Update interp_cotran_ufunc.py

src/xlnsconf/interp_cotran_ufunc.py

@@ -3,6 +3,7 @@
 import math
 
 def sbdb_ufunc_interpsb(z,s,B=None,F=None):
+  """interpolate sb with no guards, ideal db"""
   if B == None:
     B = xl.xlnsB
   if F == None:
@@ -30,6 +31,7 @@ def sbdb_ufunc_interpsb(z,s,B=None,F=None):
   return np.where(s,xl.sbdb_ufunc_ideal(z,s,B=B,F=F), 2*res)
 
 def sbdb_ufunc_cotrdb(z,s,B=None,F=None):
+  """ideal sb, flawed implementation of cotran db (doesn't handle special cases)"""
   if B == None:
     B = xl.xlnsB
   if F == None:
@@ -76,6 +78,7 @@ def sbdb_ufunc_cotrdb(z,s,B=None,F=None):
 #(-2.07022694591547e-05, 3.140714511480401e-05, -0.0009458313366082998, 4.1009107609236585e-05) interp sb+cotran db
 
 def sbdb_ufunc_interpsbcotrdb(z,s,B=None,F=None):
+  """interpolate sb with no guards, correct cotran db using same interpolate"""
   if B == None:
     B = xl.xlnsB
   if F == None:
@@ -122,3 +125,265 @@ def sbdb_ufunc_interpsbcotrdb(z,s,B=None,F=None):
 #(-2.07022694591547e-05, 3.140714511480401e-05, -1.0576641000511883e-05, 1.0576475657836816e-05) interp sb only
 #(-1.0576595498909253e-05, 1.0576516825874298e-05, -0.000967004741118746, 2.112421874103721e-05) cotran db only
 #(-2.07022694591547e-05, 3.140714511480401e-05, -2.1583566089955605e-05, 4.1009107609236585e-05) interp sb+cotran db
+
+def sbdb_ufunc_interpsb_g2extra(z,s,B=None,F=None):
+  """interpolate sb with 2 guards and extra table, ideal db"""
+  if B == None:
+    B = xl.xlnsB
+  if F == None:
+    F = -math.floor(math.log(math.log(B,2),2))
+  B = B**.25
+  F += 2
+  z = z << 2
+  N = (F-5)//2
+  J = F - N
+  #print("guard N="+str(N))
+  #print("guard J="+str(J))
+  zhmask = -(1<<J)
+  zlmask = -1 - zhmask
+  #print("guard zhmask="+str(bin(zhmask)))
+  #print("guard zlmask="+str(bin(zlmask)))
+  zh = z & zhmask
+  zl = z & zlmask
+  #print("guard zh="+str(bin(zh)))
+  #print("guard zl="+str(bin(zl)))
+  szh = xl.sbdb_ufunc_ideal(zh,0,B=B,F=F)//2
+  szhp1 = xl.sbdb_ufunc_ideal(zh-zhmask,0,B=B,F=F)//2
+  #print("guard szh="+str(bin(szh)))
+  #print("guard szhp1="+str(bin(szhp1)))
+  res = ((szhp1 - szh)* zl)>>J
+  #print("guard res="+str(bin(res)))
+  res += szh
+  return np.where(s,xl.sbdb_ufunc_ideal(z,s,B=B,F=F), ((res+2)&-4)//2)  #rounding add, mask guard, (shift right 2 guard, but shift left 1 for sign)=> /2
+
+def sbdb_ufunc_interpsb_g4extra(z,s,B=None,F=None):
+  """interpolate sb with 4 guards and extra table, ideal db"""
+  if B == None:
+    B = xl.xlnsB
+  if F == None:
+    F = -math.floor(math.log(math.log(B,2),2))
+  B = B**.0625
+  F += 4
+  z = z << 4
+  N = (F-5)//2
+  J = F - N
+  #print("guard N="+str(N))
+  #print("guard J="+str(J))
+  zhmask = -(1<<J)
+  zlmask = -1 - zhmask
+  #print("guard zhmask="+str(bin(zhmask)))
+  #print("guard zlmask="+str(bin(zlmask)))
+  zh = z & zhmask
+  zl = z & zlmask
+  #print("guard zh="+str(bin(zh)))
+  #print("guard zl="+str(bin(zl)))
+  szh = xl.sbdb_ufunc_ideal(zh,0,B=B,F=F)//2
+  szhp1 = xl.sbdb_ufunc_ideal(zh-zhmask,0,B=B,F=F)//2
+  #print("guard szh="+str(bin(szh)))
+  #print("guard szhp1="+str(bin(szhp1)))
+  res = ((szhp1 - szh)* zl)>>J
+  #print("guard res="+str(bin(res)))
+  res += szh
+  return np.where(s,xl.sbdb_ufunc_ideal(z,s,B=B,F=F), ((res+8)&-16)//8)  #rounding add, mask guard, (shift right 4 guard, but shift left 1 for sign)=> /8
+
