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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,70 +1,51 @@ | ||
| /* | ||
| * $Id$ | ||
| * | ||
| * Author: David Fournier | ||
| * Copyright (c) 2008-2012 Regents of the University of California | ||
| */ | ||
| /** | ||
| \file | ||
| Robust exponential functions for variable scalar objects. | ||
| */ | ||
| #include <fvar.hpp> | ||
| \file Robust exponential functions for variable scalar objects. | ||
| /** | ||
| Robust exponential function for variable argument > 60 or < -60. | ||
| Prevents overflow and underflow for arguments outside of the domain | ||
| of exp(). | ||
| (Note: \f$e^{60} > 10^{26}\f$.) | ||
| \param x dvariable exponent. | ||
| \return \f$\left\{\begin{array} {r@{\quad:\quad}l} | ||
| x > 60 & e^{60}\frac{(1+2(x-60))}{1+x-60}\\ | ||
| x < 60 & e^{-60}\frac{(1-x-60)}{1+2(-x-60)}\\ | ||
| {\rm else} & e^x | ||
| \end{array}\right.\f$ | ||
| \ingroup misc | ||
| */ | ||
| dvariable mfexp(const prevariable& x) | ||
| { | ||
| double b=60; | ||
| if (x<=b && x>=-b) | ||
| { | ||
| return exp(x); | ||
| } | ||
| else if (x>b) | ||
| { | ||
| return exp(b)*(1.+2.*(x-b))/(1.+x-b); | ||
| } | ||
| else | ||
| { | ||
| return exp(-b)*(1.-x-b)/(1.+2.*(-x-b)); | ||
| } | ||
| } | ||
| Author: David Fournier | ||
| Copyright (c) 2008-2015 Regents of the University of California | ||
| */ | ||
| #include <fvar.hpp> | ||
|
|
||
| /** | ||
| Robust exponential function for variable argument with user | ||
| specified domain bound. | ||
| Prevents overflow and underflow for arguments outside of the domain | ||
| \param x dvariable exponent. | ||
| \param b double user specified function domain bound. | ||
| \return \f$\left\{\begin{array} {r@{\quad:\quad}l} | ||
| Robust exponential function for variable argument with user | ||
| specified domain bound. | ||
| Prevents overflow and underflow for arguments outside of the domain | ||
| \param x dvariable exponent. | ||
| \param b double user specified function domain bound. | ||
| \return \f$\left\{\begin{array} {r@{\quad:\quad}l} | ||
| x > b & e^b\frac{(1+2(x-b))}{1+x-b}\\ | ||
| x < b & e^{-b}\frac{(1-x-b)}{1+2(-x-b)}\\ | ||
| {\rm else} & e^x | ||
| \end{array}\right.\f$ | ||
| \ingroup misc | ||
| */ | ||
| \end{array}\right.\f$ | ||
| \ingroup misc | ||
| */ | ||
| dvariable mfexp(const prevariable& x, double b) | ||
| { | ||
| if (x > b) | ||
| { | ||
| return exp(b)*(1.+2.*(x-b))/(1.+x-b); | ||
| } | ||
| else if (x < -b) | ||
| { | ||
| if (x<=b && x>=-b) | ||
| { | ||
| return exp(x); | ||
| } | ||
| else if (x>b) | ||
| { | ||
| return exp(b)*(1.+2.*(x-b))/(1.+x-b); | ||
| } | ||
| else | ||
| { | ||
| return exp(-b)*(1.-x-b)/(1.+2.*(-x-b)); | ||
| } | ||
| return exp(-b)*(1.-x-b)/(1.+2.*(-x-b)); | ||
| } | ||
| return exp(x); | ||
| } | ||
| /** | ||
| Robust exponential function for variable argument > 60 or < -60. | ||
| Prevents overflow and underflow for arguments outside of the domain | ||
| of exp(). | ||
| (Note: \f$e^{60} > 10^{26}\f$.) | ||
| \param x dvariable exponent. | ||
| \return \f$\left\{\begin{array} {r@{\quad:\quad}l} | ||
| x > 60 & e^{60}\frac{(1+2(x-60))}{1+x-60}\\ | ||
| x < 60 & e^{-60}\frac{(1-x-60)}{1+2(-x-60)}\\ | ||
| {\rm else} & e^x | ||
| \end{array}\right.\f$ | ||
| \ingroup misc | ||
| */ | ||
| dvariable mfexp(const prevariable& x) | ||
| { | ||
| double b = 60; | ||
