[xiph-commits] r8724 - trunk/theora/doc/spec

[tterribe at motherfish-iii.xiph.org]

Author: tterribe
Date: 2005-01-11 08:42:03 -0800 (Tue, 11 Jan 2005)
New Revision: 8724

Modified:
   trunk/theora/doc/spec/spec.tex
Log:
Made the spec agree with the code for the non-normative foward DCT transform.
Thanks to acolwell for pointing out the inconsistency.


Modified: trunk/theora/doc/spec/spec.tex
===================================================================
--- trunk/theora/doc/spec/spec.tex	2005-01-11 16:36:34 UTC (rev 8723)
+++ trunk/theora/doc/spec/spec.tex	2005-01-11 16:42:03 UTC (rev 8724)
@@ -6451,14 +6451,14 @@
 The column of numbers on the left represents the unpermuted input, and the
  column on the right the permuted output DCT coefficients.
 
-An offset is also added before right-shifting the output of the
- multiplications, to effect rounding with ties rounded towards positive
- infinity.
-This increases the complexity of the transform to 16 multiplications and
- 42 additions and subtractions.
+A proper division by $2^{16}$ is done after the multiplications instead of a
+ shift in the forward transform.
+This can be implemented quickly by adding an offset of $\hex{FFFF}$ if the
+ number is negative, and then shifting as before.
+This slightly increases the computational complexity of the transform.
 Unlike the inverse DCT, 16 bit registers and a $16\times16\rightarrow32$ bit
  multiply are sufficient to avoid any overflow, so long as the input is in the
- range $-6270\ldots 6270$, which is more than sufficient.
+ range $-6270\ldots 6270$, which is larger than required.
 
 \begin{enumerate}
 \item
@@ -6493,9 +6493,9 @@
 Assign \locvar{R} the value $\locvar{T}[6]-\locvar{T}[5]$.
 \item
 Assign $\locvar{T}[6]$ the value
- $(\locvar{C4}*(\locvar{T}[6]+\locvar{T}[5])+\hex{8000})>>16$.
+ $(\locvar{C4}*(\locvar{T}[6]+\locvar{T}[5]))//16$.
 \item
-Assign $\locvar{T}[5]$ the value $(\locvar{C4}*\locvar{R}+\hex{8000})>>16$.
+Assign $\locvar{T}[5]$ the value $(\locvar{C4}*\locvar{R})//16$.
 \item
 Assign \locvar{R} the value $\locvar{T}[4]+\locvar{T}[5]$.
 \item
@@ -6510,34 +6510,34 @@
 Assign $\locvar{T}[7]$ the value \locvar{R}.
 \item
 Assign $\bitvar{Y}[0]$ the value
- $(\locvar{C4}*(\locvar{T}[0]+\locvar{T}[1])+\hex{8000})>>16$.
+ $(\locvar{C4}*(\locvar{T}[0]+\locvar{T}[1]))//16$.
 \item
 Assign $\bitvar{Y}[4]$ the value
- $(\locvar{C4}*(\locvar{T}[0]-\locvar{T}[1])+\hex{8000})>>16$.
+ $(\locvar{C4}*(\locvar{T}[0]-\locvar{T}[1]))//16$.
 \item
 Assign $\bitvar{Y}[2]$ the value
- $((\locvar{S6}*\locvar{T}[3]+\hex{8000})>>16)+
- ((\locvar{C6}*\locvar{T}[2]+\hex{8000})>>16)$.
+ $((\locvar{S6}*\locvar{T}[3])//16)+
+ ((\locvar{C6}*\locvar{T}[2])//16)$.
 \item
 Assign $\bitvar{Y}[6]$ the value
- $((\locvar{C6}*\locvar{T}[3]+\hex{8000})>>16)-
- ((\locvar{S6}*\locvar{T}[2]+\hex{8000})>>16)$.
+ $((\locvar{C6}*\locvar{T}[3])//16)-
+ ((\locvar{S6}*\locvar{T}[2])//16)$.
 \item
 Assign $\bitvar{Y}[1]$ the value
- $((\locvar{S7}*\locvar{T}[7]+\hex{8000})>>16)+
- ((\locvar{C7}*\locvar{T}[4]+\hex{8000})>>16)$.
+ $((\locvar{S7}*\locvar{T}[7])//16)+
+ ((\locvar{C7}*\locvar{T}[4])//16)$.
 \item
 Assign $\bitvar{Y}[5]$ the value
- $((\locvar{S3}*\locvar{T}[6]+\hex{8000})>>16)+
- ((\locvar{C3}*\locvar{T}[5]+\hex{8000})>>16)$.
+ $((\locvar{S3}*\locvar{T}[6])//16)+
+ ((\locvar{C3}*\locvar{T}[5])//16)$.
 \item
 Assign $\bitvar{Y}[3]$ the value
- $((\locvar{C3}*\locvar{T}[6]+\hex{8000})>>16)-
- ((\locvar{S3}*\locvar{T}[5]+\hex{8000})>>16)$.
+ $((\locvar{C3}*\locvar{T}[6])//16)-
+ ((\locvar{S3}*\locvar{T}[5])//16)$.
 \item
 Assign $\bitvar{Y}[7]$ the value
- $((\locvar{C7}*\locvar{T}[7]+\hex{8000})>>16)-
- ((\locvar{S7}*\locvar{T}[4]+\hex{8000})>>16)$.
+ $((\locvar{C7}*\locvar{T}[7])//16)-
+ ((\locvar{S7}*\locvar{T}[4])//16)$.
 \end{enumerate}
 
 \subsection{The Complete Reconstruction Algorithm}