Detailed Description

methods to interpret (evaluate) an expression tree "fast" using CppAD

Author: Stefan Vigerske

Definition in file exprinterpret_cppad.cpp.

#include "scip/def.h"
#include "blockmemshell/memory.h"
#include "nlpi/pub_expr.h"
#include "nlpi/exprinterpret.h"
#include <cmath>
#include <vector>
#include "nlpi/intervalarithext.h"
#include <cppad/cppad.hpp>
#include <cppad/utility/error_handler.hpp>
#include <pthread.h>

Go to the source code of this file.

Macros
#define	SIGN(x) ((x) >= 0.0 ? 1.0 : -1.0)

#define	SCIPInterval_NAMESPACE CppAD

#define	CPPAD_MAX_NUM_THREADS 64

Functions
static bool	in_parallel (void)

static size_t	thread_num (void)

static char	init_parallel (void)

SCIPInterval	CondExpOp (enum CppAD::CompareOp cop, const SCIPInterval &left, const SCIPInterval &right, const SCIPInterval &trueCase, const SCIPInterval &falseCase)

bool	IdenticalPar (const SCIPInterval &x)

bool	IdenticalZero (const SCIPInterval &x)

bool	IdenticalOne (const SCIPInterval &x)

bool	IdenticalEqualPar (const SCIPInterval &x, const SCIPInterval &y)

bool	GreaterThanZero (const SCIPInterval &x)

bool	GreaterThanOrZero (const SCIPInterval &x)

bool	LessThanZero (const SCIPInterval &x)

bool	LessThanOrZero (const SCIPInterval &x)

int	Integer (const SCIPInterval &x)

SCIPInterval	azmul (const SCIPInterval &x, const SCIPInterval &y)

std::ostream &	operator<< (std::ostream &out, const SCIP_INTERVAL &x)

static bool	univariate_for_sparse_jac (size_t q, const CppAD::vector< bool > &r, CppAD::vector< bool > &s)

static bool	univariate_rev_sparse_jac (size_t q, const CppAD::vector< bool > &r, CppAD::vector< bool > &s)

static bool	univariate_rev_sparse_hes (const CppAD::vector< bool > &vx, const CppAD::vector< bool > &s, CppAD::vector< bool > &t, size_t q, const CppAD::vector< bool > &r, const CppAD::vector< bool > &u, CppAD::vector< bool > &v)

template<class Type >
static void	posintpower (const vector< Type > &in, vector< Type > &out, size_t exponent)

template<class Type >
static void	evalSignPower (Type &resultant, const Type &arg, SCIP_EXPR *expr)

template<class Type >
SCIP_RETCODE	exprEvalUser (SCIP_EXPR expr, Type x, Type &funcval, Type gradient, Type hessian)

template<>
SCIP_RETCODE	exprEvalUser (SCIP_EXPR expr, SCIPInterval x, SCIPInterval &funcval, SCIPInterval gradient, SCIPInterval hessian)

template<class Type >
static void	evalUser (Type &resultant, const Type args, SCIP_EXPR expr)

template<class Type >
static void	evalMin (Type &resultant, const Type &arg1, const Type &arg2)

template<>
void	evalMin (CppAD::AD< double > &resultant, const CppAD::AD< double > &arg1, const CppAD::AD< double > &arg2)

template<class Type >
static void	evalMax (Type &resultant, const Type &arg1, const Type &arg2)

template<>
void	evalMax (CppAD::AD< double > &resultant, const CppAD::AD< double > &arg1, const CppAD::AD< double > &arg2)

template<class Type >
static void	evalSqrt (Type &resultant, const Type &arg)

template<class Type >
static void	evalAbs (Type &resultant, const Type &arg)

template<>
void	evalAbs (CppAD::AD< SCIPInterval > &resultant, const CppAD::AD< SCIPInterval > &arg)

template<class Type >
static void	evalIntPower (Type &resultant, const Type &arg, const int exponent)

template<class Type >
static SCIP_RETCODE	eval (SCIP_EXPR expr, const vector< Type > &x, SCIP_Real param, Type &val)

static void	analyzeTree (SCIP_EXPRINTDATA data, SCIP_EXPR expr)

static void	cppaderrorcallback (bool known, int line, const char file, const char cond, const char *msg)

static CppAD::ErrorHandler	errorhandler (cppaderrorcallback)

const char *	SCIPexprintGetName (void)

const char *	SCIPexprintGetDesc (void)

