Annotated ECMAScript 5.1

‟Ex igne vita”

9 Type Conversion and Testing # Ⓣ Ⓔ ① Ⓐ

The ECMAScript runtime system performs automatic type conversion as needed. To clarify the semantics of certain constructs it is useful to define a set of conversion abstract operations. These abstract operations are not a part of the language; they are defined here to aid the specification of the semantics of the language. The conversion abstract operations are polymorphic; that is, they can accept a value of any ECMAScript language type, but not of specification types.

9.1 ToPrimitive # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToPrimitive takes an input argument and an optional argument PreferredType. The abstract operation ToPrimitive converts its input argument to a non-Object type. If an object is capable of converting to more than one primitive type, it may use the optional hint PreferredType to favour that type. Conversion occurs according to Table 10:

9.2 ToBoolean # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToBoolean converts its argument to a value of type Boolean according to Table 11:

9.3 ToNumber # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToNumber converts its argument to a value of type Number according to Table 12:

9.3.1 ToNumber Applied to the String Type # Ⓣ Ⓔ ① Ⓐ

ToNumber applied to Strings applies the following grammar to the input String. If the grammar cannot interpret the String as an expansion of StringNumericLiteral, then the result of ToNumber is NaN.

StringNumericLiteral :::

StrWhiteSpace_opt
StrWhiteSpace_optStrNumericLiteral StrWhiteSpace_opt

StrWhiteSpace :::

StrWhiteSpaceChar StrWhiteSpace_opt

StrWhiteSpaceChar :::

WhiteSpace
LineTerminator

StrNumericLiteral :::

StrDecimalLiteral
HexIntegerLiteral

StrDecimalLiteral :::

StrUnsignedDecimalLiteral
+ StrUnsignedDecimalLiteral
- StrUnsignedDecimalLiteral

StrUnsignedDecimalLiteral :::

Infinity
DecimalDigits . DecimalDigits_optExponentPart_opt
. DecimalDigits ExponentPart_opt
DecimalDigits ExponentPart_opt

DecimalDigits :::

DecimalDigit
DecimalDigits DecimalDigit

DecimalDigit ::: one of

0 1 2 3 4 5 6 7 8 9

ExponentPart :::

ExponentIndicator SignedInteger

ExponentIndicator ::: one of

e E

SignedInteger :::

DecimalDigits
+ DecimalDigits
- DecimalDigits

HexIntegerLiteral :::

0x HexDigit
0X HexDigit
HexIntegerLiteral HexDigit

HexDigit ::: one of

0 1 2 3 4 5 6 7 8 9 a b c d e f A B C D E F

Some differences should be noted between the syntax of a StringNumericLiteral and a NumericLiteral (see 7.8.3):

• A StringNumericLiteral may be preceded and/or followed by white space and/or line terminators.

• A StringNumericLiteral that is decimal may have any number of leading 0 digits.

• A StringNumericLiteral that is decimal may be preceded by + or - to indicate its sign.

• A StringNumericLiteral that is empty or contains only white space is converted to +0.

The conversion of a String to a Number value is similar overall to the determination of the Number value for a numeric literal (see 7.8.3), but some of the details are different, so the process for converting a String numeric literal to a value of Number type is given here in full. This value is determined in two steps: first, a mathematical value (MV) is derived from the String numeric literal; second, this mathematical value is rounded as described below.

• The MV of StringNumericLiteral ::: [empty] is 0.

• The MV of StringNumericLiteral ::: StrWhiteSpace is 0.

• The MV of StringNumericLiteral ::: StrWhiteSpace_optStrNumericLiteral StrWhiteSpace_opt is the MV of StrNumericLiteral, no matter whether white space is present or not.

• The MV of StrNumericLiteral ::: StrDecimalLiteral is the MV of StrDecimalLiteral.

• The MV of StrNumericLiteral ::: HexIntegerLiteral is the MV of HexIntegerLiteral.

• The MV of StrDecimalLiteral ::: StrUnsignedDecimalLiteral is the MV of StrUnsignedDecimalLiteral.

• The MV of StrDecimalLiteral ::: + StrUnsignedDecimalLiteral is the MV of StrUnsignedDecimalLiteral.

• The MV of StrDecimalLiteral ::: - StrUnsignedDecimalLiteral is the negative of the MV of StrUnsignedDecimalLiteral. (Note that if the MV of StrUnsignedDecimalLiteral is 0, the negative of this MV is also 0. The rounding rule described below handles the conversion of this signless mathematical zero to a floating-point +0 or −0 as appropriate.)

