{
"cells": [
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"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
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]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"include(\"program.jl\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Plots.PlotlyBackend()"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Plots\n",
"using Random\n",
"using Distributions\n",
"\n",
"plotly()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Zadanie 10, Franiszek malinka, Kacper Solecki\n",
"\n",
"# instrukcja:\n",
"# Nasz program udostępnia funkcje \n",
"\n",
"# -> taylor_sin(a, b) - sinus liczby a+bi liczony za pomocą szeregu Taylora\n",
"# -> taylor_cos(a, b) - cosinus liczby a+bi liczony za pomocą szeregu Taylora\n",
"# -> taylor_sinh(x) - sinus hiperboliczny liczby x liczony za pomocą szeregu Taylora\n",
"# -> taylor_cosh(x) - cosinus hiperboliczny liczby x liczony za pomocą szeregu Taylora\n",
"# -> cordic_sin(x) - sinus (rzeczywistej) liczby x liczony za pomocą algorytmu Cordic\n",
"# -> cordic_cos(x) - cosinus (rzeczywistej) liczby x liczony za pomocą algorytmu Cordic"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9092974268256817"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# porównianie na sin(2), cos(2)\n",
"sin(2.0)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.9092974268256817, -0.0)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"taylor_sin(2.0, 0.0)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9092974280938506"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cordic_sin(2.0)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-0.4161468365471424"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cos(2)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-0.41614683654714246, -0.0)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"taylor_cos(2.0, 0.0)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-0.4161468353122473"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"cordic_cos(2.0)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-5991.431207677988 - 9240.89014825243im"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# porównianie na sin(10 + 10i)\n",
"sin(10 + 10im)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-5991.431207678, -9240.890148252452)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"taylor_sin(10, 10)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"rel_error (generic function with 1 method)"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# w ten sposób liczony jest błąd względny zarówno dla liczb rzeczywistych jak i zespolonych\n",
"function rel_error(x, y)\n",
" if x == 0\n",
" return 0\n",
" end\n",
" return abs((x-y)/x)\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# Funkcje użyte w wykresach błędów od liczby iteracji:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
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"taylor_error_of_iterations (generic function with 1 method)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# błąd przy liczeniu sin(100 + 100i) szeregiem Taylora przy x iteracjach\n",
"function taylor_error_of_iterations(x)\n",
" set_taylor_iterations(x)\n",
" return rel_error(sin(100+100im), taylor_sin(100, 100)[1] + taylor_sin(100, 100)[2]*im)\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
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]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# błąd przy liczeniu sin(100) Cordicem przy x iteracjach\n",
"function cordic_error_of_iterations(x)\n",
" set_cordic_iterations(x)\n",
" return rel_error(sin(100), cordic_sin(100.0))\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
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]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# błąd przy liczeniu sin(100) szeregiem Taylora przy x iteracjach\n",
