From 1450c56754c1b2a1b42fc78547f384b83aa8dc13 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Mon, 14 Sep 2020 16:56:01 -0400 Subject: =?UTF-8?q?Don't=20allow=20=E2=88=9E=20with=20an=20exponent=20in?= =?UTF-8?q?=20numeric=20literals?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/spec/literal.html | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'docs/spec') diff --git a/docs/spec/literal.html b/docs/spec/literal.html index 1a5fea6a..39ac864a 100644 --- a/docs/spec/literal.html +++ b/docs/spec/literal.html @@ -9,12 +9,12 @@

Two types of literal deal with text. As the source code is considered to be a sequence of unicode code points ("characters"), and these code points are also used for BQN's character data type, the representation of a text literal is very similar to its value. In a text literal, the newline character is always represented using the ASCII line feed character, code point 10. A character literal is enclosed with single quotes ' and its value is identical to the single character between them. A string literal is enclosed in double quotes ", and any double quotes between them must come in pairs, as a lone double quote marks the end of the literal. The value of a string literal is a rank-1 array whose elements are the characters in between the enclosing quotes, after replacing each pair of double quotes with only one such quote. The null literal is the token @ and represents the null character, code point 0.

The format of a numeric literal is more complicated. From the tokenization rules, a numeric literal consists of a numeric character (one of ¯∞π.0123456789) followed by any number of numeric or alphabetic characters. Some numeric literals are valid and indicate a number, while others are invalid and cause an error. The grammar for valid numbers is given below in a BNF variant. Only four alphabetic characters are allowed: "i", which separates the real and imaginary components of a complex number, "e", which functions as in scientific notation, and the uppercase versions of these letters.

number    = component ( ( "i" | "I" ) component )?
-component = mantissa ( ( "e" | "E" ) exponent )?
+component = "¯"? ( "∞" | mantissa ( ( "e" | "E" ) exponent )? )
 exponent  = "¯"? digit+
-mantissa  = "¯"? ( "∞" | "π" | digit+ ( "." digit+ )? )
+mantissa  = "π" | digit+ ( "." digit+ )?
 digit     = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
-

The digits or arabic numerals correspond to the numbers from 0 to 9 in the conventional way (also, each corresponds to its code point value minus 48). A sequence of digits gives a natural number by evaluating it in base 10: the number is 0 for an empty sequence, and otherwise the last digit's numerical value plus ten times the number obtained from the remaining digits. The symbol ∞ indicates infinity and π indicates the ratio pi of a circle's circumference to its diameter (or, for modern mathematicians, the smallest positive real number at which the function {⋆0j1×𝕩} attains a real part of 0). The high minus symbol ¯ indicates that the number containing it is to be negated.

+

The digits or arabic numerals correspond to the numbers from 0 to 9 in the conventional way (also, each corresponds to its code point value minus 48). A sequence of digits gives a natural number by evaluating it in base 10: the number is 0 for an empty sequence, and otherwise the last digit's numerical value plus ten times the number obtained from the remaining digits. The symbol ∞ indicates infinity and π indicates the ratio pi of a circle's circumference to its diameter (or, for modern mathematicians, the smallest positive real number at which the function {⋆0i1×𝕩} attains a real part of 0). The high minus symbol ¯ indicates that the number containing it is to be negated.

When an exponent is provided (with e or E), the corresponding mantissa is multiplied by ten to that power, giving the value mantissa×10⋆exponent. If a second component is present (using i or I), that component's value is multiplied by the imaginary unit i and added to the first component; otherwise the value is the first component's value without modification. If complex numbers are not supported, then i should not be allowed in numeric literals, even when followed by 0.

The above specification describes exactly a complex number with extended real components. To obtain a BQN number, each component is rounded to its nearest representative by the rules of the number system used: for IEEE 754, smallest distance, with ties rounding to the option with even mantissa.

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