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HexNotationConstants.v
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Require Import Coq.ZArith.ZArith.
Require Export Crypto.Compilers.Syntax.
Require Import Crypto.Compilers.Z.Syntax.
Require Export bbv.WordScope.
Require Export Crypto.Util.Notations.
Notation Const x := (Op (OpConst x) TT).
(* python:
<<
#!/usr/bin/env python
from __future__ import with_statement
import math
systematic_nums \
= (list(range(128)) +
[2**i + j for i in range(256) for j in (1, 0, -1)])
nums = tuple(sorted(set(systematic_nums + [
187,
189,
317,
421,
481,
569,
765,
977,
5311,
32765,
32766,
65530,
65531,
65534,
114687,
121665,
130307,
131039,
131062,
131067,
261167,
261575,
262131,
262139,
262142,
523807,
524101,
524223,
524262,
524263,
524267,
524269,
524271,
524278,
524279,
524286,
679935,
1032192,
1044479,
1047599,
1047811,
1048202,
1048446,
1048471,
1048511,
1048526,
1048534,
1048538,
1048549,
1048557,
1048558,
1048559,
1048573,
1048574,
1359870,
2060031,
2064384,
2081439,
2088958,
2094335,
2095198,
2095622,
2096127,
2096128,
2096583,
2096942,
2097098,
2097114,
2097118,
2097127,
2097135,
2097143,
2097150,
4120062,
4162878,
4188670,
4192254,
4193166,
4193327,
4193539,
4193735,
4193823,
4193883,
4193987,
4194115,
4194240,
4194254,
4194270,
4194271,
4194275,
4194279,
4194285,
4194286,
4194287,
4194289,
4194293,
4194299,
4194301,
4194302,
8323583,
8372224,
8386654,
8387078,
8387470,
8387646,
8387766,
8387974,
8388127,
8388187,
8388230,
8388291,
8388421,
8388491,
8388503,
8388542,
8388558,
8388570,
8388574,
8388577,
8388578,
8388581,
8388591,
8388593,
8388595,
8388598,
8388599,
8388602,
8388603,
8388604,
8388605,
8388606,
11599871,
16647166,
16711679,
16775935,
16776254,
16776374,
16776582,
16776842,
16776959,
16776982,
16777006,
16777027,
16777029,
16777111,
16777162,
16777182,
16777185,
16777186,
16777187,
16777189,
16777190,
16777191,
16777197,
16777198,
16777199,
16777201,
16777205,
16777206,
16777207,
16777210,
16777211,
16777212,
16777213,
16777214,
23199742,
33423358,
33551870,
33554054,
33554058,
33554222,
33554315,
33554370,
33554374,
33554378,
33554382,
33554394,
33554398,
33554399,
33554401,
33554402,
33554407,
33554410,
33554411,
33554413,
33554414,
33554415,
33554417,
33554422,
33554423,
33554426,
33554427,
33554428,
33554429,
33554430,
67107887,
67108630,
67108798,
67108799,
67108802,
67108814,
67108822,
67108826,
67108830,
67108833,
67108834,
67108837,
67108839,
67108843,
67108845,
67108846,
67108847,
67108849,
67108854,
67108855,
67108858,
67108859,
67108860,
67108861,
67108862,
134215774,
134217598,
134217666,
134217674,
134217678,
134217686,
134217690,
134217694,
134217697,
134217698,
134217699,
134217703,
134217709,
134217710,
134217711,
134217713,
134217718,
134217719,
134217722,
134217724,
134217725,
134217726,
268431360,
268435394,
268435398,
268435406,
268435418,
268435422,
268435426,
268435438,
268435441,
268435443,
268435445,
268435447,
268435450,
268435451,
268435452,
268435453,
268435454,
536869935,
536870882,
536870886,
536870890,
536870893,
536870894,
536870902,
536870906,
536870907,
536870908,
536870909,
536870910,
678152731,
954437177,
1054736383,
1065418751,
1073709055,
1073739870,
1073741786,
1073741814,
1073741818,
1073741821,
1073741822,
1332920885,
1749801491,
2147418110,
2147483631,
2147483642,
2147483644,
2147483646,
2147483647,
2863311531,
2969567231,
3123612579,