• The MV of StrUnsignedDecimalLiteral::: Infinity is 10¹⁰⁰⁰⁰ (a value so large that it will round to +∞).

• The MV of StrUnsignedDecimalLiteral::: DecimalDigits. is the MV of DecimalDigits.

• The MV of StrUnsignedDecimalLiteral::: DecimalDigits . DecimalDigits is the MV of the first DecimalDigits plus (the MV of the second DecimalDigits times 10⁻ⁿ), where n is the number of characters in the second DecimalDigits.

• The MV of StrUnsignedDecimalLiteral::: DecimalDigits. ExponentPart is the MV of DecimalDigits times 10^e, where e is the MV of ExponentPart.

• The MV of StrUnsignedDecimalLiteral::: DecimalDigits. DecimalDigits ExponentPart is (the MV of the first DecimalDigits plus (the MV of the second DecimalDigits times 10⁻ⁿ)) times 10^e, where n is the number of characters in the second DecimalDigits and e is the MV of ExponentPart.

• The MV of StrUnsignedDecimalLiteral:::. DecimalDigits is the MV of DecimalDigits times 10⁻ⁿ, where n is the number of characters in DecimalDigits.

• The MV of StrUnsignedDecimalLiteral:::. DecimalDigits ExponentPart is the MV of DecimalDigits times 10^e−n, where n is the number of characters in DecimalDigits and e is the MV of ExponentPart.

• The MV of StrUnsignedDecimalLiteral::: DecimalDigits is the MV of DecimalDigits.

• The MV of StrUnsignedDecimalLiteral::: DecimalDigits ExponentPart is the MV of DecimalDigits times 10^e, where e is the MV of ExponentPart.

• The MV of DecimalDigits ::: DecimalDigit is the MV of DecimalDigit.

• The MV of DecimalDigits ::: DecimalDigits DecimalDigit is (the MV of DecimalDigits times 10) plus the MV of DecimalDigit.

• The MV of ExponentPart ::: ExponentIndicator SignedInteger is the MV of SignedInteger.

• The MV of SignedInteger ::: DecimalDigits is the MV of DecimalDigits.

• The MV of SignedInteger ::: + DecimalDigits is the MV of DecimalDigits.

• The MV of SignedInteger ::: - DecimalDigits is the negative of the MV of DecimalDigits.

• The MV of DecimalDigit ::: 0 or of HexDigit ::: 0 is 0.

• The MV of DecimalDigit ::: 1 or of HexDigit ::: 1 is 1.

• The MV of DecimalDigit ::: 2 or of HexDigit ::: 2 is 2.

• The MV of DecimalDigit ::: 3 or of HexDigit ::: 3 is 3.

• The MV of DecimalDigit ::: 4 or of HexDigit ::: 4 is 4.

• The MV of DecimalDigit ::: 5 or of HexDigit ::: 5 is 5.

• The MV of DecimalDigit ::: 6 or of HexDigit ::: 6 is 6.

• The MV of DecimalDigit ::: 7 or of HexDigit ::: 7 is 7.

• The MV of DecimalDigit ::: 8 or of HexDigit ::: 8 is 8.

• The MV of DecimalDigit ::: 9 or of HexDigit ::: 9 is 9.

• The MV of HexDigit ::: a or of HexDigit ::: A is 10.

• The MV of HexDigit ::: b or of HexDigit ::: B is 11.

• The MV of HexDigit ::: c or of HexDigit ::: C is 12.

• The MV of HexDigit ::: d or of HexDigit ::: D is 13.

• The MV of HexDigit ::: e or of HexDigit ::: E is 14.

• The MV of HexDigit ::: f or of HexDigit ::: F is 15.

• The MV of HexIntegerLiteral ::: 0x HexDigit is the MV of HexDigit.

• The MV of HexIntegerLiteral ::: 0X HexDigit is the MV of HexDigit.

• The MV of HexIntegerLiteral ::: HexIntegerLiteral HexDigit is (the MV of HexIntegerLiteral times 16) plus the MV of HexDigit.

