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heltonmcheltonmc
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fix SIMD
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‎src/U_polynomials.jl

Lines changed: 47 additions & 44 deletions
Original file line numberDiff line numberDiff line change
@@ -136,60 +136,63 @@ Uk_poly_Hankel(p, v, p2, x) = Uk_poly_Jn(p, v, p2, x)
136136
#####
137137

138138
function Uk_poly5(p, v, p2)
139-
u0 = 1.0
140-
u1 = evalpoly(p2, (0.125, -0.20833333333333334))
141-
u2 = evalpoly(p2, (0.0703125, -0.4010416666666667, 0.3342013888888889))
142-
u3 = evalpoly(p2, (0.0732421875, -0.8912109375, 1.8464626736111112, -1.0258125964506173))
143-
u4 = evalpoly(p2, (0.112152099609375, -2.3640869140625, 8.78912353515625, -11.207002616222994, 4.669584423426247))
144-
u5 = evalpoly(p2, (0.22710800170898438, -7.368794359479632, 42.53499874538846, -91.81824154324002, 84.63621767460073, -28.212072558200244))
145-
146-
Poly = (u0, u1, u2, u3, u4, u5)
139+
Poly = Uk_poly5(p2)
147140
return split_evalpoly(-p/v, Poly)
148141
end
149-
150-
function Uk_poly10(p, v, p2)
151-
u0 = 1.0
152-
u1 = evalpoly(p2, (0.125, -0.20833333333333334))
153-
u2 = evalpoly(p2, (0.0703125, -0.4010416666666667, 0.3342013888888889))
154-
u3 = evalpoly(p2, (0.0732421875, -0.8912109375, 1.8464626736111112, -1.0258125964506173))
155-
u4 = evalpoly(p2, (0.112152099609375, -2.3640869140625, 8.78912353515625, -11.207002616222994, 4.669584423426247))
142+
function Uk_poly5(p2)
156143
u5 = evalpoly(p2, (0.22710800170898438, -7.368794359479632, 42.53499874538846, -91.81824154324002, 84.63621767460073, -28.212072558200244))
157-
u6 = evalpoly(p2, (0.5725014209747314, -26.491430486951554, 218.1905117442116, -699.5796273761325, 1059.9904525279999, -765.2524681411817, 212.57013003921713))
158-
u7 = evalpoly(p2, (1.7277275025844574, -108.09091978839466, 1200.9029132163525, -5305.646978613403, 11655.393336864534, -13586.550006434136, 8061.722181737309, -1919.457662318407))
159-
u8 = evalpoly(p2, (6.074042001273483, -493.91530477308805, 7109.514302489364, -41192.65496889755, 122200.46498301747, -203400.17728041555, 192547.00123253153, -96980.59838863752, 20204.29133096615))
160-
u9 = evalpoly(p2, (24.380529699556064, -2499.8304818112097, 45218.76898136273, -331645.17248456355, 1.2683652733216248e6, -2.8135632265865337e6, 3.763271297656404e6, -2.998015918538107e6, 1.3117636146629772e6, -242919.18790055133))
161-
u10 = evalpoly(p2, (110.01714026924674, -13886.08975371704, 308186.40461266245, -2.7856181280864547e6, 1.3288767166421818e7, -3.7567176660763346e7, 6.634451227472903e7, -7.410514821153265e7, 5.095260249266464e7, -1.9706819118432228e7, 3.284469853072038e6))
144+
u4 = evalpoly(p2, (0.112152099609375, -2.3640869140625, 8.78912353515625, -11.207002616222994, 4.669584423426247))
145+
u3 = evalpoly(p2, (0.0732421875, -0.8912109375, 1.8464626736111112, -1.0258125964506173))
146+
u2 = evalpoly(p2, (0.0703125, -0.4010416666666667, 0.3342013888888889))
147+
u1 = evalpoly(p2, (0.125, -0.20833333333333334))
148+
return (1.0, u1, u2, u3, u4, u5)
149+
end
162150

163-
Poly = (u0, u1, u2, u3, u4, u5, u6, u7, u8, u9, u10)
151+
function Uk_poly10(p, v, p2)
152+
Poly = Uk_poly10(p2)
164153
return split_evalpoly(-p/v, Poly)
165154
end
166-
167-
function Uk_poly20(p, v, p2)
168-
u0 = 1.0
169-