"function taylor_error_of_iterations2(x)\n",
" set_taylor_iterations(x)\n",
" return rel_error(sin(100), taylor_sin(100.0, 0.0)[1])\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
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"data": {
"text/plain": [
"1:20"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X = 1:20"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"# Przykładowe błędy w zależności od liczby iteracji\n",
"# obrazują jak szybko zbiega metoda:"
]
},
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"source": [
"plot(cordic_error_of_iterations, X, title=\"CORDIC relative error calculating sin(100)\", xguide = \"iterations\", yguide = \"relative error\")"
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"rel_error_cordic (generic function with 1 method)"
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},
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"metadata": {},
"output_type": "execute_result"
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"source": [
"# funkcje do kolejnych wykresów, pokaujących błąd względny liczenia sinusa w przedziale [0, 2pi]:\n",
"\n",
"function rel_error_cordic(x)\n",
" return rel_error(sin(x), cordic_sin(x)) \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"rel_error_taylor (generic function with 1 method)"
]
},
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"metadata": {},
"output_type": "execute_result"
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"source": [
"function rel_error_taylor(x)\n",
" return rel_error(sin(x), taylor_sin(x, 0.0)[1]) \n",
"end"
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{
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"text/plain": [
"631-element Array{Real,1}:\n",
" 0\n",
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" 1.3900944467230525e-16\n",
" 0.0\n",
" 1.1592625449066459e-16\n",
" ⋮\n",
" 2.684565604502478e-15\n",
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" 3.956085449056853e-15\n",
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"source": [
"xs = range(0, stop = 6.3, step = 0.01)\n",
"OX = [x for x in xs]\n",
"\n",
"# rysowane zbiory punktów:\n",
"res_cordic = [rel_error_cordic(x) for x in xs]\n",
"res_taylor = [rel_error_taylor(x) for x in xs]"
]
},
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"text/html": [
"\n",
"\n",
" \n",
" Plots.jl\n",
" \n",
" \n",
" \n",
" \n",
" \n",
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"\n",
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"execution_count": 33,
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],
"source": [
"# Błąd względny obliczania sinusa Cordicem na przedziale (0, 6.3)\n",
"plot(OX, res_cordic, xguide = \"x\", yguide = \"relative error\", label = \"cordic_sin\")"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
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4.404261434629184e-16,
2.1651510897764416e-16,
0,
0,
2.062497865979453e-16,
2.0308052062986278e-16,
2.00026879333912e-16,
5.912493798688494e-16,
3.8848780987071593e-16,
1.9150420465215325e-16,
3.7771867286950397e-16,
0,
1.8383679219386276e-16,
0,
5.374328004375144e-16,
3.538255951266435e-16,
1.7475349614049675e-16,
0,
1.706394298924782e-16,
0,
1.6677979118636341e-16,
0,
0,
1.614244914205175e-16,
1.5974639490452063e-16,
3.162369558719701e-16,
0,
1.550059187078887e-16,
3.0703574565125046e-16,
4.562195644258387e-16,
4.520111007352465e-16,
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1.479846845085956e-16,
2.9339835201611706e-16,
4.3635068591177836e-16,
2.8847333952391093e-16,
2.861147622891691e-16,
0,
2.8159479189618573e-16,
2.794294178091305e-16,
1.3866230613540849e-16,
1.3763930022308267e-16,
0,
1.3567812292598344e-16,
1.347383644442359e-16,
