/*
* Safe function evaluator.
* by Karl Michael Westerberg
* Created: 2/6/90
* Version: $Revision: 1.10 $
* Version control file: $RCSfile: safe.h,v $
* Date last modified: $Date: 1997/07/21 16:56:51 $
* Last modified by: $Author: kt2g $
*
* This file is part of the SLV solver.
*
* Copyright (C) 1990 Karl Michael Westerberg
* Copyright (C) 1993 Joseph Zaher
* Copyright (C) 1994 Joseph Zaher, Benjamin Andrew Allan
*
* The SLV solver is free software; you can redistribute
* it and/or modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation; either version 2 of the
* License, or (at your option) any later version.
*
* The SLV solver is distributed in hope that it will be
* useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with the program; if not, write to the Free Software Foundation,
* Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check the file named
* COPYING.
*
*/
/** @file
* Safe function evaluator.
*
* Contents: Safe calculation module
*
* Authors: Karl Westerberg, Joseph Zaher
*
* Dates: 06/90 - original version in solver
* 08/93 - removed safe_D0, safe_D1, safe_D2, safe_Dn
* and added them as internal functions of the
* exprman module.
* 04/94 - enhanced error messaging
* 06/96 - dealiased and moved into compiler. BAA
*
* Description: Operations are provided for computing unary and binary
* functions. First, second, and nth derivatives may
* also be computed for all of the functions featured. A
* global boolean variable safe_ok, which is declared
* external so that it may be monitored from other
* modules, will be set to FALSE in the event of a
* calculation error. Also, to suppress printing of error
* messages in the event of an error, set the global
* variable safe_print_errors to FALSE.
* The intent here is to provide safer (if slower)
* versions of math operations with our own little
* version of errno.
* At present, not all functions here are completely safe.
* It's floating point. Can they ever be?
*
* When #including safe.h, make sure these files are #included first:
* #include "utilities/ascConfig.h"
* #include "compiler.h"
* #include "functype.h"
*
* @todo Complete documentation of compiler/safe.h.
*/
#ifndef safe__already_included
#define safe__already_included
/*extern int safe_print_errors;*/
extern void safe_error_to_stderr(enum safe_err *err);
/**<
* The variable safe_err will be set to the appropriate value whenever
* an undefined numerical calculation is attempted.
* In this case, if the variable safe_print_errors is set to TRUE,
* a description of the error will be printed to stderr.
* In order to monitor errors effectively, it is
* the responsibility of the user to set the safe_err variable to safe_ok
* before calling any of the functions below.
* (it's our on silly version of errno...)
*/
#define safe_ERF_COEF 1.1283791670955130 /**< = 2 / sqrt(PI) */
#define safe_LOG10_COEF 0.4342944819032518 /**< = log10(e) = 1/ln(10) */
#define safe_PI 3.1415926535897930 /**< pi */
extern double safe_upower(double x, unsigned y, enum safe_err *err); /**< buggy */
/**< Compute x^n. Not Verified Code! */
extern double safe_factorial(unsigned x, enum safe_err *err);
/**< Compute n!. */
extern double safe_rec(double x, enum safe_err *err);
/** even/odd int,else ==> not an int. */
/* All of the following safe_XXXX_Di must resolve to C functions
* rather than macros because safe_func_Di takes the address of them.
*/
extern double safe_sin_D0(double x, enum safe_err *safe);
extern double safe_sinh_D0(double x, enum safe_err *safe);
extern double safe_cos_D0(double x, enum safe_err *safe);
extern double safe_cosh_D0(double x, enum safe_err *safe);
extern double safe_tan_D0(double x, enum safe_err *safe);
extern double safe_tanh_D0(double x, enum safe_err *safe);
extern double safe_arctan_D0(double x, enum safe_err *safe);
extern double safe_arcsin_D0(double x, enum safe_err *safe);
extern double safe_arcsinh_D0(double x, enum safe_err *safe);
extern double safe_arccos_D0(double x, enum safe_err *safe);
extern double safe_arccosh_D0(double x, enum safe_err *safe);
extern double safe_arctanh_D0(double x, enum safe_err *safe);
#ifdef HAVE_ERF
extern double safe_erf_D0(double x, enum safe_err *safe);
#endif /* HAVE_ERF */
extern double safe_exp_D0(double x, enum safe_err *safe);
extern double safe_ln_D0(double x, enum safe_err *safe);
extern double safe_lnm_D0(double x, enum safe_err *safe);
extern double safe_log_D0(double x, enum safe_err *safe);
extern double safe_sqr_D0(double x, enum safe_err *safe);
extern double safe_sqrt_D0(double x, enum safe_err *safe);
extern double safe_cbrt_D0(double x, enum safe_err *safe);
extern double safe_fabs_D0(double x, enum safe_err *safe);
extern double safe_hold_D0(double x, enum safe_err *safe);
/*
* value = safe__D0(x)
* double value,x;
* enum safe_err *safe
*
* Computes value of unary operator.