u1 = evalpoly(p2, (0.125, -0.20833333333333334))
170-
u2 = evalpoly(p2, (0.0703125, -0.4010416666666667, 0.3342013888888889))
171-
u3 = evalpoly(p2, (0.0732421875, -0.8912109375, 1.8464626736111112, -1.0258125964506173))
172-
u4 = evalpoly(p2, (0.112152099609375, -2.3640869140625, 8.78912353515625, -11.207002616222994, 4.669584423426247))
173-
u5 = evalpoly(p2, (0.22710800170898438, -7.368794359479632, 42.53499874538846, -91.81824154324002, 84.63621767460073, -28.212072558200244))
174-
u6 = evalpoly(p2, (0.5725014209747314, -26.491430486951554, 218.1905117442116, -699.5796273761325, 1059.9904525279999, -765.2524681411817, 212.57013003921713))
175-
u7 = evalpoly(p2, (1.7277275025844574, -108.09091978839466, 1200.9029132163525, -5305.646978613403, 11655.393336864534, -13586.550006434136, 8061.722181737309, -1919.457662318407))
176-
u8 = evalpoly(p2, (6.074042001273483, -493.91530477308805, 7109.514302489364, -41192.65496889755, 122200.46498301747, -203400.17728041555, 192547.00123253153, -96980.59838863752, 20204.29133096615))
177-
u9 = evalpoly(p2, (24.380529699556064, -2499.8304818112097, 45218.76898136273, -331645.17248456355, 1.2683652733216248e6, -2.8135632265865337e6, 3.763271297656404e6, -2.998015918538107e6, 1.3117636146629772e6, -242919.18790055133))
155+
function Uk_poly10(p2)
178156
u10 = evalpoly(p2, (110.01714026924674, -13886.08975371704, 308186.40461266245, -2.7856181280864547e6, 1.3288767166421818e7, -3.7567176660763346e7, 6.634451227472903e7, -7.410514821153265e7, 5.095260249266464e7, -1.9706819118432228e7, 3.284469853072038e6))
179-
u11 = evalpoly(p2, (551.3358961220206, -84005.4336030241, 2.2437681779224495e6, -2.4474062725738727e7, 1.420629077975331e8, -4.9588978427503026e8, 1.1068428168230145e9, -1.6210805521083372e9, 1.5535968995705802e9, -9.394623596815784e8, 3.2557307418576574e8, -4.932925366450996e7))
180-
u12 = evalpoly(p2, (3038.090510922384, -549842.3275722887, 1.7395107553978164e7, -2.2510566188941526e8, 1.5592798648792574e9, -6.563293792619285e9, 1.79542137311556e10, -3.3026599749800724e10, 4.1280185579753975e10, -3.4632043388158775e10, 1.8688207509295826e10, -5.866481492051847e9, 8.147890961183121e8))
181-
u13 = evalpoly(p2, (18257.755474293175, -3.8718334425726123e6, 1.43157876718889e8, -2.167164983223795e9, 1.763473060683497e10, -8.786707217802327e10, 2.879006499061506e11, -6.453648692453765e11, 1.0081581068653821e12, -1.0983751560812233e12, 8.192186695485773e11, -3.990961752244665e11, 1.144982377320258e11, -1.4679261247695616e10))
182-
u14 = evalpoly(p2, (118838.42625678326, -2.9188388122220814e7, 1.2470092935127103e9, -2.1822927757529224e10, 2.0591450323241e11, -1.1965528801961816e12, 4.612725780849132e12, -1.2320491305598287e13, 2.334836404458184e13, -3.166708858478516e13, 3.056512551993532e13, -2.0516899410934438e13, 9.109341185239898e12, -2.406297900028504e12, 2.86464035717679e11))
183-
u15 = evalpoly(p2, (832859.3040162893, -2.3455796352225152e8, 1.1465754899448236e10, -2.2961937296824646e11, 2.4850009280340854e12, -1.663482472489248e13, 7.437312290867914e13, -2.3260483118893994e14, 5.230548825784446e14, -8.57461032982895e14, 1.0269551960827625e15, -8.894969398810265e14, 5.4273966498765975e14, -2.213496387025252e14, 5.417751075510605e13, -6.019723417234006e12))
184-