1.3382482498261752e-16,
1.3293679391630032e-16,
1.3207359088969112e-16,
0,
1.3041909020121958e-16,
1.2962657045647168e-16,
0,
0,
0,
1.266749249735528e-16,
1.2598904139149041e-16,
1.2532300997324656e-16,
1.2467638534529696e-16,
2.4809748058291475e-16,
1.2343966499087125e-16,
1.228487662980177e-16,
0,
1.217200054842107e-16,
1.211814345078375e-16,
0,
2.403084928565876e-16,
0,
1.1919160012646444e-16,
1.1873375372367847e-16,
0,
1.1786366571203686e-16,
1.1745091831979103e-16,
1.1705271597077228e-16,
1.1666883197167736e-16,
0,
1.159431612485339e-16,
1.1560096921050324e-16,
0,
0,
0,
0,
1.1408913439809627e-16,
0,
0,
1.13335576274266e-16,
1.1310913742096956e-16,
0,
0,
0,
1.1232399696452744e-16,
0,
0,
1.1185902892546942e-16,
0,
1.116068067205613e-16,
1.1149782137461506e-16,
0,
1.1131382650628477e-16,
0,
0,
0,
0,
0,
1.1103082323835086e-16,
0,
0,
1.1103952136087052e-16,
0,
1.1110087422561315e-16,
1.111482546097965e-16,
0,
1.1127654203590062e-16,
0,
0,
0,
1.116682452440973e-16,
1.1179460276394605e-16,
0,
1.1208186433579785e-16,
1.1224291488962e-16,
0,
1.1260026828125086e-16,
2.255935105086198e-16,
1.1300524934831442e-16,
0,
0,
0,
1.139615708235788e-16,
0,
1.1451492765818807e-16,
1.1481090382159398e-16,
1.1511995564462182e-16,
1.1544225107817406e-16,
1.1577796641086888e-16,
0,
1.1649040509766376e-16,
1.1686752498974867e-16,
1.172588584202073e-16,
1.1766462732973934e-16,
1.1808506369274515e-16,
0,
1.1897091891543958e-16,
0,
0,
1.2041612350137525e-16,
1.209300435268994e-16,
2.4292113410861716e-16,
1.220080203971579e-16,
0,
0,
0,
0,
1.250116608673639e-16,
1.2566836536960143e-16,
1.2634470692275536e-16,
1.270411406998836e-16,
1.2775814127819088e-16,
1.2849620351960983e-16,
1.2925584350397737e-16,
0,
1.3084203310632902e-16,
0,
1.3252130220909538e-16,
0,
1.3429865235506927e-16,
1.3522579286198734e-16,
0,
0,
2.763398071695497e-16,
4.176244571865108e-16,
0,
1.4137512447723414e-16,
2.8501141514186526e-16,
4.3100700504617343e-16,
1.4486605008501036e-16,
1.4609794609662345e-16,
1.4736583597381477e-16,
1.4867092201840918e-16,
1.5001446590650702e-16,
3.027955845229322e-16,
1.5282229249143696e-16,
4.628682867434504e-16,
3.1160147839328055e-16,
4.720735233925574e-16,
4.768873133628965e-16,
4.818489692145068e-16,
0,
4.922388773801941e-16,
4.976794250466422e-16,
3.3552831543197403e-16,
3.3939004479692484e-16,
1.7168821935212026e-16,
3.474927540733853e-16,
5.276168379658806e-16,
1.7806887700364007e-16,
3.6067860072377473e-16,
3.653737457482551e-16,
3.7023025241565105e-16,
1.8762781663467565e-16,
3.804578860517068e-16,
3.8584553321761154e-16,
1.9571383268998396e-16,
3.972139891509996e-16,
0,
4.0944144007780993e-16,
2.0795278182375914e-16,
4.2262000765257808e-16,
2.147992357893987e-16,
6.552835285415283e-16,
3.333056321357456e-16,
5.653388022234267e-16,
3.4534855765927816e-16,
4.690085762611658e-16,
5.974051962186521e-16,
4.872349332393389e-16,
4.969663806653859e-16,
6.339327832945269e-16,
3.883535282291679e-16,
6.612185522346913e-16,
5.406927923382882e-16,
5.529982124920038e-16,
5.659346964712524e-16,
4.3466270766498696e-16,
4.454235028799948e-16,
6.090366171355489e-16,
4.687734971589835e-16,
6.419547431386734e-16,
6.598879258178374e-16,
6.7892168171707615e-16,
6.991580574555936e-16,
5.405341027196453e-16,
5.577856436088656e-16,
9.603903370021445e-16,
7.946753360364779e-16,
8.229970997614497e-16,
8.53500714909746e-16,
1.1080557445894173e-15,
1.1526620823533043e-15,
1.0810220332254982e-15,
1.1285963531614852e-15,
1.0494882678197345e-15,
1.1003739582952188e-15,
1.3011380459329525e-15,
1.3713040537010517e-15,
1.4496222788057203e-15,
1.7084347734374231e-15,
1.637100998723299e-15,
1.5560615516704497e-15,
1.881140068692716e-15,
1.920035175288847e-15,
2.211721171685521e-15,
2.2904575492979325e-15,
2.684565604502478e-15,
2.839380050077419e-15,
3.0367153263107948e-15,