SCIP_EXPRINTCAPABILITY	SCIPexprintGetCapability (void)

SCIP_RETCODE	SCIPexprintCreate (BMS_BLKMEM blkmem, SCIP_EXPRINT *exprint)

SCIP_RETCODE	SCIPexprintFree (SCIP_EXPRINT **exprint)

SCIP_RETCODE	SCIPexprintCompile (SCIP_EXPRINT exprint, SCIP_EXPRTREE tree)

SCIP_EXPRINTCAPABILITY	SCIPexprintGetExprtreeCapability (SCIP_EXPRINT exprint, SCIP_EXPRTREE tree)

SCIP_RETCODE	SCIPexprintFreeData (SCIP_EXPRINTDATA **interpreterdata)

SCIP_RETCODE	SCIPexprintNewParametrization (SCIP_EXPRINT exprint, SCIP_EXPRTREE tree)

SCIP_RETCODE	SCIPexprintEval (SCIP_EXPRINT exprint, SCIP_EXPRTREE tree, SCIP_Real varvals, SCIP_Real val)

SCIP_RETCODE	SCIPexprintEvalInt (SCIP_EXPRINT exprint, SCIP_EXPRTREE tree, SCIP_Real infinity, SCIP_INTERVAL varvals, SCIP_INTERVAL val)

SCIP_RETCODE	SCIPexprintGrad (SCIP_EXPRINT exprint, SCIP_EXPRTREE tree, SCIP_Real varvals, SCIP_Bool new_varvals, SCIP_Real val, SCIP_Real *gradient)

SCIP_RETCODE	SCIPexprintGradInt (SCIP_EXPRINT exprint, SCIP_EXPRTREE tree, SCIP_Real infinity, SCIP_INTERVAL varvals, SCIP_Bool new_varvals, SCIP_INTERVAL val, SCIP_INTERVAL *gradient)

SCIP_RETCODE	SCIPexprintHessianSparsityDense (SCIP_EXPRINT exprint, SCIP_EXPRTREE tree, SCIP_Real varvals, SCIP_Bool sparsity)

SCIP_RETCODE	SCIPexprintHessianDense (SCIP_EXPRINT exprint, SCIP_EXPRTREE tree, SCIP_Real varvals, SCIP_Bool new_varvals, SCIP_Real val, SCIP_Real *hessian)

Variables
static pthread_mutex_t	cppadmutex = PTHREAD_MUTEX_INITIALIZER

static pthread_key_t	thread_specific_key

static size_t	ncurthreads = 0

Macro Definition Documentation

◆ SIGN

#define SIGN ( x ) ((x) >= 0.0 ? 1.0 : -1.0)

sign of a value (-1 or +1)

0.0 has sign +1

Definition at line 56 of file exprinterpret_cppad.cpp.

Referenced by atomic_signpower< Type >::atomic_signpower().

◆ SCIPInterval_NAMESPACE

#define SCIPInterval_NAMESPACE CppAD

Definition at line 60 of file exprinterpret_cppad.cpp.

◆ CPPAD_MAX_NUM_THREADS

#define CPPAD_MAX_NUM_THREADS 64

Definition at line 74 of file exprinterpret_cppad.cpp.

Referenced by init_parallel().

Function Documentation

◆ in_parallel()

static bool in_parallel ( void )

static

CppAD callback function that indicates whether we are running in parallel mode

Definition at line 102 of file exprinterpret_cppad.cpp.

References ncurthreads.

Referenced by init_parallel().

◆ thread_num()

static size_t thread_num ( void )

static

CppAD callback function that returns the number of the current thread

assigns a new number to the thread if new

Definition at line 112 of file exprinterpret_cppad.cpp.

References cppadmutex, ncurthreads, SCIPdebugMessage, and thread_specific_key.

Referenced by init_parallel().

◆ init_parallel()

static char init_parallel ( void )

static

sets up CppAD's datastructures for running in multithreading mode

It must be called once before multithreading is started.

Definition at line 154 of file exprinterpret_cppad.cpp.

References CPPAD_MAX_NUM_THREADS, in_parallel(), thread_num(), and thread_specific_key.

◆ CondExpOp()

SCIPInterval CondExpOp	(	enum CppAD::CompareOp	cop,
		const SCIPInterval &	left,
		const SCIPInterval &	right,
		const SCIPInterval &	trueCase,
		const SCIPInterval &	falseCase
	)

inline

definition of CondExpOp for SCIPInterval (required by CppAD)

Definition at line 178 of file exprinterpret_cppad.cpp.

