From 2282624223af05c686cfce472abee1c5447ff6ae Mon Sep 17 00:00:00 2001
From: Yan Chunwei <yanchunwei@outlook.com>
Date: Wed, 6 Sep 2017 18:16:36 -0400
Subject: [PATCH] add offset implementation to lod tensor design (#3934)

* add offset implementation to lod tensor design
---
 paddle/framework/lod_tensor.md | 40 +++++++++++++++++++++++++++-------
 1 file changed, 32 insertions(+), 8 deletions(-)

diff --git a/paddle/framework/lod_tensor.md b/paddle/framework/lod_tensor.md
index 8dfe3ee823..769b61f175 100644
--- a/paddle/framework/lod_tensor.md
+++ b/paddle/framework/lod_tensor.md
@@ -94,7 +94,7 @@ Let's go on slicing this slice.  Its <1,1>-slice is
 |||
 ```
 
-### The General Slicing Algorithm
+### The Slicing Algorithm
 
 The algorithm, with over-simplified data structure, is defined as
 
@@ -106,17 +106,41 @@ struct LoDTensor {
   float* tensor_;
 };
 
-LoDTensor Slice(const LoDTensor& lodt, int level, int sequence) {
+LoDTensor Slice(const LoDTensor& lodt, int level, int sequence);
+```
+
+Let us revisit the example above
 
-}
+```
+         3
+3           1  2
+3   2  4    1  2  3
+||| || |||| |  || |||
 ```
 
-### Slicing the Top Level
+Suppose that we want to retrieve the <1,2>-slice
 
-Please be aware that an RNN operator only slices the top level of a LoD Tensor to get the step inputs.
+```
+2
+2  3
+|| |||
+```
 
-```c++
-LoDTensor Slice(const LoDTensor& lodt, int sequence) {
+we will need to find out the starting position of this slice by summing over all leaf nodes in `LoD` to the left of the slice, i.e., 3 + 2 + 4 + 1 = 10.
+
+To avoid the traversal of the LoD tree at slcing time,  we can do it at the construction time -- instead of saving the lengths of the next level in the LoD tree, we can save the starting offset of the next level.  For example, above LoD Tensor can be transformed into
+
+```
+        0
+0           9  10
+0   3  5    9  10 12
+||| || |||| |  || |||
+```
+
+We don't really need the 0 on top, so the LoD Tensor could be
 
-}
+```
+0           9  10
+0   3  5    9  10 12
+||| || |||| |  || |||
 ```
-- 
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