Package org.sosy_lab.java_smt.api

Interface FloatingPointFormulaManager

All Known Implementing Classes:

AbstractFloatingPointFormulaManager, DebuggingFloatingPointFormulaManager

public interface FloatingPointFormulaManager

Floating point operations.

Most operations are overloaded: there is an option of either using the default rounding mode (set via the option solver.floatingPointRoundingMode), or providing the rounding mode explicitly.

If the result of an operation can not be exactly represented by the available floating-point type, i.e., the given precision is insufficient, the result is rounded to the nearest possible floating-point representation, depending on the given rounding mode.

Example: If the input number is too large to be represented as a floating point with the given type, it will be converted to positive infinity (+inf) or negative infinity (-inf). If the input number is too small to be represented with the given type (closer to zero than the smallest possible floating-point number), it will be converted to zero, with the sign preserved.

Method Summary

Modifier and Type	Method	Description
FloatingPointFormula	abs(FloatingPointFormula number)
FloatingPointFormula	add(FloatingPointFormula number1, FloatingPointFormula number2)
FloatingPointFormula	add(FloatingPointFormula number1, FloatingPointFormula number2, FloatingPointRoundingMode pFloatingPointRoundingMode)
BooleanFormula	assignment(FloatingPointFormula number1, FloatingPointFormula number2)	Create a term for assigning one floating-point term to another.
FloatingPointFormula	castFrom(Formula source, boolean signed, FormulaType.FloatingPointType targetType)	Build a FloatingPointFormula from another compatible formula.
FloatingPointFormula	castFrom(Formula source, boolean signed, FormulaType.FloatingPointType targetType, FloatingPointRoundingMode pFloatingPointRoundingMode)	Build a FloatingPointFormula from another compatible formula.
<T extends Formula> T	castTo(FloatingPointFormula source, boolean signed, FormulaType<T> targetType)	Build a formula of compatible type from a FloatingPointFormula.
<T extends Formula> T	castTo(FloatingPointFormula source, boolean signed, FormulaType<T> targetType, FloatingPointRoundingMode pFloatingPointRoundingMode)	Build a formula of compatible type from a FloatingPointFormula.
FloatingPointFormula	divide(FloatingPointFormula number1, FloatingPointFormula number2)
FloatingPointFormula	divide(FloatingPointFormula number1, FloatingPointFormula number2, FloatingPointRoundingMode pFloatingPointRoundingMode)
BooleanFormula	equalWithFPSemantics(FloatingPointFormula number1, FloatingPointFormula number2)	Create a term for comparing the equality of two floating-point terms, according to standard floating-point semantics (i.e., NaN != NaN).
FloatingPointFormula	fromIeeeBitvector(BitvectorFormula number, FormulaType.FloatingPointType pTargetType)	Create a formula that interprets the given bitvector as a floating-point value in the IEEE format, according to the given type.
BooleanFormula	greaterOrEquals(FloatingPointFormula number1, FloatingPointFormula number2)
BooleanFormula	greaterThan(FloatingPointFormula number1, FloatingPointFormula number2)
BooleanFormula	isInfinity(FloatingPointFormula number)
BooleanFormula	isNaN(FloatingPointFormula number)
BooleanFormula	isNegative(FloatingPointFormula number)	checks whether a formula is negative, including -0.0.
BooleanFormula	isNormal(FloatingPointFormula number)
BooleanFormula	isSubnormal(FloatingPointFormula number)
BooleanFormula	isZero(FloatingPointFormula number)
BooleanFormula	lessOrEquals(FloatingPointFormula number1, FloatingPointFormula number2)
BooleanFormula	lessThan(FloatingPointFormula number1, FloatingPointFormula number2)
FloatingPointFormula	makeMinusInfinity(FormulaType.FloatingPointType type)
FloatingPointFormula	makeNaN(FormulaType.FloatingPointType type)
FloatingPointFormula	makeNumber(double n, FormulaType.FloatingPointType type)	Creates a floating point formula representing the given double value with the specified type.
FloatingPointFormula	makeNumber(double n, FormulaType.FloatingPointType type, FloatingPointRoundingMode pFloatingPointRoundingMode)	Creates a floating point formula representing the given double value with the specified type and rounding mode.
FloatingPointFormula	makeNumber(String n, FormulaType.FloatingPointType type)	Creates a floating point formula representing the given string value with the specified type.
FloatingPointFormula	makeNumber(String n, FormulaType.FloatingPointType type, FloatingPointRoundingMode pFloatingPointRoundingMode)	Creates a floating point formula representing the given string value with the specified type and rounding mode.
FloatingPointFormula	makeNumber(BigDecimal n, FormulaType.FloatingPointType type)	Creates a floating point formula representing the given BigDecimal value with the specified type.
FloatingPointFormula	makeNumber(BigDecimal n, FormulaType.FloatingPointType type, FloatingPointRoundingMode pFloatingPointRoundingMode)	Creates a floating point formula representing the given BigDecimal value with the specified type and rounding mode.
FloatingPointFormula	makeNumber(BigInteger exponent, BigInteger mantissa, boolean signBit, FormulaType.FloatingPointType type)	Creates a floating point formula from the given exponent, mantissa, and sign bit with the specified type.
FloatingPointFormula	makeNumber(Rational n, FormulaType.FloatingPointType type)	Creates a floating point formula representing the given Rational value with the specified type.
FloatingPointFormula	makeNumber(Rational n, FormulaType.FloatingPointType type, FloatingPointRoundingMode pFloatingPointRoundingMode)	Creates a floating point formula representing the given Rational value with the specified type and rounding mode.
FloatingPointFormula	makePlusInfinity(FormulaType.FloatingPointType type)
FloatingPointFormula	makeVariable(String pVar, FormulaType.FloatingPointType type)	Creates a variable with exactly the given name.
FloatingPointFormula	max(FloatingPointFormula number1, FloatingPointFormula number2)
FloatingPointFormula	min(FloatingPointFormula number1, FloatingPointFormula number2)
FloatingPointFormula	multiply(FloatingPointFormula number1, FloatingPointFormula number2)
FloatingPointFormula	multiply(FloatingPointFormula number1, FloatingPointFormula number2, FloatingPointRoundingMode pFloatingPointRoundingMode)
FloatingPointFormula	negate(FloatingPointFormula number)
FloatingPointFormula	remainder(FloatingPointFormula dividend, FloatingPointFormula divisor)	remainder: x - y * n, where n in Z is nearest to x/y.
FloatingPointFormula	round(FloatingPointFormula formula, FloatingPointRoundingMode roundingMode)
FloatingPointFormula	sqrt(FloatingPointFormula number)
FloatingPointFormula	sqrt(FloatingPointFormula number, FloatingPointRoundingMode roundingMode)
FloatingPointFormula	subtract(FloatingPointFormula number1, FloatingPointFormula number2)
FloatingPointFormula	subtract(FloatingPointFormula number1, FloatingPointFormula number2, FloatingPointRoundingMode pFloatingPointRoundingMode)
BitvectorFormula	toIeeeBitvector(FloatingPointFormula number)	Create a formula that produces a representation of the given floating-point value as a bitvector conforming to the IEEE format.

