@item @code{math} mode: arbitrarily large integers and floating point numbers are available by default. The integer division and power can be overloaded for example to return a fraction. The modulo operator (@code{%}) is defined as the Euclidian
remainder. @code{^} is an alias to the power operator
(@code{**}). @code{^^} is used as the exclusive or operator.
@end itemize
The extensions are independent from each other except the @code{math}
mode which relies on BigFloat and operator overloading.
@chapter Operator overloading
Operator overloading is inspired from the proposal available at
@url{https://github.com/tc39/proposal-operator-overloading/}. It
implements the same dispatch logic but finds the operator sets by
looking at the @code{Symbol.operatorSet} property in the objects. The
changes were done in order to simplify the implementation.
More precisely, the following modifications were made:
@itemize
@item @code{with operators from} is not supported. Operator overloading is always enabled.
@item The dispatch is not based on a static @code{[[OperatorSet]]} field in all instances. Instead, a dynamic lookup of the @code{Symbol.operatorSet} property is done. This property is typically added in the prototype of each object.
@item @code{Operators.create(...dictionaries)} is used to create a new OperatorSet object. The @code{Operators} function is supported as an helper to be closer to the TC39 proposal.
@item @code{[]} cannot be overloaded.
@item In math mode, the BigInt division and power operators can be overloaded with @code{Operators.updateBigIntOperators(dictionary)}.
@end itemize
@chapter BigInt extensions
A few properties are added to the BigInt object:
@table @code
@item tdiv(a, b)
Return @math{trunc(a/b)}. @code{b = 0} raises a RangeError
exception.
@item fdiv(a, b)
Return @math{\lfloor a/b \rfloor}. @code{b = 0} raises a RangeError
exception.
@item cdiv(a, b)
Return @math{\lceil a/b \rceil}. @code{b = 0} raises a RangeError
Same semantics as the corresponding @code{Number} functions with
BigFloats. There is no limit on the accepted precision @code{p}. The
rounding mode and radix can be optionally specified. The radix must be
between 2 and 36.
@end table
@subsection @code{BigFloatEnv} constructor
The @code{BigFloatEnv([p, [,rndMode]]} constructor cannot be invoked as a
function. The floating point environment contains:
@itemize
@item the mantissa precision in bits
@item the exponent size in bits assuming an IEEE 754 representation;
@item the subnormal flag (if true, subnormal floating point numbers can
be generated by the floating point operations).
@item the rounding mode
@item the floating point status. The status flags can only be set by the floating point operations. They can be reset with @code{BigFloatEnv.prototype.clearStatus()} or with the various status flag setters.
@end itemize
@code{new BigFloatEnv([p, [,rndMode]]} creates a new floating point
environment. The status flags are reset. If no parameter is given the
precision, exponent bits and subnormal flags are copied from the
global floating point environment. Otherwise, the precision is set to
@code{p}, the number of exponent bits is set to @code{expBitsMax} and the
subnormal flags is set to @code{false}. If @code{rndMode} is
@code{undefined}, the rounding mode is set to @code{RNDN}.
@code{BigFloatEnv} properties:
@table @code
@item prec
Getter. Return the precision in bits of the global floating point
environment. The initial value is @code{113}.
@item expBits
Getter. Return the exponent size in bits of the global floating point
environment assuming an IEEE 754 representation. The initial value is
@code{15}.
@item setPrec(f, p[, e])
Set the precision of the global floating point environment to @code{p}
and the exponent size to @code{e} then call the function
@code{f}. Then the Float precision and exponent size are reset to
their precious value and the return value of @code{f} is returned (or
an exception is raised if @code{f} raised an exception). If @code{e}
is @code{undefined} it is set to @code{BigFloatEnv.expBitsMax}.
@item precMin
Read-only integer. Return the minimum allowed precision. Must be at least 2.
@item precMax
Read-only integer. Return the maximum allowed precision. Must be at least 113.
@item expBitsMin
Read-only integer. Return the minimum allowed exponent size in
bits. Must be at least 3.
@item expBitsMax
Read-only integer. Return the maximum allowed exponent size in
bits. Must be at least 15.
@item RNDN
Read-only integer. Round to nearest, with ties to even rounding mode.
@item RNDZ
Read-only integer. Round to zero rounding mode.
@item RNDD
Read-only integer. Round to -Infinity rounding mode.
