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#217 Compute acos with less cancellation near x=1
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@ -744,14 +744,13 @@
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Ctor.precision = pr + 6;
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Ctor.rounding = 1;
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x = x.asin();
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halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
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x = (new Ctor(1)).minus(x).div(x.plus(1)).sqrt().atan();
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Ctor.precision = pr;
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Ctor.rounding = rm;
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return halfPi.minus(x);
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return x.times(2);
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};
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@ -741,13 +741,12 @@ P.inverseCosine = P.acos = function () {
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Ctor.precision = pr + 6;
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Ctor.rounding = 1;
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x = x.asin();
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halfPi = getPi(Ctor, pr + 4, rm).times(0.5);
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x = (new Ctor(1)).minus(x).div(x.plus(1)).sqrt().atan();
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Ctor.precision = pr;
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Ctor.rounding = rm;
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return halfPi.minus(x);
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return x.times(2);
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};
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3
test/hypothesis/.gitignore
vendored
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3
test/hypothesis/.gitignore
vendored
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@ -0,0 +1,3 @@
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__pycache__
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.hypothesis
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.ipynb_checkpoints
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99
test/hypothesis/error_hunt.py
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99
test/hypothesis/error_hunt.py
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@ -0,0 +1,99 @@
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from decimal import Decimal, getcontext
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import json
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import subprocess
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import hypothesis
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from hypothesis import given, settings
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from hypothesis.strategies import decimals, integers, tuples
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from mpmath import mp
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import pytest
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mp.prec = 500
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getcontext().prec = 14
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node = subprocess.Popen(
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["node", "evaluate.mjs"], stdout=subprocess.PIPE, stdin=subprocess.PIPE
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)
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def get_decimal(func: str, args: list, config: dict):
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arg = json.dumps({"func": func, "args": args, "config": config}).encode() + b"\r"
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node.stdin.write(arg)
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node.stdin.flush()
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return Decimal(node.stdout.readline().strip().decode())
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def assert_matches(x, mpfunc, jsfunc=None):
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if jsfunc is None:
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jsfunc = mpfunc
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y = Decimal(str(getattr(mp, mpfunc)(x))) * Decimal("1.0")
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z = get_decimal(jsfunc, [str(x)], {"precision": 14})
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assert y == z
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@pytest.mark.parametrize("fn", "sin cos tan atan asinh".split())
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@given(
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x=tuples(
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decimals(
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allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
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),
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integers(min_value=-99, max_value=99),
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).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
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)
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@settings(max_examples=100_000)
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def test_matches(x, fn):
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assert_matches(x, fn)
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@pytest.mark.parametrize("fn", "ln log10 sqrt".split())
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@given(
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x=tuples(
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decimals(
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allow_nan=False,
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allow_infinity=False,
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min_value=1e-13,
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max_value=1,
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places=14,
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),
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integers(min_value=-99, max_value=99),
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).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
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)
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@settings(max_examples=100_000)
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def test_positive_domain(x, fn):
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assert_matches(x, fn)
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@pytest.mark.parametrize("fn", "asin acos atanh".split())
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@given(
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x=decimals(
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allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
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)
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)
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@settings(max_examples=100_000)
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def test_inverse_trig(x, fn):
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assert_matches(x, fn)
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@pytest.mark.parametrize("fn", "sinh cosh tanh exp".split())
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@given(
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x=tuples(
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decimals(
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allow_nan=False, allow_infinity=False, min_value=-1, max_value=1, places=14
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),
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integers(min_value=-99, max_value=3),
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).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
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)
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@settings(max_examples=100_000)
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def test_small_domain(x, fn):
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assert_matches(x, fn)
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@given(
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x=tuples(
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decimals(
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allow_nan=False, allow_infinity=False, min_value=1, max_value=10, places=14
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),
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integers(min_value=0, max_value=99),
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).map(lambda tup: tup[0] * Decimal(10) ** tup[1])
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)
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@settings(max_examples=100_000)
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def test_acosh(x):
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assert_matches(x, 'acosh')
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26
test/hypothesis/evaluate.mjs
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26
test/hypothesis/evaluate.mjs
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@ -0,0 +1,26 @@
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// listen for test cases, and provide the results.
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// give JSON of the test case, receive the result
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// Example:
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// > {"func":"tan", "args":["12.5"], "config":{"precision":8}}
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// -0.066468242
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import {Decimal} from '../../decimal.mjs';
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import {createInterface} from 'readline';
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const readline = createInterface({
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input: process.stdin,
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output: process.stdout
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});
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readline.on("close", () => {console.log('\n'); process.exit(0);});
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readline.on("line", (line) => {
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if (line) {
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const {func, args, config} = JSON.parse(line);
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config.defaults = true;
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Decimal.set(config);
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const result = Decimal[func](...args);
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console.log(result);
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}
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});
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3
test/hypothesis/requirements.txt
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3
test/hypothesis/requirements.txt
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@ -0,0 +1,3 @@
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hypothesis
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mpmath
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node
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@ -68,6 +68,10 @@ T('acos', function () {
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t('0.41923186648524998285699814886092351368793359300547574', 42, 3, '1.13819724675000902666504291062053681280681');
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t('-0.19508761025300975791021816036', 27, 1, '1.76714310275532020878366926');
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t('0.0623252416', 19, 0, '1.508430664767542249');
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t('0.9999999297625', 14, 4, '0.00037479994883195');
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t('0.99999999467518', 14, 4, '0.0001031970930281');
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t('0.9999999999999999995', 25, 4, '0.000000001000000000000000000041667');
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t('0.99999999999999999999995', 30, 4, '0.0000000000100000000000000000000000416667');
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/*
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t('0.95', 6, 5, '0.31756');
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@ -119,4 +119,5 @@ T('sin', function () {
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t('22011131111011111.111111611113111111111151111111', 143, 2, '0.82582504036277799386306063085803210583251158969990606609364360685569588545519071481543672724620118406694191888115120286393881609546697317692404');
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t('996270725099515169352424536636186062915113219400094989.8763797268889422850038402633796294758036260533902551191769915343780424028900449342752548782035', 46, 2, '0.6613706114081017074779805460666900787572253475');
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t('0.780360750628373', 37, 5, '0.7035358359376557390803090830882458906');
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t('5900', 14, 4, '0.088879123681079');
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});
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