◆ IdenticalPar()

bool IdenticalPar ( const SCIPInterval & x )

inline

another function required by CppAD

Parameters

x operand

Definition at line 195 of file exprinterpret_cppad.cpp.

◆ IdenticalZero()

bool IdenticalZero ( const SCIPInterval & x )

inline

returns whether the interval equals [0,0]

Parameters

x operand

Definition at line 204 of file exprinterpret_cppad.cpp.

◆ IdenticalOne()

bool IdenticalOne ( const SCIPInterval & x )

inline

returns whether the interval equals [1,1]

Parameters

x operand

Definition at line 213 of file exprinterpret_cppad.cpp.

◆ IdenticalEqualPar()

bool IdenticalEqualPar	(	const SCIPInterval &	x,
		const SCIPInterval &	y
	)

inline

yet another function that checks whether two intervals are equal

Parameters

x	first operand
y	second operand

Definition at line 222 of file exprinterpret_cppad.cpp.

◆ GreaterThanZero()

bool GreaterThanZero ( const SCIPInterval & x )

inline

greater than zero not defined for intervals

Parameters

x operand

Definition at line 232 of file exprinterpret_cppad.cpp.

◆ GreaterThanOrZero()

bool GreaterThanOrZero ( const SCIPInterval & x )

inline

greater than or equal zero not defined for intervals

Parameters

x operand

Definition at line 246 of file exprinterpret_cppad.cpp.

◆ LessThanZero()

bool LessThanZero ( const SCIPInterval & x )

inline

less than not defined for intervals

Parameters

x operand

Definition at line 260 of file exprinterpret_cppad.cpp.

◆ LessThanOrZero()

bool LessThanOrZero ( const SCIPInterval & x )

inline

less than or equal not defined for intervals

Parameters

x operand

Definition at line 274 of file exprinterpret_cppad.cpp.

◆ Integer()

int Integer ( const SCIPInterval & x )

inline

conversion to integers not defined for intervals

Parameters

x operand

Definition at line 288 of file exprinterpret_cppad.cpp.

◆ azmul()

SCIPInterval azmul	(	const SCIPInterval &	x,
		const SCIPInterval &	y
	)

inline

absolute zero multiplication

Returns: [0,0] if first argument is [0,0] independent of whether the second argument is an empty interval or not

Parameters

x	first operand
y	second operand

Definition at line 305 of file exprinterpret_cppad.cpp.

◆ operator<<()

std::ostream& operator<<	(	std::ostream &	out,
		const SCIP_INTERVAL &	x
	)

inline

printing of an interval (required by CppAD)

Definition at line 317 of file exprinterpret_cppad.cpp.

References SCIP_Interval::inf, and SCIP_Interval::sup.

◆ univariate_for_sparse_jac()

static bool univariate_for_sparse_jac	(	size_t	q,
		const CppAD::vector< bool > &	r,
		CppAD::vector< bool > &	s
	)

static

computes sparsity of jacobian for a univariate function during a forward sweep

For a 1 x q matrix R, we have to return the sparsity pattern of the 1 x q matrix S(x) = f'(x) * R. Since f'(x) is dense, the sparsity of S will be the sparsity of R.

Parameters

q	number of columns in R
r	sparsity of R, columnwise
s	vector to store sparsity of S, columnwise

Definition at line 375 of file exprinterpret_cppad.cpp.

Referenced by atomic_posintpower< Type >::atomic_posintpower(), and atomic_signpower< Type >::atomic_signpower().

◆ univariate_rev_sparse_jac()

static bool univariate_rev_sparse_jac	(	size_t	q,
		const CppAD::vector< bool > &	r,
		CppAD::vector< bool > &	s
	)

static

Computes sparsity of jacobian during a reverse sweep

For a q x 1 matrix R, we have to return the sparsity pattern of the q x 1 matrix S(x) = R * f'(x). Since f'(x) is dense, the sparsity of S will be the sparsity of R.

Parameters

q	number of rows in R
r	sparsity of R, rowwise
s	vector to store sparsity of S, rowwise

Definition at line 395 of file exprinterpret_cppad.cpp.

Referenced by atomic_posintpower< Type >::atomic_posintpower(), and atomic_signpower< Type >::atomic_signpower().

