Extensions to the PNG 1.2 Specification, Version 1.4.0
The latest versions of this document, the PNG specification, and
related information can always be found at the PNG FTP archive site,
[1]ftp://ftp.simplesystems.org/pub/png/. The maintainers of the PNG
specification can be contacted by e-mail at
[2]png-mng-misc @ lists.sourceforge.net.
Abstract
This document is an extension to the Portable Network Graphics (PNG)
specification, version 1.2 [[3]PNG-1.2], and in "Portable Network
Graphics (PNG) Specification (Second Edition)" [[4]PNG-ISO]. It
describes additional public chunk types and contains additional
information for use in PNG images.
This document, together with the PNG specification, contains the entire
list of registered "public" PNG chunks. The additional registered
chunks appearing in this document are the oFFs, pCAL, sCAL, gIFg, gIFs,
sTER, and fRAc chunks, plus the deprecated gIFt chunk. Additional chunk
types may be proposed for inclusion in this list by contacting the PNG
specification maintainers at [5]png-mng-misc @ lists.sourceforge.net.
Chunks described here are expected to be less widely supported than
those defined in the basic specification. However, application authors
are encouraged to use these chunk types whenever appropriate for their
applications.
This document also describes data representations that do not occur in
the core PNG format, but are used in one or more special-purpose
chunks. New chunks should use these representations whenever
applicable, in order to maximize portability and simplify decoders.
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Table of Contents
1. Data Representation ............................................ 1
1.1. Integer values ............................................ 1
1.2. Floating-point values ..................................... 1
2. Summary of Special-Purpose Chunks .............................. 1
3. Chunk Descriptions ............................................. 1
3.1. oFFs Image offset ......................................... 1
3.2. pCAL Calibration of pixel values .......................... 1
3.3. sCAL Physical scale of image subject ...................... 1
3.4. gIFg GIF Graphic Control Extension ........................ 1
3.5. gIFx GIF Application Extension ............................ 1
3.6. sTER Indicator of Stereo Image ........................... 1
4. Chunks Not Described Here ...................................... 1
4.1. dSIG Digital Signature .................................... 1
4.2. fRAc Fractal image parameters ............................. 1
5. Text Chunk Keywords ............................................ 1
6. Deprecated Chunks .............................................. 1
6.1. gIFt GIF Plain Text Extension ............................. 1
7. Security Considerations ........................................ 1
8. Appendix: Sample code .......................................... 1
8.1. pCAL ...................................................... 1
8.2. Fixed-point gamma correction .............................. 1
9. Appendix: Rationale ............................................ 1
9.1. pCAL ...................................................... 1
10. Appendix: Revision History .................................... 1
11. References .................................................... 1
12. Credits ....................................................... 1
1. Data Representation
1.1. Integer values
Refer to Section 2.1 of the PNG specification for the format and range
of integer values.
1.2. Floating-point values
The core of PNG does not use floating-point numbers anywhere; it uses
integers or, where applicable, fixed-point fractional values. However,
special-purpose chunks may need to represent values that do not fit
comfortably in fixed-point notation. The textual floating-point
notation defined here is recommended for use in all such cases. This
representation is simple, has no a priori limits on range or precision,
and is portable across all machines.
A floating-point value in this notation is represented by an ASCII text
string in a standardized decimal floating-point format. The string is
variable-length and must be terminated by a null (zero) character
unless it is the last item in its chunk. The string consists of an
optional sign ("+" or "-"), an integer part, a fraction part beginning
with a decimal point ("."), and an exponent part beginning with an "E"
or "e" and optional sign. The integer, fraction, and exponent parts
each contain one or more digits (ASCII "0" to "9"). Either the integer
part or the fraction part, but not both, may be omitted. A decimal
point is allowed, but not required, if there is no fraction part. The
exponent part may be omitted. No spaces or any other character besides
those specified may appear.
Note in particular that C-language "F" and "L" suffixes are not
allowed, the string "." is not allowed as a shorthand for 0 as in some
other programming languages, and no commas or underscores are allowed.
This format ought to be easily readable in all programming
environments.
2. Summary of Special-Purpose Chunks
This table summarizes some properties of the chunks described in this
document.
Name Multiple Ordering constraints
OK?
oFFs No Before IDAT
pCAL No Before IDAT
sCAL No Before IDAT
gIFg Yes None
gIFt Yes None (this chunk is deprecated)
gIFx Yes None
sTER No Before IDAT
dSIG Yes In pairs, immediately after IHDR and before IEND
fRAc Yes None
3. Chunk Descriptions
3.1. oFFs Image offset
The oFFs chunk gives the position on a printed page at which the image
should be output when printed alone. It can also be used to define the
image's location with respect to a larger screen or other
application-specific coordinate system.
The oFFs chunk contains:
X position: 4 bytes (signed integer)
Y position: 4 bytes (signed integer)
Unit specifier: 1 byte
Both position values are signed. The following values are legal for the
unit specifier:
0: unit is the pixel (true dimensions unspecified)
1: unit is the micrometer
Conversion note: one inch is equal to exactly 25400 micrometers. A
micrometer (also called a micron) is 10^-6 meter.
The X position is measured rightwards from the left edge of the page to
the left edge of the image; the Y position is measured downwards from
the top edge of the page to the top edge of the image. Note that
negative values are permitted, and denote displacement in the opposite
directions. Although oFFs can specify an image placement that is
partially or wholly outside the page boundaries, the result of such
placement is application-dependent.
If present, this chunk must precede the first IDAT chunk.
