Java中的半精度浮点
是否有一个Java库可以对数字执行计算或将数字转换为双精度 这两种方法中的任何一种都是合适的：Java中的半精度浮点,java,floating-point,ieee-754,precision,Java,Floating Point,Ieee 754,Precision,是否有一个Java库可以对数字执行计算或将数字转换为双精度 这两种方法中的任何一种都是合适的： 将数字保持为半精度格式，并使用整数算术和位旋转进行计算（单精度和双精度也是如此） 以单精度或双精度执行所有计算，转换为/转换为传输的半精度（在这种情况下，我需要的是经过良好测试的转换函数。） 编辑：转换需要100%准确-输入文件中有大量的N、无穷大和次正常值 除了JavaScript之外的相关问题：您可以使用Float.intBitsToFloat（）和Float.floatToIntBits
- 将数字保持为半精度格式，并使用整数算术和位旋转进行计算（单精度和双精度也是如此）
- 以单精度或双精度执行所有计算，转换为/转换为传输的半精度（在这种情况下，我需要的是经过良好测试的转换函数。）
编辑：转换需要100%准确-输入文件中有大量的N、无穷大和次正常值
除了JavaScript之外的相关问题：您可以使用
Float.intBitsToFloat（）Float.floatToIntBits（）// ignores the higher 16 bits
public static float toFloat( int hbits )
{
int mant = hbits & 0x03ff; // 10 bits mantissa
int exp = hbits & 0x7c00; // 5 bits exponent
if( exp == 0x7c00 ) // NaN/Inf
exp = 0x3fc00; // -> NaN/Inf
else if( exp != 0 ) // normalized value
{
exp += 0x1c000; // exp - 15 + 127
if( mant == 0 && exp > 0x1c400 ) // smooth transition
return Float.intBitsToFloat( ( hbits & 0x8000 ) << 16
| exp << 13 | 0x3ff );
}
else if( mant != 0 ) // && exp==0 -> subnormal
{
exp = 0x1c400; // make it normal
do {
mant <<= 1; // mantissa * 2
exp -= 0x400; // decrease exp by 1
} while( ( mant & 0x400 ) == 0 ); // while not normal
mant &= 0x3ff; // discard subnormal bit
} // else +/-0 -> +/-0
return Float.intBitsToFloat( // combine all parts
( hbits & 0x8000 ) << 16 // sign << ( 31 - 15 )
| ( exp | mant ) << 13 ); // value << ( 23 - 10 )
}
covered number space on either side of the returned value:
6.0E-8 ####### ##########
4.5E-8 | #
3.0E-8 ######### ########
fromFloat（）if( mant == 0 && exp > 0x1c400 ) // smooth transition
return Float.intBitsToFloat( ( hbits & 0x8000 ) << 16 | exp << 13 | 0x3ff );
{ // avoid Inf due to rounding
if( ( fbits & 0x7fffffff ) >= 0x47800000 )
...