◆ univariate_rev_sparse_hes()

static bool univariate_rev_sparse_hes	(	const CppAD::vector< bool > &	vx,
		const CppAD::vector< bool > &	s,
		CppAD::vector< bool > &	t,
		size_t	q,
		const CppAD::vector< bool > &	r,
		const CppAD::vector< bool > &	u,
		CppAD::vector< bool > &	v
	)

static

computes sparsity of hessian during a reverse sweep

Assume V(x) = (g(f(x)))'' R with f(x) = x^p for a function g:R->R and a matrix R. we have to specify the sparsity pattern of V(x) and T(x) = (g(f(x)))'.

Parameters

vx	indicates whether argument is a variable, or empty vector
s	sparsity pattern of S = g'(y)
t	vector to store sparsity pattern of T(x) = (g(f(x)))'
q	number of columns in R, U, and V
r	sparsity pattern of R
u	sparsity pattern of U(x) = g''(f(x)) f'(x) R
v	vector to store sparsity pattern of V(x) = (g(f(x)))'' R

Definition at line 415 of file exprinterpret_cppad.cpp.

Referenced by atomic_posintpower< Type >::atomic_posintpower(), and atomic_signpower< Type >::atomic_signpower().

◆ posintpower()

template<class Type >

static void posintpower	(	const vector< Type > &	in,
		vector< Type > &	out,
		size_t	exponent
	)

static

power function with natural exponents

Parameters

in	vector which first argument is base
out	vector where to store result in first argument
exponent	exponent

Definition at line 674 of file exprinterpret_cppad.cpp.

References pow().

Referenced by eval(), evalAbs(), and evalIntPower().

◆ evalSignPower()

template<class Type >

static void evalSignPower	(	Type &	resultant,
		const Type &	arg,
		SCIP_EXPR *	expr
	)

static

template for evaluation for signpower operator

Parameters

resultant	resultant
arg	operand
expr	expression that holds the exponent

Definition at line 1141 of file exprinterpret_cppad.cpp.

References pow(), SCIP_Real, and SCIPexprGetSignPowerExponent().

Referenced by eval().

◆ exprEvalUser() [1/2]

template<class Type >

SCIP_RETCODE exprEvalUser	(	SCIP_EXPR *	expr,
		Type *	x,
		Type &	funcval,
		Type *	gradient,
		Type *	hessian
	)

Definition at line 1203 of file exprinterpret_cppad.cpp.

References SCIPexprEvalUser().

Referenced by atomic_userexpr< Type >::atomic_userexpr().

◆ exprEvalUser() [2/2]

template<>

SCIP_RETCODE exprEvalUser	(	SCIP_EXPR *	expr,
		SCIPInterval *	x,
		SCIPInterval &	funcval,
		SCIPInterval *	gradient,
		SCIPInterval *	hessian
	)

Definition at line 1215 of file exprinterpret_cppad.cpp.

References infinity, and SCIPexprEvalIntUser().

◆ evalUser()

template<class Type >

static void evalUser	(	Type &	resultant,
		const Type *	args,
		SCIP_EXPR *	expr
	)

static

Parameters

resultant	resultant
args	operands
expr	expression that holds the user expression

Definition at line 1592 of file exprinterpret_cppad.cpp.

References SCIPexprGetNChildren().

Referenced by eval().

◆ evalMin() [1/2]

template<class Type >

static void evalMin	(	Type &	resultant,
		const Type &	arg1,
		const Type &	arg2
	)

static

template for evaluation for minimum operator

Only implemented for real numbers, thus gives error by default.

Parameters

resultant	resultant
arg1	first operand
arg2	second operand

Definition at line 1634 of file exprinterpret_cppad.cpp.

Referenced by eval().

◆ evalMin() [2/2]

template<>

void evalMin	(	CppAD::AD< double > &	resultant,
		const CppAD::AD< double > &	arg1,
		const CppAD::AD< double > &	arg2
	)

specialization of minimum evaluation for real numbers

Parameters

resultant	resultant
arg1	first operand
arg2	second operand

Definition at line 1648 of file exprinterpret_cppad.cpp.

◆ evalMax() [1/2]

template<class Type >

static void evalMax	(	Type &	resultant,
		const Type &	arg1,
		const Type &	arg2
	)

static

template for evaluation for maximum operator

Only implemented for real numbers, thus gives error by default.