3264175145,
3303820997,
3435973837,
3707621341,
4008636143,
4042322161,
4262789119,
4289200127,
4294639615,
4294901759,
4294963199,
4294966319,
4294966531,
4294966727,
4294966815,
4294966875,
4294966979,
4294967107,
4294967109,
4294967179,
4294967191,
4294967262,
4294967263,
4294967265,
4294967267,
4294967269,
4294967271,
4294967275,
4294967277,
4294967279,
4294967281,
4294967283,
4294967285,
4294967287,
4294967291,
4294967293,
4294967294,
4294968273,
8589934559,
8589934567,
8589934575,
8589934587,
8589934590,
17179869134,
17179869174,
17179869182,
34359738341,
34359738349,
34359738355,
34359738366,
68719476682,
68719476707,
68719476710,
68719476727,
68719476733,
68719476734,
133143985199,
137436856320,
137438952991,
137438953285,
137438953355,
137438953454,
137438953470,
266287970398,
274844352511,
274877902847,
274877906919,
274877906927,
274877906933,
274877906939,
274877906941,
274877906942,
549688705022,
549755289600,
549755813783,
549755813838,
549755813854,
549755813855,
549755813866,
549755813869,
549755813878,
549755813882,
549755813886,
1099511627566,
1099511627710,
1099511627738,
1099511627759,
1099511627761,
1099511627774,
1425929142271,
2199023255518,
2199023255522,
2199023255543,
2199023255550,
4363955208191,
4398046510080,
4398046511079,
4398046511086,
4398046511095,
4398046511099,
4398046511102,
8727910416382,
8791798053935,
8796090925055,
8796093021443,
8796093022019,
8796093022158,
8796093022179,
8796093022183,
8796093022189,
8796093022190,
8796093022193,
8796093022198,
8796093022205,
8796093022206,
17583596107870,
17592181850110,
17592186042886,
17592186044038,
17592186044358,
17592186044366,
17592186044378,
17592186044399,
17592186044410,
17592186044411,
17592186044413,
17592186044414,
35184372088715,
35184372088768,
35184372088798,
35184372088822,
35184372088826,
35184372088829,
35184372088830,
70368735789055,
70368744177430,
70368744177637,
70368744177647,
70368744177651,
70368744177655,
70368744177658,
70368744177659,
70368744177660,
70368744177661,
70368744177662,
140737471578110,
140737479966719,
140737488354759,
140737488354847,
140737488355141,
140737488355274,
140737488355294,
140737488355301,
140737488355302,
140737488355303,
140737488355310,
140737488355313,
140737488355318,
140737488355319,
140737488355326,
194613558116351,
281453501874175,
281470681743359,
281474959933438,
281474976645119,
281474976709518,
281474976709694,
281474976710235,
281474976710282,
281474976710339,
281474976710469,
281474976710551,
281474976710602,
281474976710606,
281474976710625,
281474976710626,
281474976710631,
281474976710637,
281474976710638,
281474976710639,
281474976710645,
281474976710647,
281474976710653,
281474976710654,
389227116232702,
562907003748350,
562949953290238,
562949953420470,
562949953420678,
562949953420938,
562949953421102,
562949953421250,
562949953421262,
562949953421274,
562949953421278,
562949953421279,
562949953421290,
562949953421291,
562949953421293,
562949953421294,
562949953421295,
562949953421297,
562949953421303,
562949953421306,
562949953421308,
562949953421310,
1125899873288191,
1125899906842558,
1125899906842582,
1125899906842586,
1125899906842590,
1125899906842593,
1125899906842594,
1125899906842606,
1125899906842607,
1125899906842619,
1125899906842621,
1125899906842622,
1460151441686527,
2211942517178367,
2234929182146559,
2248776156708863,
2251799813160960,
2251799813684483,
