Extensions to the PNG 1.2 Specification, Version 1.3.0
The latest versions of this document, the PNG specification, and related
information can always be found at the PNG FTP archive site,
ftp://ftp.simplesystems.org/pub/png/. The maintainers of the PNG
specification can be contacted by e-mail at png-mng-misc @
lists.sourceforge.net.
Abstract
This document is an extension to the Portable Network Graphics (PNG)
specification, version 1.2 [PNG-1.2], and in "Portable Network
Graphics (PNG) Specification (Second Edition)" [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
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.
Table of Contents
1. Data Representation
1.1. Integer values
1.2. Floating-point values
2. Summary of Special-Purpose Chunks
3. Chunk Descriptions
3.1. oFFs Image offset
3.2. pCAL Calibration of pixel values
3.3. sCAL Physical scale of image subject
3.4. gIFg GIF Graphic Control Extension
3.5. gIFx GIF Application Extension
3.6. sTER Indicator of Stereo Image
4. Chunks Not Described Here
4.1. fRAc Fractal image parameters
5. Text Chunk Keywords
6. Deprecated Chunks
6.1. gIFt GIF Plain Text Extension
7. Security Considerations
8. Appendix: Sample code
8.1. pCAL
8.2. Fixed-point gamma correction
9. Appendix: Rationale
9.1. pCAL
10. Appendix: Revision History
11. References
12. Credits
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
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 [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 (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. 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, 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
[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
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
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
* 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
[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
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
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 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, 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.
Document source
This document was built from the file pngext-master-20060914 on
14 September 2006.
Copyright Notice
Copyright (c) 1998, 1999, 2006 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