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> Macroinstructions > [fasmg] exotic constants ... 
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bitRAKE
I don't know what else to call them  exotic constants is an good as anything else I suppose. Many algorithms initialize a space with complex constants as a known basis to start some process. For example, we have SHA256  using the fractional square and cube roots of primes. Another example is ShiShua using phi (ϕ).
How would we generate these constants at compiletime? Or what if we want to use different constants for our own flavor of securitybyobscurity? Code: calminstruction hex_nibble digit*, command: display compute digit, 0FFh and '0123456789ABCDEF' shr (digit*8) arrange command, command digit assemble command end calminstruction calminstruction ROOT? result*, remainder*, N* local rem, prox, bit, temp compute rem, 0 check N = 0 jyes done compute prox, 0 compute bit, 1 shl (((bsr N) + 1) and 2) check N > 0 jyes more arrange bit, =err 'square root of negative number' assemble bit exit more: compute temp, rem + bit + prox check N < temp compute rem, rem shr 1 jyes reduce compute rem, rem + bit compute prox, temp reduce: compute bit, bit shr 2 check bit jyes more done: publish result, rem compute rem, N  prox publish remainder, rem end calminstruction ; big integer broken into integer array ; littleendian, not efficient ; grain should be a power of two calminstruction BIGHEX value*, grain:8, cmd:display local awk, digit, big, k compute big, value arrange awk, cmd '0x' assemble awk compute k, grain shl 1 jump nibs next: ; 32 bytes per line check (k  (grain shl 1)) and 63 jyes same arrange awk, cmd ',\',10,'0x' assemble awk jump nibs same: arrange awk, cmd ',0x' assemble awk nibs: compute digit, (big shr ((k1) shl 2)) and 0Fh call hex_nibble, digit, cmd compute k, k  1 check k and ((grain shl 1)  1) jyes nibs compute k, k + (grain shl 2) check big shr ((k  (grain shl 1)) shl 2) jyes next end calminstruction ; phi: square root of five, minus one; divided by two (scaled by bits bits) macro ShiShua q:16 local t0, t1, bits bits = q shl 6 ROOT t0, t1, (5 shl (bits+bits)) t0 = (t0  (1 shl bits)) shr 1 ; bigendian at the qword scale, but littleendian qwords (weird!) t1 = 0 repeat q t1 = (t1 shl 64) or (t0 and ((1) bswap 8)) t0 = t0 shr 64 end repeat BIGHEX t1 end macro ShiShua 32 Code: 0x9E3779B97F4A7C15,0xF39CC0605CEDC834,0x1082276BF3A27251,0xF86C6A11D0C18E95,\ 0x2767F0B153D27B7F,0x0347045B5BF1827F,0x01886F0928403002,0xC1D64BA40F335E36,\ 0xF06AD7AE9717877E,0x85839D6EFFBD7DC6,0x64D325D1C5371682,0xCADD0CCCFDFFBBE1,\ 0x626E33B8D04B4331,0xBBF73C790D94F79D,0x471C4AB3ED3D82A5,0xFEC507705E4AE6E5,\ 0xE73A9B91F3AA4DB2,0x87AE44F332E923A7,0x3CB91648E428E975,0xA3781EB01B49D867,\ 0x4FA1508419E0EAA4,0x038B352D9BAD30F4,0x485B71A8EF64452A,0x0DD40DC8CB8F9A2D,\ 0x4C514F1B229DCAA2,0x22AC268E9666E4A8,0x66769145F5F5880A,0x9D0ACD3B9E8C682F,\ 0x4F810320ABEB9403,0x4E70F21608C061AB,0x1C1CAEF1EBDCEFBC,0x72134ECF06ED82BF 

29 May 2022, 15:03 

bitRAKE
More constants for our fixed point needs ...
This time we are using periodic continued fractions: Code: ; integer coefficient, ; constant coefficients, ; repeating coefficients, ; precision (fractional bits) struc CFRACT a0*,a_const*,a_repeat*,N* local error, h0,k0, h1,k1, c,r,a_n, h_n,k_n h1 = 1 k1 = 0 h_n = a0 k_n = 1 n = 1 error = 1 while error <> 0 ; resolve present a(n) iterate c,a_const if n <= %% indx n a_n = c break else a_n = %% iterate r,a_repeat indx 1+((na_n1) mod %%) a_n = r break end iterate end if end iterate h0 = h1 k0 = k1 h1 = h_n k1 = k_n h_n = a_n * h1 + h0 k_n = a_n * k1 + k0 error = (h_n shl N) / k_n  (h1 shl N) / k1 n = n + 1 end while . = (h1 shl N) / k1 end struc ; SOME EXAMPLES: ; https://wikipedia.org/wiki/Golden_ratio ; https://oeis.org/A001622 golden CFRACT 1, 1, 1, 64 ; golden ratio root2 CFRACT 1, 2, 2, 64 ; square root of 2 root3 CFRACT 1, 1, <2,1>, 64 ; square root of 3 root31 CFRACT 5, 1, <1,3,5,3,1,1,10,1>, 64 ; square root of 31 tan1 CFRACT 1, 1, <1,n>, 64 ; tan(1) e64 CFRACT 2, <1,2>, <1,1,(2*n+2)/3>, 64 ; euler constant to 64bit ; see https://oeis.org/A001203 for more digits, no pattern known pi CFRACT 3, <7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,2,1,84,2,1,1>,1, 64 

03 Aug 2022, 00:07 

revolution
bitRAKE wrote: Or what if we want to use different constants for our own flavor of securitybyobscurity? 

03 Aug 2022, 01:38 

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