return sign | 0x7bff; // unrounded not quite Inf
}
fromFloat（）toFloat（）我在此将代码放入公共域。在我看到这里发布的解决方案之前，我已经想出了一些简单的方法：
public static float toFloat(int nHalf)
{
int S = (nHalf >>> 15) & 0x1;
int E = (nHalf >>> 10) & 0x1F;
int T = (nHalf ) & 0x3FF;
E = E == 0x1F
? 0xFF // it's 2^w-1; it's all 1's, so keep it all 1's for the 32-bit float
: E - 15 + 127; // adjust the exponent from the 16-bit bias to the 32-bit bias
// sign S is now bit 31
// exp E is from bit 30 to bit 23
// scale T by 13 binary digits (it grew from 10 to 23 bits)
return Float.intBitsToFloat(S << 31 | E << 23 | T << 13);
}
publicstaticfloat-toFloat（int-nHalf）
{
int S=（nHalf>>>15）和0x1；
int E=（nHalf>>>10）和0x1F；
int T=（nHalf）&0x3FF；
E=E==0x1F
0xFF//它是2^w-1；它都是1，所以保留所有1用于32位浮点
：E-15+127；//将指数从16位偏移调整为32位偏移
//符号S现在是第31位
//exp E从第30位到第23位
//按13位二进制数字缩放T（从10位增加到23位）
return Float.intBitsToFloat（Sx4u的代码将值1正确编码为0x3c00（参考：）。但是平滑度改进的解码器将其解码为1.000122。维基百科条目说整数值0..2048可以精确表示。不太好…
删除“| 0x3ff”
来自toFloat代码确保toFloat（来自float（k））==k
表示-2048..2048范围内的整数k，可能是以平滑度稍低为代价。我创建了一个名为HalfPrecisionFloat的java类，它使用x4u的解决方案。该类具有方便的方法和错误检查。它更进一步，还具有从2字节半精度值返回Double和Float的方法
希望这能帮助一些人
==>
我对小的正浮点数很感兴趣，所以我用12位尾数、无符号位和4位指数构建了这个变体，偏差为15，这样它就可以表示0到1.00之间的数字（不包括）。它在
public static float toFloat(int nHalf)
{
int S = (nHalf >>> 15) & 0x1;
int E = (nHalf >>> 10) & 0x1F;
int T = (nHalf ) & 0x3FF;
E = E == 0x1F
? 0xFF // it's 2^w-1; it's all 1's, so keep it all 1's for the 32-bit float
: E - 15 + 127; // adjust the exponent from the 16-bit bias to the 32-bit bias
// sign S is now bit 31
// exp E is from bit 30 to bit 23
// scale T by 13 binary digits (it grew from 10 to 23 bits)
return Float.intBitsToFloat(S << 31 | E << 23 | T << 13);
}
// notes from the IEEE-754 specification:
// left to right bits of a binary floating point number:
// size bit ids name description
// ---------- ------------ ---- ---------------------------
// 1 bit S sign
// w bits E[0]..E[w-1] E biased exponent
// t=p-1 bits d[1]..d[p-1] T trailing significant field
// The range of the encoding’s biased exponent E shall include:
// ― every integer between 1 and 2^w − 2, inclusive, to encode normal numbers
// ― the reserved value 0 to encode ±0 and subnormal numbers
// ― the reserved value 2w − 1 to encode +/-infinity and NaN
// The representation r of the floating-point datum, and value v of the floating-point datum
// represented, are inferred from the constituent fields as follows:
// a) If E == 2^w−1 and T != 0, then r is qNaN or sNaN and v is NaN regardless of S
// b) If E == 2^w−1 and T == 0, then r=v=(−1)^S * (+infinity)
// c) If 1 <= E <= 2^w−2, then r is (S, (E−bias), (1 + 2^(1−p) * T))
// the value of the corresponding floating-point number is
// v = (−1)^S * 2^(E−bias) * (1 + 2^(1−p) * T)
// thus normal numbers have an implicit leading significand bit of 1
// d) If E == 0 and T != 0, then r is (S, emin, (0 + 2^(1−p) * T))
// the value of the corresponding floating-point number is
// v = (−1)^S * 2^emin * (0 + 2^(1−p) * T)
// thus subnormal numbers have an implicit leading significand bit of 0
// e) If E == 0 and T ==0, then r is (S, emin, 0) and v = (−1)^S * (+0)
// parameter bin16 bin32
// -------------------------------------------- ----- -----
// k, storage width in bits 16 32
// p, precision in bits 11 24
// emax, maxiumum exponent e 15 127
// bias, E-e 15 127
// sign bit 1 1
// w, exponent field width in bits 5 8
// t, trailing significant field width in bits 10 23
import java.nio.ByteBuffer;
/**
* Accepts various forms of a floating point half-precision (2 byte) number
* and contains methods to convert to a
* full-precision floating point number Float and Double instance.
* <p>
* This implemention was inspired by x4u who is a user contributing
* to stackoverflow.com.
