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https://github.com/RGBCube/serenity
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LibM: Implement nextafter() and nexttoward()
Patch from Anonymous.
This commit is contained in:
Andreas Kling
parent
e87eac9273
commit
0269578d3e
2 changed files with 186 additions and 10 deletions
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@ -70,11 +70,14 @@ union FloatExtractor;
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template<>
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template<>
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union FloatExtractor<double> {
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union FloatExtractor<double> {
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static const int mantissa_bits = 52;
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static const int mantissa_bits = 52;
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static const unsigned long long mantissa_max = (1ull << 52) - 1;
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static const int exponent_bias = 1023;
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static const int exponent_bias = 1023;
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static const int exponent_bits = 11;
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static const unsigned exponent_max = 2047;
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struct {
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struct {
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unsigned long long mantissa : 52;
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unsigned long long mantissa : 52;
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unsigned exponent : 11;
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unsigned exponent : 11;
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int sign : 1;
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unsigned sign : 1;
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};
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};
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double d;
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double d;
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};
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};
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@ -82,11 +85,14 @@ union FloatExtractor<double> {
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template<>
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template<>
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union FloatExtractor<float> {
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union FloatExtractor<float> {
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static const int mantissa_bits = 23;
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static const int mantissa_bits = 23;
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static const unsigned mantissa_max = (1 << 23) - 1;
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static const int exponent_bias = 127;
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static const int exponent_bias = 127;
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static const int exponent_bits = 8;
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static const unsigned exponent_max = 255;
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struct {
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struct {
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unsigned long long mantissa : 23;
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unsigned long long mantissa : 23;
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unsigned exponent : 8;
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unsigned exponent : 8;
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int sign : 1;
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unsigned sign : 1;
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};
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};
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float d;
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float d;
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};
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};
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@ -152,6 +158,71 @@ static FloatType internal_to_integer(FloatType x, RoundingMode rounding_mode)
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return extractor.d;
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return extractor.d;
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}
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}
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// This is much branchier than it really needs to be
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template<typename FloatType>
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static FloatType internal_nextafter(FloatType x, bool up)
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{
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if (!isfinite(x))
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return x;
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using Extractor = FloatExtractor<decltype(x)>;
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Extractor extractor;
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extractor.d = x;
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if (x == 0) {
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if (!extractor.sign) {
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extractor.mantissa = 1;
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extractor.sign = !up;
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return extractor.d;
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}
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if (up) {
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extractor.sign = false;
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extractor.mantissa = 1;
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return extractor.d;
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}
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extractor.mantissa = 1;
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extractor.sign = up != extractor.sign;
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return extractor.d;
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}
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if (up != extractor.sign) {
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extractor.mantissa++;
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if (!extractor.mantissa) {
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// no need to normalize the mantissa as we just hit a power
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// of two.
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extractor.exponent++;
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if (extractor.exponent == Extractor::exponent_max) {
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extractor.exponent = Extractor::exponent_max - 1;
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extractor.mantissa = Extractor::mantissa_max;
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}
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}
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return extractor.d;
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}
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if (!extractor.mantissa) {
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if (extractor.exponent) {
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extractor.exponent--;
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extractor.mantissa = Extractor::mantissa_max;
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} else {
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extractor.d = 0;
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}
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return extractor.d;
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}
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extractor.mantissa--;
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if (extractor.mantissa != Extractor::mantissa_max)
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return extractor.d;
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if (extractor.exponent) {
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extractor.exponent--;
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// normalize
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extractor.mantissa <<= 1;
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} else {
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if (extractor.sign) {
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// Negative infinity
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extractor.mantissa = 0;
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extractor.exponent = Extractor::exponent_max;
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}
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}
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return extractor.d;
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}
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extern "C" {
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extern "C" {
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double trunc(double x) NOEXCEPT
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double trunc(double x) NOEXCEPT
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@ -634,14 +705,18 @@ double erfc(double x) NOEXCEPT
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return 1 - erf(x);
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return 1 - erf(x);
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}
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}
