lib/lowleveldct2x2/block.go - external/github.com/google/wuffs - Git at Google

 // Copyright 2026 The Wuffs Authors.
 //
 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
 // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
 // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 //
 // SPDX-License-Identifier: Apache-2.0 OR MIT

 // ----------------

 // Package lowleveldct2x2 provides DCT (Discrete Cosine Transform) operations
 // on 2×2 blocks of uint8 or int16 values.
 //
 // It provides a subset of the sibling github.com/google/wuffs/lib/lowleveljpeg
 // package's functionality, except that it operates on 2×2 blocks instead of
 // JPEG's 8×8 blocks.
 package lowleveldct2x2

 // ----------------

 // This file is essentially a copy-and-paste of lowleveljpeg's block.go, after
 // adjusting from 8×8 to 2×2.

 // ----------------

 // ifElse is like C's (condition ? whenTrue : whenFalse) expression.
 func ifElse(condition bool, whenTrue int64, whenFalse int64) int64 {
 	if condition {
 		return whenTrue
 	}
 	return whenFalse
 }

 const (
 	fmtHex = "0123456789ABCDEF"
 	fmtSep = " \n" // 1 space and then a new line.
 )

 const (
 	// BlockU8NeutralValue is the neutral value for a BlockU8, which holds
 	// unsigned uint8 values in the range [0x00, 0xFF].
 	BlockU8NeutralValue = 0x80

 	// BlockI16NeutralValue is the neutral value for a BlockI16, which holds
 	// signed int16 values in the range [-0x8000, +0x7FFF].
 	BlockI16NeutralValue = 0
 )

 // BlockU8 is a 2×2 block of uint8 values, such as a block of red, green, blue
 // or gray pixel values.
 //
 // It is indexed in XY (not DCT) space. If b is a BlockU8 then b[0] is the
 // top-left corner and b[2] is one pixel below that.
 type BlockU8 [4]uint8

 // String returns b in human-readable form.
 func (b BlockU8) String() string {
 	buf := [4 * 3]byte{}
 	for i, value := range b {
 		buf[(3*i)+0] = fmtHex[15&(value>>0x04)]
 		buf[(3*i)+1] = fmtHex[15&(value>>0x00)]
 		buf[(3*i)+2] = fmtSep[1&i]
 	}
 	return string(buf[:])
 }

 // SetToNeutral sets each element to BlockU8NeutralValue.
 func (b *BlockU8) SetToNeutral() {
 	if b == nil {
 		return
 	}
 	for i := range b {
 		b[i] = BlockU8NeutralValue
 	}
 }

 // ForwardDCT returns the FDCT (Forward Discrete Cosine Transform) of b.
 func (b *BlockU8) ForwardDCT() (ret BlockI16) {
 	ret.ForwardDCTFrom(b)
 	return ret
 }

 // ForwardDCTFrom sets *dst to src.ForwardDCT().
 func (dst *BlockI16) ForwardDCTFrom(src *BlockU8) {
 	if dst == nil {
 		return
 	} else if src == nil {
 		dst.SetToNeutral()
 		return
 	}

 	// This is equivalent to (but a simpler implementation than) lowleveljpeg's
 	// "Iterate in DCT space (outer) and XY space (inner)" v/u/y/x-loop, except
 	// that it operates on 2×2 blocks instead of JPEG's 8×8 blocks. Simpler
 	// also means that it has slightly more accurate rounding behavior.

 	src0 := int32(src[0]) - 0x80
 	src1 := int32(src[1]) - 0x80
 	src2 := int32(src[2]) - 0x80
 	src3 := int32(src[3]) - 0x80

 	dst[0] = int16((+src0 + src1 + src2 + src3 + 1) >> 1)
 	dst[1] = int16((+src0 - src1 + src2 - src3 + 1) >> 1)
 	dst[2] = int16((+src0 + src1 - src2 - src3 + 1) >> 1)
 	dst[3] = int16((+src0 - src1 - src2 + src3 + 1) >> 1)
 }