| return mfexp(x, b); | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,70 +1,52 @@ | ||
| /* | ||
| * $Id$ | ||
| * | ||
| * Author: David Fournier | ||
| * Copyright (c) 2008-2012 Regents of the University of California | ||
| */ | ||
| /** | ||
| * \file | ||
| Robust exponential functions for constant scalar objects. | ||
| */ | ||
| #include <fvar.hpp> | ||
| \file Robust exponential functions for constant scalar objects. | ||
| /** | ||
| Robust exponential function for constant argument > 60 or < -60. | ||
| Prevents overflow and underflow for arguments outside of the domain | ||
| of exp(). | ||
| (Note: \f$e^{60} > 10^{26}\f$.) | ||
| \param x exponent. | ||
| \return \f$\left\{\begin{array} {r@{\quad:\quad}l} | ||
| x > 60 & e^{60}\frac{(1+2(x-60))}{1+x-60}\\ | ||
| x < 60 & e^{-60}\frac{(1-x-60)}{1+2(-x-60)}\\ | ||
| {\rm else} & e^x | ||
| \end{array}\right.\f$ | ||
| \ingroup misc | ||
| */ | ||
| double mfexp(double x) | ||
| { | ||
| double b = 60; | ||
| if (x<=b && x>=-b) | ||
| { | ||
| return exp(x); | ||
| } | ||
| else if (x>b) | ||
| { | ||
| return exp(b)*(1.+2.*(x-b))/(1.+x-b); | ||
| } | ||
| else | ||
| { | ||
| return exp(-b)*(1.-x-b)/(1.+2.*(-x-b)); | ||
| } | ||
| } | ||
| Author: David Fournier | ||
| Copyright (c) 2008-2015 Regents of the University of California | ||
| */ | ||
| #include <fvar.hpp> | ||
|
|
||
| /** | ||
| Robust exponential function for constant argument with user | ||
| specified domain bound. | ||
| Prevents overflow and underflow for arguments outside of the domain | ||
| \param x exponent. | ||
| \param b ouble user specified function domain bound. | ||
| \return \f$\left\{\begin{array} {r@{\quad:\quad}l} | ||
| Robust exponential function for constant argument with user | ||
| specified domain bound. | ||
| Prevents overflow and underflow for arguments outside of the domain | ||
| \param x exponent. | ||
| \param b ouble user specified function domain bound. | ||
| \return \f$\left\{\begin{array} {r@{\quad:\quad}l} | ||
| x > b & e^b\frac{(1+2(x-b))}{1+x-b}\\ | ||
| x < b & e^{-b}\frac{(1-x-b)}{1+2(-x-b)}\\ | ||
| {\rm else} & e^x | ||
| \end{array}\right.\f$ | ||
| \ingroup misc | ||
| */ | ||
| double mfexp(double x,double b) | ||
| \end{array}\right.\f$ | ||
| \ingroup misc | ||
| */ | ||
| double mfexp(double x, double b) | ||
| { | ||
| if (x > b) | ||
| { | ||
| return exp(b)*(1.+2.*(x-b))/(1.+x-b); | ||
| } | ||
| else if (x < -b) | ||
| { | ||
| if (x<=b && x>=-b) | ||
| { | ||
| return exp(x); | ||
| } | ||
| else if (x>b) | ||
| { | ||
| return exp(b)*(1.+2.*(x-b))/(1.+x-b); | ||
| } | ||
| else | ||
| { | ||
| return exp(-b)*(1.-x-b)/(1.+2.*(-x-b)); | ||
| } | ||
| return exp(-b)*(1.-x-b)/(1.+2.*(-x-b)); | ||
| } | ||
| return exp(x); | ||
| } | ||
| /** | ||
| Robust exponential function for constant argument > 60 or < -60. | ||
| Prevents overflow and underflow for arguments outside of the domain | ||
| of exp(). | ||
| (Note: \f$e^{60} > 10^{26}\f$.) | ||
| \param x exponent. | ||
| \return \f$\left\{\begin{array} {r@{\quad:\quad}l} | ||
| x > 60 & e^{60}\frac{(1+2(x-60))}{1+x-60}\\ | ||
| x < 60 & e^{-60}\frac{(1-x-60)}{1+2(-x-60)}\\ | ||
| {\rm else} & e^x | ||
| \end{array}\right.\f$ | ||
| \ingroup misc | ||
| */ | ||
| double mfexp(double x) | ||
| { | ||
| double b = 60; | ||
| return mfexp(x, b); | ||
| } | ||
|
|
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