GHC.Num.BigNat

A BigNat

Represented as an array of limbs (Word#) stored in little-endian order (Word# themselves use machine order).

Invariant (canonical representation): higher Word# is non-zero.

As a consequence, zero is represented with a WordArray# whose size is 0.

A lifted BigNat

Represented as an array of limbs (Word#) stored in little-endian order (Word# themselves use machine order).

Invariant (canonical representation): higher Word# is non-zero.

As a consequence, zero is represented with a WordArray# whose size is 0.

Check that the BigNat is valid

Check that the BigNat is valid

Number of words in the BigNat

Number of words in the BigNat

BigNat Zero

BigNat one

Indicate if a bigNat is zero

Indicate if a bigNat is zero

Indicate if a bigNat is one

Indicate if a bigNat is one

Indicate if a bigNat is two

Indicate if a bigNat is two

Indicate if the value is a power of two and which one

Return the Word# at the given index

Return the Word# at the given index

Create a BigNat from a Word

Create a BigNat from a Word

Convert a list of non-zero Words (most-significant first) into a BigNat

Convert a list of non-zero Words (most-significant first) into a BigNat

Return the absolute value of the Int# in a BigNat

Convert a list of non-zero Words (most-significant first) into a BigNat. Don't remove most-significant zero words

Convert a BigNat into a list of non-zero Words (most-significant first)

Convert two Word# (most-significant first) into a BigNat

Convert a BigNat into a Word#

Convert a BigNat into a Word# if it fits

Convert a BigNat into a Word

Convert a BigNat into a Int#

Convert a BigNat into a Int

Convert a Word64# into a BigNat on 64-bit architectures

Convert a BigNat into a Word64# on 64-bit architectures

Encode (# BigNat mantissa, Int# exponent #) into a Double#

Test if a BigNat is greater than a Word

Test if a BigNat is equal to a Word

Test if a BigNat is greater than a Word

Test if a BigNat is lower than or equal to a Word

Test if a BigNat is lower than or equal to a Word

Equality test for BigNat

Equality test for BigNat

Inequality test for BigNat

Equality test for BigNat

Compare a BigNat and a Word#

Compare a BigNat and a Word

Compare two BigNat

Predicate: a < b

Predicate: a < b

Predicate: a <= b

Predicate: a <= b

Predicate: a > b

Predicate: a > b

Predicate: a >= b

Predicate: a >= b

Add a bigNat and a Word#

Add a bigNat and a Word

Add two bigNats

Multiply a BigNat by a Word#

Multiply a BigNAt by a Word

Square a BigNat

Multiplication (classical algorithm)

Subtract a Word# from a BigNat

The BigNat must be bigger than the Word#.

Subtract a Word# from a BigNat

The BigNat must be bigger than the Word#.

Subtract a Word# from a BigNat

Subtract two BigNat (don't check if a >= b)

Subtract two BigNat

Divide a BigNat by a Word, return the quotient

Require: b /= 0

Divide a BigNat by a Word, return the quotient

Require: b /= 0

Divide a BigNat by a Word, return the remainder

Require: b /= 0

Divide a BigNat by a Word, return the remainder

Require: b /= 0

QuotRem a BigNat by a Word

Require: b /= 0

BigNat division returning (quotient,remainder)

BigNat division returning quotient

BigNat division returning remainder

Greatest common divisor between two Word#

Greatest common divisor between two Word

Greatest common divisor between two Int#

Warning: result may become negative if (at least) one argument is minBound

Greatest common divisor between two Int

Warning: result may become negative if (at least) one argument is minBound

Greatest common divisor

Greatest common divisor

Least common multiple

Least common multiple with a Word#

Least common multiple between two Word#

Bitwise OR

Bitwise OR with Word#

Bitwise AND

Bitwise ANDNOT

Bitwise AND with Word#

Bitwise ANDNOT with Word#

Bitwise AND with Int#

Bitwise XOR

Bitwise XOR with Word#

PopCount for BigNat

PopCount for BigNat

Bit shift right

Bit shift right (two's complement)

Bit shift right

Bit shift left

Bit shift left

BigNat bit test

BigNat bit test

Return a BigNat whose bit i is the only one set.