3.2. pCAL Calibration of pixel values
When a PNG file is being used to store physical data other than color
values, such as a two-dimensional temperature field, the pCAL chunk can
be used to record the relationship (mapping) between stored pixel
samples, original samples, and actual physical values. The pCAL data
might be used to construct a reference color bar beside the image, or
to extract the original physical data values from the file. It is not
expected to affect the way the pixels are displayed. Another method
should be used if the encoder wants the decoder to modify the sample
values for display purposes.
The pCAL chunk contains:
Calibration name: 1-79 bytes (character string)
Null separator: 1 byte
Original zero (x0): 4 bytes (signed integer)
Original max (x1): 4 bytes (signed integer)
Equation type: 1 byte
Number of parameters: 1 byte
Unit name: 0 or more bytes (character string)
Null separator: 1 byte
Parameter 0 (p0): 1 or more bytes (ASCII floating-point)
Null separator: 1 byte
Parameter 1 (p1): 1 or more bytes (ASCII floating-point)
...etc...
There is no null separator after the final parameter (or after the unit
name, if there are zero parameters). The number of parameters field
must agree with the actual number of parameters present in the chunk,
and must be correct for the specified equation type (see below).
The calibration name can be any convenient name for referring to the
mapping, and is subject to the same restrictions as the keyword in a
PNG text chunk: it must contain only printable Latin-1
[[6]ISO/IEC-8859-1] characters (33-126 and 161-255) and spaces (32),
but no leading, trailing, or consecutive spaces. The calibration name
can permit applications or people to choose the appropriate pCAL chunk
when more than one is present (this could occur in a multiple-image
file, but not in a PNG file). For example, a calibration name of "SI"
or "English" could be used to identify the system of units in the pCAL
chunk as well as in other chunk types, to permit a decoder to select an
appropriate set of chunks based on their names.
The pCAL chunk defines two mappings:
1. A mapping from the stored samples, which are unsigned integers in
the range 0..max, where max=2^bitdepth-1, to the original samples,
which are signed integers. The x0 and x1 fields, together with the
bit depth for the image, define this mapping.
2. A mapping from the original samples to the physical values, which
are usually real numbers with units. This mapping is defined by x0,
x1, the equation type, parameters, and unit name.
The mapping between the stored samples and the original samples is
given by the following equations:
original_sample =
(stored_sample * (x1-x0) + max/2) / max + x0
stored_sample =
((original_sample - x0) * max + (x1-x0)/2) / (x1-x0)
clipped to the range 0..max
In these equations, "/" means integer division that rounds toward
negative infinity, so n/d = integer(floor(real(a)/real(b)))). Note that
this is the same as the "/" operator in the C programming language when
n and d are nonnegative, but not necessarily when n or d is negative.
Notice that x0 and x1 are the original samples that correspond to the
stored samples 0 and max, respectively. Encoders will usually set x0=0
and x1=max to indicate that the stored samples are equal to the
original samples. Note that x0 is not constrained to be less than x1,
and neither is constrained to be positive, but they must be different
from each other.
This mapping is lossless and reversible when abs(x1-x0) <= max and the
original sample is in the range x0..x1. If abs(x1-x0) > max then there
can be no lossless reversible mapping, but the functions provide the
best integer approximations to floating-point affine transformations.
The mapping between the original samples and the physical values is
given by one of several equations, depending on the equation type,
which may have the following values:
0: Linear mapping
1: Base-e exponential mapping
2: Arbitrary-base exponential mapping
3: Hyperbolic mapping
For equation type 0:
physical_value = p0 + p1 * original_sample / (x1-x0)
For equation type 1:
physical_value =
p0 + p1 * exp(p2 * original_sample / (x1-x0))
For equation type 2:
physical_value =
p0 + p1 * pow(p2, (original_sample / (x1-x0)))
For equation type 3:
physical_value =
p0 + p1 * sinh(p2 * (original_sample - p3) / (x1-x0))
For these physical value equations, "/" means floating-point division.
The function exp(x) is e raised to the power of x, where e is the base
of the natural logarithms, approximately 2.71828182846. The exponential
function exp() is the inverse the natural logarithm function ln().
The function pow(x,y) is x raised to the power of y.
pow(x,y) = exp(y * ln(x))
The function sinh(x) is the hyperbolic sine of x.
sinh(x) = 0.5 * (exp(x) - exp(-x))
The units for the physical values are given by the unit name, which may
contain any number of printable Latin-1 characters, with no limitation
on the number and position of blanks. For example, "K", "population
density", "MPa". A zero-length string can be used for dimensionless
data.
For color types 0 (gray) and 4 (gray-alpha), the mappings apply to the
gray sample values (but not to the alpha sample). For color types 2
(RGB), 3 (indexed RGB), and 6 (RGBA), the mappings apply independently
to each of the red, green, and blue sample values (but not the alpha
sample). In the case of color type 3 (indexed RGB), the mapping refers
to the RGB samples and not to the index values.
Linear data can be expressed with equation type 0.
Pure logarithmic data can be expressed with either equation type 1 or
2:
Equation type 1 Equation type 2
x0 = 0 x0 = 0
x1 = max x1 = max
p0 = 0 p0 = 0
p1 = bottom p1 = bottom
p2 = ln(top/bottom) p2 = top/bottom
Equation types 1 and 2 are functionally equivalent; both are defined
because authors may find one or the other more convenient.
