def pt_double(lbiX, lbiY, sgnX, sgnY):
"""See also: K. Kajiwara et al., http://arxiv.org/abs/0803.4062 and
http://arxiv.org/pdf/0903.0331.pdf
8 ADDSUBs + 10 CMPs
"""
(lbi3X, c3X), sgn3X = lbi.lbi_add(lbiX, lbiX, sgnX, sgnX)
(lbi3X, c3X), sgn3X = lbi.lbi_add(lbi3X, lbiX, sgn3X, sgnX)
(lbi3Y, c3Y), sgn3Y = lbi.lbi_add(lbiY, lbiY, sgnY, sgnY)
(lbi3Y, c3Y), sgn3Y = lbi.lbi_add(lbi3Y, lbiY, sgn3Y, sgnY)
# Get [2]P x-coordinate
if 1 == sgnX:
(lbi2X, c2X), sgn2X = lbi.lbi_add(lbiY, lbi3X, sgnY, sgn3X)
else:
(lbi2X, c2X), sgn2X = (lbiY, 0), sgnY
if 1 == lbi.lbi_cmp(lbiX, lbiY, sgnX, sgnY):
(lbi2X, c2X), sgn2X = lbi.lbi_sub(lbi2X, lbi3X, sgn2X, sgn3X)
else:
(lbi2X, c2X), sgn2X = lbi.lbi_sub(lbi2X, lbi3Y, sgn2X, sgn3Y)
# Get [2]P y-coordinate
if 1 == sgnY:
(lbi2Y, c2Y), sgn2Y = lbi.lbi_add(lbiX, lbi3Y, sgnX, sgn3Y)
else:
(lbi2Y, c2Y), sgn2Y = (lbiX, 0), sgnX
if 1 == lbi.lbi_cmp(lbiX, lbiY, sgnX, sgnY):
(lbi2Y, c2Y), sgn2Y = lbi.lbi_sub(lbi2Y, lbi3X, sgn2Y, sgn3X)
else:
(lbi2Y, c2Y), sgn2Y = lbi.lbi_sub(lbi2Y, lbi3Y, sgn2Y, sgn3Y)
return lbi2X, lbi2Y, sgn2X, sgn2Y
def pt_coord(vectors, vlbi, vsgn):
(v1, v2, v3, v4) = vectors
lbi1, sgn1 = pt_sp(v1, vlbi, vsgn)
lbi2, sgn2 = pt_sp(v2, vlbi, vsgn)
if 1 == lbi.lbi_cmp(lbi1, lbi2, sgn1, sgn2):
lbipos, sgnpos = lbi1, sgn1
else:
lbipos, sgnpos = lbi2, sgn2
lbi3, sgn3 = pt_sp(v3, vlbi, vsgn)
lbi4, sgn4 = pt_sp(v4, vlbi, vsgn)
if 1 == lbi.lbi_cmp(lbi3, lbi4, sgn3, sgn4):
lbineg, sgnneg = lbi3, sgn3
else:
lbineg, sgnneg = lbi4, sgn4
(lbiR, cR), sgnR = lbi.lbi_sub(lbipos, lbineg, sgnpos, sgnneg)
return lbiR, lbineg, sgnR, sgnneg
def pt_double_alt(lbiX, lbiY, sgnX, sgnY):
"""See also: K. Kajiwara et al., http://arxiv.org/abs/0803.4062 and
http://arxiv.org/pdf/0903.0331.pdf
5 ADDSUBs + 6 CMPs
"""
(lbi2X, c2X), sgn2X = lbi.lbi_add(lbiX, lbiX, sgnX, sgnX)
(lbi3X, c3X), sgn3X = lbi.lbi_add(lbi2X, lbiX, sgn2X, sgnX)
(lbi2Y, c2Y), sgn2Y = lbi.lbi_add(lbiY, lbiY, sgnY, sgnY)
(lbi3Y, c3Y), sgn3Y = lbi.lbi_add(lbi2Y, lbiY, sgn2Y, sgnY)
cmp = lbi.lbi_cmp(lbiX, lbiY, sgnX, sgnY)
if 1 == cmp:
if 1 == sgnX:
lbiXX, sgnXX = lbiY, sgnY
else:
(lbiXX, cXX), sgnXX = lbi.lbi_sub(lbiY, lbi3X, sgnY, sgn3X)
if 1 == sgnY:
(lbiYY, cYY), sgnYY = lbi.lbi_sub(lbi3Y, lbi2X, sgn3Y, sgn2X)
else:
lbiYY, sgnYY = lbiX, sgnX
else:
if 1 == sgnX:
(lbiXX, cXX), sgnXX = lbi.lbi_sub(lbi3X, lbi2Y, sgn3X, sgn2Y)
else:
lbiXX, sgnXX = lbi2Y, -sgn2Y
if 1 == sgnY:
lbiYY, sgnYY = lbi2X, -sgn2X
else:
(lbiXX, cXX), sgnXX = lbi.lbi_sub(lbiX, lbi3Y, sgnX, sgn3Y)
return lbiXX, lbiYY, sgnXX, sgnYY
def pt_coord_pre(vectors, vlbi, vsgn, lbineg, sgnneg):
(v1, v2, v3, v4) = vectors
lbi1, sgn1 = pt_sp(v1, vlbi, vsgn)
lbi2, sgn2 = pt_sp(v2, vlbi, vsgn)
if 1 == lbi.lbi_cmp(lbi1, lbi2, sgn1, sgn2):
lbipos, sgnpos = lbi1, sgn1
else:
lbipos, sgnpos = lbi2, sgn2
(lbiR, cR), sgnR = lbi.lbi_sub(lbipos, lbineg, sgnpos, sgnneg)
return lbiR, sgnR