*/
extern double safe_sin_D1(double x, enum safe_err *safe);
extern double safe_sinh_D1(double x, enum safe_err *safe);
extern double safe_cos_D1(double x, enum safe_err *safe);
extern double safe_cosh_D1(double x, enum safe_err *safe);
extern double safe_tan_D1(double x, enum safe_err *safe);
extern double safe_tanh_D1(double x, enum safe_err *safe);
extern double safe_arcsin_D1(double x, enum safe_err *safe);
extern double safe_arcsinh_D1(double x, enum safe_err *safe);
extern double safe_arccos_D1(double x, enum safe_err *safe);
extern double safe_arccosh_D1(double x, enum safe_err *safe);
extern double safe_arctan_D1(double x, enum safe_err *safe);
extern double safe_arctanh_D1(double x, enum safe_err *safe);
#ifdef HAVE_ERF
extern double safe_erf_D1(double x, enum safe_err *safe);
#endif /* HAVE_ERF */
extern double safe_exp_D1(double x, enum safe_err *safe);
extern double safe_ln_D1(double x, enum safe_err *safe);
extern double safe_lnm_D1(double x, enum safe_err *safe);
extern double safe_log_D1(double x, enum safe_err *safe);
extern double safe_sqr_D1(double x, enum safe_err *safe);
extern double safe_sqrt_D1(double x, enum safe_err *safe);
extern double safe_cube_D0(double x, enum safe_err *safe);
extern double safe_cube_D1(double x, enum safe_err *safe);
extern double safe_cbrt_D1(double x, enum safe_err *safe);
extern double safe_fabs_D1(double x, enum safe_err *safe);
extern double safe_hold_D1(double x, enum safe_err *safe);
/*
* value = safe__D1(x)
* double value,x;
* enum safe_err *safe
*
* Computes first derivative of unary operator.
*/
extern double safe_sin_D2(double x, enum safe_err *safe);
extern double safe_sinh_D2(double x, enum safe_err *safe);
extern double safe_cos_D2(double x, enum safe_err *safe);
extern double safe_cosh_D2(double x, enum safe_err *safe);
extern double safe_tan_D2(double x, enum safe_err *safe);
extern double safe_tanh_D2(double x, enum safe_err *safe);
extern double safe_arcsin_D2(double x, enum safe_err *safe);
extern double safe_arcsinh_D2(double x, enum safe_err *safe);
extern double safe_arccos_D2(double x, enum safe_err *safe);
extern double safe_arccosh_D2(double x, enum safe_err *safe);
extern double safe_arctan_D2(double x, enum safe_err *safe);
extern double safe_arctanh_D2(double x, enum safe_err *safe);
#ifdef HAVE_ERF
extern double safe_erf_D2(double x, enum safe_err *safe);
#endif /* HAVE_ERF */
extern double safe_exp_D2(double x, enum safe_err *safe);
extern double safe_ln_D2(double x, enum safe_err *safe);
extern double safe_lnm_D2(double x, enum safe_err *safe);
extern double safe_log_D2(double x, enum safe_err *safe);
extern double safe_sqr_D2(double x, enum safe_err *safe);
extern double safe_sqrt_D2(double x, enum safe_err *safe);
extern double safe_cube_D2(double x, enum safe_err *safe);
extern double safe_cbrt_D2(double x, enum safe_err *safe);
extern double safe_fabs_D2(double x, enum safe_err *safe);
#define safe_hold_D2 safe_hold_D1
/*
* value = safe__D2(x)
* double value,x;
* enum safe_err *safe
*
* Computes second derivative of unary operator.
