Number Systems: Operations and Properties

Number Systems: Operations and Properties
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Explore the representation of numbers and arithmetic operations, covering addition, subtraction, multiplication, and division in various number systems. Understand properties like commutative, associative, and distributive in N, Z, Q, and RQ, including working with surds, as well as concepts of natural, integer, rational, irrational, and real numbers. Dive into prime numbers, the Pythagorean theorem, and the classification of real numbers on the number line.

  • Number Systems
  • Arithmetic Operations
  • Properties
  • Rational Numbers
  • Real Numbers

Uploaded on Apr 19, 2025 | 0 Views


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  1. XDP Production Usage: DDoS Protection and L4LB Huapeng Zhou (hzhou@fb.com) Nikita (tehnerd@fb.com) Martin Lau (kafai@fb.com)

  2. Load Balancing Proxy (L7 LB) Proxy (L7 LB) SHIV (L4 LB) Proxy (L7 LB)

  3. SHIV (L4 LB) An IPVS to XDP_TX Transition

  4. SHIV: Map Lookups LRU Map (/Cache) XDP_TX Sharding Map (Proxy IPs)

  5. XDP_TX to Proxy bpf_xdp_adjust_head() ETH sport dport payload Client IP VIP Proxy IP ETH L4LB IP sport dport payload Client IP VIP XDP_TX

  6. Droplet

  7. Traffic Spike at SHIV?

  8. Droplet (Dreamlist): Fast packet drop Earliest stage in the networking stack Programmability and Flexibility Easy to develop and quick to deploy (No kernel reboot) Realized by XDP_DROP Drop at HW limited-rate

  9. Droplet: DDoS Protection Framework Loaded in kernel + Run in the NIC Driver Runtime compilation using bcc BPF program written in C Map Setup (XDP)

  10. Chaining Multiple BPF_PROG Using bpf_tail_call + BPF_MAP_TYPE_PROG_ARRAY XDP_TX #0 XDP Dump #1 #2 L4LB Droplet bpf_perf_event_output() XDP_DROP

  11. Questions?

  12. Proxy (L7 LB) SHIV (L4 LB)

  13. Droplet: DDoS Protection Framework Droplet: DDoS Protection Framework Programmability: abstract away interactions with user space Droplet handler: handles the dirty work Runtime compilation Kernel load/hook Different types of handlers GenericHandler IPHandler PrefixHandler The user only needs to write BPF code in C

  14. Lab tests (w/ pktgen) Under 99% cache hit: 3x to 6x improvement Under 0% cache hit: 10x (up to 25x w/o session tracking)

  15. TCP/IP stack processing on recv IPVS is too generic Poor DDOS survivability Hard to add new features

  16. XDP vs IPVS

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