Using equation type 3, floating-point data can be reduced (with loss)
to a set of integer samples such that the resolution of the stored data
is roughly proportional to its magnitude. For example, floating-point
data ranging from -10^31 to 10^31 (the usual range of 32-bit
floating-point numbers) can be represented with:
Equation type 3
x0 = 0
x1 = 65535
p0 = 0.0
p1 = 1.0e-30
p2 = 280.0
p3 = 32767.0
The resolution near zero is about 10^-33, while the resolution near
10^31 or -10^31 is about 10^28. Everywhere the resolution is about 0.4
percent of the magnitude.
Note that those floating-point parameters could be stored in the chunk
more compactly as follows:
p0 = 0
p1 = 1e-30
p2 = 280
p3 = 32767
Applications should use double precision arithmetic (or take other
precautions) while performing the mappings for equation types 1, 2, and
3, to prevent overflow of intermediate results when p1 is small and the
exp(), pow(), or sinh() function is large.
If present, the pCAL chunk must appear before the first IDAT chunk.
Only one instance of the pCAL chunk is permitted in a PNG datastream.
3.3. sCAL Physical scale of image subject
While the pHYs chunk is used to record the physical size of the image
itself as it was scanned or as it should be printed, certain images
(such as maps, photomicrographs, astronomical surveys, floor plans, and
others) may benefit from knowing the actual physical dimensions of the
image's subject for remote measurement and other purposes. The sCAL
chunk serves this need. It contains:
Unit specifier: 1 byte
Pixel width: 1 or more bytes (ASCII floating-point)
Null separator: 1 byte
Pixel height: 1 or more bytes (ASCII floating-point)
The following values are legal for the unit specifier:
1: unit is the meter
2: unit is the radian
Following the unit specifier are two ASCII strings. The first string
defines the physical width represented by one image pixel; the second
string defines the physical height represented by one pixel. The two
strings are separated by a zero byte (null character). As in the text
chunks, there is no trailing zero byte for the final string. Each of
these strings contains a floating-point constant in the format
specified above ([7]Floating-point values, Section 1.2). Both values
are required to be greater than zero.
If present, this chunk must precede the first IDAT chunk.
3.4. gIFg GIF Graphic Control Extension
The gIFg chunk is provided for backward compatibility with the GIF89a
Graphic Control Extension. It contains:
Disposal Method: 1 byte
User Input Flag: 1 byte
Delay Time: 2 bytes (byte order converted from GIF)
The Disposal Method indicates the way in which the graphic is to be
treated after being displayed. The User Input Flag indicates whether
user input is required before continuing. The Delay Time specifies the
number of hundredths (1/100) of a second to delay before continuing
with the processing of the datastream. Note that this field is to be
byte-order-converted.
The "Transparent Color Flag" and "Transparent Color Index" fields found
in the GIF89a Graphic Control Extension are omitted from gIFg. These
fields should be converted using the transparency features of basic
PNG.
The GIF specification allows at most one Graphic Control Extension to
preceed each graphic rendering block. Because each PNG file holds only
one image, it is expected that gIFg will appear at most once, before
IDAT, but there is no strict requirement.
3.5. gIFx GIF Application Extension
The gIFx chunk is provided for backward compatibility with the GIF89a
Application Extension. The Application Extension contains
application-specific information. This chunk contains:
Application Identifier: 8 bytes
Authentication Code: 3 bytes
Application Data: n bytes
The Application Identifier is a sequence of eight printable ASCII
characters used to identify the application creating the Application
Extension. The Authentication Code is three additional bytes that the
application may use to further validate the Application Extension. The
remainder of the chunk is application-specific data whose content is
not defined by the GIF specification.
Note that GIF-to-PNG converters should not attempt to perform byte
reordering on the contents of the Application Extension. The data is
simply transcribed without any processing except for de-blocking GIF
sub-blocks.
Applications that formerly used GIF Application Extensions may define
special-purpose PNG chunks to replace their application extensions. If
a GIF-to-PNG converter recognizes the Application Identifier and is
aware of a corresponding PNG chunk, it may choose to convert the
Application Extension into that PNG chunk type rather than using gIFx.
3.6. sTER Indicator of Stereo Image
When present, the sTER chunk indicates that the datastream contains a
stereo pair of subimages within a single PNG image.
The sTER chunk contains:
Mode: 1 byte
0: cross-fuse layout
1: diverging-fuse layout
The sTER chunk with mode==0 or mode==1 indicates that the datastream
contains two subimages, encoded within a single PNG image. They are
arranged side-by-side, with one subimage intended for presentation to
the right eye and the other subimage intended for presentation to the
left eye. The left edge of the right subimage must be on a column that
is evenly divisible by eight, so that if interlacing is employed the
two images will have coordinated interlacing. Padding columns between
the two subimages must be introduced by the encoder if necessary. The
sTER chunk imposes no requirements on the contents of the padding
pixels. For compatibility with software not supporting sTER, it does
not exempt the padding pixels from existing requirements; for example,
in palette images, the padding pixels must be valid palette indices.
The two subimages must have the same dimensions after removal of any
padding.
When mode==0, the right-eye image appears at the left and the left-eye
image appears at the right, suitable for cross-eyed free viewing. When
mode==1, the left-eye image appears at the left and the right-eye image
appears at the right, suitable for divergent (wall-eyed) free viewing.
Decoders that are aware of the sTER chunk may display the two images in
any suitable manner, with or without the padding. Decoders that are not
aware of the sTER chunk, and those that recognize the chunk but choose
not to treat stereo pairs differently from regular PNG images, will
naturally display them side-by-side in a manner suitable for free
viewing.