3.956085449056853e-15,
4.6990042927913394e-15,
5.625450115568505e-15,
7.319681171152798e-15,
1.062538454174323e-14,
1.8551186877114254e-14,
7.69251100506661e-14,
1.2727917079577463e-16,
2.0634396850290369e-16
],
"yaxis": "y",
"zmax": null,
"zmin": null
}
],
"layout": {
"annotations": [],
"height": 400,
"legend": {
"bgcolor": "rgba(255, 255, 255, 1.000)",
"bordercolor": "rgba(0, 0, 0, 1.000)",
"borderwidth": 1,
"font": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "sans-serif",
"size": 11
},
"tracegroupgap": 0,
"traceorder": "normal",
"x": 1,
"xanchor": "auto",
"y": 1,
"yanchor": "auto"
},
"margin": {
"b": 20,
"l": 0,
"r": 0,
"t": 20
},
"paper_bgcolor": "rgba(255, 255, 255, 1.000)",
"plot_bgcolor": "rgba(255, 255, 255, 1.000)",
"showlegend": true,
"width": 600,
"xaxis": {
"anchor": "y",
"domain": [
0.2986913094196558,
0.9934383202099738
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
-0.189,
6.489
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "sans-serif",
"size": 11
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"0",
"1",
"2",
"3",
"4",
"5",
"6"
],
"tickvals": [
0,
1,
2,
3,
4,
5,
6
],
"title": "x",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "sans-serif",
"size": 15
},
"type": "-",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
},
"yaxis": {
"anchor": "x",
"domain": [
0.07581474190726165,
0.9901574803149606
],
"gridcolor": "rgba(0, 0, 0, 0.100)",
"gridwidth": 0.5,
"linecolor": "rgba(0, 0, 0, 1.000)",
"mirror": false,
"range": [
-2.307753301519983e-15,
7.923286335218608e-14
],
"showgrid": true,
"showline": true,
"showticklabels": true,
"tickangle": 0,
"tickcolor": "rgb(0, 0, 0)",
"tickfont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "sans-serif",
"size": 11
},
"tickmode": "array",
"ticks": "inside",
"ticktext": [
"0",
"2×10−14",
"4×10−14",
"6×10−14"
],
"tickvals": [
0,
2e-14,
4e-14,
6e-14
],
"title": "relative error",
"titlefont": {
"color": "rgba(0, 0, 0, 1.000)",
"family": "sans-serif",
"size": 15
},
"type": "-",
"visible": true,
"zeroline": false,
"zerolinecolor": "rgba(0, 0, 0, 1.000)"
}
}
},
"text/html": [
"\n",
"\n",
" \n",
" Plots.jl\n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
"\n",
" \n",
"\n"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Błąd względny obliczania sinusa szeregiem Taylora na przedziale (0, 6.3)\n",
"plot(OX, res_taylor, xguide = \"x\", yguide = \"relative error\", label = \"taylor_sin\")"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"# Poniżej znajdują się funkcje testujące, na podstawie których powstała Tabela 2 w sprawozdaniu"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"MersenneTwister(UInt32[0x00003039], Random.DSFMT.DSFMT_state(Int32[-870096391, 1072918504, -1812426662, 1073255081, -733866021, 1073404543, 807620846, 1073368448, 1919433844, 1072852359 … -362113007, 1073100625, -166402106, 1073460158, -1907020342, 721295190, -750225566, -1300227565, 382, 0]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], UInt128[0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000 … 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000], 1002, 0)"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"TESTS = 100000000\n",
"\n",
"Random.seed!(12345)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"taylor_test_error_real (generic function with 3 methods)"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# wszystkie te funkcje wyglądają bardzo podobnie\n",
"\n",
"function taylor_test_error_real(l::Float64=floatmin(), r::Float64=floatmax())\n",
" res = BigFloat(0) # suma błędów względnych\n",
" abs_res = BigFloat(0) # suma błędów bezwzględnych\n",
" maksi_rel = BigFloat(0) # max bląd względny\n",
" maksi_abs = BigFloat(0) # max bląd bezwzględny\n",
" for i = 1:TESTS\n",
" # losujemy argument z przedziału [l, r]\n",
