Generate the previous integer exponent expPrev for the specified input base and absolute value absx = abs(x) such that the condition base**expPrev <= absx holds.
See the documentation of pm_mathExp for more information.
- Parameters
-
| [in] | absx | : The input scalar (or array of the same rank, shape, and size as other array-like arguments), of either,
-
type
integer of kind any supported by the processor (e.g., IK, IK8, IK16, IK32, or IK64), or
-
type
real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
representing the absolute value of the number for which the previous integer exponent in specified base must be computed.
|
| [in] | base | : The input positive scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as absx, representing the base of the exponentiation.
(optional, default = 2) |
- Returns
expPrev : The output scalar (or array of the same rank, shape, and size as other array-like arguments) of
-
type
integer of default kind IK if absx is of type real,
-
type
integer of the same kind as absx if absx is of type integer,
containing the previous integer exponent.
Possible calling interfaces ⛓
Generate the previous integer exponent expPrev for the specified input base and absolute value absx =...
This module contains procedures and generic interfaces for computing the previous/next integer expone...
- Warning
- The condition
1 < base must hold.
The condition 0 < absx must hold.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.
-
Note that setting
base very near 1 can lead to very large output exponents that overflow the default integer kind IK.
For example, 1.0000001**2147483647 = 1.836644819690732e+93.
-
The
pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.
- Developer Remark:
- A
real value of kind RK32 can represent integer values as large as huge(1_int128) = 170141183460469231731687303715884105727 = 1.70141183E+38 < huge(1._RK32) = 3.40282347E+38 << huge(1._RK64).
One can envision a distant future human society with advanced computers capable of representing higher precision integer value for which RK32 or RK64 would be insufficient.
- See also
- isIntPow
getExpNext
getExpPrev
Example usage ⛓
9 integer(IK),
allocatable :: expPrev(:)
11 type(display_type) :: disp
17 call disp%show(
"expPrev(1) = getExpPrev(.5)")
26 call disp%show(
"expPrev(1) = getExpPrev(1.5)")
35 call disp%show(
"expPrev(1) = getExpPrev(1.)")
44 call disp%show(
"expPrev(1) = getExpPrev(1.1)")
53 call disp%show(
"expPrev = getExpPrev(abs([1, -2, 3, -4, 5, 9, 519]))")
54 expPrev
= getExpPrev(abs([
1,
-2,
3,
-4,
5,
9,
519]))
62 call disp%show(
"expPrev = getExpPrev(abs([1, -2, 3, -4, 5, 9, 519]), base = 3)")
63 expPrev
= getExpPrev(abs([
1,
-2,
3,
-4,
5,
9,
519]), base
= 3)
71 call disp%show(
"expPrev = getExpPrev(abs([real :: 1, -2, 3, -4, 5, 9, 519]), base = exp(1.))")
72 expPrev
= getExpPrev(abs([real ::
1,
-2,
3,
-4,
5,
9,
519]), base
= exp(
1.))
This is a generic method of the derived type display_type with pass attribute.
This is a generic method of the derived type display_type with pass attribute.
This module contains classes and procedures for input/output (IO) or generic display operations on st...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort compiler ⛓
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example Windows Batch compile command via Intel ifort compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
30expPrev
= getExpPrev(abs([
1,
-2,
3,
-4,
5,
9,
519]))
32+0,
+0,
+1,
+1,
+2,
+3,
+9
34+1.00000000,
+1.00000000,
+2.00000000,
+2.00000000,
+4.00000000,
+8.00000000,
+512.000000
37expPrev
= getExpPrev(abs([
1,
-2,
3,
-4,
5,
9,
519]), base
= 3)
39+0,
+0,
+1,
+1,
+1,
+2,
+5
41+1.00000000,
+1.00000000,
+3.00000000,
+3.00000000,
+3.00000000,
+9.00000000,
+243.000000
44expPrev
= getExpPrev(abs([real ::
1,
-2,
3,
-4,
5,
9,
519]), base
= exp(
1.))
46+0,
+0,
+1,
+1,
+1,
+2,
+6
48+1.00000000,
+1.00000000,
+2.71828175,
+2.71828175,
+2.71828175,
+7.38905573,
+403.428741
- Test:
- test_pm_mathExp
Final Remarks ⛓
If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.
-
If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
-
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.
- Copyright
- Computational Data Science Lab
- Author:
- Amir Shahmoradi, April 25, 2015, 2:21 PM, National Institute for Fusion Studies, The University of Texas Austin
Definition at line 510 of file pm_mathExp.F90.
1.9.3