u16 = evalpoly(p2, (6.252951493434797e6, -2.0016469281917763e9, 1.1099740513917902e11, -2.5215584749128545e12, 3.100743647289646e13, -2.3665253045164925e14, 1.2126758042503475e15, -4.3793258383640155e15, 1.1486706978449752e16, -2.2268225133911144e16, 3.213827526858624e16, -3.4447226006485144e16, 2.705471130619708e16, -1.5129826322457682e16, 5.705782159023671e15, -1.3010127235496995e15, 1.3552215870309369e14))
185-
u17 = evalpoly(p2, (5.0069589531988926e7, -1.8078220384658062e10, 1.128709145410874e12, -2.886383763141476e13, 4.0004445704303625e14, -3.4503855118462725e15, 2.0064271476309532e16, -8.270945651585064e16, 2.4960365126160426e17, -5.62631788074636e17, 9.575335098169139e17, -1.2336116931960694e18, 1.1961991142756308e18, -8.592577980317548e17, 4.4347954614171904e17, -1.5552983504313904e17, 3.3192764720355224e16, -3.254192619642669e15))
186-
u18 = evalpoly(p2, (4.259392165047669e8, -1.722832387173505e11, 1.2030115826419191e13, -3.4396530474307594e14, 5.335106978708839e15, -5.1605093193485224e16, 3.37667624979061e17, -1.5736434765189599e18, 5.402894876715982e18, -1.3970803516443374e19, 2.757282981650519e19, -4.178861444656839e19, 4.859942729324836e19, -4.301555703831444e19, 2.846521225167657e19, -1.3639420410571592e19, 4.47020096401231e18, -8.966114215270463e17, 8.30195760673191e16))
187-
u19 = evalpoly(p2, (3.8362551802304335e9, -1.7277040123529995e12, 1.3412416915180639e14, -4.2619355104268985e15, 7.351663610930971e16, -7.921651119323832e17, 5.789887667664653e18, -3.025566598990372e19, 1.1707490535797259e20, -3.434621399768417e20, 7.756704953461136e20, -1.360203777284994e21, 1.8571089321463453e21, -1.9677247077053125e21, 1.6016898573693598e21, -9.824438427689858e20, 4.392792200888712e20, -1.351217503435996e20, 2.5563802960529236e19, -2.242438856186775e18))
188-
u20 = evalpoly(p2, (3.646840080706556e10, -1.818726203851104e13, 1.5613123930484672e15, -5.48403360388329e16, 1.0461721131134344e18, -1.2483700995047234e19, 1.0126774169536592e20, -5.8917941350694964e20, 2.548961114664972e21, -8.405915817108351e21, 2.1487414815055883e22, -4.302534303482379e22, 6.783661642951883e22, -8.423222750084323e22, 8.19433100543513e22, -6.173206302884415e22, 3.528435843903409e22, -1.4787743528433614e22, 4.285296082829494e21, -7.671943936729004e20, 6.393286613940837e19))
157+
u9 = evalpoly(p2, (24.380529699556064, -2499.8304818112097, 45218.76898136273, -331645.17248456355, 1.2683652733216248e6, -2.8135632265865337e6, 3.763271297656404e6, -2.998015918538107e6, 1.3117636146629772e6, -242919.18790055133))
158+
u8 = evalpoly(p2, (6.074042001273483, -493.91530477308805, 7109.514302489364, -41192.65496889755, 122200.46498301747, -203400.17728041555, 192547.00123253153, -96980.59838863752, 20204.29133096615))
159+
u7 = evalpoly(p2, (1.7277275025844574, -108.09091978839466, 1200.9029132163525, -5305.646978613403, 11655.393336864534, -13586.550006434136, 8061.722181737309, -1919.457662318407))
160+
u6 = evalpoly(p2, (0.5725014209747314, -26.491430486951554, 218.1905117442116, -699.5796273761325, 1059.9904525279999, -765.2524681411817, 212.57013003921713))
161+
u5 = evalpoly(p2, (0.22710800170898438, -7.368794359479632, 42.53499874538846, -91.81824154324002, 84.63621767460073, -28.212072558200244))
162+
u4 = evalpoly(p2, (0.112152099609375, -2.3640869140625, 8.78912353515625, -11.207002616222994, 4.669584423426247))
163+
u3 = evalpoly(p2, (0.0732421875, -0.8912109375, 1.8464626736111112, -1.0258125964506173))