@item RNDU
Read-only integer. Round to +Infinity rounding mode.
@item RNDNA
Read-only integer. Round to nearest, with ties away from zero rounding mode.
@item RNDA
Read-only integer. Round away from zero rounding mode.
@item RNDF@footnote{Could be removed in case a deterministic behavior for floating point operations is required.}
Read-only integer. Faithful rounding mode. The result is
non-deterministically rounded to -Infinity or +Infinity. This rounding
mode usually gives a faster and deterministic running time for the
floating point operations.
@end table
@code{BigFloatEnv.prototype} properties:
@table @code
@item prec
Getter and setter (Integer). Return or set the precision in bits.
@item expBits
Getter and setter (Integer). Return or set the exponent size in bits
assuming an IEEE 754 representation.
@item rndMode
Getter and setter (Integer). Return or set the rounding mode.
@item subnormal
Getter and setter (Boolean). subnormal flag. It is false when
@code{expBits = expBitsMax}.
@item clearStatus()
Clear the status flags.
@item invalidOperation
@item divideByZero
@item overflow
@item underflow
@item inexact
Getter and setter (Boolean). Status flags.
@end table
@chapter BigDecimal
This extension adds the @code{BigDecimal} primitive type. The
@code{BigDecimal} type represents floating point numbers in base
@code{maximumSignificantDigits} or @code{maximumFractionDigits} must
be present to specify respectively the number of significant digits
(must be >= 1) or the number of digits after the decimal point (must
be >= 0).
@end table
@subsection Properties of the @code{BigDecimal.prototype} object
@table @code
@item valueOf()
Return the bigdecimal primitive value corresponding to @code{this}.
@item toString()
Convert @code{this} to a string with infinite precision in base 10.
@item toPrecision(p, rnd_mode = "half-up")
@item toFixed(p, rnd_mode = "half-up")
@item toExponential(p, rnd_mode = "half-up")
Convert the BigDecimal @code{this} to string with the specified
precision @code{p}. There is no limit on the accepted precision
@code{p}. The rounding mode can be optionally
specified. @code{toPrecision} outputs either in decimal fixed notation
or in decimal exponential notation with a @code{p} digits of
precision. @code{toExponential} outputs in decimal exponential
notation with @code{p} digits after the decimal point. @code{toFixed}
outputs in decimal notation with @code{p} digits after the decimal
point.
@end table
@chapter Math mode
A new @emph{math mode} is enabled with the @code{"use math"}
directive. It propagates the same way as the @emph{strict mode}. It is
designed so that arbitrarily large integers and floating point numbers
are available by default. In order to minimize the number of changes
in the Javascript semantics, integers are represented either as Number
or BigInt depending on their magnitude. Floating point numbers are
always represented as BigFloat.
The following changes are made to the Javascript semantics:
@itemize
@item Floating point literals (i.e. number with a decimal point or an exponent) are @code{BigFloat} by default (i.e. a @code{l} suffix is implied). Hence @code{typeof 1.0 === "bigfloat"}.
@item Integer literals (i.e. numbers without a decimal point or an exponent) with or without the @code{n} suffix are @code{BigInt} if their value cannot be represented as a safe integer. A safe integer is defined as a integer whose absolute value is smaller or equal to @code{2**53-1}. Hence @code{typeof 1 === "number "}, @code{typeof 1n === "number"} but @code{typeof 9007199254740992 === "bigint" }.
@item All the bigint builtin operators and functions are modified so that their result is returned as a Number if it is a safe integer. Otherwise the result stays a BigInt.
@item The builtin operators are modified so that they return an exact result (which can be a BigInt) if their operands are safe integers. Operands between Number and BigInt are accepted provided the Number operand is a safe integer. The integer power with a negative exponent returns a BigFloat as result. The integer division returns a BigFloat as result.
@item The @code{^} operator is an alias to the power operator (@code{**}).
@item The power operator (both @code{^} and @code{**}) grammar is modified so that @code{-2^2} is allowed and yields @code{-4}.
@item The logical xor operator is still available with the @code{^^} operator.
@item The modulo operator (@code{%}) returns the Euclidian remainder (always positive) instead of the truncated remainder.
@item The integer division operator can be overloaded with @code{Operators.updateBigIntOperators(dictionary)}.
@item The integer power operator with a non zero negative exponent can be overloaded with @code{Operators.updateBigIntOperators(dictionary)}.