If present, the sTER chunk must appear before the first IDAT chunk.
Given two subimages with width subimage_width, encoders can calculate
the inter-subimage padding and total width W using the following
pseudocode:
padding := 7 - ((subimage_width - 1) mod 8)
W := 2 * subimage_width + padding
Given an image with width W, decoders can calculate the subimage width
and inter-subimage padding using the following pseudocode:
padding := 15 - ((W - 1) mod 16)
if (padding > 7) then error
subimage_width := (W - padding) / 2
Decoders can assume that the samples in the left and right subimages
are cosited, such that the subimages and their centers are coincident
at the projection plane. Decoders can also assume that the left and
right subimages are intended to be presented directly to the right and
left eyes of the user/viewer without independent scaling, rotation or
displacement. I.e., the subimages will be presented at the same size in
the same relative position and orientation to each eye of the viewer.
Encoders should use the pHYs chunk to indicate the pixel's size ratio
when it is not 1:1.
It is recommended that encoders use the cross-fusing layout (mode==0),
especially when the image centers are separated by more than 65
millimeters when displayed on a typical monitor.
4. Chunks Not Described Here
The definitions of some public chunks are being maintained by groups
other than the core PNG group. In general, these are chunks that are
useful to more than one application (and thus are not private chunks),
but are considered too specialized to list in the core PNG
documentation.
4.1. dSIG Digital signature
The dSIG chunk provides a digital signature that guarantees that the
contents of the prtion of the entire datastream enclosed in a pair of
such chunks has not changed since the digital signature was added. This
chunk is described in detail in a separate document, [[8]dSIG-spec],
which is accompanied by an example provided in [[9]dSIG-example].
4.2. fRAc Fractal image parameters
The fRAc chunk will describe the parameters used to generate a fractal
image. The specification for the contents of the fRAc chunk is being
developed by Tim Wegner, [10]twegner @ phoenix.net.
In the future, chunks will be fully specified before they are
registered.
5. Text Chunk Keywords
It is expected that special-purpose keywords for PNG text chunks will
be registered and will appear in this document. However, no such
keywords have yet been assigned.
All registered textual keywords in text chunks and all other chunk
types are limited to the ASCII characters A-Z, a-z, 0-9, space, and the
following 20 symbols:
! " % & ' ( ) * + , - . / : ; < = > ? _
but not the remaining 12 symbols:
# $ @ [ \ ] ^ ` { | } ~
This restricted set is the ISO-646 "invariant" character set
[[11]ISO-646]. These characters have the same numeric codes in all ISO
character sets, including all national variants of ASCII.
6. Deprecated Chunks
The chunks listed in this section are registered, but deprecated.
Encoders are discouraged from using them, and decoders are not
encouraged to support them.
6.1. gIFt GIF Plain Text Extension
The gIFt chunk was originally provided for backward compatibility with
the GIF89a Plain Text Extension, but gIFt is now deprecated because it
suffers from some fundamental design flaws.
* GIF considers a Plain Text Extension to be a Graphic Rendering
Block, just like an image, so a GIF datastream containing an image
and a Plain Text Extension is really a multi-image datastream with
ordering issues (like associating each Graphic Control Extension
with the proper Graphic Rendering Block). PNG, being a single-image
format with no provisions for handling these ordering issues, is
not equipped to contain both IDAT and gIFt simultaneously. Since
IDAT is required, gIFt must be discouraged.
* The Text Foreground Color and Text Background Color fields of the
Plain Text Extension are converted to RGB, rather than being
converted to RGBA or left as palette indexes. Therefore,
transparency information can be lost.
The gIFt chunk contains:
Text Grid Left Position: 4 bytes (signed integer,
byte order and size converted)
Text Grid Top Position: 4 bytes (signed integer,
byte order and size converted)
Text Grid Width: 4 bytes (unsigned integer,
byte order and size converted)
Text Grid Height: 4 bytes (unsigned integer,
byte order and size converted)
Character Cell Width: 1 byte
Character Cell Height: 1 byte
Text Foreground Color: 3 bytes (R,G,B samples)
Text Background Color: 3 bytes (R,G,B samples)
Plain Text Data: n bytes
Text Grid Left Position, Top Position, Width, and Height specify the
text area position and size in pixels. The converter must reformat
these fields from 2-byte LSB-first unsigned integers to 4-byte
MSB-first signed or unsigned integers. Note that GIF defines the
position to be relative to the upper left corner of the logical screen.
If an oFFs chunk is also present, a decoder should assume that the oFFs
chunk defines the offset of the image relative to the GIF logical
screen; hence subtracting the oFFs values (converted from micrometers
to pixels if necessary) from the Text Grid Left and Top Positions gives
the text area position relative to the main PNG image.
Character Cell Width and Height give the dimensions of each character
in pixels.
Text Foreground and Background Color give the colors to be used to
render text foreground and background. Note that the GIF-to-PNG
converter must replace the palette index values found in the GIF Plain
Text Extension block with the corresponding palette entry.
The remainder of the chunk is the text to be displayed. Note that this
data is not in GIF sub-block format, but is a continuous datastream.
7. Security Considerations
The normal precautions (see the Security considerations section of the
PNG specification) should be taken when displaying text contained in
the sCAL calibration name, pCAL unit name, or any ASCII floating-point
fields.
Applications must take care to avoid underflow and overflow of
intermediate results when converting data from one form to another
according to the pCAL mappings.
