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Previously real constants were parsed by an unproved OCaml code. The
parser and printer are now implemented in Coq, which will enable a
proof and hopefully make it easier to maintain / make evolve.
Previously reals were all parsed as an integer, an integer multiplied
by a power of ten or an integer divided by a power of ten. This means
1.02 and 102e-2 were both parsed as 102 / 100 and could not be tell
apart when printing. So the printer had to choose between two
representations : without exponent or without decimal dot. The choice
was made heuristically toward a most compact representation.
Now, decimal dot is parsed as a rational and exponents are parsed as a
product or division by a power of ten. For instance, 1.02 is parsed as
Q2R (102 # 100) whereas 102e-2 is parsed as IZR 102 / IZR (Z.pow_pos
10 2).
1.02 and 102e-2 remain equal (proved by reflexivity) but 1.02e1 = Q2R
(102 # 100) * 10 and 10.2 = Q2R (102 # 10) no longer are.
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We add hexadecimal numerals according to the following regexp
0[xX][0-9a-fA-F][0-9a-fA-F_]*(\.[0-9a-fA-F_]+)?([pP][+-]?[0-9][0-9_]*)?
This is unfortunately a rather large commit. I suggest reading it in
the following order:
* test-suite/output/ZSyntax.{v,out} new test
* test-suite/output/Int63Syntax.{v,out} ''
* test-suite/output/QArithSyntax.{v,out} ''
* test-suite/output/RealSyntax.{v,out} ''
* test-suite/output/FloatSyntax.{v,out} ''
* interp/numTok.ml{i,} extending numeral tokens
* theories/Init/Hexadecimal.v adaptation of Decimal.v
for the new hexadecimal Numeral Notation
* theories/Init/Numeral.v new interface for Numeral Notation (basically,
a numeral is either a decimal or an hexadecimal)
* theories/Init/Nat.v add hexadecimal numeral notation to nat
* theories/PArith/BinPosDef.v '' positive
* theories/ZArith/BinIntDef.v '' Z
* theories/NArith/BinNatDef.v '' N
* theories/QArith/QArith_base.v '' Q
* interp/notation.ml{i,} adapting implementation of numeral notations
* plugins/syntax/numeral.ml ''
* plugins/syntax/r_syntax.ml adapt parser for real numbers
* plugins/syntax/float_syntax.ml adapt parser for primitive floats
* theories/Init/Prelude.v register parser for nat
* adapting the test-suite (test-suite/output/NumeralNotations.{v,out}
and test-suite/output/SearchPattern.out)
* remaining ml files (interp/constrex{tern,pr_ops}.ml where two open
had to be permuted)
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Print 1.5 as 1.5 and not 15e-1.
We choose the shortest representation
with tie break to the dot notation (0.01 rather than 1e-3).
The printing remains injective, i.e. 12*10^2 is printed 12e2 in order
not to mix it with 1200 and 12/10^1 is not mixed with 120/10^2, the
first being printed as 1.2 and the last as 1.20.
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Four types of numerals are introduced:
- positive natural numbers (may include "_", e.g. to separate thousands, and leading 0)
- integer numbers (may start with a minus sign)
- positive numbers with mantisse and signed exponent
- signed numbers with mantisse and signed exponent
In passing, we clarify that the lexer parses only positive numerals,
but the numeral interpreters may accept signed numerals.
Several improvements and fixes come from Pierre Roux. See
https://github.com/coq/coq/pull/11703 for details. Thanks to him.
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'e' was not displayed when printing decimal notations in R :
Require Import Reals.
Check (1.23e1, 32e+1, 0.1)%R.
was giving
< (123-1%R, 321%R, 1-1%R)
instead of
< (123e-1%R, 32e1%R, 1e-1%R)
This was introduced in #8764 (in Coq 8.10).
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@7693 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2127 85f007b7-540e-0410-9357-904b9bb8a0f7
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