+def sbdb_ufunc_interpsb_g6extra(z,s,B=None,F=None):
+  """interpolate sb with 6 guards and extra table, ideal db"""
+  if B == None:
+    B = xl.xlnsB
+  if F == None:
+    F = -math.floor(math.log(math.log(B,2),2))
+  B = B**.015625
+  F += 6
+  z = z << 6
+  N = (F-5)//2
+  J = F - N
+  #print("guard N="+str(N))
+  #print("guard J="+str(J))
+  zhmask = -(1<<J)
+  zlmask = -1 - zhmask
+  #print("guard zhmask="+str(bin(zhmask)))
+  #print("guard zlmask="+str(bin(zlmask)))
+  zh = z & zhmask
+  zl = z & zlmask
+  #print("guard zh="+str(bin(zh)))
+  #print("guard zl="+str(bin(zl)))
+  szh = xl.sbdb_ufunc_ideal(zh,0,B=B,F=F)//2
+  szhp1 = xl.sbdb_ufunc_ideal(zh-zhmask,0,B=B,F=F)//2
+  #print("guard szh="+str(bin(szh)))
+  #print("guard szhp1="+str(bin(szhp1)))
+  res = ((szhp1 - szh)* zl)>>J
+  #print("guard res="+str(bin(res)))
+  res += szh
+  return np.where(s,xl.sbdb_ufunc_ideal(z,s,B=B,F=F), ((res+32)&-64)//32)  #rounding add, mask guard, (shift right 6 guard, but shift left 1 for sign)=> /32
+
+def sbdb_ufunc_interpsb_g4(z,s,B=None,F=None):
+  """interpolate sb with 4 guards, ideal db"""
+  if B == None:
+    B = xl.xlnsB
+  if F == None:
+    F = -math.floor(math.log(math.log(B,2),2))
+  N = (F-5)//2
+  J = F - N
+  #print("guard N="+str(N))
+  #print("guard J="+str(J))
+  zhmask = -(1<<J)
+  zlmask = -1 - zhmask
+  #print("guard zhmask="+str(bin(zhmask)))
+  #print("guard zlmask="+str(bin(zlmask)))
+  zh = z & zhmask
+  zl = z & zlmask
+  #print("guard zh="+str(bin(zh)))
+  #print("guard zl="+str(bin(zl)))
+
+  B = B**.0625
+  F += 4
+  zh = zh << 4
+  zhmask = zhmask << 4
+
+  szh = xl.sbdb_ufunc_ideal(zh,0,B=B,F=F)//2
+  szhp1 = xl.sbdb_ufunc_ideal(zh-zhmask,0,B=B,F=F)//2
+  #print("guard szh="+str(bin(szh)))
+  #print("guard szhp1="+str(bin(szhp1)))
+  res = ((szhp1 - szh)* zl)>>J
+  #print("guard res="+str(bin(res)))
+  res += szh
+  return np.where(s,xl.sbdb_ufunc_ideal(z,s,B=B,F=F), ((res+8)&-16)//8)  #rounding add, mask guard, (shift right 4 guard, but shift left 1 for sign)=> /8
+
+def sbdb_ufunc_interpsb_g6(z,s,B=None,F=None):
+  """interpolate sb with 4 guards, ideal db"""
+  if B == None:
+    B = xl.xlnsB
+  if F == None:
+    F = -math.floor(math.log(math.log(B,2),2))
+  N = (F-5)//2
+  J = F - N
+  #print("guard N="+str(N))
+  #print("guard J="+str(J))
+  zhmask = -(1<<J)
+  zlmask = -1 - zhmask
+  #print("guard zhmask="+str(bin(zhmask)))
+  #print("guard zlmask="+str(bin(zlmask)))
+  zh = z & zhmask
+  zl = z & zlmask
+
+  B = B**.015625
+  F += 6
+  zh = zh << 6
+  zhmask = zhmask << 6
+
+  #print("guard zh="+str(bin(zh)))
+  #print("guard zl="+str(bin(zl)))
+  szh = xl.sbdb_ufunc_ideal(zh,0,B=B,F=F)//2
+  szhp1 = xl.sbdb_ufunc_ideal(zh-zhmask,0,B=B,F=F)//2
+  #print("guard szh="+str(bin(szh)))
+  #print("guard szhp1="+str(bin(szhp1)))
+  res = ((szhp1 - szh)* zl)>>J
+  #print("guard res="+str(bin(res)))
+  res += szh
+  return np.where(s,xl.sbdb_ufunc_ideal(z,s,B=B,F=F), ((res+32)&-64)//32)  #rounding add, mask guard, (shift right 6 guard, but shift left 1 for sign)=> /32
+
+def sbdb_ufunc_interpsb_g2(z,s,B=None,F=None):
+  """interpolate sb with 2 guards, ideal db"""
+  if B == None:
+    B = xl.xlnsB
+  if F == None:
+    F = -math.floor(math.log(math.log(B,2),2))
+  N = (F-5)//2
+  J = F - N
+  #print("guard N="+str(N))
+  #print("guard J="+str(J))
+  zhmask = -(1<<J)
+  zlmask = -1 - zhmask
