/usr/share/julia/base/special/erf.jl is in julia-common 0.4.7-6.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 | # This file is a part of Julia. License is MIT: http://julialang.org/license
for f in (:erf, :erfc, :erfcx, :erfi, :Dawson)
fname = (f === :Dawson) ? :dawson : f
@eval begin
($fname)(z::Complex128) = Complex128(ccall(($(string("Faddeeva_",f)),openspecfun), Complex{Float64}, (Complex{Float64}, Float64), z, zero(Float64)))
($fname)(z::Complex64) = Complex64(ccall(($(string("Faddeeva_",f)),openspecfun), Complex{Float64}, (Complex{Float64}, Float64), Complex128(z), Float64(eps(Float32))))
($fname)(z::Complex) = ($fname)(Complex128(z))
end
end
for f in (:erfcx, :erfi, :Dawson)
fname = (f === :Dawson) ? :dawson : f
@eval begin
($fname)(x::Float64) = ccall(($(string("Faddeeva_",f,"_re")),openspecfun), Float64, (Float64,), x)
($fname)(x::Float32) = Float32(ccall(($(string("Faddeeva_",f,"_re")),openspecfun), Float64, (Float64,), Float64(x)))
($fname)(x::Integer) = ($fname)(float(x))
@vectorize_1arg Number $fname
end
end
# Compute the inverse of the error function: erf(erfinv(x)) == x,
# using the rational approximants tabulated in:
# J. M. Blair, C. A. Edwards, and J. H. Johnson, "Rational Chebyshev
# approximations for the inverse of the error function," Math. Comp. 30,
# pp. 827--830 (1976).
# http://dx.doi.org/10.1090/S0025-5718-1976-0421040-7
# http://www.jstor.org/stable/2005402
function erfinv(x::Float64)
a = abs(x)
if a >= 1.0
if x == 1.0
return Inf
elseif x == -1.0
return -Inf
end
throw(DomainError())
elseif a <= 0.75 # Table 17 in Blair et al.
t = x*x - 0.5625
return x * @horner(t, 0.16030_49558_44066_229311e2,
-0.90784_95926_29603_26650e2,
0.18644_91486_16209_87391e3,
-0.16900_14273_46423_82420e3,
0.65454_66284_79448_7048e2,
-0.86421_30115_87247_794e1,
0.17605_87821_39059_0) /
@horner(t, 0.14780_64707_15138_316110e2,
-0.91374_16702_42603_13936e2,
0.21015_79048_62053_17714e3,
-0.22210_25412_18551_32366e3,
0.10760_45391_60551_23830e3,
-0.20601_07303_28265_443e2,
0.1e1)
elseif a <= 0.9375 # Table 37 in Blair et al.
t = x*x - 0.87890625
return x * @horner(t, -0.15238_92634_40726_128e-1,
0.34445_56924_13612_5216,
-0.29344_39867_25424_78687e1,
0.11763_50570_52178_27302e2,
-0.22655_29282_31011_04193e2,
0.19121_33439_65803_30163e2,
-0.54789_27619_59831_8769e1,
0.23751_66890_24448) /
@horner(t, -0.10846_51696_02059_954e-1,
0.26106_28885_84307_8511,
-0.24068_31810_43937_57995e1,
0.10695_12997_33870_14469e2,
-0.23716_71552_15965_81025e2,
0.24640_15894_39172_84883e2,
-0.10014_37634_97830_70835e2,
0.1e1)
else # Table 57 in Blair et al.
t = 1.0 / sqrt(-log(1.0 - a))
return @horner(t, 0.10501_31152_37334_38116e-3,
0.10532_61131_42333_38164_25e-1,
0.26987_80273_62432_83544_516,
0.23268_69578_89196_90806_414e1,
0.71678_54794_91079_96810_001e1,
0.85475_61182_21678_27825_185e1,
0.68738_08807_35438_39802_913e1,
0.36270_02483_09587_08930_02e1,
0.88606_27392_96515_46814_9) /
(copysign(t, x) *
@horner(t, 0.10501_26668_70303_37690e-3,
0.10532_86230_09333_27531_11e-1,
0.27019_86237_37515_54845_553,
0.23501_43639_79702_53259_123e1,
0.76078_02878_58012_77064_351e1,
0.11181_58610_40569_07827_3451e2,
0.11948_78791_84353_96667_8438e2,
0.81922_40974_72699_07893_913e1,
0.40993_87907_63680_15361_45e1,
0.1e1))
end
end
function erfinv(x::Float32)
a = abs(x)
if a >= 1.0f0
if x == 1.0f0
return Inf32
elseif x == -1.0f0
return -Inf32
end
throw(DomainError())
elseif a <= 0.75f0 # Table 10 in Blair et al.
