Re: [math-fun] Japanese Temple Geometry, and misc comments
At 11:09 PM 4/2/2017, rcs@xmission.com wrote:
In a different direction: The IBM 1620 computer (c.1962) used tables in memory for single-digit addition and multiplication. This might have been used to do arithmetic in other bases < 10.
It's been 58 years; do we have to file a FOIA request to ask NSA if they ever used the 1620 table lookup for bases other than base 10? I hacked the 1620 while still in high school, but didn't know enough math at that time to really utilize the table lookup feature for anything other than base ten. Also, I don't recall whether the machine could even boot if the arithmetic tables got wiped, so trying experiments of this form could be very dangerous. (Core memories retain their data when powered off, so wiping these tables was rare.) BTW, modern GPU's are *really good* at interpolating large tables; Google "texture mapping": https://en.wikipedia.org/wiki/Texture_mapping_unit "In GPGPU, texture maps in 1,2, or 3 dimensions may be used to store arbitrary data. By providing interpolation, the texture mapping unit provides a convenient means of approximating arbitrary functions with data tables."
The add table was in hardware for the model II, but the multiply table was still present. I think the standard boot sequence (hitting “insert storage key” then typing magic digits at the keyboard, which inserted them directly into memory, and the hitting the “reset and start” key on the keyboard) would load these tables from the card deck which you had carefully placed in the card reader.
On Apr 3, 2017, at 12:52 PM, Henry Baker <hbaker1@pipeline.com> wrote:
At 11:09 PM 4/2/2017, rcs@xmission.com wrote:
In a different direction: The IBM 1620 computer (c.1962) used tables in memory for single-digit addition and multiplication. This might have been used to do arithmetic in other bases < 10.
It's been 58 years; do we have to file a FOIA request to ask NSA if they ever used the 1620 table lookup for bases other than base 10?
I hacked the 1620 while still in high school, but didn't know enough math at that time to really utilize the table lookup feature for anything other than base ten.
Also, I don't recall whether the machine could even boot if the arithmetic tables got wiped, so trying experiments of this form could be very dangerous. (Core memories retain their data when powered off, so wiping these tables was rare.)
BTW, modern GPU's are *really good* at interpolating large tables; Google "texture mapping":
https://en.wikipedia.org/wiki/Texture_mapping_unit
"In GPGPU, texture maps in 1,2, or 3 dimensions may be used to store arbitrary data. By providing interpolation, the texture mapping unit provides a convenient means of approximating arbitrary functions with data tables."
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On the model I, I don't see how the card reader could even operate without performing addition, since each column from the card needed to be stored in the "next" location in memory; that "next" location required an *increment** to compute its address. How could the program counter even increment? BTW, early microcodes had explicit next addresses for precisely this reason; this made the microcode into a Lisp-like linked list. At 10:08 AM 4/3/2017, Tom Knight wrote:
The add table was in hardware for the model II, but the multiply table was still present.
I think the standard boot sequence (hitting "insert storage key" then typing magic digits at the keyboard, which inserted them directly into memory, and the hitting the "reset and start" key on the keyboard) would load these tables from the card deck which you had carefully placed in the card reader.
On Apr 3, 2017, at 12:52 PM, Henry Baker <hbaker1@pipeline.com> wrote:
At 11:09 PM 4/2/2017, rcs@xmission.com wrote:
In a different direction: The IBM 1620 computer (c.1962) used tables in memory for single-digit addition and multiplication. This might have been used to do arithmetic in other bases < 10.
Also, I don't recall whether the machine could even boot if the arithmetic tables got wiped, so trying experiments of this form could be very dangerous. (Core memories retain their data when powered off, so wiping these tables was rare.)
participants (2)
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Henry Baker -
Tom Knight