/-
Copyright (c) 2022 Henrik Böving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henrik Böving
-/
module

prelude
public import Init.Data.Fin.Log2

public section

/--
Base-two logarithm of 8-bit unsigned integers. Returns `⌊max 0 (log₂ a)⌋`.

This function is overridden at runtime with an efficient implementation. This definition is
the logical model.

Examples:
 * `UInt8.log2 0 = 0`
 * `UInt8.log2 1 = 0`
 * `UInt8.log2 2 = 1`
 * `UInt8.log2 4 = 2`
 * `UInt8.log2 7 = 2`
 * `UInt8.log2 8 = 3`
-/
@[extern "lean_uint8_log2"]
def UInt8.log2 (a : UInt8) : UInt8 := ⟨⟨Fin.log2 a.toFin⟩⟩

/--
Base-two logarithm of 16-bit unsigned integers. Returns `⌊max 0 (log₂ a)⌋`.

This function is overridden at runtime with an efficient implementation. This definition is
the logical model.

Examples:
 * `UInt16.log2 0 = 0`
 * `UInt16.log2 1 = 0`
 * `UInt16.log2 2 = 1`
 * `UInt16.log2 4 = 2`
 * `UInt16.log2 7 = 2`
 * `UInt16.log2 8 = 3`
-/
@[extern "lean_uint16_log2"]
def UInt16.log2 (a : UInt16) : UInt16 := ⟨⟨Fin.log2 a.toFin⟩⟩

/--
Base-two logarithm of 32-bit unsigned integers. Returns `⌊max 0 (log₂ a)⌋`.

This function is overridden at runtime with an efficient implementation. This definition is
the logical model.

Examples:
 * `UInt32.log2 0 = 0`
 * `UInt32.log2 1 = 0`
 * `UInt32.log2 2 = 1`
 * `UInt32.log2 4 = 2`
 * `UInt32.log2 7 = 2`
 * `UInt32.log2 8 = 3`
-/
@[extern "lean_uint32_log2"]
def UInt32.log2 (a : UInt32) : UInt32 := ⟨⟨Fin.log2 a.toFin⟩⟩

/--
Base-two logarithm of 64-bit unsigned integers. Returns `⌊max 0 (log₂ a)⌋`.

This function is overridden at runtime with an efficient implementation. This definition is
the logical model.

Examples:
 * `UInt64.log2 0 = 0`
 * `UInt64.log2 1 = 0`
 * `UInt64.log2 2 = 1`
 * `UInt64.log2 4 = 2`
 * `UInt64.log2 7 = 2`
 * `UInt64.log2 8 = 3`
-/
@[extern "lean_uint64_log2"]
def UInt64.log2 (a : UInt64) : UInt64 := ⟨⟨Fin.log2 a.toFin⟩⟩

/--
Base-two logarithm of word-sized unsigned integers. Returns `⌊max 0 (log₂ a)⌋`.

This function is overridden at runtime with an efficient implementation. This definition is
the logical model.

Examples:
 * `USize.log2 0 = 0`
 * `USize.log2 1 = 0`
 * `USize.log2 2 = 1`
 * `USize.log2 4 = 2`
 * `USize.log2 7 = 2`
 * `USize.log2 8 = 3`
-/
@[extern "lean_usize_log2"]
def USize.log2 (a : USize) : USize := ⟨⟨Fin.log2 a.toFin⟩⟩