Method Details

makeNumber

FloatingPointFormula makeNumber(double n,
 FormulaType.FloatingPointType type)

Creates a floating point formula representing the given double value with the specified type.

makeNumber

FloatingPointFormula makeNumber(double n,
 FormulaType.FloatingPointType type,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

Creates a floating point formula representing the given double value with the specified type and rounding mode.

makeNumber

FloatingPointFormula makeNumber(BigDecimal n,
 FormulaType.FloatingPointType type)

Creates a floating point formula representing the given BigDecimal value with the specified type.

makeNumber

FloatingPointFormula makeNumber(BigDecimal n,
 FormulaType.FloatingPointType type,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

Creates a floating point formula representing the given BigDecimal value with the specified type and rounding mode.

makeNumber

FloatingPointFormula makeNumber(String n,
 FormulaType.FloatingPointType type)

Creates a floating point formula representing the given string value with the specified type.

makeNumber

FloatingPointFormula makeNumber(String n,
 FormulaType.FloatingPointType type,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

Creates a floating point formula representing the given string value with the specified type and rounding mode.

makeNumber

FloatingPointFormula makeNumber(Rational n,
 FormulaType.FloatingPointType type)

Creates a floating point formula representing the given Rational value with the specified type.

makeNumber

FloatingPointFormula makeNumber(Rational n,
 FormulaType.FloatingPointType type,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

Creates a floating point formula representing the given Rational value with the specified type and rounding mode.

makeNumber

FloatingPointFormula makeNumber(BigInteger exponent,
 BigInteger mantissa,
 boolean signBit,
 FormulaType.FloatingPointType type)

Creates a floating point formula from the given exponent, mantissa, and sign bit with the specified type.