 // BlockI16 is a 2×2 block of int16 values, such as a block of JPEG
 // coefficients (except that it's 2×2 instead of JPEG's 8×8).
 //
 // It is indexed in DCT (not XY) space. If b is a BlockI16 then b[0] is the DC
 // coefficient and every other element is an AC coefficient.
 //
 // The horizontal-only AC coefficient is b[1].
 //
 // The vertical-only AC coefficient is b[2].
 type BlockI16 [4]int16

 // String returns b in human-readable form.
 func (b BlockI16) String() string {
 	buf := [4 * 5]byte{}
 	for i, value := range b {
 		buf[(5*i)+0] = fmtHex[15&(value>>0x0C)]
 		buf[(5*i)+1] = fmtHex[15&(value>>0x08)]
 		buf[(5*i)+2] = fmtHex[15&(value>>0x04)]
 		buf[(5*i)+3] = fmtHex[15&(value>>0x00)]
 		buf[(5*i)+4] = fmtSep[1&i]
 	}
 	return string(buf[:])
 }

 // Abs returns the elementwise absolute value of b.
 func (b *BlockI16) Abs() (ret BlockI16) {
 	if b == nil {
 		return ret
 	}
 	for i, v := range b {
 		if v < 0 {
 			ret[i] = -v
 		} else {
 			ret[i] = +v
 		}
 	}
 	return ret
 }

 // SetToNeutral sets each element to BlockI16NeutralValue.
 func (b *BlockI16) SetToNeutral() {
 	if b == nil {
 		return
 	}
 	for i := range b {
 		b[i] = BlockI16NeutralValue
 	}
 }

 // InverseDCT returns the IDCT (Inverse Discrete Cosine Transform) of b.
 func (b *BlockI16) InverseDCT() (ret BlockU8) {
 	ret.InverseDCTFrom(b)
 	return ret
 }

 // InverseDCTFrom sets *dst to src.InverseDCT().
 func (dst *BlockU8) InverseDCTFrom(src *BlockI16) {
 	if dst == nil {
 		return
 	} else if src == nil {
 		dst.SetToNeutral()
 		return
 	}

 	// This is equivalent to (but a simpler implementation than) lowleveljpeg's
 	// "Iterate in XY space (outer) and DCT space (inner)" y/x/v/u-loop, except
 	// that it operates on 2×2 blocks instead of JPEG's 8×8 blocks. Simpler
 	// also means that it has slightly more accurate rounding behavior.

 	src0 := int32(src[0])
 	src1 := int32(src[1])
 	src2 := int32(src[2])
 	src3 := int32(src[3])

 	dst[0] = biasAndClamp[((+src0+src1+src2+src3+1)>>1)&1023]
 	dst[1] = biasAndClamp[((+src0-src1+src2-src3+1)>>1)&1023]
 	dst[2] = biasAndClamp[((+src0+src1-src2-src3+1)>>1)&1023]
 	dst[3] = biasAndClamp[((+src0-src1-src2+src3+1)>>1)&1023]
 }

 // IsValid returns whether b does not contain unexpectedly extreme values for
 // an 8-bit-depth JPEG - one that is invalid to pass to AddN. ForwardDCT or
 // ForwardDCTFrom always returns or sets a BlockI16 that IsValid.
 //
 // Specifically:
 //   - a  DC element is out of range when outside [-256, +255].
 //   - an AC element is out of range when outside [-255, +255].
 //
 // A BlockI16 is valid when none of its elements are out of range.
 func (b *BlockI16) IsValid() bool {
 	if b == nil {
 		return false
 	}
 	if (b[0] < -256) || (+255 < b[0]) {
 		return false
 	}
 	for _, v := range b[1:] {
 		if (v < -255) || (+255 < v) {
 			return false
 		}
 	}
 	return true
 }

