// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.


/*
Package big implements arbitrary-precision arithmetic (big numbers).
The following numeric types are supported:

	Int    signed integers
	Rat    rational numbers
	Float  floating-point numbers

The zero value for an Int, Rat, or Float correspond to 0. Thus, new
values can be declared in the usual ways and denote 0 without further
initialization:

	var x Int        // &x is an *Int of value 0
	var r = &Rat{}   // r is a *Rat of value 0
	y := new(Float)  // y is a *Float of value 0

Alternatively, new values can be allocated and initialized with factory
functions of the form:

	func NewT(v V) *T

For instance, NewInt(x) returns an *Int set to the value of the int64
argument x, NewRat(a, b) returns a *Rat set to the fraction a/b where
a and b are int64 values, and NewFloat(f) returns a *Float initialized
to the float64 argument f. More flexibility is provided with explicit
setters, for instance:

	var z1 Int
	z1.SetUint64(123)                 // z1 := 123
	z2 := new(Rat).SetFloat64(1.25)   // z2 := 5/4
	z3 := new(Float).SetInt(z1)       // z3 := 123.0

Setters, numeric operations and predicates are represented as methods of
the form:

	func (z *T) SetV(v V) *T          // z = v
	func (z *T) Unary(x *T) *T        // z = unary x
	func (z *T) Binary(x, y *T) *T    // z = x binary y
	func (x *T) Pred() P              // p = pred(x)

with T one of Int, Rat, or Float. For unary and binary operations, the
result is the receiver (usually named z in that case; see below); if it
is one of the operands x or y it may be safely overwritten (and its memory
reused).

Arithmetic expressions are typically written as a sequence of individual
method calls, with each call corresponding to an operation. The receiver
denotes the result and the method arguments are the operation's operands.
For instance, given three *Int values a, b and c, the invocation

	c.Add(a, b)

computes the sum a + b and stores the result in c, overwriting whatever
value was held in c before. Unless specified otherwise, operations permit
aliasing of parameters, so it is perfectly ok to write

	sum.Add(sum, x)

to accumulate values x in a sum.

(By always passing in a result value via the receiver, memory use can be
much better controlled. Instead of having to allocate new memory for each
result, an operation can reuse the space allocated for the result value,
and overwrite that value with the new result in the process.)

Notational convention: Incoming method parameters (including the receiver)
are named consistently in the API to clarify their use. Incoming operands
are usually named x, y, a, b, and so on, but never z. A parameter specifying
the result is named z (typically the receiver).

For instance, the arguments for (*Int).Add are named x and y, and because
the receiver specifies the result destination, it is called z:

	func (z *Int) Add(x, y *Int) *Int

Methods of this form typically return the incoming receiver as well, to
enable simple call chaining.

Methods which don't require a result value to be passed in (for instance,
Int.Sign), simply return the result. In this case, the receiver is typically
the first operand, named x:

	func (x *Int) Sign() int

Various methods support conversions between strings and corresponding
numeric values, and vice versa: *Int, *Rat, and *Float values implement
the Stringer interface for a (default) string representation of the value,
but also provide SetString methods to initialize a value from a string in
a variety of supported formats (see the respective SetString documentation).

Finally, *Int, *Rat, and *Float satisfy the fmt package's Scanner interface
for scanning and (except for *Rat) the Formatter interface for formatted
printing.
*/
package big