Parameters:

exponent - the exponent part of the floating point number

mantissa - the mantissa part of the floating point number

signBit - the sign bit of the floating point number, e.g., true for negative numbers

makeVariable

FloatingPointFormula makeVariable(String pVar,
 FormulaType.FloatingPointType type)

Creates a variable with exactly the given name.

Please make sure that the given name is valid in SMT-LIB2. Take a look at FormulaManager.isValidName(java.lang.String) for further information.

This method does not quote or unquote the given name, but uses the plain name "AS IS". Formula.toString() can return a different String than the given one.

makePlusInfinity

FloatingPointFormula makePlusInfinity(FormulaType.FloatingPointType type)

makeMinusInfinity

FloatingPointFormula makeMinusInfinity(FormulaType.FloatingPointType type)

makeNaN

FloatingPointFormula makeNaN(FormulaType.FloatingPointType type)

castTo

<T extends Formula> T castTo(FloatingPointFormula source,
 boolean signed,
 FormulaType<T> targetType)

Build a formula of compatible type from a FloatingPointFormula. This method uses the default rounding mode.

Compatible formula types are all numeral types and (signed/unsigned) bitvector types. It is also possible to cast a floating-point number into another floating-point type. We do not support casting from boolean or array types. We try to keep an exact representation, however fall back to rounding if needed.

Parameters:

source - the source formula of floating-point type

signed - if a BitvectorFormula is given as target, we additionally use this flag. Otherwise, we ignore it.

targetType - the type of the resulting formula

Throws:

IllegalArgumentException - if an incompatible type is used, e.g. a FloatingPointFormula cannot be cast to BooleanFormula.

castTo

<T extends Formula> T castTo(FloatingPointFormula source,
 boolean signed,
 FormulaType<T> targetType,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

Build a formula of compatible type from a FloatingPointFormula.

Compatible formula types are all numeral types and (signed/unsigned) bitvector types. It is also possible to cast a floating-point number into another floating-point type. We do not support casting from boolean or array types. We try to keep an exact representation, however fall back to rounding if needed.

Parameters:

source - the source formula of floating-point type

signed - if a BitvectorFormula is given as target, we additionally use this flag. Otherwise, we ignore it.

targetType - the type of the resulting formula

pFloatingPointRoundingMode - if rounding is needed, we apply the rounding mode.

Throws:

IllegalArgumentException - if an incompatible type is used, e.g. a FloatingPointFormula cannot be cast to BooleanFormula.

castFrom

FloatingPointFormula castFrom(Formula source,
 boolean signed,
 FormulaType.FloatingPointType targetType)

Build a FloatingPointFormula from another compatible formula. This method uses the default rounding mode.

Compatible formula types are all numeral types and (signed/unsigned) bitvector types. It is also possible to cast a floating-point number into another floating-point type. We do not support casting from boolean or array types. We try to keep an exact representation, however fall back to rounding if needed.

Parameters:

source - the source formula of compatible type

signed - if a BitvectorFormula is given as source, we additionally use this flag. Otherwise, we ignore it.

targetType - the type of the resulting formula

Throws:

IllegalArgumentException - if an incompatible type is used, e.g. a BooleanFormula cannot be cast to FloatingPointFormula.

castFrom

FloatingPointFormula castFrom(Formula source,
 boolean signed,
 FormulaType.FloatingPointType targetType,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

Build a FloatingPointFormula from another compatible formula.

Compatible formula types are all numeral types and (signed/unsigned) bitvector types. It is also possible to cast a floating-point number into another floating-point type. We do not support casting from boolean or array types. We try to keep an exact representation, however fall back to rounding if needed.

Parameters:

source - the source formula of compatible type

signed - if a BitvectorFormula is given as source, we additionally use this flag. Otherwise, we ignore it.

targetType - the type of the resulting formula

pFloatingPointRoundingMode - if rounding is needed, we apply the rounding mode.