8. Appendix: Sample code
This appendix provides some sample code that can be used in encoding
and decoding PNG chunks. It does not form a part of the specification.
In the event of a discrepancy between the sample code in this appendix
and the chunk definition, the chunk definition prevails.
8.1. pCAL
The latest version of this code, including test routines not shown
here, is available at
[12]ftp://ftp.simplesystems.org/pub/png/src/pcal.c.
#if 0
pcal.c 0.2.2 (Sat 19 Dec 1998)
Adam M. Costello
This is public domain example code for computing
the mappings defined for the PNG pCAL chunk.
#endif
#if __STDC__ != 1
#error This code relies on ANSI C conformance.
#endif
#include
#include
#include
#include
/* In this program a type named uintN denotes an unsigned */
/* type that handles at least all values 0 through (2^N)-1. */
/* A type named intN denotes a signed type that handles at */
/* least all values 1-2^(N-1) through 2^(N-1)-1. It is not */
/* necessarily the smallest such type; we are more concerned */
/* with speed. */
typedef unsigned int uint16;
#if UINT_MAX >= 0xffffffff
typedef unsigned int uint32;
#else
typedef unsigned long uint32;
#endif
#if INT_MAX >= 0x7fffffff && INT_MIN + 0x7fffffff <= 0
typedef int int32;
#else
typedef long int32;
#endif
/* Testing for 48-bit integers is tricky because we cannot */
/* safely use constants greater than 0xffffffff. Also, */
/* shifting by the entire width of a type is undefined, so */
/* for unsigned int, which might be only 16 bits wide, we */
/* must shift in two steps. */
#if (UINT_MAX - 0xffff) >> 8 >> 8 >= 0xffffffff
typedef unsigned int uint48;
#define HAVE_UINT48 1
#elif (ULONG_MAX - 0xffff) >> 16 >= 0xffffffff
typedef unsigned long uint48;
#define HAVE_UINT48 1
#elif defined(ULLONG_MAX)
#if (ULLONG_MAX - 0xffff) >> 16 >= 0xffffffff
typedef unsigned long long uint48;
#define HAVE_UINT48 1
#endif
#else
#define HAVE_UINT48 0
#endif
/*******************/
/* Program failure */
void
fail(const char *msg)
{
fputs(msg,stderr);
fputc('\n', stderr);
exit(EXIT_FAILURE);
}
/*************************/
/* Check max, x0, and x1 */
int
samp_params_ok(uint16 max, int32 x0, int32 x1)
/* Returns 1 if max, x0, and x1 have */
/* allowed values, 0 otherwise. */
{
const int32 xlimit = 0x7fffffff;
return max > 0 && max <= 0xffff
&& x0 <= xlimit && x0 >= -xlimit
&& x1 <= xlimit && x1 >= -xlimit
&& x0 != x1;
}
/***********************************************/
/* Map from stored samples to original samples */
int32
stored_to_orig(uint16 stored, uint16 max, int32 x0, int32 x1)
#if 0
Returns the original sample corresponding to the given stored
sample, which must be <= max. The parameters max, x0, and x1
must have been approved by samp_params_ok().
The pCAL spec says:
orig = (stored * (x1-x0) + max/2) / max + x0 [1]
Equivalently:
orig = (stored * (x1-x0) + max/2) / max
+ (x0-x1) - (x0-x1) + x0
orig = (stored * (x1-x0) + max * (x0-x1) + max/2) / max
- (x0-x1) + x0
orig = ((max - stored) * (x0-x1) + max/2) / max + x1
So we can check whether x0 < x1 and coerce the formula so that
the numerators and denominators are always nonnegative:
orig = (offset * xspan + max/2) / max + xbottom [2]
This will come in handy later.
But the multiplication and the subtraction can overflow, so we
have to be trickier. For the subtraction, we can convert to
unsigned integers. For the multiplication, we can use 48-bit
integers if we have them, otherwise observe that:
b = (b/c)*c + b%c
a*b = a*(b/c)*c + a*(b%c) ; let d = a*(b%c)
(a*b)/c = a*(b/c) + d/c remainder d%c [3]
These are true no matter which way the division rounds. If
(a*b)/c is in-range, a*(b/c) is guaranteed to be in-range if
b/c rounds toward zero. Here is another observation:
sum{x_i} / c = sum{x_i / c} + sum{x_i % c} / c [4]
This one also avoids overflow if the division rounds toward
zero. The pCAL spec requires rounding toward -infinity. ANSI
C leaves the rounding direction implementation-defined except
when both the numerator and denominator are nonnegative, in
which case it rounds downward. So if we arrange for all
numerators and denominators to be nonnegative, everything
works. Starting with equation 2 and applying identity 4, then
3, we obtain the final formula:
d = offset * (xspan % max)
xoffset = offset * (xspan / max) + d/max
+ (d%max + max/2) / max
orig = xoffset + xbottom
#endif
{
uint16 offset;
uint32 xspan, q, r, d, xoffset;
int32 xbottom;
if (stored > max) fail("stored_to_orig: stored > max");
if (x1 >= x0) {
xbottom = x0;
xspan = (uint32)x1 - (uint32)x0;
offset = stored;
}
else {
xbottom = x1;
xspan = (uint32)x0 - (uint32)x1;
offset = max - stored;
}
/* We knew xspan would fit in a uint32, but we needed to */
/* cast x0 and x1 before subtracting because otherwise the */
/* subtraction could overflow, and ANSI doesn't say what */
/* the result will be in that case. */
/* Let's optimize two common simple cases */
/* before handling the general case: */
if (xspan == max) {
xoffset = offset;
}
else if (xspan <= 0xffff) {
/* Equation 2 won't overflow and does only one division. */
xoffset = (offset * xspan + (max>>1)) / max;
}
else {
#if HAVE_UINT48
/* We can use equation 2 and do one uint48 */
/* division instead of three uint32 divisions. */
xoffset = (offset * (uint48)xspan + (max>>1)) / max;
#else
q = xspan / max;
r = xspan % max;
/* Hopefully those were compiled into one instruction. */
d = offset * r;
xoffset = offset * q + d/max + (d%max + (max>>1)) / max;
#endif
}
/* xoffset might not fit in an int32, but we know the sum */
/* xbottom + xoffset will, so we can do the addition on */
/* unsigned integers and then cast. */
return (int32)((uint32)xbottom + xoffset);
}
/***********************************************/
/* Map from original samples to stored samples */
uint16
orig_to_stored(int32 orig, uint16 max, int32 x0, int32 x1)
#if 0
Returns the stored sample corresponding to the given original
sample. The parameters max, x0, and x1 must have been
approved by samp_params_ok().