164+
u2 = evalpoly(p2, (0.0703125, -0.4010416666666667, 0.3342013888888889))
165+
u1 = evalpoly(p2, (0.125, -0.20833333333333334))
166+
return (1.0, u1, u2, u3, u4, u5, u6, u7, u8, u9, u10)
167+
end
189168

190-
Poly = (u0, u1, u2, u3, u4, u5, u6, u7, u8, u9, u10, u11, u12, u13, u14, u15, u16, u17, u18, u19, u20)
169+
function Uk_poly20(p, v, p2)
170+
Poly = Uk_poly20(p2)
191171
return split_evalpoly(-p/v, Poly)
192172
end
173+
function Uk_poly20(p2)
174+
u20 = evalpoly(p2, (3.646840080706556e10, -1.818726203851104e13, 1.5613123930484672e15, -5.48403360388329e16, 1.0461721131134344e18, -1.2483700995047234e19, 1.0126774169536592e20, -5.8917941350694964e20, 2.548961114664972e21, -8.405915817108351e21, 2.1487414815055883e22, -4.302534303482379e22, 6.783661642951883e22, -8.423222750084323e22, 8.19433100543513e22, -6.173206302884415e22, 3.528435843903409e22, -1.4787743528433614e22, 4.285296082829494e21, -7.671943936729004e20, 6.393286613940837e19))
175+
u19 = evalpoly(p2, (3.8362551802304335e9, -1.7277040123529995e12, 1.3412416915180639e14, -4.2619355104268985e15, 7.351663610930971e16, -7.921651119323832e17, 5.789887667664653e18, -3.025566598990372e19, 1.1707490535797259e20, -3.434621399768417e20, 7.756704953461136e20, -1.360203777284994e21, 1.8571089321463453e21, -1.9677247077053125e21, 1.6016898573693598e21, -9.824438427689858e20, 4.392792200888712e20, -1.351217503435996e20, 2.5563802960529236e19, -2.242438856186775e18))
176+
u18 = evalpoly(p2, (4.259392165047669e8, -1.722832387173505e11, 1.2030115826419191e13, -3.4396530474307594e14, 5.335106978708839e15, -5.1605093193485224e16, 3.37667624979061e17, -1.5736434765189599e18, 5.402894876715982e18, -1.3970803516443374e19, 2.757282981650519e19, -4.178861444656839e19, 4.859942729324836e19, -4.301555703831444e19, 2.846521225167657e19, -1.3639420410571592e19, 4.47020096401231e18, -8.966114215270463e17, 8.30195760673191e16))
177+
u17 = evalpoly(p2, (5.0069589531988926e7, -1.8078220384658062e10, 1.128709145410874e12, -2.886383763141476e13, 4.0004445704303625e14, -3.4503855118462725e15, 2.0064271476309532e16, -8.270945651585064e16, 2.4960365126160426e17, -5.62631788074636e17, 9.575335098169139e17, -1.2336116931960694e18, 1.1961991142756308e18, -8.592577980317548e17, 4.4347954614171904e17, -1.5552983504313904e17, 3.3192764720355224e16, -3.254192619642669e15))
178+
u16 = evalpoly(p2, (6.252951493434797e6, -2.0016469281917763e9, 1.1099740513917902e11, -2.5215584749128545e12, 3.100743647289646e13, -2.3665253045164925e14, 1.2126758042503475e15, -4.3793258383640155e15, 1.1486706978449752e16, -2.2268225133911144e16, 3.213827526858624e16, -3.4447226006485144e16, 2.705471130619708e16, -1.5129826322457682e16, 5.705782159023671e15, -1.3010127235496995e15, 1.3552215870309369e14))
179+
u15 = evalpoly(p2, (832859.3040162893, -2.3455796352225152e8, 1.1465754899448236e10, -2.2961937296824646e11, 2.4850009280340854e12, -1.663482472489248e13, 7.437312290867914e13, -2.3260483118893994e14, 5.230548825784446e14, -8.57461032982895e14, 1.0269551960827625e15, -8.894969398810265e14, 5.4273966498765975e14, -2.213496387025252e14, 5.417751075510605e13, -6.019723417234006e12))
180+
