def cint_cint_division(a, b, k, f): """ Goldschmidt method implemented with SE aproximation: http://stackoverflow.com/questions/2661541/picking-good-first-estimates-for-goldschmidt-division """ # theta can be replaced with something smaller # for safety we assume that is the same theta from previous GS method theta = int(ceil(log(k / 3.5) / log(2))) two = cint(2) * two_power(f) sign_b = cint(1) - 2 * cint(b < 0) sign_a = cint(1) - 2 * cint(a < 0) absolute_b = b * sign_b absolute_a = a * sign_a w0 = approximate_reciprocal(absolute_b, k, f, theta) A = Array(theta, cint) B = Array(theta, cint) W = Array(theta, cint) A[0] = absolute_a B[0] = absolute_b W[0] = w0 for i in range(1, theta): A[i] = shift_two(A[i - 1] * W[i - 1], f) B[i] = shift_two(B[i - 1] * W[i - 1], f) W[i] = two - B[i] return (sign_a * sign_b) * A[theta - 1]
def cint_cint_division(a, b, k, f): """ Goldschmidt method implemented with SE aproximation: http://stackoverflow.com/questions/2661541/picking-good-first-estimates-for-goldschmidt-division """ # theta can be replaced with something smaller # for safety we assume that is the same theta from previous GS method theta = int(ceil(log(k/3.5) / log(2))) two = cint(2) * two_power(f) sign_b = cint(1) - 2 * cint(b < 0) sign_a = cint(1) - 2 * cint(a < 0) absolute_b = b * sign_b absolute_a = a * sign_a w0 = approximate_reciprocal(absolute_b, k, f, theta) A = Array(theta, cint) B = Array(theta, cint) W = Array(theta, cint) A[0] = absolute_a B[0] = absolute_b W[0] = w0 for i in range(1, theta): A[i] = shift_two(A[i - 1] * W[i - 1], f) B[i] = shift_two(B[i - 1] * W[i - 1], f) W[i] = two - B[i] return (sign_a * sign_b) * A[theta - 1]
def approximate_reciprocal(divisor, k, f, theta): """ returns aproximation of 1/divisor where type(divisor) = cint """ def twos_complement(x): bits = x.bit_decompose(k)[::-1] bit_array = Array(k, cint) bit_array.assign(bits) twos_result = MemValue(cint(0)) @for_range(k) def block(i): val = twos_result.read() val <<= 1 val += 1 - bit_array[i] twos_result.write(val) return twos_result.read() + 1 bit_array = Array(k, cint) bits = divisor.bit_decompose(k)[::-1] bit_array.assign(bits) cnt_leading_zeros = MemValue(regint(0)) flag = MemValue(regint(0)) cnt_leading_zeros = MemValue(regint(0)) normalized_divisor = MemValue(divisor) @for_range(k) def block(i): flag.write(flag.read() | bit_array[i] == 1) @if_(flag.read() == 0) def block(): cnt_leading_zeros.write(cnt_leading_zeros.read() + 1) normalized_divisor.write(normalized_divisor << 1) q = MemValue(two_power(k)) e = MemValue(twos_complement(normalized_divisor.read())) qr = q.read() er = e.read() for i in range(theta): qr = qr + shift_two(qr * er, k) er = shift_two(er * er, k) q = qr res = shift_two(q, (2 * k - 2 * f - cnt_leading_zeros)) return res
def approximate_reciprocal(divisor, k, f, theta): """ returns aproximation of 1/divisor where type(divisor) = cint """ def twos_complement(x): bits = x.bit_decompose(k)[::-1] bit_array = Array(k, cint) bit_array.assign(bits) twos_result = MemValue(cint(0)) @for_range(k) def block(i): val = twos_result.read() val <<= 1 val += 1 - bit_array[i] twos_result.write(val) return twos_result.read() + 1 bit_array = Array(k, cint) bits = divisor.bit_decompose(k)[::-1] bit_array.assign(bits) cnt_leading_zeros = MemValue(regint(0)) flag = MemValue(regint(0)) cnt_leading_zeros = MemValue(regint(0)) normalized_divisor = MemValue(divisor) @for_range(k) def block(i): flag.write(flag.read() | bit_array[i] == 1) @if_(flag.read() == 0) def block(): cnt_leading_zeros.write(cnt_leading_zeros.read() + 1) normalized_divisor.write(normalized_divisor << 1) q = MemValue(two_power(k)) e = MemValue(twos_complement(normalized_divisor.read())) qr = q.read() er = e.read() for i in range(theta): qr = qr + shift_two(qr * er, k) er = shift_two(er * er, k) q = qr res = shift_two(q, (2*k - 2*f - cnt_leading_zeros)) return res
def block(i): A[i] = TruncPr(A[i - 1] * W[i - 1], 2 * k, f, kappa) temp = shift_two(B[i - 1] * W[i - 1], f) # no reading and writing to the same variable in a for loop. W[i] = two - temp B[i] = temp
def block(i): A[i] = TruncPr(A[i - 1] * W[i - 1], 2*k, f, kappa) temp = shift_two(B[i - 1] * W[i - 1], f) # no reading and writing to the same variable in a for loop. W[i] = two - temp B[i] = temp