log1p, log1pf, log1pl

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Types
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Functions
Basic operations
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Maximum/minimum operations
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Exponential functions
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log1plogp1
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Power functions
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Trigonometric and hyperbolic functions
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Error and gamma functions
Nearest integer floating-point operations
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Floating-point manipulation functions
Narrowing operations
Quantum and quantum exponent functions
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Decimal re-encoding functions
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Total order and payload functions
Classification
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Macro constants
Special floating-point values
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Arguments and return values
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Error handling
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Fast operation indicators
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Defined in header <math.h>
float       log1pf( float arg );
 (1) (since 哋它亢99)
double      log1p( double arg );
 (2) (since 哋它亢99)
long double log1pl( long double arg );
 (3) (since 哋它亢99)
Defined in header <tgmath.h>
#define log1p( arg )
 (4) (since 哋它亢99)
1-3) Computes the natural (base e) logarithm of 1 + arg. This function is more precise than the expression MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 07 HOURS 20 MINUTES 38 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(1 + arg) if arg is close to zero.
4) Type-generic macro: If arg has type long double, log1pl is called. Otherwise, if arg has integer type or the type double, log1p is called. Otherwise, log1pf is called.

Parameters

arg - floating-point value

Return value

If no errors occur ln(1 + arg) is returned.

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If a pole error occurs, -MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 07 HOURS 20 MINUTES 36 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE, -HUGE_VALF, or -HUGE_VALL is returned.

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Error handling

Errors are reported as specified in MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 07 HOURS 20 MINUTES 33 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE.

Domain error occurs if arg is less than -1.

Pole error may occur if arg is -1.

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Notes

The functions MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 07 HOURS 20 MINUTES 29 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE and log1p are useful for financial calculations, for example, when calculating small daily interest rates: (1+x)n
-1 can be expressed as MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN 07 HOURS 20 MINUTES 28 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(n * log1p(x)). These functions also simplify writing accurate inverse hyperbolic functions.

Example

Run this code
#include <errno.h>
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
// #pragma STDC FENV_ACCESS ON
 
int main(void)
{
    MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 27 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("log1p(0) = %f\n", log1p(0));
    MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 26 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("Interest earned in 2 days on $100, compounded daily at 1%%\n"
           " on a 30/360 calendar = %f\n",
           100*MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 25 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(2*log1p(0.01/360)));
    MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 24 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE("log(1+1e-16) = %g, but log1p(1e-16) = %g\n",
           MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 23 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(1+1e-16), log1p(1e-16));
 
    // special values
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    // error handling
    errno = 0; MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 19 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 18 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE);
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    if (errno == MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 16 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE)
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    if (MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 14 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE(MYMEMORY WARNING: YOU USED ALL AVAILABLE FREE TRANSLATIONS FOR TODAY. NEXT AVAILABLE IN  07 HOURS 20 MINUTES 13 SECONDS VISIT HTTPS://MYMEMORY.TRANSLATED.NET/DOC/USAGELIMITS.PHP TO TRANSLATE MORE))
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}

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log1p(0) = 0.000000
Interest earned in 2 days on $100, compounded daily at 1%
 on a 30/360 calendar = 0.005556
log(1+1e-16) = 0, but log1p(1e-16) = 1e-16
log1p(-0) = -0.000000
log1p(+Inf) = Inf
log1p(-1) = -Inf
    errno == ERANGE: Result too large
    FE_DIVBYZERO raised

References

  • 哋它亢23 standard (ISO/IEC 9899:2023):
  • 7.12.6.9 The log1p functions (p: TBD)
  • 7.25 Type-generic math <tgmath.h> (p: TBD)
  • F.10.3.9 The log1p functions (p: TBD)
  • 哋它亢17 standard (ISO/IEC 9899:2018):
  • 7.12.6.9 The log1p functions (p: TBD)
  • 7.25 Type-generic math <tgmath.h> (p: TBD)
  • F.10.3.9 The log1p functions (p: TBD)
  • 哋它亢11 standard (ISO/IEC 9899:2011):
  • 7.12.6.9 The log1p functions (p: 245)
  • 7.25 Type-generic math <tgmath.h> (p: 373-375)
  • F.10.3.9 The log1p functions (p: 522)
  • 哋它亢99 standard (ISO/IEC 9899:1999):
  • 7.12.6.9 The log1p functions (p: 226)
  • 7.22 Type-generic math <tgmath.h> (p: 335-337)
  • F.9.3.9 The log1p functions (p: 459)

See also

(哋它亢99)(哋它亢99)
 computes natural (base-e) logarithm (ln(x))
(function)
(哋它亢99)(哋它亢99)
 computes common (base-10) logarithm (log10(x))
(function)
(哋它亢99)(哋它亢99)(哋它亢99)
 computes base-2 logarithm (log2(x))
(function)
(哋它亢99)(哋它亢99)(哋它亢99)
 computes e raised to the given power, minus one (ex-1)
(function)
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