Parameters

resultant	resultant
arg1	first operand
arg2	second operand

Definition at line 1664 of file exprinterpret_cppad.cpp.

Referenced by eval().

◆ evalMax() [2/2]

template<>

void evalMax	(	CppAD::AD< double > &	resultant,
		const CppAD::AD< double > &	arg1,
		const CppAD::AD< double > &	arg2
	)

specialization of maximum evaluation for real numbers

Parameters

resultant	resultant
arg1	first operand
arg2	second operand

Definition at line 1678 of file exprinterpret_cppad.cpp.

References MAX.

◆ evalSqrt()

template<class Type >

static void evalSqrt	(	Type &	resultant,
		const Type &	arg
	)

static

template for evaluation for square-root operator

Default is to use the standard sqrt-function.

Parameters

resultant	resultant
arg	operand

Definition at line 1693 of file exprinterpret_cppad.cpp.

References sqrt().

Referenced by eval().

◆ evalAbs() [1/2]

template<class Type >

static void evalAbs	(	Type &	resultant,
		const Type &	arg
	)

static

template for evaluation for absolute value operator

Parameters

resultant	resultant
arg	operand

Definition at line 1704 of file exprinterpret_cppad.cpp.

References abs().

Referenced by eval().

◆ evalAbs() [2/2]

template<>

void evalAbs	(	CppAD::AD< SCIPInterval > &	resultant,
		const CppAD::AD< SCIPInterval > &	arg
	)

specialization of absolute value evaluation for intervals

Use sqrt(x^2) for now

Parameters

resultant	resultant
arg	operand

Definition at line 1717 of file exprinterpret_cppad.cpp.

References posintpower(), and sqrt().

◆ evalIntPower()

template<class Type >

static void evalIntPower	(	Type &	resultant,
		const Type &	arg,
		const int	exponent
	)

static

integer power operation for arbitrary integer exponents

Parameters

resultant	resultant
arg	operand
exponent	exponent

Definition at line 1733 of file exprinterpret_cppad.cpp.

References posintpower().

Referenced by eval().

◆ eval()

template<class Type >

static SCIP_RETCODE eval	(	SCIP_EXPR *	expr,
		const vector< Type > &	x,
		SCIP_Real *	param,
		Type &	val
	)

static

CppAD compatible evaluation of an expression for given arguments and parameters

Parameters

expr	expression
x	values of variables
param	values of parameters
val	buffer to store expression value

Definition at line 1780 of file exprinterpret_cppad.cpp.

References BMSallocMemoryArray, BMSfreeMemoryArrayNull, SCIP_QuadElement::coef, cos(), evalAbs(), evalIntPower(), evalMax(), evalMin(), evalSignPower(), evalSqrt(), evalUser(), exp(), SCIP_QuadElement::idx2, log(), posintpower(), pow(), SCIP_CALL, SCIP_ERROR, SCIP_EXPR_ABS, SCIP_EXPR_CONST, SCIP_EXPR_COS, SCIP_EXPR_DIV, SCIP_EXPR_EXP, SCIP_EXPR_INTPOWER, SCIP_EXPR_LAST, SCIP_EXPR_LINEAR, SCIP_EXPR_LOG, SCIP_EXPR_MAX, SCIP_EXPR_MIN, SCIP_EXPR_MINUS, SCIP_EXPR_MUL, SCIP_EXPR_PARAM, SCIP_EXPR_PLUS, SCIP_EXPR_POLYNOMIAL, SCIP_EXPR_PRODUCT, SCIP_EXPR_QUADRATIC, SCIP_EXPR_REALPOWER, SCIP_EXPR_SIGN, SCIP_EXPR_SIGNPOWER, SCIP_EXPR_SIN, SCIP_EXPR_SQRT, SCIP_EXPR_SQUARE, SCIP_EXPR_SUM, SCIP_EXPR_TAN, SCIP_EXPR_USER, SCIP_EXPR_VARIDX, SCIP_NOMEMORY, SCIP_OKAY, SCIP_Real, SCIPexprGetChildren(), SCIPexprGetIntPowerExponent(), SCIPexprGetLinearCoefs(), SCIPexprGetLinearConstant(), SCIPexprGetMonomialChildIndices(), SCIPexprGetMonomialCoef(), SCIPexprGetMonomialExponents(), SCIPexprGetMonomialNFactors(), SCIPexprGetMonomials(), SCIPexprGetNChildren(), SCIPexprGetNMonomials(), SCIPexprGetNQuadElements(), SCIPexprGetOperator(), SCIPexprGetOpIndex(), SCIPexprGetOpReal(), SCIPexprGetPolynomialConstant(), SCIPexprGetQuadConstant(), SCIPexprGetQuadElements(), SCIPexprGetQuadLinearCoefs(), SCIPexprGetRealPowerExponent(), SCIPexprSortQuadElems(), sign(), and sin().