The pCAL spec says:
stored = ((orig - x0) * max + (x1-x0)/2) / (x1-x0)
clipped to the range 0..max
Notice that all three terms are nonnegative, or else all
are nonpositive. Just as in stored_to_orig(), we can avoid
overflow and rounding problems by transforming the equation to
use unsigned quantities:
stored = (xoffset * max + xspan/2) / xspan
#endif
{
uint32 xoffset, xspan;
if (x0 < x1) {
if (orig < x0) return 0;
if (orig > x1) return max;
xspan = (uint32)x1 - (uint32)x0;
xoffset = (uint32)orig - (uint32)x0;
}
else {
if (orig < x1) return 0;
if (orig > x0) return max;
xspan = (uint32)x0 - (uint32)x1;
xoffset = (uint32)x0 - (uint32)orig;
}
/* For 16-bit xspan the calculation is straightforward: */
if (xspan <= 0xffff)
return (xoffset * max + (xspan>>1)) / xspan;
/* Otherwise, the numerator is more than 32 bits and the */
/* denominator is more than 16 bits. The tricks we played */
/* in stored_to_orig() depended on the denominator being */
/* 16-bit, so they won't help us here. */
#if HAVE_UINT48
return ((uint48)xoffset * max + (xspan>>1)) / xspan;
#else
/* Doing the exact integer calculation with 32-bit */
/* arithmetic would be very difficult. But xspan > 0xffff */
/* implies xspan > max, in which case the pCAL spec says */
/* "there can be no lossless reversible mapping, but the */
/* functions provide the best integer approximations to */
/* floating-point affine transformations." So why insist */
/* on using the integer calculation? Let's just use */
/* floating-point. */
return ((double)xoffset * max + (xspan>>1)) / xspan;
#endif
}
/*********************************************/
/* Check x0, x1, eqtype, n, and p[0]..p[n-1] */
int
phys_params_ok(int32 x0, int32 x1, int eqtype, int n, double *p)
/* Returns 1 if x0, x1, eqtype, n, and p[0]..p[n-1] */
/* have allowed values, 0 otherwise. */
{
if (!samp_params_ok(1,x0,x1)) return 0;
switch (eqtype) {
case 0: return n == 2;
case 1: return n == 3;
case 2: break;
case 3: return n == 4;
}
/* eqtype is 2, check for pow() domain error: */
if (p[2] > 0) return 1;
if (p[2] < 0) return 0;
return (x0 <= x1) ? (x0 > 0 && x1 > 0) : (x0 < 0 && x1 < 0);
}
/************************************************/
/* Map from original samples to physical values */
double
orig_to_phys(int32 orig, int32 x0, int32 x1,
int eqtype, double *p)
/* Returns the physical value corresponding to the given */
/* original sample. The parameters x0, x1, eqtype, and p[] */
/* must have been approved by phys_params_ok(). The array */
/* p[] must hold enough parameters for the equation type. */
{
double xdiff, f;
xdiff = (double)x1 - x0;
switch (eqtype) {
case 0: f = orig / xdiff;
break;
case 1: f = exp(p[2] * orig / xdiff);
break;
case 2: f = pow(p[2], orig / xdiff);
break;
case 3: f = sinh(p[2] * (orig - p[3]) / xdiff);
break;
default: fail("orig_to_phys: unknown equation type");
}
return p[0] + p[1] * f;
}
8.2. Fixed-point gamma correction
The latest version of this code, including test routines not shown
here, is available at
[13]ftp://ftp.simplesystems.org/pub/png/src/gamma-lookup.c.
#if 0
gamma-lookup.c 0.1.4 (Sat 19 Dec 1998)
by Adam M. Costello
This is public domain example code for computing gamma
correction lookup tables using integer arithmetic.
#endif
#if __STDC__ != 1
#error This code relies on ANSI C conformance.