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double nextafter(double, double) NOEXCEPT
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double nextafter(double x, double target) NOEXCEPT
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{
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{
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TODO();
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if (x == target)
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return target;
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return internal_nextafter(x, target >= x);
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}
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}
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float nextafterf(float, float) NOEXCEPT
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float nextafterf(float x, float target) NOEXCEPT
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{
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{
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TODO();
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if (x == target)
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return target;
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return internal_nextafter(x, target >= x);
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}
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}
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long double nextafterl(long double, long double) NOEXCEPT
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long double nextafterl(long double, long double) NOEXCEPT
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@ -649,14 +724,18 @@ long double nextafterl(long double, long double) NOEXCEPT
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TODO();
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TODO();
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}
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}
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double nexttoward(double, long double) NOEXCEPT
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double nexttoward(double x, long double target) NOEXCEPT
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{
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{
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TODO();
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if (x == target)
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return target;
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return internal_nextafter(x, target >= x);
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}
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}
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float nexttowardf(float, long double) NOEXCEPT
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float nexttowardf(float x, long double target) NOEXCEPT
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{
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{
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TODO();
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if (x == target)
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return target;
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return internal_nextafter(x, target >= x);
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}
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}
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long double nexttowardl(long double, long double) NOEXCEPT
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long double nexttowardl(long double, long double) NOEXCEPT
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@ -111,4 +111,101 @@ TEST_CASE(logarithms)
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EXPECT_CLOSE(log10(5), 0.698988)
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EXPECT_CLOSE(log10(5), 0.698988)
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}
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}
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union Extractor {
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explicit Extractor(double d)
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: d(d)
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{
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}
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Extractor(unsigned sign, unsigned exponent, unsigned long long mantissa)
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: mantissa(mantissa)
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, exponent(exponent)
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, sign(sign)
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{
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}
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struct {
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unsigned long long mantissa : 52;
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unsigned exponent : 11;
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unsigned sign : 1;
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};
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double d;
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bool operator==(const Extractor& other) const
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{
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return other.sign == sign && other.exponent == exponent && other.mantissa == mantissa;
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}
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};
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namespace AK {
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template<>
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struct Formatter<Extractor> : StandardFormatter {
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void format(FormatBuilder& builder, const Extractor& value)
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{
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builder.put_literal("{");
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builder.put_u64(value.sign);
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builder.put_literal(", ");
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builder.put_u64(value.exponent, 16, true);
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builder.put_literal(", ");
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builder.put_u64(value.mantissa, 16, true);
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builder.put_literal("}");
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}
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};
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}
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static Extractor nextafter_translator(Extractor x, Extractor target)
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{
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return Extractor(nextafter(x.d, target.d));
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}
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TEST_CASE(nextafter)
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{
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x1, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x0, 0x412, 0xe848200000000)), Extractor(0x0, 0x3ff, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x412, 0xe847e00000000)), Extractor(0x1, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x2));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x1, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848200000000), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x0, 0x412, 0xe8481ffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x1, 0x0, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe847e00000000), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x412, 0xe847dffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x0, 0x1)), Extractor(0x0, 0x412, 0xe847fffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x0, 0x1, 0x0)), Extractor(0x0, 0x1, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x0, 0x3ff, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x1, 0x3ff, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x0, 0x0, 0x1)), Extractor(0x0, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x1, 0x7fe, 0xffffffffffffe));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x1, 0x0), Extractor(0x0, 0x1, 0x0)), Extractor(0x1, 0x0, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x1), Extractor(0x0, 0x0, 0x1)), Extractor(0x1, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x1, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xffffffffffffe));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x1, 0x1, 0x0)), Extractor(0x0, 0x0, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x1, 0x0, 0x1)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x0, 0x0, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x419, 0x7d783fc000000)), Extractor(0x0, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x1, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x1, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x1, 0x419, 0x7d78404000000)), Extractor(0x1, 0x3ff, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x1, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d783fc000000), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x419, 0x7d783fbffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x0, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78404000000), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x1, 0x419, 0x7d78403ffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x0, 0x1)), Extractor(0x1, 0x419, 0x7d783ffffffff));
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}
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TEST_MAIN(Math)
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TEST_MAIN(Math)
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