def point_face(xr, sxr, yr, syr):
if (1, -1) == (sxr, syr): return 5
if (-1, 1) == (sxr, syr): return 2
cmpyx = lbi.lbi_cmp(xr, yr, sxr, syr)
if (1, 1) == (sxr, syr):
if 1 == cmpyx: return 6
else: return 1
elif (-1, -1) == (sxr, syr):
if 1 == cmpyx: return 4
else: return 3
else:
return 0
def line_center(xp, sxp, yp, syp, xq, sxq, yq, syq):
xcmp = lbi.lbi_cmp(xp, xq, sxp, sxq)
ycmp = lbi.lbi_cmp(yp, yq, syp, syq)
# P, Q are on edges 2 and 3
if -1 == xcmp * ycmp:
if xcmp == 1:
(xb, sxb, yb, syb) = (xq, sxq, yq, syq)
(xc, sxc, yc, syc) = (xp, sxp, yp, syp)
conf = 'CB'
else:
(xb, sxb, yb, syb) = (xp, sxp, yp, syp)
(xc, sxc, yc, syc) = (xq, sxq, yq, syq)
conf = 'BC'
return (xc, sxc, yb, syb, conf)
# One of P or Q in on edge 2 or 3
else:
if 1 == xcmp:
(subyxinf, cyxinf), sgnyxinf = lbi.lbi_sub(yq, xq, syq, sxq)
(subyx, cyx), sgnyx = lbi.lbi_sub(yp, xp, syp, sxp)
cmpyx = lbi.lbi_cmp(subyx, subyxinf, sgnyx, sgnyxinf)
if 1 == cmpyx:
(add, cadd), sadd = lbi.lbi_add(xq, subyx, sxq, sgnyx)
return (xq, sxq, add, sadd, 'AC')
else:
(sub, csub), ssub = lbi.lbi_sub(yq, subyx, syq, sgnyx)
return (sub, ssub, yq, syq, 'AB')
else:
(subyxinf, cyxinf), sgnyxinf = lbi.lbi_sub(yp, xp, syp, sxp)
(subyx, cyx), sgnyx = lbi.lbi_sub(yq, xq, syq, sxq)
cmpyx = lbi.lbi_cmp(subyx, subyxinf, sgnyx, sgnyxinf)
if 1 == cmpyx:
(add, cadd), sadd = lbi.lbi_add(xp, subyx, sxp, sgnyx)
return (xp, sxp, add, sadd, 'CA')
else:
(sub, csub), ssub = lbi.lbi_sub(yp, subyx, syp, sgnyx)
return (sub, ssub, yp, syp, 'BA')
return (0, 0, 0, 0, '')
def pt_K(lbiX, lbiY, sgnX, sgnY, verbose=False):
(lbi3X, c3X), sgn3X = lbi.lbi_add(lbiX, lbiX, sgnX, sgnX)
(lbi3X, c3X), sgn3X = lbi.lbi_add(lbi3X, lbiX, sgn3X, sgnX)
(lbi3Y, c3Y), sgn3Y = lbi.lbi_add(lbiY, lbiY, sgnY, sgnY)
(lbi3Y, c3Y), sgn3Y = lbi.lbi_add(lbi3Y, lbiY, sgn3Y, sgnY)
(lbisum, csum), sgnsum = lbi.lbi_add(lbiX, lbiY, sgnX, sgnY)
if verbose:
print "In K: 3X, 3Y", lbi.lbi_lbi2dec(lbi3X, sgn3X), lbi.lbi_lbi2dec(
lbi3Y, sgn3Y)
print "In K: X+Y ", lbi.lbi_lbi2dec(lbisum, sgnsum)
if 1 == lbi.lbi_cmp(lbiX, lbiY, sgnX, sgnY):
lbimax, sgnmax = lbi3X, sgn3X
else:
lbimax, sgnmax = lbi3Y, sgn3Y
if 1 == sgnmax:
(lbiR, cR), sgnR = lbi.lbi_sub(lbimax, lbisum, sgnmax, sgnsum)
else:
(lbiR, cR), sgnR = (lbisum, csum), -sgnsum
return lbiR, sgnR
def pt_K_alt(lbiX, lbiY, sgnX, sgnY, verbose=False):
"""Hessian Pencil parameter from a cyce point.
4 ADDSUBs + 5 CMPs
"""
(lbisum, csum), sgnsum = lbi.lbi_add(lbiX, lbiY, sgnX, sgnY)
(lbi2X, c2X), sgn2X = lbi.lbi_add(lbiX, lbiX, sgnX, sgnX)
(lbi2Y, c2Y), sgn2Y = lbi.lbi_add(lbiY, lbiY, sgnY, sgnY)
cmp = lbi.lbi_cmp(lbiX, lbiY, sgnX, sgnY)
if 1 == cmp:
if 1 == sgnX:
(lbiR, cR), sgnR = lbi.lbi_sub(lbi2X, lbiY, sgn2X, sgnY)
return lbiR, sgnR
else:
return lbisum, -sgnsum
else:
if 1 == sgnY:
(lbiR, cR), sgnR = lbi.lbi_sub(lbi2Y, lbiX, sgn2Y, sgnX)
return lbiR, sgnR
else:
return lbisum, -sgnsum