Bit bias in hash functions

MD5
-------------------
bit   0: 0.50071500
bit   1: 0.49974200
bit   2: 0.50015200
bit   3: 0.50050000
bit   4: 0.50026200
bit   5: 0.50019500
bit   6: 0.49985800
bit   7: 0.49950000
bit   8: 0.50062500
bit   9: 0.50058900
bit  10: 0.50014800
bit  11: 0.50072800
bit  12: 0.49934700
bit  13: 0.50010400
bit  14: 0.50089000
bit  15: 0.50012500
bit  16: 0.50055400
bit  17: 0.50046900
bit  18: 0.50022600
bit  19: 0.50003100
bit  20: 0.49888600
bit  21: 0.50003500
bit  22: 0.49898500
bit  23: 0.49891900
bit  24: 0.50063600
bit  25: 0.49981500
bit  26: 0.49960200
bit  27: 0.49986300
bit  28: 0.50051600
bit  29: 0.49996000
bit  30: 0.49980400
bit  31: 0.50007100
bit  32: 0.49976500
bit  33: 0.50014500
bit  34: 0.49967600
bit  35: 0.50034000
bit  36: 0.49997200
bit  37: 0.50049800
bit  38: 0.49929900
bit  39: 0.50032000
bit  40: 0.49983500
bit  41: 0.49990700
bit  42: 0.50033900
bit  43: 0.50091400
bit  44: 0.49939000
bit  45: 0.50037500
bit  46: 0.50013700
bit  47: 0.50077100
bit  48: 0.50001300
bit  49: 0.50115600
bit  50: 0.50042800
bit  51: 0.50033900
bit  52: 0.50018600
bit  53: 0.49984200
bit  54: 0.50065600
bit  55: 0.49985400
bit  56: 0.49938100
bit  57: 0.50053900
bit  58: 0.49980500
bit  59: 0.50044600
bit  60: 0.50048700
bit  61: 0.49959300
bit  62: 0.49971100
bit  63: 0.49947900
bit  64: 0.50061700
bit  65: 0.50083900
bit  66: 0.49952900
bit  67: 0.49949900
bit  68: 0.50060400
bit  69: 0.50050900
bit  70: 0.50050900
bit  71: 0.50029400
bit  72: 0.50017800
bit  73: 0.49977200
bit  74: 0.50050300
bit  75: 0.49951400
bit  76: 0.49933900
bit  77: 0.49963800
bit  78: 0.49918400
bit  79: 0.50054800
bit  80: 0.49999900
bit  81: 0.49999600
bit  82: 0.50034800
bit  83: 0.50010800
bit  84: 0.50000500
bit  85: 0.49978200
bit  86: 0.49999200
bit  87: 0.49944400
bit  88: 0.50063500
bit  89: 0.50107400
bit  90: 0.50008700
bit  91: 0.50065700
bit  92: 0.49990500
bit  93: 0.49988300
bit  94: 0.49920800
bit  95: 0.50003600
bit  96: 0.50060700
bit  97: 0.50087800
bit  98: 0.50053200
bit  99: 0.50067500
bit 100: 0.50060400
bit 101: 0.49939900
bit 102: 0.49960400
bit 103: 0.50051800
bit 104: 0.50034900
bit 105: 0.49993100
bit 106: 0.50030200
bit 107: 0.49951000
bit 108: 0.49999100
bit 109: 0.50052200
bit 110: 0.50081800
bit 111: 0.49981800
bit 112: 0.49950200
bit 113: 0.50053400
bit 114: 0.50024300
bit 115: 0.49987000
bit 116: 0.49951500
bit 117: 0.49964500
bit 118: 0.50027300
bit 119: 0.49913800
bit 120: 0.50011100
bit 121: 0.50007900
bit 122: 0.50051700
bit 123: 0.49911800
bit 124: 0.50052100
bit 125: 0.50003600
bit 126: 0.49940500
bit 127: 0.50019600

SHA-256
-------------------
bit   0: 0.49952500
bit   1: 0.50017100
bit   2: 0.49945700
bit   3: 0.50040100
bit   4: 0.49960200
bit   5: 0.49988500
bit   6: 0.50126600
bit   7: 0.50129700
bit   8: 0.50019600
bit   9: 0.49988700
bit  10: 0.49981100
bit  11: 0.50051800
bit  12: 0.50003100
bit  13: 0.49962000
bit  14: 0.50006700
bit  15: 0.50086700
bit  16: 0.49994500
bit  17: 0.50076100
bit  18: 0.50065600
bit  19: 0.50009600
bit  20: 0.49909900
bit  21: 0.49948500
bit  22: 0.50057400
bit  23: 0.49996600
bit  24: 0.50038500
bit  25: 0.50015900
bit  26: 0.50015200
bit  27: 0.49963600
bit  28: 0.50012100
bit  29: 0.49963400
bit  30: 0.49927900
bit  31: 0.49966100
bit  32: 0.50033000
bit  33: 0.50059500
bit  34: 0.50038000
bit  35: 0.50074900
bit  36: 0.50017900
bit  37: 0.49937000
bit  38: 0.49979700
bit  39: 0.50018600
bit  40: 0.49992500
bit  41: 0.49906700
bit  42: 0.50071900
bit  43: 0.49987300
bit  44: 0.49987500
bit  45: 0.50034700
bit  46: 0.49964200
bit  47: 0.49872900
bit  48: 0.49958600
bit  49: 0.50051000
bit  50: 0.50167700
bit  51: 0.49950900
bit  52: 0.50007600
bit  53: 0.50042700
bit  54: 0.49932200
bit  55: 0.50020000
bit  56: 0.50008800
bit  57: 0.49981300
bit  58: 0.49974000
bit  59: 0.50009800
bit  60: 0.50087100
bit  61: 0.50020500
bit  62: 0.49968300
bit  63: 0.49980500
bit  64: 0.50001700
bit  65: 0.50032800
bit  66: 0.50009000
bit  67: 0.50050700
bit  68: 0.49964300
bit  69: 0.49938200
bit  70: 0.49990200
bit  71: 0.50002300
bit  72: 0.50098600
bit  73: 0.49941400
bit  74: 0.49985600
bit  75: 0.50006500
bit  76: 0.49970000
bit  77: 0.50071000
bit  78: 0.49981700
bit  79: 0.50078200
bit  80: 0.49926800
bit  81: 0.50061500
bit  82: 0.50012900
bit  83: 0.50110600
bit  84: 0.50017700
bit  85: 0.50026400
bit  86: 0.50110600
bit  87: 0.49942500
bit  88: 0.49930100
bit  89: 0.49983600
bit  90: 0.49991200
bit  91: 0.50014700
bit  92: 0.50015400
bit  93: 0.49975400
bit  94: 0.49994000
bit  95: 0.50018900
bit  96: 0.50026000
bit  97: 0.49923600
bit  98: 0.49920900
bit  99: 0.49948500
bit 100: 0.50050100
bit 101: 0.49995700
bit 102: 0.50015600
bit 103: 0.49990500
bit 104: 0.50101800
bit 105: 0.50061500
bit 106: 0.50012500
bit 107: 0.50054000
bit 108: 0.49972100
bit 109: 0.49997300
bit 110: 0.50068700
bit 111: 0.49985100
bit 112: 0.50048200
bit 113: 0.50021700
bit 114: 0.50047800
bit 115: 0.50022200
bit 116: 0.50011300
bit 117: 0.49944700
bit 118: 0.50003700
bit 119: 0.50016500
bit 120: 0.50069100
bit 121: 0.49956500
bit 122: 0.49920900
bit 123: 0.49936100
bit 124: 0.50013700
bit 125: 0.50044700
bit 126: 0.49950800
bit 127: 0.49961100
bit 128: 0.50091600
bit 129: 0.50052600
bit 130: 0.50051700
bit 131: 0.50043600
bit 132: 0.49920400
bit 133: 0.49927500
bit 134: 0.50032600
bit 135: 0.50044200
bit 136: 0.50018300
bit 137: 0.50006600
bit 138: 0.50027200
bit 139: 0.50030000
bit 140: 0.49974300
bit 141: 0.49897000
bit 142: 0.50004500
bit 143: 0.49933900
bit 144: 0.50020900
bit 145: 0.49991000
bit 146: 0.49986400
bit 147: 0.49891600
bit 148: 0.50069700
bit 149: 0.50019800
bit 150: 0.49953500
bit 151: 0.49980400
bit 152: 0.49981800
bit 153: 0.49975900
bit 154: 0.49943300
bit 155: 0.49897100
bit 156: 0.50039200
bit 157: 0.49982300
bit 158: 0.49995200
bit 159: 0.50054000
bit 160: 0.50000700
bit 161: 0.49977400
bit 162: 0.49955400
bit 163: 0.49998300
bit 164: 0.50001900
bit 165: 0.49996500
bit 166: 0.50038100
bit 167: 0.50007500
bit 168: 0.49951800
bit 169: 0.49980400
bit 170: 0.50024500
bit 171: 0.49947400
bit 172: 0.50094800
bit 173: 0.49983000
bit 174: 0.49998600
bit 175: 0.49928100
bit 176: 0.50044300
bit 177: 0.49999200
bit 178: 0.49987600
bit 179: 0.50061500
bit 180: 0.49929600
bit 181: 0.49964000
bit 182: 0.49935600
bit 183: 0.49963400
bit 184: 0.49994600
bit 185: 0.49967000
bit 186: 0.49960800
bit 187: 0.49953600
bit 188: 0.50082300
bit 189: 0.50020700
bit 190: 0.49940500
bit 191: 0.50076900
bit 192: 0.49964100
bit 193: 0.50127600
bit 194: 0.49996700
bit 195: 0.49907300
bit 196: 0.50004500
bit 197: 0.50110200
bit 198: 0.49979300
bit 199: 0.49967200
bit 200: 0.49914300
bit 201: 0.50013000
bit 202: 0.49980200
bit 203: 0.49993000
bit 204: 0.49947400
bit 205: 0.49981600
bit 206: 0.50107900
bit 207: 0.49886700
bit 208: 0.49977300
bit 209: 0.50016900
bit 210: 0.49990800
bit 211: 0.49920300
bit 212: 0.50005900
bit 213: 0.50065700
bit 214: 0.49958500
bit 215: 0.49935200
bit 216: 0.49970500
bit 217: 0.50015400
bit 218: 0.49977900
bit 219: 0.50036400
bit 220: 0.50103500
bit 221: 0.49940400
bit 222: 0.49982000
bit 223: 0.49921100
bit 224: 0.49984500
bit 225: 0.49955700
bit 226: 0.50068200
bit 227: 0.49977000
bit 228: 0.49987600
bit 229: 0.50029800
bit 230: 0.49949900
bit 231: 0.50047800
bit 232: 0.50033800
bit 233: 0.50043400
bit 234: 0.49989200
bit 235: 0.49982900
bit 236: 0.50024100
bit 237: 0.50055800
bit 238: 0.50017600
bit 239: 0.49965600
bit 240: 0.49955900
bit 241: 0.50028000
bit 242: 0.49921400
bit 243: 0.49969300
bit 244: 0.49989500
bit 245: 0.50052100
bit 246: 0.50103000
bit 247: 0.49980700
bit 248: 0.49938200
bit 249: 0.49967500
bit 250: 0.49925300
bit 251: 0.50050500
bit 252: 0.49978200
bit 253: 0.49947300
bit 254: 0.49939900
bit 255: 0.50032300