* (https://stackoverflow.com/users/237321/x4u).
*
* @author dougestep
*/
public class HalfPrecisionFloat {
private short halfPrecision;
private Float fullPrecision;
/**
* Creates an instance of the class from the supplied the supplied
* byte array. The byte array must be exactly two bytes in length.
*
* @param bytes the two-byte byte array.
*/
public HalfPrecisionFloat(byte[] bytes) {
if (bytes.length != 2) {
throw new IllegalArgumentException("The supplied byte array " +
"must be exactly two bytes in length");
}
final ByteBuffer buffer = ByteBuffer.wrap(bytes);
this.halfPrecision = buffer.getShort();
}
/**
* Creates an instance of this class from the supplied short number.
*
* @param number the number defined as a short.
*/
public HalfPrecisionFloat(final short number) {
this.halfPrecision = number;
this.fullPrecision = toFullPrecision();
}
/**
* Creates an instance of this class from the supplied
* full-precision floating point number.
*
* @param number the float number.
*/
public HalfPrecisionFloat(final float number) {
if (number > Short.MAX_VALUE) {
throw new IllegalArgumentException("The supplied float is too "
+ "large for a two byte representation");
}
if (number < Short.MIN_VALUE) {
throw new IllegalArgumentException("The supplied float is too "
+ "small for a two byte representation");
}
final int val = fromFullPrecision(number);
this.halfPrecision = (short) val;
this.fullPrecision = number;
}
/**
* Returns the half-precision float as a number defined as a short.
*
* @return the short.
*/
public short getHalfPrecisionAsShort() {
return halfPrecision;
}
/**
* Returns a full-precision floating pointing number from the
* half-precision value assigned on this instance.
*
* @return the full-precision floating pointing number.
*/
public float getFullFloat() {
if (fullPrecision == null) {
fullPrecision = toFullPrecision();
}
return fullPrecision;
}
/**
* Returns a full-precision double floating point number from the
* half-precision value assigned on this instance.
*
* @return the full-precision double floating pointing number.
*/
public double getFullDouble() {
return new Double(getFullFloat());
}
/**
* Returns the full-precision float number from the half-precision
* value assigned on this instance.
*
* @return the full-precision floating pointing number.
*/
private float toFullPrecision() {
int mantisa = halfPrecision & 0x03ff;
int exponent = halfPrecision & 0x7c00;
if (exponent == 0x7c00) {
exponent = 0x3fc00;
} else if (exponent != 0) {
exponent += 0x1c000;
if (mantisa == 0 && exponent > 0x1c400) {
return Float.intBitsToFloat(
(halfPrecision & 0x8000) << 16 | exponent << 13 | 0x3ff);
}
} else if (mantisa != 0) {
exponent = 0x1c400;
do {
mantisa <<= 1;
exponent -= 0x400;
} while ((mantisa & 0x400) == 0);
mantisa &= 0x3ff;
}
return Float.intBitsToFloat(
(halfPrecision & 0x8000) << 16 | (exponent | mantisa) << 13);
}
/**
* Returns the integer representation of the supplied
* full-precision floating pointing number.
*
* @param number the full-precision floating pointing number.
* @return the integer representation.
