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/* |
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* Safe function evaluator. |
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* by Karl Michael Westerberg |
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* Created: 2/6/90 |
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* Version: $Revision: 1.10 $ |
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* Version control file: $RCSfile: safe.h,v $ |
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* Date last modified: $Date: 1997/07/21 16:56:51 $ |
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* Last modified by: $Author: kt2g $ |
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* |
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* This file is part of the SLV solver. |
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* |
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* Copyright (C) 1990 Karl Michael Westerberg |
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* Copyright (C) 1993 Joseph Zaher |
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* Copyright (C) 1994 Joseph Zaher, Benjamin Andrew Allan |
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* |
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* The SLV solver is free software; you can redistribute |
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* it and/or modify it under the terms of the GNU General Public License as |
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* published by the Free Software Foundation; either version 2 of the |
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* License, or (at your option) any later version. |
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* |
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* The SLV solver is distributed in hope that it will be |
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* useful, but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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* General Public License for more details. |
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* |
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* You should have received a copy of the GNU General Public License |
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* along with the program; if not, write to the Free Software Foundation, |
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* Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check the file named |
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* COPYING. |
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* |
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*/ |
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|
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/** @file |
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* Safe function evaluator. |
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* <pre> |
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* Contents: Safe calculation module |
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* |
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* Authors: Karl Westerberg, Joseph Zaher |
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* |
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* Dates: 06/90 - original version in solver |
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* 08/93 - removed safe_D0, safe_D1, safe_D2, safe_Dn |
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* and added them as internal functions of the |
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* exprman module. |
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* 04/94 - enhanced error messaging |
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* 06/96 - dealiased and moved into compiler. BAA |
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* |
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* Description: Operations are provided for computing unary and binary |
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* functions. First, second, and nth derivatives may |
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* also be computed for all of the functions featured. A |
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* global boolean variable safe_ok, which is declared |
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* external so that it may be monitored from other |
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* modules, will be set to FALSE in the event of a |
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* calculation error. Also, to suppress printing of error |
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* messages in the event of an error, set the global |
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* variable safe_print_errors to FALSE. |
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* The intent here is to provide safer (if slower) |
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* versions of math operations with our own little |
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* version of errno. |
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* At present, not all functions here are completely safe. |
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* It's floating point. Can they ever be? |
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* |
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* When #including safe.h, make sure these files are #included first: |
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* #include "utilities/ascConfig.h" |
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* #include "compiler.h" |
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* #include "functype.h" |
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* </pre> |
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* @todo Complete documentation of compiler/safe.h. |
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*/ |
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|
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#ifndef safe__already_included |
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#define safe__already_included |
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|
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/*extern int safe_print_errors;*/ |
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|
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extern void safe_error_to_stderr(enum safe_err *err); |
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/**< |
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* The variable safe_err will be set to the appropriate value whenever |
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* an undefined numerical calculation is attempted. |
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* In this case, if the variable safe_print_errors is set to TRUE, |
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* a description of the error will be printed to stderr. |
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* In order to monitor errors effectively, it is |
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* the responsibility of the user to set the safe_err variable to safe_ok |
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* before calling any of the functions below. |
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* (it's our on silly version of errno...) |
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*/ |
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|
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#define safe_ERF_COEF 1.1283791670955130 /**< = 2 / sqrt(PI) */ |
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#define safe_LOG10_COEF 0.4342944819032518 /**< = log10(e) = 1/ln(10) */ |
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#define safe_PI 3.1415926535897930 /**< pi */ |
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|
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extern double safe_upower(double x, unsigned y, enum safe_err *err); /**< buggy */ |
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/**< Compute x^n. Not Verified Code! */ |
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extern double safe_factorial(unsigned x, enum safe_err *err); |
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/**< Compute n!. */ |
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extern double safe_rec(double x, enum safe_err *err); |
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/**<Compute 1/x. */ |
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extern double safe_cube(register double x, enum safe_err *err); |
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/**<Compute x^3 with range check. */ |
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extern double safe_Dn_rec(double x, int y, enum safe_err *err); |
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/**< Compute n-th derivative of 1/x. */ |
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#ifdef HAVE_ERF |
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extern double safe_erf_inv(double x, enum safe_err *err); |
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/**< Compute inverse of erf. */ |
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#endif /* HAVE_ERF */ |