2251799813685186,
2251799813685210,
2251799813685214,
2251799813685217,
2251799813685229,
2251799813685231,
2251799813685238,
2251799813685239,
2251799813685242,
2251799813685245,
2251799813685246,
2920302883373054,
4423885034356734,
4469858364293118,
4497552313417726,
4503595332402223,
4503599627368966,
4503599627369927,
4503599627370015,
4503599627370307,
4503599627370309,
4503599627370434,
4503599627370458,
4503599627370462,
4503599627370475,
4503599627370478,
4503599627370479,
4503599627370490,
4503599627370491,
4503599627370494,
9007190664804446,
9007199187632127,
9007199254739854,
9007199254740030,
9007199254740614,
9007199254740618,
9007199254740950,
9007199254740958,
9007199254740963,
9007199254740967,
9007199254740977,
9007199254740982,
9007199254740988,
9007199254740990,
18014398509481926,
18014398509481934,
18014398509481954,
18014398509481975,
18014398509481981,
18014398509481982,
36028797018963547,
36028797018963651,
36028797018963781,
36028797018963863,
36028797018963937,
36028797018963943,
36028797018963947,
36028797018963949,
36028797018963950,
36028797018963951,
36028797018963962,
36028797018963964,
36028797018963966,
72056494526300160,
72057594037927094,
72057594037927302,
72057594037927562,
72057594037927726,
72057594037927819,
72057594037927874,
72057594037927886,
72057594037927894,
72057594037927898,
72057594037927902,
72057594037927915,
72057594037927919,
72057594037927931,
72057594037927933,
72057594037927934,
144115188075855638,
144115188075855830,
144115188075855838,
144115188075855853,
144115188075855857,
144115188075855862,
144115188075855863,
144115188075855866,
144115188075855867,
144115188075855868,
144115188075855869,
144115188075855870,
288230376151711706,
288230376151711713,
288230376151711714,
288230376151711717,
288230376151711726,
288230376151711727,
288230376151711734,
288230376151711738,
288230376151711740,
288230376151711741,
288230376151711742,
576460752303423426,
576460752303423434,
576460752303423454,
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])))
def log2_up(i):
return int(math.ceil(math.log(i, 2)))
def word(i, width=None):
assert(i >= 0)
if width is None:
if i == 0: return word(i, width=1)
return word(i, width=2**log2_up(log2_up(i + 1)))
return 'WO~' + '~'.join(bin(i)[2:].rjust(width, '0'))
word_formats = tuple(sorted([(n, hex(n), bin(n), word(n)) for n in nums]))
def header():
return (r"""Require Import Coq.ZArith.ZArith.
Require Export Crypto.Compilers.Syntax.
Require Import Crypto.Compilers.Z.Syntax.
Require Export bbv.WordScope.
Require Export Crypto.Util.Notations.
Notation Const x := (Op (OpConst x) TT).
(""" + r"""* python:
<<
""" +
open(__file__).read() +
r""">>
*""" + r""")""")
def hex_nots():
return ('\n'.join('''Notation "'%s'" (* %d (%s) *)\n := (Const %s%%Z).\nNotation "'%s'" (* %d (%s) *)\n := (Const %s).''' % (h, d, h, d, h, d, h, w)
for d, h, b, w in word_formats))
def bin_nots():
return ('\n'.join('''Notation "'%s'" (* %d (%s) *)\n := (Const %s).''' % (b, d, h, w)
for d, h, b, w in word_formats))
with open('HexNotationConstants.v', 'w') as f:
f.write(header() + '\n' + hex_nots() + '\n')
with open('BinaryNotationConstants.v', 'w') as f:
f.write(header() + '\n' + bin_nots() + '\n')
>>
*)
Notation "'0x0'" (* 0 (0x0) *)
:= (Const 0%Z).
Notation "'0x0'" (* 0 (0x0) *)
:= (Const WO~0).
Notation "'0x1'" (* 1 (0x1) *)
:= (Const 1%Z).
Notation "'0x1'" (* 1 (0x1) *)
:= (Const WO~1).