*/
private int fromFullPrecision(final float number) {
int fbits = Float.floatToIntBits(number);
int sign = fbits >>> 16 & 0x8000;
int val = (fbits & 0x7fffffff) + 0x1000;
if (val >= 0x47800000) {
if ((fbits & 0x7fffffff) >= 0x47800000) {
if (val < 0x7f800000) {
return sign | 0x7c00;
}
return sign | 0x7c00 | (fbits & 0x007fffff) >>> 13;
}
return sign | 0x7bff;
}
if (val >= 0x38800000) {
return sign | val - 0x38000000 >>> 13;
}
if (val < 0x33000000) {
return sign;
}
val = (fbits & 0x7fffffff) >>> 23;
return sign | ((fbits & 0x7fffff | 0x800000)
+ (0x800000 >>> val - 102) >>> 126 - val);
}
import org.junit.Assert;
import org.junit.Test;
import java.nio.ByteBuffer;
public class TestHalfPrecision {
private byte[] simulateBytes(final float fullPrecision) {
HalfPrecisionFloat halfFloat = new HalfPrecisionFloat(fullPrecision);
short halfShort = halfFloat.getHalfPrecisionAsShort();
ByteBuffer buffer = ByteBuffer.allocate(2);
buffer.putShort(halfShort);
return buffer.array();
}
@Test
public void testHalfPrecisionToFloatApproach() {
final float startingValue = 1.2f;
final float closestValue = 1.2001953f;
final short shortRepresentation = (short) 15565;
byte[] bytes = simulateBytes(startingValue);
HalfPrecisionFloat halfFloat = new HalfPrecisionFloat(bytes);
final float retFloat = halfFloat.getFullFloat();
Assert.assertEquals(new Float(closestValue), new Float(retFloat));
HalfPrecisionFloat otherWay = new HalfPrecisionFloat(retFloat);
final short shrtValue = otherWay.getHalfPrecisionAsShort();
Assert.assertEquals(new Short(shortRepresentation), new Short(shrtValue));
HalfPrecisionFloat backAgain = new HalfPrecisionFloat(shrtValue);
final float backFlt = backAgain.getFullFloat();
Assert.assertEquals(new Float(closestValue), new Float(backFlt));
HalfPrecisionFloat dbl = new HalfPrecisionFloat(startingValue);
final double retDbl = dbl.getFullDouble();
Assert.assertEquals(new Double(startingValue), new Double(retDbl));
}
@Test(expected = IllegalArgumentException.class)
public void testInvalidByteArray() {
ByteBuffer buffer = ByteBuffer.allocate(4);
buffer.putFloat(Float.MAX_VALUE);
byte[] bytes = buffer.array();
new HalfPrecisionFloat(bytes);
}
@Test(expected = IllegalArgumentException.class)
public void testInvalidMaxFloat() {
new HalfPrecisionFloat(Float.MAX_VALUE);
}
@Test(expected = IllegalArgumentException.class)
public void testInvalidMinFloat() {
new HalfPrecisionFloat(-35000);
}
@Test
public void testCreateWithShort() {
HalfPrecisionFloat sut = new HalfPrecisionFloat(Short.MAX_VALUE);
Assert.assertEquals(Short.MAX_VALUE, sut.getHalfPrecisionAsShort());
}
}
Smallest subnormal float : 0.0000000149
Largest subnormal float : 0.0000610203
Smallest normal float : 0.0000610352
Smallest normal float + ups: 0.0000610501
E=1, M=fff (max) : 0.0001220554
Largest normal float : 0.0078115463
0.9990000129 => 3f7fbe77 => eff8 => 0.9990234375 | error: 0.002%