*/
extern double safe_arcsin_Dn(double x, int n, enum safe_err *safe);
extern double safe_arccos_Dn(double x, int n, enum safe_err *safe);
extern double safe_arctan_Dn(double x, int n, enum safe_err *safe);
extern double safe_cos_Dn(double x, int n, enum safe_err *safe);
extern double safe_sin_Dn(double x, int n, enum safe_err *safe);
#ifdef HAVE_ERF
extern double safe_erf_Dn(double x, int n, enum safe_err *safe);
#endif /* HAVE_ERF */
extern double safe_exp_Dn(double x, int n, enum safe_err *safe);
extern double safe_ln_Dn(double x, int n, enum safe_err *safe);
extern double safe_log_Dn(double x, int n, enum safe_err *safe);
extern double safe_sqr_Dn(double x, int n, enum safe_err *safe);
extern double safe_sqrt_Dn(double x, int n, enum safe_err *safe);
extern double safe_tan_Dn(double x, int n, enum safe_err *safe);
extern double safe_fabs_Dn(double x, int n, enum safe_err *safe);
#define safe_hold_Dn safe_hold_D1
/*
* value = safe__Dn(x,n)
* double value,x;
* int n; n >= 0
* enum safe_err *safe
*
* Computes n-th derivative of unary operator.
*/
#define safe_add_D0(x,y,safe) ((x)+(y))
#define safe_sub_D0(x,y,safe) ((x)-(y))
#define safe_mul_D0(x,y,safe) ((x)*(y))
#define safe_div_D0(x,y,safe) safe_mul_D0((x),safe_rec(y,safe),(safe))
#define safe_ipow_D0(x,y,safe) asc_ipow((x),ascnint(y))
extern double safe_pow_D0(double x, double y, enum safe_err *safe);
/**<
*
*
*
*
* Computes x y and returns the value.
*/
#define safe_add_D1(x,y,wrt,safe) (1.0)
#define safe_sub_D1(x,y,wrt,safe) (1.0 - 2.0*(wrt))
#define safe_mul_D1(x,y,wrt,safe) ((wrt)==0 ? (y) : (x))
extern double safe_div_D1(double x, double y, int wrt, enum safe_err *safe);
extern double safe_ipow_D1(double x, double y, int wrt, enum safe_err *safe);
extern double safe_pow_D1(double x, double y, int wrt, enum safe_err *safe);
/*
* diff = safe__D1(x,y,wrt)
* double diff,x,y;
* int wrt; 0 ==> d/dx, 1 ==> d/dy
* enum safe_err *safe
*
* Computes derivative of x y w.r.t. x or y depending on wrt.
*/
#define safe_add_D2(x,y,wrt1,wrt2,safe) (0.0)
#define safe_sub_D2(x,y,wrt1,wrt2,safe) (0.0)
#define safe_mul_D2(x,y,wrt1,wrt2,safe) ((wrt1)!=(wrt2)?1.0:0.0)
extern double safe_div_D2(double x, double y, int wrt1, int wrt2, enum safe_err *safe);
extern double safe_ipow_D2(double x, double y, int wrt1, int wrt2, enum safe_err *safe);
extern double safe_pow_D2(double x, double y, int wrt1, int wrt2, enum safe_err *safe);
/*
* diff2 = safe__D2(x,y,wrt1,wrt2,safe)
* double diff2,x,y;
* int wrt1,wrt2; 0 ==> w.r.t 1st arg, 1 ==> w.r.t. 2nd arg
* enum safe_err *safe
*
* Computes 2nd derivative of x y w.r.t. x or y depending on
* wrt1 and wrt2. (so you can get d^2(f)/dx^2, d^2(f)/dy^2 or d^2(f)/dy/dx
*
* At least in the CASE of pow/ipow
* wrt1 = 0 wrt2 = 0 ==> d^2f/dx^2
* wrt1 = 0 wrt2 = 1 ==> d^2f/dy/dx
* wrt1 = 1 wrt2 = 0 ==> d^2f/dy/dx
* wrt1 = 1 wrt2 = 1 ==> d^2f/dy^2
*/
extern double safe_add_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe);
extern double safe_sub_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe);
extern double safe_mul_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe);
extern double safe_div_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe);
extern double
safe_pow_Dn(double x, double y, int nwrt0, int nwrt1, enum safe_err *safe);
/**< @todo this one not verified!*/
/*
* diffn = safe__Dn(x,y,nwrt0,nwrt1)
* double diffn,x,y;
* int nwrt0,nwrt1;
*
* Computes nwrt0'th derivative wrt x of the nwrt1'th derivative wrt y
* of x y.
*/
#endif /* safe__already_included */