#endif
#include
#include
/* In this program a type named uintN denotes the */
/* smallest unsigned type we can find that handles */
/* at least all values 0 through (2^N)-1. */
typedef unsigned char uint8;
#if UCHAR_MAX >= 0xffff
typedef unsigned char uint16;
#else
typedef unsigned short uint16;
#endif
#if UCHAR_MAX >= 0xffffffff
typedef unsigned char uint32;
#elif USHRT_MAX >= 0xffffffff
typedef unsigned short uint32;
#elif UINT_MAX >= 0xffffffff
typedef unsigned int uint32;
#else
typedef unsigned long uint32;
#endif
/*********************/
/* 16-bit arithmetic */
void
precompute16(uint16 L[511])
/* Precomputes the log table (this requires floating point). */
{
int j;
double f;
/* L[j] will hold an integer representation of */
/* -log(j / 510.0). Knowing that L[1] (the largest) is */
/* 0xfe00 will help avoid overflow later, so we set the */
/* scale factor accordingly. */
f = 0xfe00 / log(1 / 510.0);
for (j = 1; j <= 510; ++j)
L[j] = log(j / 510.0) * f + 0.5;
}
void
gamma16(uint16 L[511], uint8 G[256], uint16 g)
/* Makes a 256-entry gamma correction lookup table G[] with */
/* exponent g/pow(2,14), where g must not exceed 0xffff. */
{
int i, j;
uint16 x, y, xhi, ghi, xlo, glo;
j = 1;
G[0] = 0;
for (i = 1; i <= 255; ++i) {
x = L[i << 1];
xhi = x >> 8;
ghi = g >> 8;
y = xhi * ghi;
if (y > 0x3f80) {
/* We could have overflowed later. */
/* But now we know y << 2 > L[1]. */
G[i] = 0;
continue;
}
xlo = x & 0xff;
glo = g & 0xff;
y = (y << 2) + ((xhi * glo) >> 6) + ((xlo * ghi) >> 6);
while (L[j] > y) ++j;
G[i] = j >> 1;
}
}
/*********************/
/* 32-bit arithmetic */
void
precompute32(uint32 L[511])
/* Precomputes the log table (this requires floating point). */
{
int j;
double f;
/* L[j] will hold an integer representation of */
/* -log(j / 510.0). Knowing that L[1] (the largest) */
/* is 0x3ffffff will help avoid overflow later, so we */
/* set the scale factor accordingly. */
f = 0x3fffffff / log(1 / 510.0);
for (j = 1; j <= 510; ++j)
L[j] = log(j / 510.0) * f + 0.5;
}
void
gamma32(uint32 L[511], uint8 G[256], uint16 g)
/* Makes a 256-entry gamma correction lookup table G[] with */
/* exponent g/pow(2,14), where g must not exceed 0xffff. */
{
int i, j;
uint32 x, y;
j = 1;
G[0] = 0;
for (i = 1; i <= 255; ++i) {
x = L[i << 1];
y = (x >> 14) * g;
while (L[j] > y) ++j;
G[i] = j >> 1;
}
}
/**********************************************/
/* Floating-point arithmetic (for comparison) */
void
gamma_fp(uint8 G[256], double g)
/* Makes a 256-entry gamma correction */
/* lookup table G[i] with exponent g. */
{
int i;
G[0] = 0;
for (i = 1; i <= 255; ++i)
G[i] = pow(i/255.0, g) * 255 + 0.5;
}
9. Appendix: Rationale
This appendix gives the reasoning behind some of the design decisions
in the PNG extension chunks. It does not form a part of the
specification.
9.1. pCAL
This section gives the reasoning behind some of the design decisions in
the pCAL chunk. It does not form a part of the specification.
Redundant equation types
Equation types 1 and 2 seem to be equivalent. Why have both?
* We don't want to force people to do the exponentiation using ln()
and exp(), since pow() may provide better accuracy in some
floating-point math libraries. We also don't want to force people
using base-10 logs to store a sufficiently accurate value of ln(10)
in the pCAL chunk.
* When the base is e, we don't want to force people to encode a
sufficiently accurate value of e in the pCAL chunk, or to use pow()
when exp() is sufficient.
What are x0 and x1 for?
* First, x0 and x1 provide a way to recover the original data,
losslessly, when the original range is not a power of two.
Sometimes the digitized values do not have a range that fills the
full depth of a PNG. For example, if the original samples range
from 0 (corresponding to black) to 800 (corresponding to white),
PNG requires that these samples be scaled to the range 0 to 65535.
By recording x0=0 and x1=800 we can recover the original samples,
and we indicate the precision of the data.
* Even if the original data had a range identical to a valid PNG
image sample, like 0 (black) to 65535 (white), one might want to
create a derived image by stretching the contrast in a limited
intensity range containing the important details. For example, we
might want to scale the samples so that 46000 becomes 0 (black) and
47000 becomes 65535 (white). As in the previous case, by recording
x0=46000 and x1=47000, we can recover the original data samples
that fell between 46000 and 47000.
Integer division
Why define integer divison to round toward negative infinity? This is
different from many C implementations and from all Fortran
implementations, which round toward zero.
We cannot leave the choice unspecified. If we were to specify rounding
toward zero, we'd have to account for a discontinuity at zero. A
division by positive d would map the 2d-1 values from -(d-1) through
d-1 to zero, but would map only d values to any other value; for
example, 3d through 4d-1 would be mapped to 3. Achieving lossless
mappings in spite of this anomaly would be difficult.
10. Appendix: Revision History
* 1 May 2008 (version 1.4.0):
+ Added the dSIG chunk.
* 31 August 2006 (version 1.3.0):
+ Added the sTER chunk.
* 14 July 1999 (version 1.2.0):
+ Deleted the iTXt chunk, which has been moved to the core spec.