u14 = evalpoly(p2, (118838.42625678326, -2.9188388122220814e7, 1.2470092935127103e9, -2.1822927757529224e10, 2.0591450323241e11, -1.1965528801961816e12, 4.612725780849132e12, -1.2320491305598287e13, 2.334836404458184e13, -3.166708858478516e13, 3.056512551993532e13, -2.0516899410934438e13, 9.109341185239898e12, -2.406297900028504e12, 2.86464035717679e11))
181+
u13 = evalpoly(p2, (18257.755474293175, -3.8718334425726123e6, 1.43157876718889e8, -2.167164983223795e9, 1.763473060683497e10, -8.786707217802327e10, 2.879006499061506e11, -6.453648692453765e11, 1.0081581068653821e12, -1.0983751560812233e12, 8.192186695485773e11, -3.990961752244665e11, 1.144982377320258e11, -1.4679261247695616e10))
182+
u12 = evalpoly(p2, (3038.090510922384, -549842.3275722887, 1.7395107553978164e7, -2.2510566188941526e8, 1.5592798648792574e9, -6.563293792619285e9, 1.79542137311556e10, -3.3026599749800724e10, 4.1280185579753975e10, -3.4632043388158775e10, 1.8688207509295826e10, -5.866481492051847e9, 8.147890961183121e8))
183+
u11 = evalpoly(p2, (551.3358961220206, -84005.4336030241, 2.2437681779224495e6, -2.4474062725738727e7, 1.420629077975331e8, -4.9588978427503026e8, 1.1068428168230145e9, -1.6210805521083372e9, 1.5535968995705802e9, -9.394623596815784e8, 3.2557307418576574e8, -4.932925366450996e7))
184+
u10 = evalpoly(p2, (110.01714026924674, -13886.08975371704, 308186.40461266245, -2.7856181280864547e6, 1.3288767166421818e7, -3.7567176660763346e7, 6.634451227472903e7, -7.410514821153265e7, 5.095260249266464e7, -1.9706819118432228e7, 3.284469853072038e6))
185+
u9 = evalpoly(p2, (24.380529699556064, -2499.8304818112097, 45218.76898136273, -331645.17248456355, 1.2683652733216248e6, -2.8135632265865337e6, 3.763271297656404e6, -2.998015918538107e6, 1.3117636146629772e6, -242919.18790055133))
186+
u8 = evalpoly(p2, (6.074042001273483, -493.91530477308805, 7109.514302489364, -41192.65496889755, 122200.46498301747, -203400.17728041555, 192547.00123253153, -96980.59838863752, 20204.29133096615))
187+
u7 = evalpoly(p2, (1.7277275025844574, -108.09091978839466, 1200.9029132163525, -5305.646978613403, 11655.393336864534, -13586.550006434136, 8061.722181737309, -1919.457662318407))
188+
u6 = evalpoly(p2, (0.5725014209747314, -26.491430486951554, 218.1905117442116, -699.5796273761325, 1059.9904525279999, -765.2524681411817, 212.57013003921713))
189+
u5 = evalpoly(p2, (0.22710800170898438, -7.368794359479632, 42.53499874538846, -91.81824154324002, 84.63621767460073, -28.212072558200244))
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u4 = evalpoly(p2, (0.112152099609375, -2.3640869140625, 8.78912353515625, -11.207002616222994, 4.669584423426247))
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u3 = evalpoly(p2, (0.0732421875, -0.8912109375, 1.8464626736111112, -1.0258125964506173))
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u2 = evalpoly(p2, (0.0703125, -0.4010416666666667, 0.3342013888888889))
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u1 = evalpoly(p2, (0.125, -0.20833333333333334))
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return (1.0, u1, u2, u3, u4, u5, u6, u7, u8, u9, u10, u11, u12, u13, u14, u15, u16, u17, u18, u19, u20)
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end
193196

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# implementation for arbitrary precision
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function Uk_poly_Jn(p, v, p2, x::T) where T

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