" x = rand(Uniform(l, r))\n",
" lib_sin = sin(x)\n",
" # sprawdzanie błędu względnego z zerem nie ma sensu\n",
" if lib_sin == 0\n",
" continue\n",
" end\n",
" my_sin = taylor_sin(x, 0)\n",
" # obliczamy błąd względny względem funkcji bibliotecznej\n",
" error = rel_error(lib_sin, my_sin[1])\n",
" # obliczamy błąd bezwzględny względem funkcji bibliotecznej\n",
" abs_error = abs(my_sin[1] - lib_sin)\n",
" # aktualizujemy błędy\n",
" res += error\n",
" abs_res += abs_error\n",
" maksi_rel = max(maksi_rel, error)\n",
" maksi_abs = max(maksi_abs, abs_error)\n",
" end\n",
" return (res/TESTS, maksi_rel, abs_res/TESTS, maksi_abs)\n",
"end\n",
"\n",
"# (floatmin(), floatmax()):\n",
"# (1.887844299668514797145972383393008309519973773948872165524132116232181033410611e-15, \n",
"# 3.16719187748669057932019506480803006098767582443542778491973876953125e-08,\n",
"# 1.1794041986528804301572959036155385792454808324691839516162872314453125e-16,\n",
"# 8.8817841970012523233890533447265625e-16)\n",
"\n",
"# (-pi/2, pi/2):\n",
"# (1.471587646915289673578957365178574707202863924359834292944840261618821841693717e-15, \n",
"# 1.1848604479598457485905096801294400510329296594136394560337066650390625e-08, \n",
"# 9.765754183892570637182101557852154094518937199609354138374328613281249999999994e-17, \n",
"# 5.5511151231257827021181583404541015625e-16)\n",
"\n",
"# (0, 1):\n",
"# (8.693695902799099432701533207691913249153884601349429181102457242502623557811573e-17,\n",
"# 6.661260307992334044328275268948192015174572739102942797728701407322660088539124e-16,\n",
"# 4.293257315426284893844499634951716871000826358795166015624999999999999999999994e-17,\n",
"# 4.44089209850062616169452667236328125e-16)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"taylor_test_error_complex (generic function with 3 methods)"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function taylor_test_error_complex(l::Float64=-100.0, r::Float64=100.0)\n",
" res = BigFloat(0)\n",
" abs_res = BigFloat(0)\n",
" maksi_rel = BigFloat(0)\n",
" maksi_abs = BigFloat(0)\n",
" for i = 1:TESTS\n",
" x = rand(Uniform(l, r))\n",
" y = rand(Uniform(max(l, -Float64(√(BigFloat(r)*r - BigFloat(x)*x))), \n",
" Float64(√(BigFloat(r)*r - BigFloat(x)*x))))\n",
" lib_sin = sin(x + y*im)\n",
" my_sin = taylor_sin(x, y)\n",
" error = rel_error(lib_sin, my_sin[1] + my_sin[2]*im)\n",
" abs_error = abs(lib_sin - (my_sin[1] + my_sin[2]*im))\n",
" res += error\n",
" abs_res += abs_error\n",
" maksi_rel = max(maksi_rel, error)\n",
" maksi_abs = max(maksi_abs, abs_error)\n",
" end\n",
" return (res/TESTS, maksi_rel, abs_res/TESTS, maksi_abs)\n",
"end\n",
"\n",
"# (-100, 100):\n",
"# (4.932205036590292360305897845543684560590114030155004375572792447173773555907229e-15, \n",
"# 1.3111008357751143737471652583705182364137709072338111582212150096893310546875e-13, \n",
"# 1.688623533003329462861070079404255492323042928202526655997186385923664654746476e+26, \n",
"# 5.89784569029861503624382775296e+29)\n",
"\n",
"# (-2pi, 2pi):\n",
"# (4.338436856498561167962902801400526155223569336855327458414068651872587652334067e-16, \n",
"# 1.48720543982594402760972427363260419015678071019692652043886482715606689453125e-11, \n",
"# 1.364745868545483273874507699553481910023596725366415789061836204439613629002538e-14, \n",
"# 8.7095846425677781478128738959826782468909289747216462274082005023956298828125e-13)\n",
"\n",
"# (0, 1):\n",
"# (1.596935223079780368874812440778376297707878344605454825588075017177200118204992e-16, \n",
"# 1.098997011961567777204023105931451003520679665648174250236479565501213073730469e-15, \n",
"# 1.124298405324025732059699593805301650508046127888472394113736655893442950571177e-16, \n",
