2025-03-03

age vs youth, Tesla protests, Mozilla fan fluff, how Pentiums multiplied by 3, Firefly sticks lunar landing, Trump's crypto reserve, "US out of the UN", 50 years of white men's complaints, friendly fire



Religion / Tribal / Culture War and Re-Segregation

Edumacationalizing / Acedemia Nuts

TechSuck / Geek Bait

  • (2022) The very weird Hewlett Packard FreeDOS option – Interesting things

    When ordering a HP machine with FreeDOS what you are getting is the following: + A Linux installation on the “bare metal” which boots a VM + This VM boots either an old version of FreeDOS or + An old version of Linux in a kiosk mode

  • The Pentium contains a complicated circuit to multiply by three

    this multiplier is a small part of the Pentium's floating-point multiplier circuit. In particular, the Pentium multiplies two 64-bit numbers using base-8 multiplication, which is faster than binary multiplication. However, multiplying by 3 needs to be handled as a special case. Moreover, since the rest of the multiplication process can't start until the multiplication by 3 finishes, this circuit must be very fast. If you've studied digital design, you may have heard of techniques such as carry lookahead, Kogge-Stone addition, and carry-select addition. I'll explain how the ×3 circuit combines all these techniques to maximize performance.

    The downside to radix-8 multiplication is that multiplying by a number from 0 to 7 is much more complicated than multiplying by 0 or 1, which is almost trivial. Fortunately, there are some shortcuts. Note that multiplying by 2 is the same as shifting the number to the left by 1 bit position, which is very easy in hardware—you wire each bit one position to the left. Similarly, to multiply by 4, shift the multiplicand two bit positions to the left. Multiplying by 7 seems inconvenient, but there is a trick, known as Booth's multiplication algorithm. Instead of multiplying by 7, you add 8 times the number and subtract the number, ending up with 7 times the number. You might think this requires two steps, but the trick is to multiply by one more in the digit to the left, so you get the factor of 8 without an additional step. (A base-10 analogy is that if you want to multiply by 19, you can multiply by 20 and subtract the multiplicand.) Thus, you can get the ×7 by subtracting. Similarly, for a ×6 term, you can subtract a ×2 multiple and add ×8 in the next digit. Thus, the only difficult multiple is ×3. (What about ×5? If you can compute ×3, you can subtract that from ×8 to get ×5.) To summarize, the Pentium's radix-8 Booth's algorithm is a fast way to multiply, but it requires a special circuit to produce the ×3 multiple of the multiplicand.

Left Angst

External Security / Militaria / Diplomania