Notation "'0x2'" (* 2 (0x2) *)
:= (Const 2%Z).
Notation "'0x2'" (* 2 (0x2) *)
:= (Const WO~1~0).
Notation "'0x3'" (* 3 (0x3) *)
:= (Const 3%Z).
Notation "'0x3'" (* 3 (0x3) *)
:= (Const WO~1~1).
Notation "'0x4'" (* 4 (0x4) *)
:= (Const 4%Z).
Notation "'0x4'" (* 4 (0x4) *)
:= (Const WO~0~1~0~0).
Notation "'0x5'" (* 5 (0x5) *)
:= (Const 5%Z).
Notation "'0x5'" (* 5 (0x5) *)
:= (Const WO~0~1~0~1).
Notation "'0x6'" (* 6 (0x6) *)
:= (Const 6%Z).
Notation "'0x6'" (* 6 (0x6) *)
:= (Const WO~0~1~1~0).
Notation "'0x7'" (* 7 (0x7) *)
:= (Const 7%Z).
Notation "'0x7'" (* 7 (0x7) *)
:= (Const WO~0~1~1~1).
Notation "'0x8'" (* 8 (0x8) *)
:= (Const 8%Z).
Notation "'0x8'" (* 8 (0x8) *)
:= (Const WO~1~0~0~0).
Notation "'0x9'" (* 9 (0x9) *)
:= (Const 9%Z).
Notation "'0x9'" (* 9 (0x9) *)
:= (Const WO~1~0~0~1).
Notation "'0xa'" (* 10 (0xa) *)
:= (Const 10%Z).
Notation "'0xa'" (* 10 (0xa) *)
:= (Const WO~1~0~1~0).
Notation "'0xb'" (* 11 (0xb) *)
:= (Const 11%Z).
Notation "'0xb'" (* 11 (0xb) *)
:= (Const WO~1~0~1~1).
Notation "'0xc'" (* 12 (0xc) *)
:= (Const 12%Z).
Notation "'0xc'" (* 12 (0xc) *)
:= (Const WO~1~1~0~0).
Notation "'0xd'" (* 13 (0xd) *)
:= (Const 13%Z).
Notation "'0xd'" (* 13 (0xd) *)
:= (Const WO~1~1~0~1).
Notation "'0xe'" (* 14 (0xe) *)
:= (Const 14%Z).
Notation "'0xe'" (* 14 (0xe) *)
:= (Const WO~1~1~1~0).
Notation "'0xf'" (* 15 (0xf) *)
:= (Const 15%Z).
Notation "'0xf'" (* 15 (0xf) *)
:= (Const WO~1~1~1~1).
Notation "'0x10'" (* 16 (0x10) *)
:= (Const 16%Z).
Notation "'0x10'" (* 16 (0x10) *)
:= (Const WO~0~0~0~1~0~0~0~0).
Notation "'0x11'" (* 17 (0x11) *)
:= (Const 17%Z).
Notation "'0x11'" (* 17 (0x11) *)
:= (Const WO~0~0~0~1~0~0~0~1).
Notation "'0x12'" (* 18 (0x12) *)
:= (Const 18%Z).
Notation "'0x12'" (* 18 (0x12) *)
:= (Const WO~0~0~0~1~0~0~1~0).
Notation "'0x13'" (* 19 (0x13) *)
:= (Const 19%Z).
Notation "'0x13'" (* 19 (0x13) *)
:= (Const WO~0~0~0~1~0~0~1~1).
Notation "'0x14'" (* 20 (0x14) *)
:= (Const 20%Z).
Notation "'0x14'" (* 20 (0x14) *)
:= (Const WO~0~0~0~1~0~1~0~0).
Notation "'0x15'" (* 21 (0x15) *)
:= (Const 21%Z).
Notation "'0x15'" (* 21 (0x15) *)
:= (Const WO~0~0~0~1~0~1~0~1).
Notation "'0x16'" (* 22 (0x16) *)
:= (Const 22%Z).