t = x*x - 0.5625f0
return x * @horner(t, -0.13095_99674_22f2,
0.26785_22576_0f2,
-0.92890_57365f1) /
@horner(t, -0.12074_94262_97f2,
0.30960_61452_9f2,
-0.17149_97799_1f2,
0.1f1)
elseif a <= 0.9375f0 # Table 29 in Blair et al.
t = x*x - 0.87890625f0
return x * @horner(t, -0.12402_56522_1f0,
0.10688_05957_4f1,
-0.19594_55607_8f1,
0.42305_81357f0) /
@horner(t, -0.88276_97997f-1,
0.89007_43359f0,
-0.21757_03119_6f1,
0.1f1)
else # Table 50 in Blair et al.
t = 1.0f0 / sqrt(-log(1.0f0 - a))
return @horner(t, 0.15504_70003_116f0,
0.13827_19649_631f1,
0.69096_93488_87f0,
-0.11280_81391_617f1,
0.68054_42468_25f0,
-0.16444_15679_1f0) /
(copysign(t, x) *
@horner(t, 0.15502_48498_22f0,
0.13852_28141_995f1,
0.1f1))
end
end
erfinv(x::Integer) = erfinv(float(x))
@vectorize_1arg Real erfinv
# Inverse complementary error function: use Blair tables for y = 1-x,
# exploiting the greater accuracy of y (vs. x) when y is small.
function erfcinv(y::Float64)
if y > 0.0625
return erfinv(1.0 - y)
elseif y <= 0.0
if y == 0.0
return Inf
end
throw(DomainError())
elseif y >= 1e-100 # Table 57 in Blair et al.
t = 1.0 / sqrt(-log(y))
return @horner(t, 0.10501_31152_37334_38116e-3,
0.10532_61131_42333_38164_25e-1,
0.26987_80273_62432_83544_516,
0.23268_69578_89196_90806_414e1,
0.71678_54794_91079_96810_001e1,
0.85475_61182_21678_27825_185e1,
0.68738_08807_35438_39802_913e1,
0.36270_02483_09587_08930_02e1,
0.88606_27392_96515_46814_9) /
(t *
@horner(t, 0.10501_26668_70303_37690e-3,
0.10532_86230_09333_27531_11e-1,
0.27019_86237_37515_54845_553,
0.23501_43639_79702_53259_123e1,
0.76078_02878_58012_77064_351e1,
0.11181_58610_40569_07827_3451e2,
0.11948_78791_84353_96667_8438e2,
0.81922_40974_72699_07893_913e1,
0.40993_87907_63680_15361_45e1,
0.1e1))
else # Table 80 in Blair et al.
t = 1.0 / sqrt(-log(y))
return @horner(t, 0.34654_29858_80863_50177e-9,
0.25084_67920_24075_70520_55e-6,
0.47378_13196_37286_02986_534e-4,
0.31312_60375_97786_96408_3388e-2,
0.77948_76454_41435_36994_854e-1,
0.70045_68123_35816_43868_271e0,
0.18710_42034_21679_31668_683e1,
0.71452_54774_31351_45428_3e0) /
(t * @horner(t, 0.34654_29567_31595_11156e-9,
0.25084_69079_75880_27114_87e-6,
0.47379_53129_59749_13536_339e-4,
0.31320_63536_46177_68848_0813e-2,
0.78073_48906_27648_97214_733e-1,
0.70715_04479_95337_58619_993e0,
0.19998_51543_49112_15105_214e1,
0.15072_90269_27316_80008_56e1,
0.1e1))
end
end
function erfcinv(y::Float32)
if y > 0.0625f0
return erfinv(1.0f0 - y)
elseif y <= 0.0f0
if y == 0.0f0
return Inf32
end
throw(DomainError())
else # Table 50 in Blair et al.
t = 1.0f0 / sqrt(-log(y))
return @horner(t, 0.15504_70003_116f0,
0.13827_19649_631f1,
0.69096_93488_87f0,
-0.11280_81391_617f1,
0.68054_42468_25f0,
-0.16444_15679_1f0) /
(t *
@horner(t, 0.15502_48498_22f0,
0.13852_28141_995f1,
0.1f1))
end
end
erfcinv(x::Integer) = erfcinv(float(x))
@vectorize_1arg Real erfcinv
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