GHC.Num.Natural

Add two naturals

Check Natural invariants

Check Natural invariants

Compare two Natural

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

Encode (# Natural mantissa, Int# exponent #) into a Float#

TODO: Not sure if it's worth to write Float optimized versions here

Equality test for Natural

Equality test for Natural

Read a Natural 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 trimed.

Read a Natural 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 trimed.

Create a Natural from a BigNat# (respect the invariants)

Read a Natural 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 trimed.

Create a Natural from a Word

Create a Natural from a Word#

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

Create a Natural from a list of Word

Compute greatest common divisor.

Greater or equal test for Natural

Greater or equal test for Natural

Greater test for Natural

Greater test for Natural

Test One Natural

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

Test Zero Natural

Compute least common multiple.

Lower or equal test for Natural

Lower or equal test for Natural

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

Lower test for Natural

Lower test for Natural

Multiplication

Inequality test for Natural

Inequality test for Natural

Negate for Natural

One Natural

PopCount for Natural

PopCount for Natural

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

Return division quotient

Return division quotient and remainder

Return division quotient and remainder

Division by zero is handled by BigNat

Return division remainder

Left shift

Left shift

Right shift for Natural

Right shift for Natural

Signum for Natural

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

base must be > 1

Square a Natural

Sub two naturals

Sub two naturals

Throw an Underflow exception if x < y

Sub two naturals

Unsafe: don't check that x >= y Undefined results if it happens

Write a Natural to addr in base-256 representation and return the number of bytes written.

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

Write a Natural to addr in base-256 representation and return the number of bytes written.

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

Convert a Natural into a BigNat#

Write a Natural 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#.

Convert the lower bits of a Natural into a Word

Convert the lower bits of a Natural into a Word#

Convert a Natural into a Word# clamping to (maxBound :: Word).

Convert a Natural into a Word# clamping to (maxBound :: Word#).

Try downcasting Natural to Word value. Returns (##) if value doesn't fit in Word.

Zero Natural

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor