#!/usr/bin/env python
import sys
+import string
+from collections import namedtuple
-class Output(object):
- def __init__(self, bignum_int_bits):
- self.bignum_int_bits = bignum_int_bits
- self.text = ""
- self.vars = []
- def stmt(self, statement):
- self.text += " %s;\n" % statement
- def register_var(self, var):
- self.vars.append(var)
- def finalise(self):
- for var in self.vars:
- assert var.maxval == 0, "Variable not clear: %s" % var.name
- return self.text
-
-class Variable(object):
- def __init__(self, out, name):
- self.out = out
- self.maxval = 0
- self.name = name
- self.placeval = None
- self.out.stmt("BignumDblInt %s" % (self.name))
- self.out.register_var(self)
- def clear(self, placeval):
- self.maxval = 0
- self.placeval = placeval
- self.out.stmt("%s = 0" % (self.name))
- def set_word(self, name, limit=None):
- if limit is not None:
- self.maxval = limit-1
- else:
- self.maxval = (1 << self.out.bignum_int_bits) - 1
- assert self.maxval < (1 << 2*self.out.bignum_int_bits)
- self.out.stmt("%s = %s" % (self.name, name))
- def add_word(self, name, limit=None):
- if limit is not None:
- self.maxval += limit-1
- else:
- self.maxval += (1 << self.out.bignum_int_bits) - 1
- assert self.maxval < (1 << 2*self.out.bignum_int_bits)
- self.out.stmt("%s += %s" % (self.name, name))
- def add_input_word(self, fmt, wordpos, limit=None):
- assert self.placeval == wordpos * self.out.bignum_int_bits
- self.add_word(fmt % wordpos, limit)
- def set_to_product(self, a, b, placeval):
- self.maxval = ((1 << self.out.bignum_int_bits) - 1) ** 2
- assert self.maxval < (1 << 2*self.out.bignum_int_bits)
- self.out.stmt("%s = (BignumDblInt)(%s) * (%s)" % (self.name, a, b))
- self.placeval = placeval
- def add_bottom_half(self, srcvar):
- self.add_word("%s & BIGNUM_INT_MASK" % (srcvar.name))
- def add_top_half(self, srcvar):
- self.add_word("%s >> %d" % (srcvar.name, self.out.bignum_int_bits))
- def unload_into(self, topvar, botvar):
- assert botvar.placeval == self.placeval
- botvar.add_bottom_half(self)
- assert topvar.placeval == self.placeval + self.out.bignum_int_bits
- topvar.add_top_half(self)
- self.maxval = 0
- def output_word(self, bitpos, bits, destfmt, destwordpos):
- assert bitpos == 0
- assert self.placeval == destwordpos * self.out.bignum_int_bits
- dest = destfmt % destwordpos
- if bits == self.out.bignum_int_bits:
- self.out.stmt("%s = %s" % (dest, self.name))
- else:
- self.out.stmt("%s = %s & (((BignumInt)1 << %d)-1)" %
- (dest, self.name, bits))
- def transfer_to_next_acc(self, bitpos, bits, pow5, destvar):
- destbitpos = self.placeval + bitpos - 130 * pow5 - destvar.placeval
- #print "transfer", "*%d" % 5**pow5, self.name, self.placeval, bitpos, destvar.name, destvar.placeval, destbitpos, bits
- assert 0 <= bitpos < bitpos+bits <= self.out.bignum_int_bits
- assert 0 <= destbitpos < destbitpos+bits <= self.out.bignum_int_bits
- expr = self.name
- if bitpos > 0:
- expr = "(%s >> %d)" % (expr, bitpos)
- expr = "(%s & (((BignumInt)1 << %d)-1))" % (expr, bits)
- self.out.stmt("%s += %s * ((BignumDblInt)%d << %d)" %
- (destvar.name, expr, 5**pow5, destbitpos))
- destvar.maxval += (((1 << bits)-1) << destbitpos) * (5**pow5)
- def shift_down_from(self, top):
- if top is not None:
- self.out.stmt("%s = %s + (%s >> %d)" %
- (self.name, top.name, self.name,
- self.out.bignum_int_bits))
- topmaxval = top.maxval
- else:
- self.out.stmt("%s >>= %d" % (self.name, self.out.bignum_int_bits))
- topmaxval = 0
- self.maxval = topmaxval + self.maxval >> self.out.bignum_int_bits
- assert self.maxval < (1 << 2*self.out.bignum_int_bits)
- if top is not None:
- assert self.placeval + self.out.bignum_int_bits == top.placeval
- top.clear(top.placeval + self.out.bignum_int_bits)
- self.placeval += self.out.bignum_int_bits
-
-def gen_add(bignum_int_bits):
- out = Output(bignum_int_bits)
-
- inbits = 130
- inwords = (inbits + bignum_int_bits - 1) / bignum_int_bits
+class Multiprecision(object):
+ def __init__(self, target, minval, maxval, words):
+ self.target = target
+ self.minval = minval
+ self.maxval = maxval
+ self.words = words
+ assert 0 <= self.minval
+ assert self.minval <= self.maxval
+ assert self.target.nwords(self.maxval) == len(words)
+ def getword(self, n):
+ return self.words[n] if n < len(self.words) else "0"
+
+ def __add__(self, rhs):
+ newmin = self.minval + rhs.minval
+ newmax = self.maxval + rhs.maxval
+ nwords = self.target.nwords(newmax)
+ words = []
+
+ addfn = self.target.add
+ for i in range(nwords):
+ words.append(addfn(self.getword(i), rhs.getword(i)))
+ addfn = self.target.adc
+
+ return Multiprecision(self.target, newmin, newmax, words)
+
+ def __mul__(self, rhs):
+ newmin = self.minval * rhs.minval
+ newmax = self.maxval * rhs.maxval
+ nwords = self.target.nwords(newmax)
+ words = []
+
+ # There are basically two strategies we could take for
+ # multiplying two multiprecision integers. One is to enumerate
+ # the space of pairs of word indices in lexicographic order,
+ # essentially computing a*b[i] for each i and adding them
+ # together; the other is to enumerate in diagonal order,
+ # computing everything together that belongs at a particular
+ # output word index.
+ #
+ # For the moment, I've gone for the former.
+
+ sprev = []
+ for i, sword in enumerate(self.words):
+ rprev = None
+ sthis = sprev[:i]
+ for j, rword in enumerate(rhs.words):
+ prevwords = []
+ if i+j < len(sprev):
+ prevwords.append(sprev[i+j])
+ if rprev is not None:
+ prevwords.append(rprev)
+ vhi, vlo = self.target.muladd(sword, rword, *prevwords)
+ sthis.append(vlo)
+ rprev = vhi
+ sthis.append(rprev)
+ sprev = sthis
+
+ # Remove unneeded words from the top of the output, if we can
+ # prove by range analysis that they'll always be zero.
+ sprev = sprev[:self.target.nwords(newmax)]
+
+ return Multiprecision(self.target, newmin, newmax, sprev)
+
+ def extract_bits(self, start, bits=None):
+ if bits is None:
+ bits = (self.maxval >> start).bit_length()
+
+ # Overly thorough range analysis: if min and max have the same
+ # *quotient* by 2^bits, then the result of reducing anything
+ # in the range [min,max] mod 2^bits has to fall within the
+ # obvious range. But if they have different quotients, then
+ # you can wrap round the modulus and so any value mod 2^bits
+ # is possible.
+ newmin = self.minval >> start
+ newmax = self.maxval >> start
+ if (newmin >> bits) != (newmax >> bits):
+ newmin = 0
+ newmax = (1 << bits) - 1
+
+ nwords = self.target.nwords(newmax)
+ words = []
+ for i in range(nwords):
+ srcpos = i * self.target.bits + start
+ maxbits = min(self.target.bits, start + bits - srcpos)
+ wordindex = srcpos / self.target.bits
+ if srcpos % self.target.bits == 0:
+ word = self.getword(srcpos / self.target.bits)
+ elif (wordindex+1 >= len(self.words) or
+ srcpos % self.target.bits + maxbits < self.target.bits):
+ word = self.target.new_value(
+ "(%%s) >> %d" % (srcpos % self.target.bits),
+ self.getword(srcpos / self.target.bits))
+ else:
+ word = self.target.new_value(
+ "((%%s) >> %d) | ((%%s) << %d)" % (
+ srcpos % self.target.bits,
+ self.target.bits - (srcpos % self.target.bits)),
+ self.getword(srcpos / self.target.bits),
+ self.getword(srcpos / self.target.bits + 1))
+ if maxbits < self.target.bits and maxbits < bits:
+ word = self.target.new_value(
+ "(%%s) & ((((BignumInt)1) << %d)-1)" % maxbits,
+ word)
+ words.append(word)
+
+ return Multiprecision(self.target, newmin, newmax, words)
+
+# Each Statement has a list of variables it reads, and a list of ones
+# it writes. 'forms' is a list of multiple actual C statements it
+# could be generated as, depending on which of its output variables is
+# actually used (e.g. no point calling BignumADC if the generated
+# carry in a particular case is unused, or BignumMUL if nobody needs
+# the top half). It is indexed by a bitmap whose bits correspond to
+# the entries in wvars, with wvars[0] the MSB and wvars[-1] the LSB.
+Statement = namedtuple("Statement", "rvars wvars forms")
+
+class CodegenTarget(object):
+ def __init__(self, bits):
+ self.bits = bits
+ self.valindex = 0
+ self.stmts = []
+ self.generators = {}
+ self.bv_words = (130 + self.bits - 1) / self.bits
+ self.carry_index = 0
+
+ def nwords(self, maxval):
+ return (maxval.bit_length() + self.bits - 1) / self.bits
+
+ def stmt(self, stmt, needed=False):
+ index = len(self.stmts)
+ self.stmts.append([needed, stmt])
+ for val in stmt.wvars:
+ self.generators[val] = index
+
+ def new_value(self, formatstr=None, *deps):
+ name = "v%d" % self.valindex
+ self.valindex += 1
+ if formatstr is not None:
+ self.stmt(Statement(
+ rvars=deps, wvars=[name],
+ forms=[None, name + " = " + formatstr % deps]))
+ return name
+
+ def bigval_input(self, name, bits):
+ words = (bits + self.bits - 1) / self.bits
+ # Expect not to require an entire extra word
+ assert words == self.bv_words
+
+ return Multiprecision(self, 0, (1<<bits)-1, [
+ self.new_value("%s->w[%d]" % (name, i)) for i in range(words)])
+
+ def const(self, value):
+ # We only support constants small enough to both fit in a
+ # BignumInt (of any size supported) _and_ be expressible in C
+ # with no weird integer literal syntax like a trailing LL.
+ #
+ # Supporting larger constants would be possible - you could
+ # break 'value' up into word-sized pieces on the Python side,
+ # and generate a legal C expression for each piece by
+ # splitting it further into pieces within the
+ # standards-guaranteed 'unsigned long' limit of 32 bits and
+ # then casting those to BignumInt before combining them with
+ # shifts. But it would be a lot of effort, and since the
+ # application for this code doesn't even need it, there's no
+ # point in bothering.
+ assert value < 2**16
+ return Multiprecision(self, value, value, ["%d" % value])
+
+ def current_carry(self):
+ return "carry%d" % self.carry_index
+
+ def add(self, a1, a2):
+ ret = self.new_value()
+ adcform = "BignumADC(%s, carry, %s, %s, 0)" % (ret, a1, a2)
+ plainform = "%s = %s + %s" % (ret, a1, a2)
+ self.carry_index += 1
+ carryout = self.current_carry()
+ self.stmt(Statement(
+ rvars=[a1,a2], wvars=[ret,carryout],
+ forms=[None, adcform, plainform, adcform]))
+ return ret
+
+ def adc(self, a1, a2):
+ ret = self.new_value()
+ adcform = "BignumADC(%s, carry, %s, %s, carry)" % (ret, a1, a2)
+ plainform = "%s = %s + %s + carry" % (ret, a1, a2)
+ carryin = self.current_carry()
+ self.carry_index += 1
+ carryout = self.current_carry()
+ self.stmt(Statement(
+ rvars=[a1,a2,carryin], wvars=[ret,carryout],
+ forms=[None, adcform, plainform, adcform]))
+ return ret
+
+ def muladd(self, m1, m2, *addends):
+ rlo = self.new_value()
+ rhi = self.new_value()
+ wideform = "BignumMUL%s(%s)" % (
+ { 0:"", 1:"ADD", 2:"ADD2" }[len(addends)],
+ ", ".join([rhi, rlo, m1, m2] + list(addends)))
+ narrowform = " + ".join(["%s = %s * %s" % (rlo, m1, m2)] +
+ list(addends))
+ self.stmt(Statement(
+ rvars=[m1,m2]+list(addends), wvars=[rhi,rlo],
+ forms=[None, narrowform, wideform, wideform]))
+ return rhi, rlo
+
+ def write_bigval(self, name, val):
+ for i in range(self.bv_words):
+ word = val.getword(i)
+ self.stmt(Statement(
+ rvars=[word], wvars=[],
+ forms=["%s->w[%d] = %s" % (name, i, word)]),
+ needed=True)
+
+ def compute_needed(self):
+ used_vars = set()
+
+ self.queue = [stmt for (needed,stmt) in self.stmts if needed]
+ while len(self.queue) > 0:
+ stmt = self.queue.pop(0)
+ deps = []
+ for var in stmt.rvars:
+ if var[0] in string.digits:
+ continue # constant
+ deps.append(self.generators[var])
+ used_vars.add(var)
+ for index in deps:
+ if not self.stmts[index][0]:
+ self.stmts[index][0] = True
+ self.queue.append(self.stmts[index][1])
+
+ forms = []
+ for i, (needed, stmt) in enumerate(self.stmts):
+ if needed:
+ formindex = 0
+ for (j, var) in enumerate(stmt.wvars):
+ formindex *= 2
+ if var in used_vars:
+ formindex += 1
+ forms.append(stmt.forms[formindex])
+
+ # Now we must check whether this form of the statement
+ # also writes some variables we _don't_ actually need
+ # (e.g. if you only wanted the top half from a mul, or
+ # only the carry from an adc, you'd be forced to
+ # generate the other output too). Easiest way to do
+ # this is to look for an identical statement form
+ # later in the array.
+ maxindex = max(i for i in range(len(stmt.forms))
+ if stmt.forms[i] == stmt.forms[formindex])
+ extra_vars = maxindex & ~formindex
+ bitpos = 0
+ while extra_vars != 0:
+ if extra_vars & (1 << bitpos):
+ extra_vars &= ~(1 << bitpos)
+ var = stmt.wvars[-1-bitpos]
+ used_vars.add(var)
+ # Also, write out a cast-to-void for each
+ # subsequently unused value, to prevent gcc
+ # warnings when the output code is compiled.
+ forms.append("(void)" + var)
+ bitpos += 1
+
+ used_carry = any(v.startswith("carry") for v in used_vars)
+ used_vars = [v for v in used_vars if v.startswith("v")]
+ used_vars.sort(key=lambda v: int(v[1:]))
+
+ return used_carry, used_vars, forms
+
+ def text(self):
+ used_carry, values, forms = self.compute_needed()
+
+ ret = ""
+ while len(values) > 0:
+ prefix, sep, suffix = " BignumInt ", ", ", ";"
+ currline = values.pop(0)
+ while (len(values) > 0 and
+ len(prefix+currline+sep+values[0]+suffix) < 79):
+ currline += sep + values.pop(0)
+ ret += prefix + currline + suffix + "\n"
+ if used_carry:
+ ret += " BignumCarry carry;\n"
+ if ret != "":
+ ret += "\n"
+ for stmtform in forms:
+ ret += " %s;\n" % stmtform
+ return ret
+
+def gen_add(target):
# This is an addition _without_ reduction mod p, so that it can be
# used both during accumulation of the polynomial and for adding
# on the encrypted nonce at the end (which is mod 2^128, not mod
# Because one of the inputs will have come from our
# not-completely-reducing multiplication function, we expect up to
# 3 extra bits of input.
- acclo = Variable(out, "acclo")
-
- acclo.clear(0)
-
- for wordpos in range(inwords):
- limit = min(1 << bignum_int_bits, 1 << (130 - wordpos*bignum_int_bits))
- acclo.add_input_word("a->w[%d]", wordpos, limit)
- acclo.add_input_word("b->w[%d]", wordpos, limit)
- acclo.output_word(0, bignum_int_bits, "r->w[%d]", wordpos)
- acclo.shift_down_from(None)
-
- return out.finalise()
-def gen_mul_1305(bignum_int_bits):
- out = Output(bignum_int_bits)
-
- inbits = 130
- inwords = (inbits + bignum_int_bits - 1) / bignum_int_bits
+ a = target.bigval_input("a", 133)
+ b = target.bigval_input("b", 133)
+ ret = a + b
+ target.write_bigval("r", ret)
+ return """\
+static void bigval_add(bigval *r, const bigval *a, const bigval *b)
+{
+%s}
+\n""" % target.text()
+def gen_mul(target):
# The inputs are not 100% reduced mod p. Specifically, we can get
# a full 130-bit number from the pow5==0 pass, and then a 130-bit
# number times 5 from the pow5==1 pass, plus a possible carry. The
# total of that can be easily bounded above by 2^130 * 8, so we
# need to assume we're multiplying two 133-bit numbers.
- outbits = (inbits + 3) * 2
- outwords = (outbits + bignum_int_bits - 1) / bignum_int_bits + 1
-
- tmp = Variable(out, "tmp")
- acclo = Variable(out, "acclo")
- acchi = Variable(out, "acchi")
- acc2lo = Variable(out, "acc2lo")
-
- pow5, bits_at_pow5 = 0, inbits
-
- acclo.clear(0)
- acchi.clear(bignum_int_bits)
- bits_needed_in_acc2 = bignum_int_bits
-
- for outwordpos in range(outwords):
- for a in range(inwords):
- b = outwordpos - a
- if 0 <= b < inwords:
- tmp.set_to_product("a->w[%d]" % a, "b->w[%d]" % b,
- outwordpos * bignum_int_bits)
- tmp.unload_into(acchi, acclo)
-
- bits_in_word = bignum_int_bits
- bitpos = 0
- #print "begin output"
- while bits_in_word > 0:
- chunk = min(bits_in_word, bits_at_pow5)
- if pow5 > 0:
- chunk = min(chunk, bits_needed_in_acc2)
- if pow5 == 0:
- acclo.output_word(bitpos, chunk, "r->w[%d]", outwordpos)
- else:
- acclo.transfer_to_next_acc(bitpos, chunk, pow5, acc2lo)
- bits_needed_in_acc2 -= chunk
- if bits_needed_in_acc2 == 0:
- assert acc2lo.placeval % bignum_int_bits == 0
- other_outwordpos = acc2lo.placeval / bignum_int_bits
- acc2lo.add_input_word("r->w[%d]", other_outwordpos)
- acc2lo.output_word(bitpos, bignum_int_bits, "r->w[%d]",
- other_outwordpos)
- acc2lo.shift_down_from(None)
- bits_needed_in_acc2 = bignum_int_bits
- bits_in_word -= chunk
- bits_at_pow5 -= chunk
- bitpos += chunk
- if bits_at_pow5 == 0:
- if pow5 > 0:
- assert acc2lo.placeval % bignum_int_bits == 0
- other_outwordpos = acc2lo.placeval / bignum_int_bits
- acc2lo.add_input_word("r->w[%d]", other_outwordpos)
- acc2lo.output_word(0, bignum_int_bits, "r->w[%d]",
- other_outwordpos)
- pow5 += 1
- bits_at_pow5 = inbits
- acc2lo.clear(0)
- bits_needed_in_acc2 = bignum_int_bits
- acclo.shift_down_from(acchi)
-
- while acc2lo.maxval > 0:
- other_outwordpos = acc2lo.placeval / bignum_int_bits
- bitsleft = inbits - other_outwordpos * bignum_int_bits
- limit = 1<<bitsleft if bitsleft < bignum_int_bits else None
- acc2lo.add_input_word("r->w[%d]", other_outwordpos, limit=limit)
- acc2lo.output_word(0, bignum_int_bits, "r->w[%d]", other_outwordpos)
- acc2lo.shift_down_from(None)
-
- return out.finalise()
-
-def gen_final_reduce_1305(bignum_int_bits):
- out = Output(bignum_int_bits)
-
- inbits = 130
- inwords = (inbits + bignum_int_bits - 1) / bignum_int_bits
-
- # We take our input number n, and compute k = 5 + 5*(n >> 130).
+
+ a = target.bigval_input("a", 133)
+ b = target.bigval_input("b", 133)
+ ab = a * b
+ ab0 = ab.extract_bits(0, 130)
+ ab1 = ab.extract_bits(130, 130)
+ ab2 = ab.extract_bits(260)
+ ab1_5 = target.const(5) * ab1
+ ab2_25 = target.const(25) * ab2
+ ret = ab0 + ab1_5 + ab2_25
+ target.write_bigval("r", ret)
+ return """\
+static void bigval_mul_mod_p(bigval *r, const bigval *a, const bigval *b)
+{
+%s}
+\n""" % target.text()
+
+def gen_final_reduce(target):
+ # We take our input number n, and compute k = n + 5*(n >> 130).
# Then k >> 130 is precisely the multiple of p that needs to be
# subtracted from n to reduce it to strictly less than p.
- acclo = Variable(out, "acclo")
-
- acclo.clear(0)
- # Hopefully all the bits we're shifting down fit in the same word.
- assert 130 / bignum_int_bits == (130 + 3 - 1) / bignum_int_bits
- acclo.add_word("5 * ((n->w[%d] >> %d) + 1)" %
- (130 / bignum_int_bits, 130 % bignum_int_bits),
- limit = 5 * (7 + 1))
- for wordpos in range(inwords):
- acclo.add_input_word("n->w[%d]", wordpos)
- # Notionally, we could call acclo.output_word here to store
- # our adjusted value k. But we don't need to, because all we
- # actually want is the very top word of it.
- if wordpos == 130 / bignum_int_bits:
- break
- acclo.shift_down_from(None)
-
- # Now we can find the right multiple of p to subtract. We actually
- # subtract it by adding 5 times it, and then finally discarding
- # the top bits of the output.
-
- # Hopefully all the bits we're shifting down fit in the same word.
- assert 130 / bignum_int_bits == (130 + 3 - 1) / bignum_int_bits
- acclo.set_word("5 * (acclo >> %d)" % (130 % bignum_int_bits),
- limit = 5 * (7 + 1))
- acclo.placeval = 0
- for wordpos in range(inwords):
- acclo.add_input_word("n->w[%d]", wordpos)
- acclo.output_word(0, bignum_int_bits, "n->w[%d]", wordpos)
- acclo.shift_down_from(None)
-
- out.stmt("n->w[%d] &= (1 << %d) - 1" %
- (130 / bignum_int_bits, 130 % bignum_int_bits))
-
- # Here we don't call out.finalise(), because that will complain
- # that there are bits of output we never dealt with. This is true,
- # but all the bits in question are above 2^130, so they're bits
- # we're discarding anyway.
- return out.text # not out.finalise()
-
-ops = { "mul" : gen_mul_1305,
- "add" : gen_add,
- "final_reduce" : gen_final_reduce_1305 }
-
-args = sys.argv[1:]
-if len(args) != 2 or args[0] not in ops:
- sys.stderr.write("usage: make1305.py (%s) <bits>\n" % (" | ".join(sorted(ops))))
- sys.exit(1)
-
-sys.stdout.write(" /* ./contrib/make1305.py %s %s */\n" % tuple(args))
-s = ops[args[0]](int(args[1]))
-sys.stdout.write(s)
+ a = target.bigval_input("n", 133)
+ a1 = a.extract_bits(130, 130)
+ k = a + target.const(5) * a1
+ q = k.extract_bits(130)
+ adjusted = a + target.const(5) * q
+ ret = adjusted.extract_bits(0, 130)
+ target.write_bigval("n", ret)
+ return """\
+static void bigval_final_reduce(bigval *n)
+{
+%s}
+\n""" % target.text()
+
+pp_keyword = "#if"
+for bits in [16, 32, 64]:
+ sys.stdout.write("%s BIGNUM_INT_BITS == %d\n\n" % (pp_keyword, bits))
+ pp_keyword = "#elif"
+ sys.stdout.write(gen_add(CodegenTarget(bits)))
+ sys.stdout.write(gen_mul(CodegenTarget(bits)))
+ sys.stdout.write(gen_final_reduce(CodegenTarget(bits)))
+sys.stdout.write("""#else
+#error Add another bit count to contrib/make1305.py and rerun it
+#endif
+""")
projects / PuTTY.git / blobdiff