Is java.lang.Math.PI equal to GCC M_PI?

Question

I encode several reference algorithms in both Java and C / C ++. Some of these algorithms use & pi ;. I would like for two implementations of each algorithm to get identical results , without rounding differently. One way to do this, which has worked so far, is to use a custom constant pi, which in both languages ​​is exactly the same as 3.14159. However, it seems silly to me to define pi when there are already high-precision constants defined both in Java libraries and in GCC.

I spent some time creating quick test programs, looking at the documentation for each library, and reading on floating point types. But I could not convince myself that java.lang.Math.PI (or java.lang.StrictMath.PI) is equal or not equal to M_PI in math.h.

GCC 3.4.4 (cygwin) math.h contains:

#define M_PI            3.14159265358979323846
                                         ^^^^^

but this one

printf("%.20f", M_PI);

produces

3.14159265358979311600
                 ^^^^^

which suggests that the last 5 digits cannot be trusted.

Meanwhile, Javadocs says java.lang.Math.PI:

A value doublethat is closer than any other to pi is the ratio of the circumference of a circle to its diameter.

and

public static final double PI  3.141592653589793d

which omits the dubious last five digits of the constant.

System.out.printf("%.20f\n", Math.PI);

produces

3.14159265358979300000
                 ^^^^^

If you have experience with floating point data types, can you convince me that these library constants are exactly equal? Or that they are definitely not equal?

Answer 1

, , , GCC Java ; ndash; , , pi, , ^{& dagger;}.

, S. Lott, , GCC M_PI double, long double, . Java, GCC, , 64- IEEE-754 double. (MSB to LSB) , double, ( JeeBee):

pi_bytes.c:

#include <math.h>
#include <stdio.h>
int main()
{
   double pi = M_PI;
   printf("%016llx\n", *((uint64_t*)&pi));
}

pi_bytes.java:

class pi_bytes
{
   public static void main(String[] a)
   {
      System.out.printf("%016x\n", Double.doubleToRawLongBits( Math.PI ) );
   }
}

:

$ gcc -lm -o pi_bytes pi_bytes.c && ./pi_bytes
400921fb54442d18

$ javac pi_bytes.java && java pi_bytes
400921fb54442d18

M_PI ( double) Math.PI , .

& ; – , , sin, cos, exp .., , .

Answer 2

.

16 . 48 , .

64- IEEE , .

#define M_PI 21 ; 63 , 80- IEEE .

, , M_PI.

Answer 3

, - PI .

Java http://java.sun.com/j2se/1.5.0/docs/api/java/lang/Double.html#doubleToRawLongBits(double), , .

Java 5 :

• PI - 3.141592653589793
• : 4614256656552045848
• Binary - 100000000001001001000011111101101010100010001000010110100011000

C double pi = M_PI; printf("%lld\n", pi);, 64- : 4614256656552045848 ( ).

Answer 4

, .

(, , x86/PowerPC), (, GCC/MS ++) , . , ( ). , ( )

- , gamestate ( node , ).

, (C/++) : Java .

:

, , Sun .

, java.lang.Math.PI GCCs M_PI . . IEEE (sin, cos, exp,...). , .

Answer 5

double 52 signficand, , 15 10 , , 5 , 20 .

Answer 6

BigDecimal , :

private static final BigDecimal PI = new BigDecimal(
"3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679" +
    "8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196" +
    "4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273" +
    "7245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094" +
    "3305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912" +
    "9833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132" +
    "0005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235" +
    "4201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859" +
    "5024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303" +
    "5982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989" +
    "3809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151" +
    "5574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012" +
    "8583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912" +
    "9331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279" +
    "6782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955" +
    "3211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000" +
    "8164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333" +
    "4547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383" +
    "8279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863" +
    "0674427862203919494504712371378696095636437191728746776465757396241389086583264599581339047802759009" +
    "9465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203" +
    "4962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382" +
    "6868386894277415599185592524595395943104997252468084598727364469584865383673622262609912460805124388" +
    "4390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506" +
    "0168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125"
);

public static void main(String... args) throws InterruptedException {
    System.out.println("PI to " + PI.scale() + " digits is " + PI);
    System.out.println("PI^2 to " + PI.scale() + " digits is " + 
            PI.multiply(PI).setScale(PI.scale(), BigDecimal.ROUND_HALF_UP));
}

Answer 7

Returns memories of the need to obtain a value for pi in fortran.

Since there were no constant libraries, I either used 4 * atan (1.) or acos (-1.).

Answer 8

No, they are not equal, they have a different representation in memory.

In general, if you want to compare 2 floating point values, you should not use == (and if you cannot work with termin 'equals'). You should use a comparison with epsilon.

double eps = 0.0000001;
if (Math.abs (Java_PI - Another_Pi) <= eps)
  System.out.println ("equals");