0.8991000056 => 3f662b6b => ecc5 => 0.8990478516 | error: 0.006%
0.8091899753 => 3f4f2713 => e9e5 => 0.8092041016 | error: 0.002%
0.7282709479 => 3f3a6ff7 => e74e => 0.7282714844 | error: 0.000%
0.6554438472 => 3f27cb2b => e4f9 => 0.6553955078 | error: 0.007%
0.5898994207 => 3f1703a6 => e2e0 => 0.5898437500 | error: 0.009%
0.5309094787 => 3f07e9af => e0fd => 0.5308837891 | error: 0.005%
0.4778185189 => 3ef4a4a1 => de95 => 0.4778442383 | error: 0.005%
0.4300366640 => 3edc2dc4 => db86 => 0.4300537109 | error: 0.004%
0.3870329857 => 3ec62930 => d8c5 => 0.3870239258 | error: 0.002%
0.3483296633 => 3eb25844 => d64b => 0.3483276367 | error: 0.001%
0.3134966791 => 3ea082a3 => d410 => 0.3134765625 | error: 0.006%
0.2821469903 => 3e907592 => d20f => 0.2821655273 | error: 0.007%
0.2539322972 => 3e82036a => d040 => 0.2539062500 | error: 0.010%
0.2285390645 => 3e6a0625 => cd41 => 0.2285461426 | error: 0.003%
0.2056851536 => 3e529f21 => ca54 => 0.2056884766 | error: 0.002%
0.1851166338 => 3e3d8f37 => c7b2 => 0.1851196289 | error: 0.002%
0.1666049659 => 3e2a9a7e => c553 => 0.1665954590 | error: 0.006%
0.1499444693 => 3e198b0b => c331 => 0.1499328613 | error: 0.008%
0.1349500120 => 3e0a3056 => c146 => 0.1349487305 | error: 0.001%
0.1214550063 => 3df8bd67 => bf18 => 0.1214599609 | error: 0.004%
0.1093095019 => 3ddfdda9 => bbfc => 0.1093139648 | error: 0.004%
0.0983785465 => 3dc97ab1 => b92f => 0.0983734131 | error: 0.005%
0.0885406882 => 3db554d2 => b6ab => 0.0885467529 | error: 0.007%
0.0796866193 => 3da332bd => b466 => 0.0796813965 | error: 0.007%
0.0717179552 => 3d92e0dd => b25c => 0.0717163086 | error: 0.002%
0.0645461604 => 3d8430c7 => b086 => 0.0645446777 | error: 0.002%
0.0580915436 => 3d6df166 => adbe => 0.0580902100 | error: 0.002%
0.0522823893 => 3d56260f => aac5 => 0.0522842407 | error: 0.004%
0.0470541492 => 3d40bbda => a817 => 0.0470504761 | error: 0.008%
0.0423487313 => 3d2d75dd => a5af => 0.0423507690 | error: 0.005%
0.0381138586 => 3d1c1d47 => a384 => 0.0381164551 | error: 0.007%
0.0343024731 => 3d0c80c0 => a190 => 0.0343017578 | error: 0.002%
0.0308722258 => 3cfce7c0 => 9f9d => 0.0308723450 | error: 0.000%
0.0277850032 => 3ce39d60 => 9c74 => 0.0277862549 | error: 0.005%
0.0250065029 => 3cccda70 => 999b => 0.0250053406 | error: 0.005%
0.0225058515 => 3cb85e31 => 970c => 0.0225067139 | error: 0.004%
0.0202552658 => 3ca5ee5f => 94be => 0.0202560425 | error: 0.004%
0.0182297379 => 3c955688 => 92ab => 0.0182304382 | error: 0.004%
0.0164067633 => 3c86677a => 90cd => 0.0164070129 | error: 0.002%
0.0147660868 => 3c71ed75 => 8e3e => 0.0147666931 | error: 0.004%
0.0132894777 => 3c59bc1c => 8b38 => 0.0132904053 | error: 0.007%
0.0119605297 => 3c43f619 => 887f => 0.0119609833 | error: 0.004%
0.0107644768 => 3c305d7d => 860c => 0.0107650757 | error: 0.006%
0.0096880291 => 3c1eba8a => 83d7 => 0.0096874237 | error: 0.006%
0.0087192263 => 3c0edb16 => 81db => 0.0087184906 | error: 0.008%