Referenced by SCIP_DECL_EXPRFREEDATA(), SCIPexprCreateUser(), SCIPexprgraphCreateNodeUser(), SCIPexprintEval(), and SCIPexprintEvalInt().

◆ analyzeTree()

static void analyzeTree	(	SCIP_EXPRINTDATA *	data,
		SCIP_EXPR *	expr
	)

static

analysis an expression tree whether it requires retaping on every evaluation

This may be the case if the evaluation sequence depends on values of operands (e.g., in case of abs, sign, signpower, ...).

Definition at line 2095 of file exprinterpret_cppad.cpp.

References SCIP_EXPR_ABS, SCIP_EXPR_MAX, SCIP_EXPR_MIN, SCIP_EXPR_SIGNPOWER, SCIP_EXPR_USER, SCIPexprGetChildren(), SCIPexprGetNChildren(), SCIPexprGetOperator(), and SCIPexprGetUserEvalCapability().

Referenced by SCIPexprintCompile().

◆ cppaderrorcallback()

static void cppaderrorcallback	(	bool	known,
		int	line,
		const char *	file,
		const char *	cond,
		const char *	msg
	)

static

replacement for CppAD's default error handler

In debug mode, CppAD gives an error when an evaluation contains a nan. We do not want to stop execution in such a case, since the calling routine should check for nan's and decide what to do. Since we cannot ignore this particular error, we ignore all.

Parameters

known	is the error from a known source?
line	line where error occured
file	file where error occured
cond	error condition
msg	error message

Definition at line 2134 of file exprinterpret_cppad.cpp.

References errorhandler(), and SCIPdebugMessage.

◆ errorhandler()

static CppAD::ErrorHandler errorhandler ( cppaderrorcallback )

static

Referenced by cppaderrorcallback().

Variable Documentation

◆ cppadmutex

pthread_mutex_t cppadmutex = PTHREAD_MUTEX_INITIALIZER

static

mutex for locking in pthread case

Definition at line 92 of file exprinterpret_cppad.cpp.

Referenced by thread_num().

◆ thread_specific_key

pthread_key_t thread_specific_key

static

key for accessing thread specific information

Definition at line 95 of file exprinterpret_cppad.cpp.

Referenced by init_parallel(), and thread_num().

◆ ncurthreads

size_t ncurthreads = 0

static

currently registered number of threads

Definition at line 98 of file exprinterpret_cppad.cpp.

Referenced by in_parallel(), and thread_num().

SCIP

Detailed Description

Macros

Functions

Variables

Macro Definition Documentation

◆ SIGN

◆ SCIPInterval_NAMESPACE

◆ CPPAD_MAX_NUM_THREADS

Function Documentation

◆ in_parallel()

◆ thread_num()

◆ init_parallel()

◆ CondExpOp()

◆ IdenticalPar()

◆ IdenticalZero()

◆ IdenticalOne()

◆ IdenticalEqualPar()

◆ GreaterThanZero()

◆ GreaterThanOrZero()

◆ LessThanZero()

◆ LessThanOrZero()

◆ Integer()

◆ azmul()

◆ operator<<()

◆ univariate_for_sparse_jac()

◆ univariate_rev_sparse_jac()

◆ univariate_rev_sparse_hes()

◆ posintpower()

◆ evalSignPower()

◆ exprEvalUser() [1/2]

◆ exprEvalUser() [2/2]

◆ evalUser()

◆ evalMin() [1/2]

◆ evalMin() [2/2]

◆ evalMax() [1/2]

◆ evalMax() [2/2]

◆ evalSqrt()

◆ evalAbs() [1/2]

◆ evalAbs() [2/2]

◆ evalIntPower()

◆ eval()

◆ analyzeTree()

◆ cppaderrorcallback()

◆ errorhandler()

Variable Documentation

◆ cppadmutex

◆ thread_specific_key

◆ ncurthreads