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83 lines
2.3 KiB
Python
83 lines
2.3 KiB
Python
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#!/usr/bin/python
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# This file is part of the Luau programming language and is licensed under MIT License; see LICENSE.txt for details
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# This code can be used to generate power tables for Schubfach algorithm (see lnumprint.cpp)
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import math
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import sys
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(_, pow10min, pow10max, compact) = sys.argv
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pow10min = int(pow10min)
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pow10max = int(pow10max)
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compact = compact == "True"
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# extract high 128 bits of the value
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def high128(n, roundup):
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L = math.ceil(math.log2(n))
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r = 0
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for i in range(L - 128, L):
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if i >= 0 and (n & (1 << i)) != 0:
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r |= (1 << (i - L + 128))
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return r + (1 if roundup else 0)
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def pow10approx(n):
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if n == 0:
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return 1 << 127
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elif n > 0:
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return high128(10**n, 5**n >= 2**128)
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else:
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# 10^-n is a binary fraction that can't be represented in floating point
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# we need to extract top 128 bits of the fraction starting from the first 1
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# to get there, we need to divide 2^k by 10^n for a sufficiently large k and repeat the extraction process
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p = 10**-n
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k = 2**128 * 16**-n # this guarantees that the fraction has more than 128 extra bits
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return high128(k // p, True)
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def pow5_64(n):
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assert(n >= 0)
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if n == 0:
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return 1 << 63
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else:
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return high128(5**n, False) >> 64
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if not compact:
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print("// kPow10Table", pow10min, "..", pow10max)
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print("{")
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for p in range(pow10min, pow10max + 1):
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h = hex(pow10approx(p))[2:]
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assert(len(h) == 32)
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print(" {0x%s, 0x%s}," % (h[0:16].upper(), h[16:32].upper()))
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print("}")
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else:
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print("// kPow5Table")
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print("{")
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for i in range(16):
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print(" " + hex(pow5_64(i)) + ",")
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print("}")
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print("// kPow10Table", pow10min, "..", pow10max)
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print("{")
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for p in range(pow10min, pow10max + 1, 16):
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base = pow10approx(p)
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errw = 0
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for i in range(16):
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real = pow10approx(p + i)
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appr = (base * pow5_64(i)) >> 64
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scale = 1 if appr < (1 << 127) else 0 # 1-bit scale
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offset = (appr << scale) - real
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assert(offset >= -4 and offset <= 3) # 3-bit offset
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assert((appr << scale) >> 64 == real >> 64) # offset only affects low half
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assert((appr << scale) - offset == real) # validate full reconstruction
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err = (scale << 3) | (offset + 4)
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errw |= err << (i * 4)
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hbase = hex(base)[2:]
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assert(len(hbase) == 32)
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assert(errw < 1 << 64)
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print(" {0x%s, 0x%s, 0x%16x}," % (hbase[0:16], hbase[16:32], errw))
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print("}")
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