I am recently reading the book "computer architecture: a quantitative approach" by Jonh  L. Hennessy & David A. Patterson.
I find that the term "Lane" is extensively used in Chapter 4 but not explicitly and formally defined.   
The first places it appears is as follows:
"All modern vector computers have vector functional units with multiple parallel pipelines (or lanes) that can produce two or more results per clock cycle ..." in Page 290 (6th version).
I am a little confused about the terms "Lane" and "pipeline". Are they the same thing?
A "lane" in this context is a SIMD element. (They're talking about vector execution units, not superscalar CPUs that run more than one instruction in parallel throughout "the pipeline" of the whole CPU. In practice you have both)
e.g. x86 SSE addps xmm0, xmm1 does 4x float32 additions with one instruction, treating the XMM registers as 4 lanes of 32-bit float.
It runs on a SIMD execution unit that has 4 single-precision FP adders in parallel. This execution unit is pipelined, typically 3 or 4 cycle latency and 1/clock throughput.
In this case your textbook is talking about the pipeline(s) inside one execution unit. As far as pipelining is concerned, it makes little different what the operation is, and whether it's 4x 32-bit or 2x 64-bit or whatever. At the buffers between pipeline stages, there's a certain number of bits to latch, and the latches don't really care how it's interpreted.
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