"# 1.110569915127177230816030746289393434073728902933275719533412484452128410339355e-15)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"cordic_test_error (generic function with 3 methods)"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function cordic_test_error(l::Float64=floatmin(), r::Float64=floatmax())\n",
" res = BigFloat(0)\n",
" abs_res = BigFloat(0)\n",
" maksi_rel = BigFloat(0)\n",
" maksi_abs = BigFloat(0)\n",
" for i = 1:TESTSd\n",
" x = rand(Uniform(l, r))\n",
" lib_sin = sin(x)\n",
" my_sin = cordic_sin(x)\n",
" error = rel_error(lib_sin, my_sin)\n",
" abs_error = abs(lib_sin - my_sin)\n",
" res += error\n",
" abs_res += abs_error\n",
" if error > maksi_rel\n",
" worst_rel = x\n",
" end\n",
" maksi_rel = max(maksi_rel, error)\n",
" maksi_abs = max(maksi_abs, abs_error)\n",
" end\n",
" return (res/TESTS, maksi_rel, abs_res/TESTS, maksi_abs)\n",
"end\n",
"\n",
"# (floatmin(), floatmax()):\n",
"# (3.099880824631376815575307358441341907045753361742215192539218280437518515668677e-08, \n",
"# 0.457561153670805575988111968399607576429843902587890625, \n",
"# 2.459716652636021482355597144179802356154379561203882076370064169168472290039072e-09, \n",
"# 0.0006041780891818948617810747236944735050201416015625)\n",
"\n",
"# (-2pi, 2pi):\n",
"# (2.769658715752475495709394998775060901506630522496771093654899307916206208091117e-08, \n",
"# 0.11834204003306579566778822254491387866437435150146484375, \n",
"# 2.532059440779907667675144447194875727078638982803227008844260126352310180664052e-09,\n",
"# 0.00552917548107156875403234153054654598236083984375)\n",
"\n",
"# (0, 1):\n",
"# (4.176404604808155838824592152607760760141260709650975486490997166423577713345588e-08, \n",
"# 0.091828765031669201679420666550868190824985504150390625, \n",
"# 2.613683444981852927700279986835644064485650872597943816799670457839965820312493e-09, \n",
"# 0.00052619288922584050993691562325693666934967041015625)"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"taylor_without_reduction_test_error (generic function with 3 methods)"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function taylor_without_reduction_test_error(l::Float64=-100.0, r::Float64=100.0)\n",
" res = BigFloat(0)\n",
" abs_res = BigFloat(0)\n",
" maksi_rel = BigFloat(0)\n",
" maksi_abs = BigFloat(0)\n",
" for i = 1:TESTS\n",
" x = rand(Uniform(l, r))\n",
" y = rand(Uniform(max(l, -Float64(√(BigFloat(r)*r - BigFloat(x)*x))), \n",
" Float64(√(BigFloat(r)*r - BigFloat(x)*x))))\n",
" lib_sin = sin(x + y*im)\n",
" my_sin = taylor_sin_no_reduction(x, y)\n",
" error = rel_error(lib_sin, my_sin[1] + my_sin[2]*im)\n",
" abs_error = abs(lib_sin - (my_sin[1] + my_sin[2]*im))\n",
" res += error\n",
" abs_res += abs_error\n",
" maksi_rel = max(maksi_rel, error)\n",
" maksi_abs = max(maksi_abs, abs_error)\n",
" end\n",
" return (res/TESTS, maksi_rel, abs_res/TESTS, maksi_abs)\n",
"end\n",
"\n",
"# (-100, 100)\n",
"# (4.774091809397734982069398193189465079787514988283523440828527859306283137571149e+23, \n",
"# 4.48814142545670189837451264e+26, \n",
"# 7.758560481134976967771949796127369173267383351574525337904198599731007318070319e+40, \n",
"# 2.20832987186165589366506156220211970162294784e+44)\n",
"\n",
"# (-2pi, 2pi)\n",
"# (0.6332711088634405192103194531076134843075526902544601426097735760298574150340518, \n",
"# 1.0, \n",
"# 23.44057586605533515691829807979128873527513778367553433852055381911453864572971, \n",
"# 267.74654227273646256435313262045383453369140625)\n",
"\n",
"# (0, 1)\n",
"# (1.589482169544726703219739509256918022523030217883325972454504856003547167066932e-16, \n",
"# 1.291897416767691567199962520855285151964115327068161054313577551511116325855255e-15, \n",
"# 1.118367257755837281340217148887719929595000777959128862241583039814976641146415e-16, \n",
"# 1.115760330918745818020084658567032229219617364690542160587938269600272178649902e-15)"
]
}
],
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