y-cruncher Multi-Precision Library
	A Multi-threaded Multi-Precision Arithmetic Library (Powered by y-cruncher)

(Last updated: March 3, 2016)

 

BigFloat - Large Floating-Point

 

BigFloat is a large floating-point object:

• It can represent arbitrarily precise numbers limited only by memory address space.
• The range of numbers that it can represent are approximately base^(±2⁶³).
• It supports both positive and negative numbers. It also supports zero.
• It does not support infinity or not-a-number.
• Overflow/underflow of the exponent range is not handled. (they will fail silently)
• It supports fast algorithms and parallelism for large multiplication and dependent operations. Multiplication runs in approximately O(N log(N)) time.

 

Types:

 

BigFloat is an abstract base class for BigFloatR and BigFloatO. So it cannot be used directly.

• BigFloatO is a standard RAII object that is easy to use but has a lot of overhead.
• BigFloatR is a low-level object that is difficult to use and has little overhead.

These subclasses differ in only their resource ownership policies. But otherwise, they have nearly identical functionality.

 

 

Representation:

 

The current representation of the BigFloat object is as follows:

BigFloat = sign * ( A[0] + A[1]*base¹ + A[2]*base² + A[3]*base³ + ... ) * base^exp

with the following relevant fields:

• T - The pointer to the start of the array.
• L - The length of the array.
• exp - The exponent.
• sign - The sign.

 

Function List:

• Headers: Objects/GenericFloat/GenericFloat.h
• Sources: none
• Namespace: ymp

 

Being the abstract base class, there isn't much functionality here.

 

Const Getters:

• get_T()
• get_L()
• get_exp()
• get_mag()
• get_sign()
• get_buffersize()
• to_double()
• is_zero()
• operator[]
• get_range()
• operator<(), operator>()
• operator<=(), operator>=()
• operator==()
• cmp()
• iPsize()

 

Getters:

 

Get Array Pointer:

const u32_t* BigFloat<u32_t>::get_T () const;

const u64_t* BigFloat<u64_t>::get_T () const;

 

Returns a pointer to the start of the internal array.

Get Length:

upL_t BigFloat<u32_t>::get_L () const;

upL_t BigFloat<u64_t>::get_L () const;

 

Return the logical length of the array. (the mantissa)

Get Exponent:

siL_t BigFloat<u32_t>::get_exp () const;

siL_t BigFloat<u64_t>::get_exp () const;

 

Return the exponent.

If the object has a value of zero, the returned value is undefined.

Get Magnitude:

siL_t BigFloat<u32_t>::get_mag () const;

siL_t BigFloat<u64_t>::get_mag () const;

 

Return the magnitude of the object. The magnitude is defined as the smallest power of the base that is larger in magnitude than the object.

If the object has a value of zero, the returned value is undefined.

 

Mathematically:

magnitude = Floor( Log_base( Abs(this) ) ) + 1

Internally: get_mag() = get_exp() + get_L().

Get Sign:

int BigFloat<u32_t>::get_sign () const;

int BigFloat<u64_t>::get_sign () const;

 

Returns:

• 1 if the object is positive.
• 0 if the object is zero.
• -1 if the object is negative.

Get Buffer Size:

upL_t BigFloat<u32_t>::get_buffersize () const;

upL_t BigFloat<u64_t>::get_buffersize () const;

 

Returns the size of the internal buffer. This gives the largest number (in words) that can be stored in the object.

 

---

Convert to Double-Precision:

double BigFloat<u32_t>::to_double (siL_t& exp) const;

double BigFloat<u64_t>::to_double (siL_t& exp) const;

Description:

Converts the current object to double-precision. The exponent is stored into exp. This exponent is there to avoid overflow.

this = (return value) * base^exp

 

---

Is Zero:

bool BigFloat<u32_t>::is_zero () const;

bool BigFloat<u64_t>::is_zero () const;

Description:

Returns true if the current object is zero.

 

---

Operator[]:

u32_t BigFloat<u32_t>::operator[] (siL_t mag) const;

u64_t BigFloat<u64_t>::operator[] (siL_t mag) const;

Description:

Returns the word at the specified magnitude.

 

Mathematically:

(return value) = Floor( Abs(this) / base^mag ) mod base

 

---

Get Range:

void BigFloat<u32_t>::get_range (u32_t* buffer, siL_t s, upL_t L) const;

void BigFloat<u64_t>::get_range (u64_t* buffer, siL_t s, upL_t L) const;

Description:

Get the words in the range [s, s + L) and write them to buffer. This is a multi-word version of operator[].

 

Mathematically:

{buffer, L} = Floor( Abs(this) / base^s ) mod base^L

 

---

Compare:

bool operator< (const BigFloat<u32_t>& A, const BigFloat<u32_t>& B);

bool operator< (const BigFloat<u64_t>& A, const BigFloat<u64_t>& B);

 

bool operator> (const BigFloat<u32_t>& A, const BigFloat<u32_t>& B);

bool operator> (const BigFloat<u64_t>& A, const BigFloat<u64_t>& B);

 

bool operator<= (const BigFloat<u32_t>& A, const BigFloat<u32_t>& B);

bool operator<= (const BigFloat<u64_t>& A, const BigFloat<u64_t>& B);

 

bool operator>= (const BigFloat<u32_t>& A, const BigFloat<u32_t>& B);

bool operator>= (const BigFloat<u64_t>& A, const BigFloat<u64_t>& B);

 

bool operator== (const BigFloat<u32_t>& A, const BigFloat<u32_t>& B);

bool operator== (const BigFloat<u64_t>& A, const BigFloat<u64_t>& B);

 

int BigFloat<u32_t>::cmp (const BigFloat<u32_t>& B) const;

int BigFloat<u64_t>::cmp (const BigFloat<u64_t>& B) const;

Description:

Standard comparison operators.

 

cmp() returns:

• 1 if this > B
• 0 if this == B
• -1 if this < B

 

---

Incremental Scratch Buffer Size:

static uiL_t BigFloat<u32_t>::iPsize (uiL_t p, upL_t tds = 1);

static uiL_t BigFloat<u64_t>::iPsize (uiL_t p, upL_t tds = 1);

Description:

Similar to mul_iPsize().

 

Returns the size of the scratch buffer needed to call any large multiplication on a BigFloat object with a precision of at most p and using a task decomposition of at most tds.

 

This is mainly used for populating the BasicParameters object.