0.0078473035 => 3c0091fa => 8012 => 0.0078468323 | error: 0.006%
0.0070625730 => 3be76d28 => 7cee => 0.0070629120 | error: 0.005%
0.0063563157 => 3bd048a4 => 7a09 => 0.0063562393 | error: 0.001%
0.0057206838 => 3bbb7493 => 776f => 0.0057210922 | error: 0.007%
0.0051486152 => 3ba8b5b7 => 7517 => 0.0051488876 | error: 0.005%
0.0046337536 => 3b97d6be => 72fb => 0.0046339035 | error: 0.003%
0.0041703782 => 3b88a7ab => 7115 => 0.0041704178 | error: 0.001%
0.0037533403 => 3b75fa9a => 6ebf => 0.0037531853 | error: 0.004%
0.0033780062 => 3b5d618a => 6bac => 0.0033779144 | error: 0.003%
0.0030402055 => 3b473e2f => 68e8 => 0.0030403137 | error: 0.004%
0.0027361847 => 3b335190 => 666a => 0.0027360916 | error: 0.003%
0.0024625661 => 3b216301 => 642c => 0.0024623871 | error: 0.007%
0.0022163095 => 3b113f81 => 6228 => 0.0022163391 | error: 0.001%
0.0019946785 => 3b02b927 => 6057 => 0.0019946098 | error: 0.003%
0.0017952106 => 3aeb4d46 => 5d6a => 0.0017952919 | error: 0.005%
0.0016156895 => 3ad3c58b => 5a79 => 0.0016157627 | error: 0.005%
0.0014541205 => 3abe9830 => 57d3 => 0.0014541149 | error: 0.000%
0.0013087085 => 3aab88f8 => 5571 => 0.0013086796 | error: 0.002%
0.0011778376 => 3a9a61ac => 534c => 0.0011777878 | error: 0.004%
0.0010600538 => 3a8af181 => 515e => 0.0010600090 | error: 0.004%
0.0009540484 => 3a7a191b => 4f43 => 0.0009540319 | error: 0.002%
0.0008586436 => 3a611698 => 4c23 => 0.0008586645 | error: 0.002%
0.0007727792 => 3a4a9455 => 4953 => 0.0007728338 | error: 0.007%
0.0006955012 => 3a36524c => 46ca => 0.0006954670 | error: 0.005%
0.0006259511 => 3a2416de => 4483 => 0.0006259680 | error: 0.003%
0.0005633560 => 3a13ae2e => 4276 => 0.0005633831 | error: 0.005%
0.0005070204 => 3a04e990 => 409d => 0.0005069971 | error: 0.005%
0.0004563183 => 39ef3e03 => 3de8 => 0.0004563332 | error: 0.003%
0.0004106865 => 39d75169 => 3aea => 0.0004106760 | error: 0.003%
0.0003696179 => 39c1c945 => 3839 => 0.0003696084 | error: 0.003%
0.0003326561 => 39ae6857 => 35cd => 0.0003326535 | error: 0.001%
0.0002993904 => 399cf781 => 339f => 0.0002993941 | error: 0.001%
0.0002694514 => 398d4527 => 31a9 => 0.0002694726 | error: 0.008%
0.0002425062 => 397e4946 => 2fc9 => 0.0002425015 | error: 0.002%
0.0002182556 => 3964db8b => 2c9b => 0.0002182424 | error: 0.006%
0.0001964300 => 394df8ca => 29bf => 0.0001964271 | error: 0.001%
0.0001767870 => 39395fe9 => 272c => 0.0001767874 | error: 0.000%
0.0001591083 => 3926d651 => 24db => 0.0001591146 | error: 0.004%
0.0001431975 => 39162749 => 22c5 => 0.0001432002 | error: 0.002%
0.0001288777 => 3907235b => 20e4 => 0.0001288652 | error: 0.010%
0.0001159900 => 38f33fa3 => 1e68 => 0.0001159906 | error: 0.001%
0.0001043910 => 38daec79 => 1b5e => 0.0001043975 | error: 0.006%
0.0000939519 => 38c50806 => 18a1 => 0.0000939518 | error: 0.000%
0.0000845567 => 38b15405 => 162b => 0.0000845641 | error: 0.009%