Specialized version of `bigNatShiftL (bigNatFromWord# 1##)`

Return a BigNat whose bit i is the only one set.

Specialized version of `bigNatShiftL (bigNatFromWord# 1##)`

BigNat clear bit

BigNat set bit

Reverse the given bit

Base 2 logarithm

Base 2 logarithm

Logarithm for an arbitrary base

Logarithm for an arbitrary base

Logarithm for an arbitrary base

Logarithm for an arbitrary base

Compute the number of digits of the BigNat in the given base.

base must be > 1

Compute the number of digits of the BigNat in the given base.

base must be > 1

"bigNatPowModWord# b e m" computes base b raised to exponent e modulo m.

"bigNatPowMod b e m" computes base b raised to exponent e modulo m.

Return count of trailing zero bits

Return 0 for zero BigNat

Return count of trailing zero bits

Return 0 for zero BigNat

Return count of trailing zero words

Return 0 for zero BigNat

Return count of trailing zero words

Return 0 for zero BigNat

Write a BigNat in base-256 little-endian representation and return the number of bytes written.

Use "bigNatSizeInBase 256# i" to compute the exact number of bytes written in advance. In case of i == 0, the function will write and report zero bytes written.

Write a BigNat in base-256 big-endian representation and return the number of bytes written.

Use "bigNatSizeInBase 256# i" to compute the exact number of bytes written in advance. In case of i == 0, the function will write and report zero bytes written.

Write a BigNat in base-256 representation and return the number of bytes written.

The endianness is selected with the Bool# parameter: most significant byte first (big-endian) if 1# or least significant byte first (little-endian) if 0#.

Use "bigNatSizeInBase 256# i" to compute the exact number of bytes written in advance. In case of i == 0, the function will write and report zero bytes written.

Write a BigNat in base-256 representation and return the number of bytes written.

The endianness is selected with the Bool# parameter: most significant byte first (big-endian) if 1# or least significant byte first (little-endian) if 0#.

Use "bigNatSizeInBase 256# i" to compute the exact number of bytes written in advance. In case of i == 0, the function will write and report zero bytes written.

Read a BigNat in base-256 little-endian representation from an Addr#.

The size is given in bytes.

Higher limbs equal to 0 are automatically trimmed.

Read a BigNat in base-256 big-endian representation from an Addr#.

The size is given in bytes.

Null higher limbs are automatically trimmed.

Read a BigNat in base-256 representation from an Addr#.

The size is given in bytes.

The endianness is selected with the Bool# parameter: most significant byte first (big-endian) if 1# or least significant byte first (little-endian) if 0#.

Null higher limbs are automatically trimmed.

Write a BigNat in base-256 little-endian representation and return the number of bytes written.

Use "bigNatSizeInBase 256# i" to compute the exact number of bytes written in advance. In case of i == 0, the function will write and report zero bytes written.

Write a BigNat in base-256 big-endian representation and return the number of bytes written.

Use "bigNatSizeInBase 256# i" to compute the exact number of bytes written in advance. In case of i == 0, the function will write and report zero bytes written.

Write a BigNat in base-256 representation and return the number of bytes written.

The endianness is selected with the Bool# parameter: most significant byte first (big-endian) if 1# or least significant byte first (little-endian) if 0#.

Use "bigNatSizeInBase 256# i" to compute the exact number of bytes written in advance. In case of i == 0, the function will write and report zero bytes written.

Read a BigNat in base-256 little-endian representation from a ByteArray#.

The size is given in bytes.

Null higher limbs are automatically trimmed.

Read a BigNat in base-256 big-endian representation from a ByteArray#.

The size is given in bytes.

Null higher limbs are automatically trimmed.

Read a BigNat in base-256 representation from a ByteArray#.

The size is given in bytes.

The endianness is selected with the Bool# parameter: most significant byte first (big-endian) if 1# or least significant byte first (little-endian) if 0#.

Null higher limbs are automatically trimmed.

Create a BigNat# from a WordArray# containing n limbs in least-significant-first order.

If possible WordArray#, will be used directly (i.e. shared without cloning the WordArray# into a newly allocated one)

Create a BigNat from a WordArray# containing n limbs in least-significant-first order.

If possible WordArray#, will be used directly (i.e. shared without cloning the WordArray# into a newly allocated one)