If the type of the multiplication expression is double, then the double value set must be chosen in Java

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If the type of the multiplication expression is double, then the double value set must be chosen
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If the multiplication expression is not FP-strict:
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Entia non sunt multiplicanda praeter necessitatem
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Division Operator / 15172
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If the type of the multiplication expression is float, then either the oat value set or the oat-extended-exponent value set may be chosen, at the whim of the implementation If the type of the multiplication expression is double, then either the double value set or the double-extended-exponent value set may be chosen, at the whim of the implementation
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Despite the fact that over ow, under ow, or loss of information may occur, evaluation of a multiplication operator * never throws a run-time exception 15172 Division Operator /
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The binary / operator performs division, producing the quotient of its operands The left-hand operand is the dividend and the right-hand operand is the divisor Integer division rounds toward 0 That is, the quotient produced for operands n and d that are integers after binary numeric promotion ( 562) is an integer value q whose magnitude is as large as possible while satisfying d q n ; moreover, q is positive when n d and n and d have the same sign, but q is negative when n d and n and d have opposite signs There is one special case that does not satisfy this rule: if the dividend is the negative integer of largest possible magnitude for its type, and the divisor is -1, then integer over ow occurs and the result is equal to the dividend Despite the over ow, no exception is thrown in this case On the other hand, if the value of the divisor in an integer division is 0, then an ArithmeticException is thrown The result of a oating-point division is determined by the speci cation of IEEE arithmetic: If either operand is NaN, the result is NaN If the result is not NaN, the sign of the result is positive if both operands have the same sign, negative if the operands have different signs
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Gallia est omnis divisa in partes tres Commentaries on the Gallic Wars 493
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Next, a value must be chosen from the chosen value set to represent the product If the magnitude of the product is too large to represent, we say the operation over ows; the result is then an in nity of appropriate sign Otherwise, the product is rounded to the nearest value in the chosen value set using IEEE 754 round-to-nearest mode The Java programming language requires support of gradual under ow as de ned by IEEE 754 ( 424)
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15172 Division Operator /
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EXPRESSIONS
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Division of an in nity by an in nity results in NaN Division of an in nity by a nite value results in a signed in nity The sign is determined by the rule stated above Division of a nite value by an in nity results in a signed zero The sign is determined by the rule stated above Division of a zero by a zero results in NaN; division of zero by any other nite value results in a signed zero The sign is determined by the rule stated above
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In the remaining cases, where neither an in nity nor NaN is involved, the exact mathematical quotient is computed A oating-point value set is then chosen:
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If the division expression is FP-strict ( 154):
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If the type of the division expression is float, then the oat value set must be chosen If the type of the division expression is double, then the double value set must be chosen
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Next, a value must be chosen from the chosen value set to represent the quotient If the magnitude of the quotient is too large to represent, we say the operation over ows; the result is then an in nity of appropriate sign Otherwise, the quotient is rounded to the nearest value in the chosen value set using IEEE 754 round-to-nearest mode The Java programming language requires support of gradual under ow as de ned by IEEE 754 ( 424)
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Despite the fact that over ow, under ow, division by zero, or loss of information may occur, evaluation of a oating-point division operator / never throws a run-time exception
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If the division expression is not FP-strict:
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If the type of the division expression is float, then either the oat value set or the oat-extended-exponent value set may be chosen, at the whim of the implementation
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If the type of the division expression is double, then either the double value set or the double-extended-exponent value set may be chosen, at the whim of the implementation
Division of a nonzero nite value by a zero results in a signed in nity The sign is determined by the rule stated above