+  #print("guard zhmask="+str(bin(zhmask)))
+  #print("guard zlmask="+str(bin(zlmask)))
+  zh = z & zhmask
+  zl = z & zlmask
+
+  B = B**.25
+  F += 2
+  zh = zh << 2
+  zhmask = zhmask << 2
+
+  #print("guard zh="+str(bin(zh)))
+  #print("guard zl="+str(bin(zl)))
+  szh = xl.sbdb_ufunc_ideal(zh,0,B=B,F=F)//2
+  szhp1 = xl.sbdb_ufunc_ideal(zh-zhmask,0,B=B,F=F)//2
+  #print("guard szh="+str(bin(szh)))
+  #print("guard szhp1="+str(bin(szhp1)))
+  res = ((szhp1 - szh)* zl)>>J
+  #print("guard res="+str(bin(res)))
+  res += szh
+  return np.where(s,xl.sbdb_ufunc_ideal(z,s,B=B,F=F), ((res+2)&-4)//2)  #rounding add, mask guard, (shift right 2 guard, but shift left 1 for sign)=> /2
+
+def sbdb_ufunc_interpsbcotrdb_g2(z,s,B=None,F=None):
+  """interpolate sb with 2 guards, correct cotran db with same interpolate"""
+  if B == None:
+    B = xl.xlnsB
+  if F == None:
+    #F = xl.xlnsF
+    F = -math.floor(math.log(math.log(B,2),2))
+
+  N = (F-5)//2
+  J = F - N
+  zhmask = -(1<<J)  #masks arbitrary, similar to interp about balanced
+  zp = -z
+  z2 = zp & zhmask
+  z1 = zp - z2
+  #instead of 1, use s, which==1 only for cases dz1,dz2 needed
+  # won't blow up when s==0 and meaningless results discarded
+  dz1 = xl.sbdb_ufunc_ideal(-z1,s,B=B,F=F)//2
+  dz2 = xl.sbdb_ufunc_ideal(-z2,s,B=B,F=F)//2
+  return np.where(s, np.where(z2==0, 2*dz1, 
+                              np.where(z1==0, 2*dz2, 
+                                              2*dz2 + sbdb_ufunc_interpsb_g2(-z2-dz2+dz1,0,B=B,F=F))), 
+                     sbdb_ufunc_interpsb_g2(z,s,B=B,F=F)) 
+
+
+def sbdb_ufunc_interpsbcotrdb_g4(z,s,B=None,F=None):
+  """interpolate sb with 4 guards, correct cotran db with same interpolate"""
+  if B == None:
+    B = xl.xlnsB
+  if F == None:
+    #F = xl.xlnsF
+    F = -math.floor(math.log(math.log(B,2),2))
+
+  N = (F-5)//2
+  J = F - N
+  zhmask = -(1<<J)  #masks arbitrary, similar to interp about balanced
+  zp = -z
+  z2 = zp & zhmask
+  z1 = zp - z2
+  #instead of 1, use s, which==1 only for cases dz1,dz2 needed
+  # won't blow up when s==0 and meaningless results discarded
+  dz1 = xl.sbdb_ufunc_ideal(-z1,s,B=B,F=F)//2
+  dz2 = xl.sbdb_ufunc_ideal(-z2,s,B=B,F=F)//2
+  return np.where(s, np.where(z2==0, 2*dz1, 
+                              np.where(z1==0, 2*dz2, 
+                                              2*dz2 + sbdb_ufunc_interpsb_g4(-z2-dz2+dz1,0,B=B,F=F))), 
+                     sbdb_ufunc_interpsb_g4(z,s,B=B,F=F)) 
+
+
+def sbdb_ufunc_interpsbcotrdb_g6(z,s,B=None,F=None):
+  """interpolate sb with 6 guards, correct cotran db with same interpolate"""
+  if B == None:
+    B = xl.xlnsB
+  if F == None:
+    #F = xl.xlnsF
+    F = -math.floor(math.log(math.log(B,2),2))
+
+  N = (F-5)//2
+  J = F - N
+  zhmask = -(1<<J)  #masks arbitrary, similar to interp about balanced
+  zp = -z
+  z2 = zp & zhmask
+  z1 = zp - z2
+  #instead of 1, use s, which==1 only for cases dz1,dz2 needed
+  # won't blow up when s==0 and meaningless results discarded
+  dz1 = xl.sbdb_ufunc_ideal(-z1,s,B=B,F=F)//2
+  dz2 = xl.sbdb_ufunc_ideal(-z2,s,B=B,F=F)//2
+  return np.where(s, np.where(z2==0, 2*dz1, 
+                              np.where(z1==0, 2*dz2, 
+                                              2*dz2 + sbdb_ufunc_interpsb_g6(-z2-dz2+dz1,0,B=B,F=F))), 
+                     sbdb_ufunc_interpsb_g6(z,s,B=B,F=F)) 
+
+