0.0000761010 => 389f986b => 13f3 => 0.0000761002 | error: 0.001%
0.0000684909 => 388fa2c6 => 11f4 => 0.0000684857 | error: 0.008%
0.0000616418 => 388145b2 => 1029 => 0.0000616461 | error: 0.007%
0.0000554776 => 3868b0a6 => 0e8b => 0.0000554770 | error: 0.001%
0.0000499299 => 38516bc8 => 0d17 => 0.0000499338 | error: 0.008%
0.0000449369 => 383c7a9a => 0bc8 => 0.0000449419 | error: 0.011%
0.0000404432 => 3829a18a => 0a9a => 0.0000404418 | error: 0.004%
0.0000363989 => 3818aafc => 098b => 0.0000364035 | error: 0.013%
0.0000327590 => 380966af => 0896 => 0.0000327528 | error: 0.019%
0.0000294831 => 37f7526e => 07bb => 0.0000294894 | error: 0.021%
0.0000265348 => 37de96fc => 06f5 => 0.0000265390 | error: 0.016%
0.0000238813 => 37c854af => 0643 => 0.0000238866 | error: 0.022%
0.0000214932 => 37b44c37 => 05a2 => 0.0000214875 | error: 0.026%
0.0000193438 => 37a24498 => 0512 => 0.0000193417 | error: 0.011%
0.0000174095 => 37920a89 => 0490 => 0.0000174046 | error: 0.028%
0.0000156685 => 37836fe1 => 041b => 0.0000156611 | error: 0.047%
0.0000141017 => 376c962e => 03b2 => 0.0000140965 | error: 0.037%
0.0000126915 => 3754ed8f => 0354 => 0.0000126958 | error: 0.034%
0.0000114223 => 373fa29a => 02ff => 0.0000114292 | error: 0.060%
0.0000102801 => 372c78be => 02b2 => 0.0000102818 | error: 0.016%
0.0000092521 => 371b3978 => 026d => 0.0000092536 | error: 0.016%
0.0000083269 => 370bb3b9 => 022f => 0.0000083297 | error: 0.034%
0.0000074942 => 36fb76b3 => 01f7 => 0.0000074953 | error: 0.014%
0.0000067448 => 36e2513a => 01c5 => 0.0000067502 | error: 0.081%
0.0000060703 => 36cbaf81 => 0197 => 0.0000060648 | error: 0.091%
0.0000054633 => 36b75127 => 016f => 0.0000054687 | error: 0.100%
0.0000049169 => 36a4fc3c => 014a => 0.0000049174 | error: 0.009%
0.0000044253 => 36947c9c => 0129 => 0.0000044256 | error: 0.009%
0.0000039827 => 3685a359 => 010b => 0.0000039786 | error: 0.103%
0.0000035845 => 36708c6d => 00f1 => 0.0000035912 | error: 0.188%
0.0000032260 => 36587e62 => 00d8 => 0.0000032187 | error: 0.228%
0.0000029034 => 3642d825 => 00c3 => 0.0000029057 | error: 0.080%
0.0000026131 => 362f5c21 => 00af => 0.0000026077 | error: 0.205%
0.0000023518 => 361dd2ea => 009e => 0.0000023544 | error: 0.112%
0.0000021166 => 360e0a9f => 008e => 0.0000021160 | error: 0.029%
0.0000019049 => 35ffacb7 => 0080 => 0.0000019073 | error: 0.127%
0.0000017144 => 35e61b71 => 0073 => 0.0000017136 | error: 0.047%
0.0000015430 => 35cf18b2 => 0068 => 0.0000015497 | error: 0.436%
0.0000013887 => 35ba6306 => 005d => 0.0000013858 | error: 0.208%
0.0000012498 => 35a7bf85 => 0054 => 0.0000012517 | error: 0.150%
0.0000011248 => 3596f92b => 004b => 0.0000011176 | error: 0.645%
0.0000010124 => 3587e040 => 0044 => 0.0000010133 | error: 0.091%
0.0000009111 => 357493a6 => 003d => 0.0000009090 | error: 0.236%
0.0000008200 => 355c1e7b => 0037 => 0.0000008196 | error: 0.054%
0.0000007380 => 35461b6e => 0032 => 0.0000007451 | error: 0.955%