 // biasAndClamp[x & 1023] is (x + 0x80), clamped to the range [0x00, 0xFF], for
 // a signed integer x in the range [-512, +511].
 var biasAndClamp = [1024]uint8{
 	0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8A, 0x8B, 0x8C, 0x8D, 0x8E, 0x8F,
 	0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9A, 0x9B, 0x9C, 0x9D, 0x9E, 0x9F,
 	0xA0, 0xA1, 0xA2, 0xA3, 0xA4, 0xA5, 0xA6, 0xA7, 0xA8, 0xA9, 0xAA, 0xAB, 0xAC, 0xAD, 0xAE, 0xAF,
 	0xB0, 0xB1, 0xB2, 0xB3, 0xB4, 0xB5, 0xB6, 0xB7, 0xB8, 0xB9, 0xBA, 0xBB, 0xBC, 0xBD, 0xBE, 0xBF,
 	0xC0, 0xC1, 0xC2, 0xC3, 0xC4, 0xC5, 0xC6, 0xC7, 0xC8, 0xC9, 0xCA, 0xCB, 0xCC, 0xCD, 0xCE, 0xCF,
 	0xD0, 0xD1, 0xD2, 0xD3, 0xD4, 0xD5, 0xD6, 0xD7, 0xD8, 0xD9, 0xDA, 0xDB, 0xDC, 0xDD, 0xDE, 0xDF,
 	0xE0, 0xE1, 0xE2, 0xE3, 0xE4, 0xE5, 0xE6, 0xE7, 0xE8, 0xE9, 0xEA, 0xEB, 0xEC, 0xED, 0xEE, 0xEF,
 	0xF0, 0xF1, 0xF2, 0xF3, 0xF4, 0xF5, 0xF6, 0xF7, 0xF8, 0xF9, 0xFA, 0xFB, 0xFC, 0xFD, 0xFE, 0xFF,

 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,

 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,

 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
 	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,

 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,

 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,

 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
 	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,

 	0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0A, 0x0B, 0x0C, 0x0D, 0x0E, 0x0F,
 	0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1A, 0x1B, 0x1C, 0x1D, 0x1E, 0x1F,
 	0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2A, 0x2B, 0x2C, 0x2D, 0x2E, 0x2F,
 	0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3A, 0x3B, 0x3C, 0x3D, 0x3E, 0x3F,
 	0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4A, 0x4B, 0x4C, 0x4D, 0x4E, 0x4F,
 	0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5A, 0x5B, 0x5C, 0x5D, 0x5E, 0x5F,
 	0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6A, 0x6B, 0x6C, 0x6D, 0x6E, 0x6F,
 	0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7A, 0x7B, 0x7C, 0x7D, 0x7E, 0x7F,
 }
	// Copyright 2026 The Wuffs Authors.
	//
	// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
	// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
	// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
	// option. This file may not be copied, modified, or distributed
	// except according to those terms.
	//
	// SPDX-License-Identifier: Apache-2.0 OR MIT

	// ----------------

	// Package lowleveldct2x2 provides DCT (Discrete Cosine Transform) operations
	// on 2×2 blocks of uint8 or int16 values.
	//
	// It provides a subset of the sibling github.com/google/wuffs/lib/lowleveljpeg
	// package's functionality, except that it operates on 2×2 blocks instead of
	// JPEG's 8×8 blocks.
	package lowleveldct2x2

	// ----------------

	// This file is essentially a copy-and-paste of lowleveljpeg's block.go, after
	// adjusting from 8×8 to 2×2.

	// ----------------

	// ifElse is like C's (condition ? whenTrue : whenFalse) expression.
	func ifElse(condition bool, whenTrue int64, whenFalse int64) int64 {
	if condition {
	return whenTrue
	}
	return whenFalse
	}

	const (
	fmtHex = "0123456789ABCDEF"
	fmtSep = " \n" // 1 space and then a new line.
	)

	const (
	// BlockU8NeutralValue is the neutral value for a BlockU8, which holds
	// unsigned uint8 values in the range [0x00, 0xFF].
	BlockU8NeutralValue = 0x80

	// BlockI16NeutralValue is the neutral value for a BlockI16, which holds
	// signed int16 values in the range [-0x8000, +0x7FFF].
	BlockI16NeutralValue = 0
	)

	// BlockU8 is a 2×2 block of uint8 values, such as a block of red, green, blue
	// or gray pixel values.
	//
	// It is indexed in XY (not DCT) space. If b is a BlockU8 then b[0] is the
	// top-left corner and b[2] is one pixel below that.
	type BlockU8 [4]uint8