* 9 February 1999 (version 1.1.1):
+ Added the iTXt chunk
+ Limited the character set for future registered keywords
* 30 December 1998 (version 1.1.0):
+ Added pCAL chunk and related sample code
+ Deprecated the gIFT chunk
+ Added sample gamma-correction code that uses integer
arithmetic
* 11 March 1996 (version 0.96): First public release
11. References
[dSIG-example]
Bosslet, Martin, and Thomas Kopp, "PNG Digital Signatures:
Commented Example", 17 April 2008, available at
[14]ftp://ftp.simplesystems.org/pub/png/documents/signatures/.
[dSIG-Spec]
Kopp, Thomas, "PNG Digital Signatures: Extension Specification",
17 April 2008, available at
[15]ftp://ftp.simplesystems.org/pub/png/documents/signatures/.
[ISO/IEC-8859-1]
International Organization for Standardization and International
Electrotechnical Commission, "Information Technology--8-bit
Single-Byte Coded Graphic Character Sets--Part 1: Latin Alphabet
No. 1", IS 8859-1, 1998.
Also see sample files at
[16]ftp://ftp.simplesystems.org/pub/png/documents/iso_8859-1.*
[ISO-646]
International Organization for Standardization and International
Electrotechnical Commission, "Information Technology--ISO 7-bit
Coded Character Set for Information Exchange", 1991.
[PNG-1.2]
Randers-Pehrson, G., et. al., "PNG (Portable Network Graphics
Format) Version 1.2", which is available at
[17]ftp://ftp.simplesystems.org/pub/png/documents/.
[PNG-ISO]
"Portable Network Graphics (PNG) Specification (Second
Edition)," 10 November 2003, also released as "International
Standard 15948:2003 -- Portable Network Graphics (PNG):
Functional specification" available at
[18]http://png-mng.sourceforge.net/pub/png/spec/iso/
12. Credits
Editors
* Glenn Randers-Pehrson, glennrp @ users.sourceforge.net
* Tom Lane, tgl @ sss.pgh.pa.us (edited the first release of this
document)
Contributors
Names of contributors not already listed in the PNG specification are
presented in alphabetical order:
* Adeluc, [19]www.adeluc.com, png @ adeluc.com
* Todd French, tfrench @ sandia.gov
* Alaric B. Snell, alaric @ alaric-snell.com
Trademarks
GIF is a service mark of CompuServe Incorporated. PostScript is a
trademark of Adobe Systems.
Copyright Notice
Copyright © 1998, 1999, 2006, 2008 by: Glenn Randers-Pehrson
This specification is being provided by the copyright holder under the
following license. By obtaining, using and/or copying this
specification, you agree that you have read, understood, and will
comply with the following terms and conditions:
Permission to use, copy, and distribute this specification for any
purpose and without fee or royalty is hereby granted, provided that the
full text of this NOTICE appears on ALL copies of the specification or
portions thereof, including modifications, that you make.
THIS SPECIFICATION IS PROVIDED "AS IS," AND COPYRIGHT HOLDER MAKES NO
REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED. BY WAY OF EXAMPLE,
BUT NOT LIMITATION, COPYRIGHT HOLDERS MAKE NO REPRESENTATIONS OR
WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE OR
THAT THE USE OF THE SPECIFICATION WILL NOT INFRINGE ANY THIRD PARTY
PATENTS, COPYRIGHTS, TRADEMARKS OR OTHER RIGHTS. COPYRIGHT HOLDER WILL
BEAR NO LIABILITY FOR ANY USE OF THIS SPECIFICATION.
The name and trademarks of copyright holder may NOT be used in
advertising or publicity pertaining to the specification without
specific, written prior permission. Title to copyright in this
specification and any associated documentation will at all times remain
with copyright holder.
The "Appendix: Sample Code" has been placed in the public domain, and
the conditions described above do not apply to that appendix.
End of Extensions to the PNG 1.2 Specification
References
1. ftp://ftp.simplesystems.org/pub/png/
2. mailto:png-mng-misc%C2%A0@%C2%A0lists.sourceforge.net
3. file://localhost/ftp/pub/libpng/png/documents/pngext-1.4.0-pdg.html#PNG-1.2
4. file://localhost/ftp/pub/libpng/png/documents/pngext-1.4.0-pdg.html#PNG-ISO
5. file://localhost/ftp/pub/libpng/png/documents/pngext-1.4.0-pdg.html#64;%C2%A0lists.sourceforge.net
6. file://localhost/ftp/pub/libpng/png/documents/pngext-1.4.0-pdg.html#I-8859-1
7. file://localhost/ftp/pub/libpng/png/documents/pngext-1.4.0-pdg.html#DR.Floating-point-values
8. file://localhost/ftp/pub/libpng/png/documents/pngext-1.4.0-pdg.html#dSIG-spec
9. file://localhost/ftp/pub/libpng/png/documents/pngext-1.4.0-pdg.html#dSIG-example
10. file://localhost/ftp/pub/libpng/png/documents/pngext-1.4.0-pdg.html#64;%C2%A0phoenix.net
11. file://localhost/ftp/pub/libpng/png/documents/pngext-1.4.0-pdg.html#ISO-646
12. ftp://ftp.simplesystems.org/pub/png/src/pcal.c
13. ftp://ftp.simplesystems.org/pub/png/src/gamma-lookup.c
14. ftp://ftp.simplesystems.org/pub/png/documents/signatures/index.html
15. ftp://ftp.simplesystems.org/pub/png/documents/signatures/index.html
16. ftp://ftp.simplesystems.org/pub/png/documents/
17. ftp://ftp.simplesystems.org/pub/png/documents/
18. http://png-mng.sourceforge.net/pub/png/spec/iso/
19. http://www.adeluc.com/
}