Throws:

IllegalArgumentException - if an incompatible type is used, e.g. a BooleanFormula cannot be cast to FloatingPointFormula.

fromIeeeBitvector

FloatingPointFormula fromIeeeBitvector(BitvectorFormula number,
 FormulaType.FloatingPointType pTargetType)

Create a formula that interprets the given bitvector as a floating-point value in the IEEE format, according to the given type. The sum of the sizes of exponent and mantissa of the target type plus 1 (for the sign bit) needs to be equal to the size of the bitvector.

Note: This method will return a value that is (numerically) far away from the original value. This method is completely different from castFrom(org.sosy_lab.java_smt.api.Formula, boolean, org.sosy_lab.java_smt.api.FormulaType.FloatingPointType), which will produce a floating-point value close to the numeral value.

toIeeeBitvector

BitvectorFormula toIeeeBitvector(FloatingPointFormula number)

Create a formula that produces a representation of the given floating-point value as a bitvector conforming to the IEEE format. The size of the resulting bitvector is the sum of the sizes of the exponent and mantissa of the input formula plus 1 (for the sign bit).

round

FloatingPointFormula round(FloatingPointFormula formula,
 FloatingPointRoundingMode roundingMode)

negate

FloatingPointFormula negate(FloatingPointFormula number)

abs

FloatingPointFormula abs(FloatingPointFormula number)

max

FloatingPointFormula max(FloatingPointFormula number1,
 FloatingPointFormula number2)

min

FloatingPointFormula min(FloatingPointFormula number1,
 FloatingPointFormula number2)

sqrt

FloatingPointFormula sqrt(FloatingPointFormula number)

sqrt

FloatingPointFormula sqrt(FloatingPointFormula number,
 FloatingPointRoundingMode roundingMode)

add

FloatingPointFormula add(FloatingPointFormula number1,
 FloatingPointFormula number2)

add

FloatingPointFormula add(FloatingPointFormula number1,
 FloatingPointFormula number2,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

subtract

FloatingPointFormula subtract(FloatingPointFormula number1,
 FloatingPointFormula number2)

subtract

FloatingPointFormula subtract(FloatingPointFormula number1,
 FloatingPointFormula number2,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

divide

FloatingPointFormula divide(FloatingPointFormula number1,
 FloatingPointFormula number2)

divide

FloatingPointFormula divide(FloatingPointFormula number1,
 FloatingPointFormula number2,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

multiply

FloatingPointFormula multiply(FloatingPointFormula number1,
 FloatingPointFormula number2)

multiply

FloatingPointFormula multiply(FloatingPointFormula number1,
 FloatingPointFormula number2,
 FloatingPointRoundingMode pFloatingPointRoundingMode)

remainder

FloatingPointFormula remainder(FloatingPointFormula dividend,
 FloatingPointFormula divisor)

remainder: x - y * n, where n in Z is nearest to x/y. The result can be negative even for two positive arguments, e.g. "rem(5, 4) == 1" and "rem(5, 6) == -1", as opposed to integer modulo operators.

assignment

BooleanFormula assignment(FloatingPointFormula number1,
 FloatingPointFormula number2)

Create a term for assigning one floating-point term to another. This means both terms are considered equal afterwards. This method is the same as the method equal for other theories.

equalWithFPSemantics

BooleanFormula equalWithFPSemantics(FloatingPointFormula number1,
 FloatingPointFormula number2)

Create a term for comparing the equality of two floating-point terms, according to standard floating-point semantics (i.e., NaN != NaN). Be careful to not use this method when you really need assignment(FloatingPointFormula, FloatingPointFormula).

greaterThan

BooleanFormula greaterThan(FloatingPointFormula number1,
 FloatingPointFormula number2)

greaterOrEquals

BooleanFormula greaterOrEquals(FloatingPointFormula number1,
 FloatingPointFormula number2)

lessThan

BooleanFormula lessThan(FloatingPointFormula number1,
 FloatingPointFormula number2)

lessOrEquals

BooleanFormula lessOrEquals(FloatingPointFormula number1,
 FloatingPointFormula number2)

isNaN

BooleanFormula isNaN(FloatingPointFormula number)

isInfinity

BooleanFormula isInfinity(FloatingPointFormula number)

isZero

BooleanFormula isZero(FloatingPointFormula number)

isNormal

BooleanFormula isNormal(FloatingPointFormula number)

isSubnormal

BooleanFormula isSubnormal(FloatingPointFormula number)

isNegative

BooleanFormula isNegative(FloatingPointFormula number)

checks whether a formula is negative, including -0.0.