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%2Fexpm1.html | 83 +++++++++++++++++++++++++++++++++++ 1 file changed, 83 insertions(+) create mode 100644 devdocs/c/numeric%2Fmath%2Fexpm1.html (limited to 'devdocs/c/numeric%2Fmath%2Fexpm1.html') diff --git a/devdocs/c/numeric%2Fmath%2Fexpm1.html b/devdocs/c/numeric%2Fmath%2Fexpm1.html new file mode 100644 index 00000000..75918aa8 --- /dev/null +++ b/devdocs/c/numeric%2Fmath%2Fexpm1.html @@ -0,0 +1,83 @@ +

expm1, expm1f, expm1l

Defined in header <math.h> 
float       expm1f( float arg );
+		 (1) (since C99) 
double      expm1( double arg );
+		 (2) (since C99) 
long double expm1l( long double arg );
+		 (3) (since C99)
Defined in header <tgmath.h> 
#define expm1( arg )
+		 (4) (since C99)
+1-3) Computes the e (Euler's number, 2.7182818) raised to the given power arg, minus 1.0. This function is more accurate than the expression exp(arg)-1.0 if arg is close to zero.
+4) Type-generic macro: If arg has type long double, expm1l is called. Otherwise, if arg has integer type or the type double, expm1 is called. Otherwise, expm1f is called.

Parameters

+ +
arg - floating point value

Return value

If no errors occur earg-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),

+

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.

+

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

+

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("expm1(1) = %f\n", expm1(1));
+    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("exp(1e-16)-1 = %g, but expm1(1e-16) = %g\n",
+           exp(1e-16)-1, expm1(1e-16));
+    // special values
+    printf("expm1(-0) = %f\n", expm1(-0.0));
+    printf("expm1(-Inf) = %f\n", expm1(-INFINITY));
+    //error handling
+    errno = 0; feclearexcept(FE_ALL_EXCEPT);
+    printf("expm1(710) = %f\n", expm1(710));
+    if(errno == ERANGE) perror("    errno == ERANGE");
+    if(fetestexcept(FE_OVERFLOW)) puts("    FE_OVERFLOW raised");
+}

Possible output:

+
expm1(1) = 1.718282
+Interest earned in 2 days on $100, compounded daily at 1%
+ on a 30/360 calendar = 0.005556
+exp(1e-16)-1 = 0, but expm1(1e-16) = 1e-16
+expm1(-0) = -0.000000
+expm1(-Inf) = -1.000000
+expm1(710) = inf
+    errno == ERANGE: Result too large
+    FE_OVERFLOW raised

References

See also

+ + + +
+
(C99)(C99)
 computes e raised to the given power (\({\small e^x}\)ex)
(function)
+
(C99)(C99)(C99)
 computes 2 raised to the given power (\({\small 2^x}\)2x)
(function)
+
(C99)(C99)(C99)
 computes natural (base-e) logarithm of 1 plus the given number (\({\small \ln{(1+x)} }\)ln(1+x))
(function)
C++ documentation for expm1
+

+ © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
+ https://en.cppreference.com/w/c/numeric/math/expm1 +

+
-- cgit v1.2.3