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extern double safe_lnm_inv(double x, enum safe_err *err); |
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extern int safe_is_int(double x, enum safe_err *err); |
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/**< 0,1 ==> even/odd int,else ==> not an int. */ |
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|
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/* All of the following safe_XXXX_Di must resolve to C functions |
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* rather than macros because safe_func_Di takes the address of them. |
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*/ |
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|
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extern double safe_sin_D0(double x, enum safe_err *safe); |
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extern double safe_sinh_D0(double x, enum safe_err *safe); |
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extern double safe_cos_D0(double x, enum safe_err *safe); |
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extern double safe_cosh_D0(double x, enum safe_err *safe); |
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extern double safe_tan_D0(double x, enum safe_err *safe); |
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extern double safe_tanh_D0(double x, enum safe_err *safe); |
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extern double safe_arctan_D0(double x, enum safe_err *safe); |
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extern double safe_arcsin_D0(double x, enum safe_err *safe); |
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extern double safe_arcsinh_D0(double x, enum safe_err *safe); |
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extern double safe_arccos_D0(double x, enum safe_err *safe); |
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extern double safe_arccosh_D0(double x, enum safe_err *safe); |
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extern double safe_arctanh_D0(double x, enum safe_err *safe); |
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#ifdef HAVE_ERF |
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extern double safe_erf_D0(double x, enum safe_err *safe); |
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#endif /* HAVE_ERF */ |
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extern double safe_exp_D0(double x, enum safe_err *safe); |
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extern double safe_ln_D0(double x, enum safe_err *safe); |
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extern double safe_lnm_D0(double x, enum safe_err *safe); |
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extern double safe_log_D0(double x, enum safe_err *safe); |
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extern double safe_sqr_D0(double x, enum safe_err *safe); |
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extern double safe_sqrt_D0(double x, enum safe_err *safe); |
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extern double safe_cbrt_D0(double x, enum safe_err *safe); |
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extern double safe_fabs_D0(double x, enum safe_err *safe); |
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extern double safe_hold_D0(double x, enum safe_err *safe); |
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/* |
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* value = safe_<uop>_D0(x) |
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* double value,x; |
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* enum safe_err *safe |
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* |
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* Computes value of unary operator. |
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*/ |
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|
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extern double safe_sin_D1(double x, enum safe_err *safe); |
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extern double safe_sinh_D1(double x, enum safe_err *safe); |
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extern double safe_cos_D1(double x, enum safe_err *safe); |
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extern double safe_cosh_D1(double x, enum safe_err *safe); |
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extern double safe_tan_D1(double x, enum safe_err *safe); |
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extern double safe_tanh_D1(double x, enum safe_err *safe); |
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extern double safe_arcsin_D1(double x, enum safe_err *safe); |
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extern double safe_arcsinh_D1(double x, enum safe_err *safe); |
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extern double safe_arccos_D1(double x, enum safe_err *safe); |
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extern double safe_arccosh_D1(double x, enum safe_err *safe); |
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extern double safe_arctan_D1(double x, enum safe_err *safe); |
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extern double safe_arctanh_D1(double x, enum safe_err *safe); |
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#ifdef HAVE_ERF |
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extern double safe_erf_D1(double x, enum safe_err *safe); |
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#endif /* HAVE_ERF */ |
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extern double safe_exp_D1(double x, enum safe_err *safe); |
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extern double safe_ln_D1(double x, enum safe_err *safe); |
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extern double safe_lnm_D1(double x, enum safe_err *safe); |
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extern double safe_log_D1(double x, enum safe_err *safe); |
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extern double safe_sqr_D1(double x, enum safe_err *safe); |
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extern double safe_sqrt_D1(double x, enum safe_err *safe); |
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extern double safe_cube_D0(double x, enum safe_err *safe); |
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extern double safe_cube_D1(double x, enum safe_err *safe); |
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extern double safe_cbrt_D1(double x, enum safe_err *safe); |
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extern double safe_fabs_D1(double x, enum safe_err *safe); |
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extern double safe_hold_D1(double x, enum safe_err *safe); |
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/* |
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* value = safe_<uop>_D1(x) |
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* double value,x; |
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* enum safe_err *safe |
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* |
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* Computes first derivative of unary operator. |
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*/ |
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|
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extern double safe_sin_D2(double x, enum safe_err *safe); |
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extern double safe_sinh_D2(double x, enum safe_err *safe); |
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extern double safe_cos_D2(double x, enum safe_err *safe); |
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extern double safe_cosh_D2(double x, enum safe_err *safe); |
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extern double safe_tan_D2(double x, enum safe_err *safe); |
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extern double safe_tanh_D2(double x, enum safe_err *safe); |
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extern double safe_arcsin_D2(double x, enum safe_err *safe); |
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extern double safe_arcsinh_D2(double x, enum safe_err *safe); |
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extern double safe_arccos_D2(double x, enum safe_err *safe); |
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extern double safe_arccosh_D2(double x, enum safe_err *safe); |
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extern double safe_arctan_D2(double x, enum safe_err *safe); |
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extern double safe_arctanh_D2(double x, enum safe_err *safe); |
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#ifdef HAVE_ERF |
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extern double safe_erf_D2(double x, enum safe_err *safe); |
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#endif /* HAVE_ERF */ |
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extern double safe_exp_D2(double x, enum safe_err *safe); |
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extern double safe_ln_D2(double x, enum safe_err *safe); |
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extern double safe_lnm_D2(double x, enum safe_err *safe); |
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extern double safe_log_D2(double x, enum safe_err *safe); |