	// String returns b in human-readable form.
	func (b BlockU8) String() string {
	buf := [4 * 3]byte{}
	for i, value := range b {
	buf[(3*i)+0] = fmtHex[15&(value>>0x04)]
	buf[(3*i)+1] = fmtHex[15&(value>>0x00)]
	buf[(3*i)+2] = fmtSep[1&i]
	}
	return string(buf[:])
	}

	// SetToNeutral sets each element to BlockU8NeutralValue.
	func (b *BlockU8) SetToNeutral() {
	if b == nil {
	return
	}
	for i := range b {
	b[i] = BlockU8NeutralValue
	}
	}

	// ForwardDCT returns the FDCT (Forward Discrete Cosine Transform) of b.
	func (b *BlockU8) ForwardDCT() (ret BlockI16) {
	ret.ForwardDCTFrom(b)
	return ret
	}

	// ForwardDCTFrom sets *dst to src.ForwardDCT().
	func (dst BlockI16) ForwardDCTFrom(src BlockU8) {
	if dst == nil {
	return
	} else if src == nil {
	dst.SetToNeutral()
	return
	}

	// This is equivalent to (but a simpler implementation than) lowleveljpeg's
	// "Iterate in DCT space (outer) and XY space (inner)" v/u/y/x-loop, except
	// that it operates on 2×2 blocks instead of JPEG's 8×8 blocks. Simpler
	// also means that it has slightly more accurate rounding behavior.

	src0 := int32(src[0]) - 0x80
	src1 := int32(src[1]) - 0x80
	src2 := int32(src[2]) - 0x80
	src3 := int32(src[3]) - 0x80

	dst[0] = int16((+src0 + src1 + src2 + src3 + 1) >> 1)
	dst[1] = int16((+src0 - src1 + src2 - src3 + 1) >> 1)
	dst[2] = int16((+src0 + src1 - src2 - src3 + 1) >> 1)
	dst[3] = int16((+src0 - src1 - src2 + src3 + 1) >> 1)
	}

	// BlockI16 is a 2×2 block of int16 values, such as a block of JPEG
	// coefficients (except that it's 2×2 instead of JPEG's 8×8).
	//
	// It is indexed in DCT (not XY) space. If b is a BlockI16 then b[0] is the DC
	// coefficient and every other element is an AC coefficient.
	//
	// The horizontal-only AC coefficient is b[1].
	//
	// The vertical-only AC coefficient is b[2].
	type BlockI16 [4]int16

	// String returns b in human-readable form.
	func (b BlockI16) String() string {
	buf := [4 * 5]byte{}
	for i, value := range b {
	buf[(5*i)+0] = fmtHex[15&(value>>0x0C)]
	buf[(5*i)+1] = fmtHex[15&(value>>0x08)]
	buf[(5*i)+2] = fmtHex[15&(value>>0x04)]
	buf[(5*i)+3] = fmtHex[15&(value>>0x00)]
	buf[(5*i)+4] = fmtSep[1&i]
	}
	return string(buf[:])
	}

	// Abs returns the elementwise absolute value of b.
	func (b *BlockI16) Abs() (ret BlockI16) {
	if b == nil {
	return ret
	}
	for i, v := range b {
	if v < 0 {
	ret[i] = -v
	} else {
	ret[i] = +v
	}
	}
	return ret
	}

	// SetToNeutral sets each element to BlockI16NeutralValue.
	func (b *BlockI16) SetToNeutral() {
	if b == nil {
	return
	}
	for i := range b {
	b[i] = BlockI16NeutralValue
	}
	}

	// InverseDCT returns the IDCT (Inverse Discrete Cosine Transform) of b.
	func (b *BlockI16) InverseDCT() (ret BlockU8) {
	ret.InverseDCTFrom(b)
	return ret
	}

	// InverseDCTFrom sets *dst to src.InverseDCT().
	func (dst BlockU8) InverseDCTFrom(src BlockI16) {
	if dst == nil {
	return
	} else if src == nil {
	dst.SetToNeutral()
	return
	}

