) raised to the given power {{c|num}}, minus {{c|1.0}}. This function is more accurate than the expression {{c|std::exp(num) - 1.0}} if {{c|num}} is close to zero.{{rev inl|since=c++23| The library provides overloads of {{tt|std::expm1}} for all cv-unqualified floating-point types as the type of the parameter {{c|num}}.}}
 
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@A@ Additional overloads are provided for all integer types, which are treated as {{c/core|double}}.
 
  
 
===Parameters===
 
===Parameters===

Revision as of 09:12, 28 June 2023

 
C++
 
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expm1
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Macro constants
 
Defined in header <cmath>
(1)
float       expm1 ( float num );

double      expm1 ( double num );

long double expm1 ( long 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)
long double expm1l( long double num );
 (3) (since C++11)
(constexpr since C++26)
Additional overloads (since C++11)
Defined in header <cmath>
template< class Integer >
double      expm1 ( Integer num );
 (A) (constexpr since C++26)
1-3) Computes the e (Euler's number, 2.7182818...) raised to the given power num, minus 1.0. This function is more accurate than the expression std::exp(num) - 1.0 if num is close to zero. The library provides overloads of std::expm1 for all cv-unqualified floating-point types as the type of the parameter.(since C++23)
A) Additional overloads are provided for all integer types, which are treated as double.
 (since C++11)

Contents

Parameters

num - floating-point or integer value

Return value

If no errors occur enum-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.

Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

  • If the argument is ±0, it is returned, unmodified
  • If the argument is -∞, -1 is returned
  • If the argument is +∞, +∞ is returned
  • If the argument is NaN, NaN is returned

Notes

The functions std::expm1 and std::log1p are useful for financial calculations, for example, when calculating small daily interest rates: (1+x)n-1 can be expressed as std::expm1(n * std::log1p(x)). These functions also simplify writing accurate inverse hyperbolic functions.

For IEEE-compatible type double, overflow is guaranteed if 709.8 < num.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::expm1(num) has the same effect as std::expm1(static_cast<double>(num)).

Example

Run this code
#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 values
    std::cout << "expm1(-0) = " << std::expm1(-0.0) << '\n'
              << "expm1(-Inf) = " << std::expm1(-INFINITY) << '\n';
 
    // error handling
    errno = 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) = 1.71828
Interest earned in 2 days on $100, compounded daily at 1%
    on a 30/360 calendar = 0.00555563
exp(1e-16)-1 = 0, but expm1(1e-16) = 1e-16
expm1(-0) = -0
expm1(-Inf) = -1
expm1(710) = inf
    errno == ERANGE: Result too large
    FE_OVERFLOW raised

See also

(C++11)(C++11)
 returns e raised to the given power (ex)
(function) [edit]
(C++11)(C++11)(C++11)
 returns 2 raised to the given power (2x)
(function) [edit]
(C++11)(C++11)(C++11)
 natural logarithm (to base e) of 1 plus the given number (ln(1+x))
(function) [edit]
C documentation for expm1
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