0.0000006642 => 35324be3 => 002d => 0.0000006706 | error: 0.955%
0.0000005978 => 3520777f => 0028 => 0.0000005960 | error: 0.291%
0.0000005380 => 35106b8c => 0024 => 0.0000005364 | error: 0.291%
0.0000004842 => 3501fa64 => 0020 => 0.0000004768 | error: 1.522%
0.0000004358 => 34e9f5e7 => 001d => 0.0000004321 | error: 0.838%
0.0000003922 => 34d29083 => 001a => 0.0000003874 | error: 1.218%
0.0000003530 => 34bd820f => 0018 => 0.0000003576 | error: 1.315%
0.0000003177 => 34aa8ea7 => 0015 => 0.0000003129 | error: 1.499%
0.0000002859 => 34998063 => 0013 => 0.0000002831 | error: 0.978%
0.0000002573 => 348a26bf => 0011 => 0.0000002533 | error: 1.557%
0.0000002316 => 3478ac24 => 0010 => 0.0000002384 | error: 2.947%
0.0000002084 => 345fce20 => 000e => 0.0000002086 | error: 0.087%
0.0000001876 => 34496cb6 => 000d => 0.0000001937 | error: 3.264%
0.0000001688 => 3435483d => 000b => 0.0000001639 | error: 2.914%
0.0000001519 => 3423276a => 000a => 0.0000001490 | error: 1.933%
0.0000001368 => 3412d6ac => 0009 => 0.0000001341 | error: 1.933%
0.0000001231 => 3404279b => 0008 => 0.0000001192 | error: 3.144%
0.0000001108 => 33ede0e3 => 0007 => 0.0000001043 | error: 5.834%
0.0000000997 => 33d61732 => 0007 => 0.0000001043 | error: 4.629%
0.0000000897 => 33c0ae79 => 0006 => 0.0000000894 | error: 0.354%
0.0000000808 => 33ad69d3 => 0005 => 0.0000000745 | error: 7.735%
0.0000000727 => 339c1271 => 0005 => 0.0000000745 | error: 2.517%
0.0000000654 => 338c76ff => 0004 => 0.0000000596 | error: 8.874%
0.0000000589 => 337cd631 => 0004 => 0.0000000596 | error: 1.251%
0.0000000530 => 33638d92 => 0004 => 0.0000000596 | error: 12.501%
0.0000000477 => 334ccc36 => 0003 => 0.0000000447 | error: 6.249%
0.0000000429 => 33385163 => 0003 => 0.0000000447 | error: 4.168%
0.0000000386 => 3325e2d9 => 0003 => 0.0000000447 | error: 15.742%
0.0000000348 => 33154c29 => 0002 => 0.0000000298 | error: 14.265%
0.0000000313 => 33065e25 => 0002 => 0.0000000298 | error: 4.739%
0.0000000282 => 32f1dca9 => 0002 => 0.0000000298 | error: 5.846%
0.0000000253 => 32d9acfe => 0002 => 0.0000000298 | error: 17.606%
0.0000000228 => 32c3e87e => 0002 => 0.0000000298 | error: 30.673%
0.0000000205 => 32b0513e => 0001 => 0.0000000149 | error: 27.404%
0.0000000185 => 329eaf84 => 0001 => 0.0000000149 | error: 19.337%
0.0000000166 => 328ed12a => 0001 => 0.0000000149 | error: 10.375%
0.0000000150 => 3280890c => 0001 => 0.0000000149 | error: 0.416%
0.0000000135 => 32675d15 => 0001 => 0.0000000149 | error: 10.648%
0.0000000121 => 32503a2c => 0001 => 0.0000000149 | error: 22.943%
0.0000000109 => 323b678e => 0001 => 0.0000000149 | error: 36.603%
0.0000000098 => 3228aa00 => 0001 => 0.0000000149 | error: 51.781%
0.0000000088 => 3217cc33 => 0001 => 0.0000000149 | error: 68.646%
0.0000000080 => 32089e2e => 0001 => 0.0000000149 | error: 87.384%
0.0000000072 => 31f5e986 => 0000 => 0.0000000000 | error: 100.000%