	// This is equivalent to (but a simpler implementation than) lowleveljpeg's
	// "Iterate in XY space (outer) and DCT space (inner)" y/x/v/u-loop, except
	// that it operates on 2×2 blocks instead of JPEG's 8×8 blocks. Simpler
	// also means that it has slightly more accurate rounding behavior.

	src0 := int32(src[0])
	src1 := int32(src[1])
	src2 := int32(src[2])
	src3 := int32(src[3])

	dst[0] = biasAndClamp[((+src0+src1+src2+src3+1)>>1)&1023]
	dst[1] = biasAndClamp[((+src0-src1+src2-src3+1)>>1)&1023]
	dst[2] = biasAndClamp[((+src0+src1-src2-src3+1)>>1)&1023]
	dst[3] = biasAndClamp[((+src0-src1-src2+src3+1)>>1)&1023]
	}

	// IsValid returns whether b does not contain unexpectedly extreme values for
	// an 8-bit-depth JPEG - one that is invalid to pass to AddN. ForwardDCT or
	// ForwardDCTFrom always returns or sets a BlockI16 that IsValid.
	//
	// Specifically:
	// - a DC element is out of range when outside [-256, +255].
	// - an AC element is out of range when outside [-255, +255].
	//
	// A BlockI16 is valid when none of its elements are out of range.
	func (b *BlockI16) IsValid() bool {
	if b == nil {
	return false
	}
	if (b[0] < -256) \|\| (+255 < b[0]) {
	return false
	}
	for _, v := range b[1:] {
	if (v < -255) \|\| (+255 < v) {
	return false
	}
	}
	return true
	}

	// biasAndClamp[x & 1023] is (x + 0x80), clamped to the range [0x00, 0xFF], for
	// a signed integer x in the range [-512, +511].
	var biasAndClamp = [1024]uint8{
	0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8A, 0x8B, 0x8C, 0x8D, 0x8E, 0x8F,
	0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9A, 0x9B, 0x9C, 0x9D, 0x9E, 0x9F,
	0xA0, 0xA1, 0xA2, 0xA3, 0xA4, 0xA5, 0xA6, 0xA7, 0xA8, 0xA9, 0xAA, 0xAB, 0xAC, 0xAD, 0xAE, 0xAF,
	0xB0, 0xB1, 0xB2, 0xB3, 0xB4, 0xB5, 0xB6, 0xB7, 0xB8, 0xB9, 0xBA, 0xBB, 0xBC, 0xBD, 0xBE, 0xBF,
	0xC0, 0xC1, 0xC2, 0xC3, 0xC4, 0xC5, 0xC6, 0xC7, 0xC8, 0xC9, 0xCA, 0xCB, 0xCC, 0xCD, 0xCE, 0xCF,
	0xD0, 0xD1, 0xD2, 0xD3, 0xD4, 0xD5, 0xD6, 0xD7, 0xD8, 0xD9, 0xDA, 0xDB, 0xDC, 0xDD, 0xDE, 0xDF,
	0xE0, 0xE1, 0xE2, 0xE3, 0xE4, 0xE5, 0xE6, 0xE7, 0xE8, 0xE9, 0xEA, 0xEB, 0xEC, 0xED, 0xEE, 0xEF,
	0xF0, 0xF1, 0xF2, 0xF3, 0xF4, 0xF5, 0xF6, 0xF7, 0xF8, 0xF9, 0xFA, 0xFB, 0xFC, 0xFD, 0xFE, 0xFF,

	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,

	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,

	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
	0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,

	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,

	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,

	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,

	0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0A, 0x0B, 0x0C, 0x0D, 0x0E, 0x0F,
	0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1A, 0x1B, 0x1C, 0x1D, 0x1E, 0x1F,
	0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2A, 0x2B, 0x2C, 0x2D, 0x2E, 0x2F,
	0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3A, 0x3B, 0x3C, 0x3D, 0x3E, 0x3F,
	0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4A, 0x4B, 0x4C, 0x4D, 0x4E, 0x4F,
	0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5A, 0x5B, 0x5C, 0x5D, 0x5E, 0x5F,
	0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6A, 0x6B, 0x6C, 0x6D, 0x6E, 0x6F,
	0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7A, 0x7B, 0x7C, 0x7D, 0x7E, 0x7F,
	}