Once the exact MV for a String numeric literal has been determined, it is then rounded to a value of the Number type. If the MV is 0, then the rounded value is +0 unless the first non white space character in the String numeric literal is ‘-’, in which case the rounded value is −0. Otherwise, the rounded value must be the Number value for the MV (in the sense defined in 8.5), unless the literal includes a StrUnsignedDecimalLiteral and the literal has more than 20 significant digits, in which case the Number value may be either the Number value for the MV of a literal produced by replacing each significant digit after the 20th with a 0 digit or the Number value for the MV of a literal produced by replacing each significant digit after the 20th with a 0 digit and then incrementing the literal at the 20th digit position. A digit is significant if it is not part of an ExponentPart and

• it is not 0; or

• there is a nonzero digit to its left and there is a nonzero digit, not in the ExponentPart, to its right.

9.4 ToInteger # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToInteger converts its argument to an integral numeric value. This abstract operation functions as follows:

1. Let number be the result of calling ToNumber on the input argument.

2. If number is NaN, return +0.

3. If number is +0, −0, +∞, or −∞, return number.

4. Return the result of computing sign(number) * floor(abs(number)).

9.5 ToInt32: (Signed 32 Bit Integer) # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToInt32 converts its argument to one of 2³² integer values in the range −2³¹ through 2³¹−1, inclusive. This abstract operation functions as follows:

1. Let number be the result of calling ToNumber on the input argument.

2. If number is NaN, +0, −0, +∞, or −∞, return +0.

3. Let posInt be sign(number) * floor(abs(number)).

4. Let int32bit be posInt modulo 2³²; that is, a finite integer value k of Number type with positive sign and less than 2³² in magnitude such that the mathematical difference of posInt and k is mathematically an integer multiple of 2³².

5. If int32bit is greater than or equal to 2³¹, return int32bit − 2³², otherwise return int32bit.

NOTE Given the above definition of ToInt32:

• The ToInt32 abstract operation is idempotent: if applied to a result that it produced, the second application leaves that value unchanged.

• ToInt32(ToUint32(x)) is equal to ToInt32(x) for all values of x. (It is to preserve this latter property that +∞ and −∞ are mapped to +0.)

• ToInt32 maps −0 to +0.

9.6 ToUint32: (Unsigned 32 Bit Integer) # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToUint32 converts its argument to one of 2³² integer values in the range 0 through 2³²−1, inclusive. This abstraction operation functions as follows:

1. Let number be the result of calling ToNumber on the input argument.

2. If number is NaN, +0, −0, +∞, or −∞, return +0.

3. Let posInt be sign(number) * floor(abs(number)).

4. Let int32bit be posInt modulo 2³²; that is, a finite integer value k of Number type with positive sign and less than 2³² in magnitude such that the mathematical difference of posInt and k is mathematically an integer multiple of 2³².

5. Return int32bit.

NOTE Given the above definition of ToUInt32:

• Step 5 is the only difference between ToUint32 and ToInt32.

• The ToUint32 abstract operation is idempotent: if applied to a result that it produced, the second application leaves that value unchanged.

• ToUint32(ToInt32(x)) is equal to ToUint32(x) for all values of x. (It is to preserve this latter property that +∞ and −∞ are mapped to +0.)

• ToUint32 maps −0 to +0.

9.7 ToUint16: (Unsigned 16 Bit Integer) # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToUint16 converts its argument to one of 2¹⁶ integer values in the range 0 through 2¹⁶−1, inclusive. This abstract operation functions as follows:

1. Let number be the result of calling ToNumber on the input argument.

2. If number is NaN, +0, −0, +∞, or −∞, return +0.

3. Let posInt be sign(number) * floor(abs(number)).

4. Let int16bit be posInt modulo 2¹⁶; that is, a finite integer value k of Number type with positive sign and less than 2¹⁶ in magnitude such that the mathematical difference of posInt and k is mathematically an integer multiple of 2¹⁶.

5. Return int16bit.

NOTE Given the above definition of ToUint16:

• The substitution of 2¹⁶ for 2³² in step 4 is the only difference between ToUint32 and ToUint16.

• ToUint16 maps −0 to +0.

9.8 ToString # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToString converts its argument to a value of type String according to Table 13:

9.8.1 ToString Applied to the Number Type # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToString converts a Number m to String format as follows:

1. If m is NaN, return the String "NaN".

2. If m is +0 or −0, return the String "0".

3. If m is less than zero, return the String concatenation of the String "-" and ToString(−m).

4. If m is infinity, return the String "Infinity".

5. Otherwise, let n, k, and s be integers such that k ≥ 1, 10^k−1≤ s < 10^k, the Number value for s × 10^n−k is m, and k is as small as possible. Note that k is the number of digits in the decimal representation of s, that s is not divisible by 10, and that the least significant digit of s is not necessarily uniquely determined by these criteria.