Notation "'0x16'" (* 22 (0x16) *)
:= (Const WO~0~0~0~1~0~1~1~0).
Notation "'0x17'" (* 23 (0x17) *)
:= (Const 23%Z).
Notation "'0x17'" (* 23 (0x17) *)
:= (Const WO~0~0~0~1~0~1~1~1).
Notation "'0x18'" (* 24 (0x18) *)
:= (Const 24%Z).
Notation "'0x18'" (* 24 (0x18) *)
:= (Const WO~0~0~0~1~1~0~0~0).
Notation "'0x19'" (* 25 (0x19) *)
:= (Const 25%Z).
Notation "'0x19'" (* 25 (0x19) *)
:= (Const WO~0~0~0~1~1~0~0~1).
Notation "'0x1a'" (* 26 (0x1a) *)
:= (Const 26%Z).
Notation "'0x1a'" (* 26 (0x1a) *)
:= (Const WO~0~0~0~1~1~0~1~0).
Notation "'0x1b'" (* 27 (0x1b) *)
:= (Const 27%Z).
Notation "'0x1b'" (* 27 (0x1b) *)
:= (Const WO~0~0~0~1~1~0~1~1).
Notation "'0x1c'" (* 28 (0x1c) *)
:= (Const 28%Z).
Notation "'0x1c'" (* 28 (0x1c) *)
:= (Const WO~0~0~0~1~1~1~0~0).
Notation "'0x1d'" (* 29 (0x1d) *)
:= (Const 29%Z).
Notation "'0x1d'" (* 29 (0x1d) *)
:= (Const WO~0~0~0~1~1~1~0~1).
Notation "'0x1e'" (* 30 (0x1e) *)
:= (Const 30%Z).
Notation "'0x1e'" (* 30 (0x1e) *)
:= (Const WO~0~0~0~1~1~1~1~0).
Notation "'0x1f'" (* 31 (0x1f) *)
:= (Const 31%Z).
Notation "'0x1f'" (* 31 (0x1f) *)
:= (Const WO~0~0~0~1~1~1~1~1).
Notation "'0x20'" (* 32 (0x20) *)
:= (Const 32%Z).
Notation "'0x20'" (* 32 (0x20) *)
:= (Const WO~0~0~1~0~0~0~0~0).
Notation "'0x21'" (* 33 (0x21) *)
:= (Const 33%Z).
Notation "'0x21'" (* 33 (0x21) *)
:= (Const WO~0~0~1~0~0~0~0~1).
Notation "'0x22'" (* 34 (0x22) *)
:= (Const 34%Z).
Notation "'0x22'" (* 34 (0x22) *)
:= (Const WO~0~0~1~0~0~0~1~0).
Notation "'0x23'" (* 35 (0x23) *)
:= (Const 35%Z).
Notation "'0x23'" (* 35 (0x23) *)
:= (Const WO~0~0~1~0~0~0~1~1).
Notation "'0x24'" (* 36 (0x24) *)
:= (Const 36%Z).
Notation "'0x24'" (* 36 (0x24) *)
:= (Const WO~0~0~1~0~0~1~0~0).
Notation "'0x25'" (* 37 (0x25) *)
:= (Const 37%Z).
Notation "'0x25'" (* 37 (0x25) *)
:= (Const WO~0~0~1~0~0~1~0~1).
Notation "'0x26'" (* 38 (0x26) *)
:= (Const 38%Z).
Notation "'0x26'" (* 38 (0x26) *)
:= (Const WO~0~0~1~0~0~1~1~0).
Notation "'0x27'" (* 39 (0x27) *)
:= (Const 39%Z).
Notation "'0x27'" (* 39 (0x27) *)
:= (Const WO~0~0~1~0~0~1~1~1).
Notation "'0x28'" (* 40 (0x28) *)
:= (Const 40%Z).
Notation "'0x28'" (* 40 (0x28) *)
:= (Const WO~0~0~1~0~1~0~0~0).
Notation "'0x29'" (* 41 (0x29) *)
:= (Const 41%Z).
