The problem with large integers
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C has data types for 8-bit, 16-bit, 32-bit, and 64-bit integers
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Why are there no data types for 256-bit integers?
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Magma does not have problems with large integers
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Python has datatype long for arbitrary-size integers
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Java has BigInteger class
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C is “portable assembly”, very close to what computers really do
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Computers work on data in registers (very small, very fast storage
units)
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Typical register sizes: 8 bit, 16 bit, 32 bit, 64 bit . . . but not 256 bit
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That’s a lie!
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Yeah, you’re right. We do have 256-bit registers (AVX on Intel and
AMD processors)
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But those do not hold a single 256-bit integer (but vectors of
integers or floats)
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Why can’t they just hold a 256-bit integer?
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Because arithmetic units cannot perform arithmetic on 256-bit
integers (only on 8-bit, 16-bit, 32-bit, and 64-bit integers)
Efficient implementation of finite-field arithmetic 4