6. If k ≤ n ≤ 21, return the String consisting of the k digits of the decimal representation of s (in order, with no leading zeroes), followed by n−k occurrences of the character ‘0’.

7. If 0 < n ≤ 21, return the String consisting of the most significant n digits of the decimal representation of s, followed by a decimal point ‘.’, followed by the remaining k−n digits of the decimal representation of s.

8. If −6 < n ≤ 0, return the String consisting of the character ‘0’, followed by a decimal point ‘.’, followed by −n occurrences of the character ‘0’, followed by the k digits of the decimal representation of s.

9. Otherwise, if k = 1, return the String consisting of the single digit of s, followed by lowercase character ‘e’, followed by a plus sign ‘+’ or minus sign ‘−’ according to whether n−1 is positive or negative, followed by the decimal representation of the integer abs(n−1) (with no leading zeros).

10. Return the String consisting of the most significant digit of the decimal representation of s, followed by a decimal point ‘.’, followed by the remaining k−1 digits of the decimal representation of s, followed by the lowercase character ‘e’, followed by a plus sign ‘+’ or minus sign ‘−’ according to whether n−1 is positive or negative, followed by the decimal representation of the integer abs(n−1) (with no leading zeros).

NOTE 1 The following observations may be useful as guidelines for implementations, but are not part of the normative requirements of this Standard:

• If x is any Number value other than −0, then ToNumber(ToString(x)) is exactly the same Number value as x.

• The least significant digit of s is not always uniquely determined by the requirements listed in step 5.

NOTE 2 For implementations that provide more accurate conversions than required by the rules above, it is recommended that the following alternative version of step 5 be used as a guideline:

Otherwise, let n, k, and s be integers such that k ≥ 1, 10^k−1≤ s < 10^k, the Number value for s × 10^n−k is m, and k is as small as possible. If there are multiple possibilities for s, choose the value of s for which s × 10^n−k is closest in value to m. If there are two such possible values of s, choose the one that is even. Note that k is the number of digits in the decimal representation of s and that s is not divisible by 10.

NOTE 3 Implementers of ECMAScript may find useful the paper and code written by David M. Gay for binary-to-decimal conversion of floating-point numbers:

Gay, David M. Correctly Rounded Binary-Decimal and Decimal-Binary Conversions. Numerical Analysis, Manuscript 90-10. AT&T Bell Laboratories (Murray Hill, New Jersey). November 30, 1990. Available as
http://cm.bell-labs.com/cm/cs/doc/90/4-10.ps.gz. Associated code available as
http://cm.bell-labs.com/netlib/fp/dtoa.c.gz and as
http://cm.bell-labs.com/netlib/fp/g_fmt.c.gz and may also be found at the various netlib mirror sites.

9.9 ToObject # Ⓣ Ⓔ ① Ⓐ

The abstract operation ToObject converts its argument to a value of type Object according to Table 14:

9.10 CheckObjectCoercible # Ⓣ Ⓔ ① Ⓐ

The abstract operation CheckObjectCoercible throws an error if its argument is a value that cannot be converted to an Object using ToObject. It is defined by Table 15:

9.11 IsCallable # Ⓣ Ⓔ ① Ⓐ

The abstract operation IsCallable determines if its argument, which must be an ECMAScript language value, is a callable function Object according to Table 16:

9.12 The SameValue Algorithm # Ⓣ Ⓔ ① Ⓐ

The internal comparison abstract operation SameValue(x, y), where x and y are ECMAScript language values, produces true or false. Such a comparison is performed as follows:

1. If Type(x) is different from Type(y), return false.

2. If Type(x) is Undefined, return true.

3. If Type(x) is Null, return true.

4. If Type(x) is Number, then.

   1. If x is NaN and y is NaN, return true.

   2. If x is +0 and y is -0, return false.

   3. If x is -0 and y is +0, return false.

   4. If x is the same Number value as y, return true.

   5. Return false.

5. If Type(x) is String, then return true if x and y are exactly the same sequence of characters (same length and same characters in corresponding positions); otherwise, return false.

6. If Type(x) is Boolean, return true if x and y are both true or both false; otherwise, return false.

7. Return true if x and y refer to the same object. Otherwise, return false.