From 754bbf7a25a8dda49b5d08ef0d0443bbf5af0e36 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Sun, 7 Apr 2024 13:41:34 -0500 Subject: new repository --- devdocs/c/numeric%2Fmath%2Flog1p.html | 82 +++++++++++++++++++++++++++++++++++ 1 file changed, 82 insertions(+) create mode 100644 devdocs/c/numeric%2Fmath%2Flog1p.html (limited to 'devdocs/c/numeric%2Fmath%2Flog1p.html') diff --git a/devdocs/c/numeric%2Fmath%2Flog1p.html b/devdocs/c/numeric%2Fmath%2Flog1p.html new file mode 100644 index 00000000..792b8a08 --- /dev/null +++ b/devdocs/c/numeric%2Fmath%2Flog1p.html @@ -0,0 +1,82 @@ +

log1p, log1pf, log1pl

Defined in header <math.h> 
float       log1pf( float arg );
+		 (1) (since C99) 
double      log1p( double arg );
+		 (2) (since C99) 
long double log1pl( long double arg );
+		 (3) (since C99)
Defined in header <tgmath.h> 
#define log1p( arg )
+		 (4) (since C99)
+1-3) Computes the natural (base e) logarithm of 1+arg. This function is more precise than the expression log(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.

+

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

+

If a pole error 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.

+

Domain error occurs if arg is less than -1.

+

Pole error may occur if arg is -1.

+

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

+

Notes

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

+

Example

#include <stdio.h>
+#include <math.h>
+#include <float.h>
+#include <errno.h>
+#include <fenv.h>
+#pragma STDC FENV_ACCESS ON
+int main(void)
+{
+    printf("log1p(0) = %f\n", log1p(0));
+    printf("Interest earned in 2 days on $100, compounded daily at 1%%\n"
+           " on a 30/360 calendar = %f\n",
+           100*expm1(2*log1p(0.01/360)));
+    printf("log(1+1e-16) = %g, but log1p(1e-16) = %g\n",
+           log(1+1e-16), log1p(1e-16));
+    // special values
+    printf("log1p(-0) = %f\n", log1p(-0.0));
+    printf("log1p(+Inf) = %f\n", log1p(INFINITY));
+    //error handling
+    errno = 0; feclearexcept(FE_ALL_EXCEPT);
+    printf("log1p(-1) = %f\n", log1p(-1));
+    if(errno == ERANGE) perror("    errno == ERANGE");
+    if(fetestexcept(FE_DIVBYZERO)) puts("    FE_DIVBYZERO raised");
+}

Possible output:

+
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

See also

+ + + + +
+
(C99)(C99)
 computes natural (base-e) logarithm (\({\small \ln{x} }\)ln(x))
(function)
+
(C99)(C99)
 computes common (base-10) logarithm (\({\small \log_{10}{x} }\)log10(x))
(function)
+
(C99)(C99)(C99)
 computes base-2 logarithm (\({\small \log_{2}{x} }\)log2(x))
(function)
+
(C99)(C99)(C99)
 computes e raised to the given power, minus one (\({\small e^x-1}\)ex-1)
(function)
C++ documentation for log1p
+

+ © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
+ https://en.cppreference.com/w/c/numeric/math/log1p +

+
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