Notation "'0x29'" (* 41 (0x29) *)
:= (Const WO~0~0~1~0~1~0~0~1).
Notation "'0x2a'" (* 42 (0x2a) *)
:= (Const 42%Z).
Notation "'0x2a'" (* 42 (0x2a) *)
:= (Const WO~0~0~1~0~1~0~1~0).
Notation "'0x2b'" (* 43 (0x2b) *)
:= (Const 43%Z).
Notation "'0x2b'" (* 43 (0x2b) *)
:= (Const WO~0~0~1~0~1~0~1~1).
Notation "'0x2c'" (* 44 (0x2c) *)
:= (Const 44%Z).
Notation "'0x2c'" (* 44 (0x2c) *)
:= (Const WO~0~0~1~0~1~1~0~0).
Notation "'0x2d'" (* 45 (0x2d) *)
:= (Const 45%Z).
Notation "'0x2d'" (* 45 (0x2d) *)
:= (Const WO~0~0~1~0~1~1~0~1).
Notation "'0x2e'" (* 46 (0x2e) *)
:= (Const 46%Z).
Notation "'0x2e'" (* 46 (0x2e) *)
:= (Const WO~0~0~1~0~1~1~1~0).
Notation "'0x2f'" (* 47 (0x2f) *)
:= (Const 47%Z).
Notation "'0x2f'" (* 47 (0x2f) *)
:= (Const WO~0~0~1~0~1~1~1~1).
Notation "'0x30'" (* 48 (0x30) *)
:= (Const 48%Z).
Notation "'0x30'" (* 48 (0x30) *)
:= (Const WO~0~0~1~1~0~0~0~0).
Notation "'0x31'" (* 49 (0x31) *)
:= (Const 49%Z).
Notation "'0x31'" (* 49 (0x31) *)
:= (Const WO~0~0~1~1~0~0~0~1).
Notation "'0x32'" (* 50 (0x32) *)
:= (Const 50%Z).
Notation "'0x32'" (* 50 (0x32) *)
:= (Const WO~0~0~1~1~0~0~1~0).
Notation "'0x33'" (* 51 (0x33) *)
:= (Const 51%Z).
Notation "'0x33'" (* 51 (0x33) *)
:= (Const WO~0~0~1~1~0~0~1~1).
Notation "'0x34'" (* 52 (0x34) *)
:= (Const 52%Z).
Notation "'0x34'" (* 52 (0x34) *)
:= (Const WO~0~0~1~1~0~1~0~0).
Notation "'0x35'" (* 53 (0x35) *)
:= (Const 53%Z).
Notation "'0x35'" (* 53 (0x35) *)
:= (Const WO~0~0~1~1~0~1~0~1).
Notation "'0x36'" (* 54 (0x36) *)
:= (Const 54%Z).
Notation "'0x36'" (* 54 (0x36) *)
:= (Const WO~0~0~1~1~0~1~1~0).
Notation "'0x37'" (* 55 (0x37) *)
:= (Const 55%Z).
Notation "'0x37'" (* 55 (0x37) *)
:= (Const WO~0~0~1~1~0~1~1~1).
Notation "'0x38'" (* 56 (0x38) *)
:= (Const 56%Z).
Notation "'0x38'" (* 56 (0x38) *)
:= (Const WO~0~0~1~1~1~0~0~0).
Notation "'0x39'" (* 57 (0x39) *)
:= (Const 57%Z).
Notation "'0x39'" (* 57 (0x39) *)
:= (Const WO~0~0~1~1~1~0~0~1).
Notation "'0x3a'" (* 58 (0x3a) *)
:= (Const 58%Z).
Notation "'0x3a'" (* 58 (0x3a) *)
:= (Const WO~0~0~1~1~1~0~1~0).
Notation "'0x3b'" (* 59 (0x3b) *)
:= (Const 59%Z).
Notation "'0x3b'" (* 59 (0x3b) *)
:= (Const WO~0~0~1~1~1~0~1~1).
Notation "'0x3c'" (* 60 (0x3c) *)