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extern double safe_sqr_D2(double x, enum safe_err *safe); |
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extern double safe_sqrt_D2(double x, enum safe_err *safe); |
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extern double safe_cube_D2(double x, enum safe_err *safe); |
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extern double safe_cbrt_D2(double x, enum safe_err *safe); |
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extern double safe_fabs_D2(double x, enum safe_err *safe); |
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#define safe_hold_D2 safe_hold_D1 |
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/* |
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* value = safe_<uop>_D2(x) |
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* double value,x; |
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* enum safe_err *safe |
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* |
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* Computes second derivative of unary operator. |
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*/ |
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|
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extern double safe_arcsin_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_arccos_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_arctan_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_cos_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_sin_Dn(double x, int n, enum safe_err *safe); |
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#ifdef HAVE_ERF |
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extern double safe_erf_Dn(double x, int n, enum safe_err *safe); |
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#endif /* HAVE_ERF */ |
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extern double safe_exp_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_ln_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_log_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_sqr_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_sqrt_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_tan_Dn(double x, int n, enum safe_err *safe); |
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extern double safe_fabs_Dn(double x, int n, enum safe_err *safe); |
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#define safe_hold_Dn safe_hold_D1 |
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/* |
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* value = safe_<uop>_Dn(x,n) |
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* double value,x; |
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* int n; n >= 0 |
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* enum safe_err *safe |
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* |
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* Computes n-th derivative of unary operator. |
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*/ |
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|
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#define safe_add_D0(x,y,safe) ((x)+(y)) |
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#define safe_sub_D0(x,y,safe) ((x)-(y)) |
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#define safe_mul_D0(x,y,safe) ((x)*(y)) |
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#define safe_div_D0(x,y,safe) safe_mul_D0((x),safe_rec(y,safe),(safe)) |
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#define safe_ipow_D0(x,y,safe) asc_ipow((x),ascnint(y)) |
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extern double safe_pow_D0(double x, double y, enum safe_err *safe); |
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/**< |
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* <!-- value = safe_<binop>_D0(x,y,safe) --> |
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* <!-- double value,x,y; --> |
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* <!-- enum safe_err *safe --> |
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* |
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* Computes x <binop> y and returns the value. |
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*/ |
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|
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#define safe_add_D1(x,y,wrt,safe) (1.0) |
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#define safe_sub_D1(x,y,wrt,safe) (1.0 - 2.0*(wrt)) |
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#define safe_mul_D1(x,y,wrt,safe) ((wrt)==0 ? (y) : (x)) |
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extern double safe_div_D1(double x, double y, int wrt, enum safe_err *safe); |
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extern double safe_ipow_D1(double x, double y, int wrt, enum safe_err *safe); |
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extern double safe_pow_D1(double x, double y, int wrt, enum safe_err *safe); |
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/* |
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* diff = safe_<binop>_D1(x,y,wrt) |
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* double diff,x,y; |
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* int wrt; 0 ==> d/dx, 1 ==> d/dy |
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* enum safe_err *safe |
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* |
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* Computes derivative of x <binop> y w.r.t. x or y depending on wrt. |
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*/ |
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|
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#define safe_add_D2(x,y,wrt1,wrt2,safe) (0.0) |
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#define safe_sub_D2(x,y,wrt1,wrt2,safe) (0.0) |
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#define safe_mul_D2(x,y,wrt1,wrt2,safe) ((wrt1)!=(wrt2)?1.0:0.0) |
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extern double safe_div_D2(double x, double y, int wrt1, int wrt2, enum safe_err *safe); |
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extern double safe_ipow_D2(double x, double y, int wrt1, int wrt2, enum safe_err *safe); |
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extern double safe_pow_D2(double x, double y, int wrt1, int wrt2, enum safe_err *safe); |
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/* |
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* diff2 = safe_<binop>_D2(x,y,wrt1,wrt2,safe) |
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* double diff2,x,y; |
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* int wrt1,wrt2; 0 ==> w.r.t 1st arg, 1 ==> w.r.t. 2nd arg |
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* enum safe_err *safe |
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* |
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* Computes 2nd derivative of x <binop> y w.r.t. x or y depending on |
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* wrt1 and wrt2. (so you can get d^2(f)/dx^2, d^2(f)/dy^2 or d^2(f)/dy/dx |
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* |
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* At least in the CASE of pow/ipow |
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* wrt1 = 0 wrt2 = 0 ==> d^2f/dx^2 |
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* wrt1 = 0 wrt2 = 1 ==> d^2f/dy/dx |
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* wrt1 = 1 wrt2 = 0 ==> d^2f/dy/dx |
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* wrt1 = 1 wrt2 = 1 ==> d^2f/dy^2 |
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*/ |
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|
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extern double safe_add_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe); |
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extern double safe_sub_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe); |
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extern double safe_mul_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe); |
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extern double safe_div_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe); |
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extern double |
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safe_pow_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe); |
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/**< @todo this one not verified!*/ |
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/* |
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* diffn = safe_<binop>_Dn(x,y,nwrt0,nwrt1) |
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* double diffn,x,y; |
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* int nwrt0,nwrt1; |
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* |
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* Computes nwrt0'th derivative wrt x of the nwrt1'th derivative wrt y |
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* of x <binop> y. |
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*/ |
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|
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#endif /* safe__already_included */ |
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