JDK 9 RFR of JDK-7130085 Port fdlibm hypot to Java

[joe darcy]

Hi Brian,

Thanks for the review; I plan to push a slightly amended version later 
today. The new version

* rewords the paragraph you suggested
* declares the method strictfp
* fixes a comparison that mixes integer and floating-point values
* add more test cases near the subnormal threshold

Diff of patches below.

Cheers,

-Joe
# FdLibm.java

77c97
< +        public static double compute(double x, double y) {
---
 > +        public static strictfp double compute(double x, double y) {
99,107c119,134
< +            // Note: the uses of ha and hb in hypot could be
< +            // eliminated by changing the relative magnitude
< +            // comparison below to either a floating-point divide or a
< +            // comparison of getExponent results coupled initializing
< +            // t1 and t2 using a split generated by floating-point
< +            // operations. The range filtering and exponent
< +            // adjustments already done by hypot implies should a
< +            // split would not need to worry about overflow or
< +            // underflow cases.
---
 > +            // Note: the ha and hb variables are the high-order
 > +            // 32-bits of a and b stored as integer values. The ha and
 > +            // hb values are used first for a rough magnitude
 > +            // comparison of a and b and second for simulating higher
 > +            // precision by allowing a and b, respectively, to be
 > +            // decomposed into non-overlapping portions. Both of these
 > +            // uses could be eliminated. The magnitude comparison
 > +            // could be eliminated by extracting and comparing the
 > +            // exponents of a and b or just be performing a
 > +            // floating-point divide.  Splitting a floating-point
 > +            // number into non-overlapping portions can be
 > +            // accomplished by judicious use of multiplies and
 > +            // additions. For details see T. J. Dekker, A Floating
 > +            // Point Technique for Extending the Available Precision ,
 > +            // Numerische Mathematik, vol. 18, 1971, pp.224-242 and
 > +            // subsequent work.
127c154
< +                if (hb <= Double.MIN_NORMAL) {      // subnormal b or 
0 */
---
 > +                if (b < Double.MIN_NORMAL) {      // subnormal b or 0 */
169a197,205
 > @@ -97,7 +239,7 @@
 >       *      1. Compute and return log2(x) in two pieces:
 >       *              log2(x) = w1 + w2,
 >       *         where w1 has 53 - 24 = 29 bit trailing zeros.
 > -     *      2. Perform y*log2(x) = n+y' by simulating muti-precision
 > +     *      2. Perform y*log2(x) = n+y' by simulating multi-precision
 >       *         arithmetic, where |y'| <= 0.5.
 >       *      3. Return x**y = 2**n*exp(y'*log2)
 >       *

# HypotTests.java

452,460c488,496
< +            {0x1.0p500,             0x1.0p440, 0x1.0p500},
< +            {0x1.0000000000001p500, 0x1.0p440, 0x1.0000000000001p500},
< +            {0x1.0p500,             0x1.0p439, 0x1.0p500},
< +            {0x1.0000000000001p500, 0x1.0p439, 0x1.0000000000001p500},
< +
< +            {0x1.0p-450,             0x1.0p-500, 0x1.0p-450},
< +            {0x1.0000000000001p-450, 0x1.0p-500, 0x1.0000000000001p-450},
< +            {0x1.0p-450,             0x1.fffffffffffffp-499, 0x1.0p-450},
< +            {0x1.0000000000001p-450, 0x1.fffffffffffffp-499, 
0x1.0000000000001p-450},
---
 > +            {0x1.0p500,               0x1.0p440, 0x1.0p500},
 > +            {0x1.0000000000001p500,   0x1.0p440, 0x1.0000000000001p500},
 > +            {0x1.0p500,               0x1.0p439, 0x1.0p500},
 > +            {0x1.0000000000001p500,   0x1.0p439, 0x1.0000000000001p500},
 > +
 > +            {0x1.0p-450,              0x1.0p-500, 0x1.0p-450},
 > +            {0x1.0000000000001p-450,  0x1.0p-500, 
0x1.0000000000001p-450},
 > +            {0x1.0p-450,              0x1.fffffffffffffp-499, 
0x1.0p-450},
 > +            {0x1.0000000000001p-450,  0x1.fffffffffffffp-499, 
0x1.0000000000001p-450},
473a510,518
 > +
 > +            {0x1.0000000000000p-1022, 0x0.fffffffffffffp-1022, 
0x1.6a09e667f3bccp-1022},
 > +            {0x1.0000000000000p-1021, 0x0.fffffffffffffp-1022, 
0x1.1e3779b97f4a8p-1021},
 > +            {0x1.0000000000000p-1020, 0x0.fffffffffffffp-1022, 
0x1.07e0f66afed07p-1020},
 > +
 > +            // 0x0.0000000000001P-1022 is MIN_VALUE (smallest 
nonzero number)
 > +            {0x0.0000000000001p-1022, 0x0.0000000000001p-1022, 
0x0.0000000000001p-1022},
 > +            {0x0.0000000000002p-1022, 0x0.0000000000001p-1022, 
0x0.0000000000002p-1022},
 > +            {0x0.0000000000003p-1022, 0x0.0000000000002p-1022, 
0x0.0000000000004p-1022},


-Joe

On 9/22/2015 4:20 PM, Brian Burkhalter wrote:
> Hi Joe,
>
> Overall this looks good. I only have a couple of minor observations 
> related to internal documentation.
>
> 1. FdLibm.java
>
> Lines 158-166: The verbiage in the note might benefit from a little 
> reworking.
>
> 2. HypotTests.java
>
> Line 46: “Commutative” is misspelled.
>
> Thanks,
>
> Brian
>
> On Sep 21, 2015, at 6:22 PM, Joseph D. Darcy <Joe.Darcy at Oracle.Com 
> <mailto:Joe.Darcy at Oracle.Com>> wrote:
>
>> Please review the next portion of the port of fdlibm to Java:
>>
>>    JDK-7130085 Port fdlibm hypot to Java
>> http://cr.openjdk.java.net/~darcy/7130085.0/ 
>> <http://cr.openjdk.java.net/%7Edarcy/7130085.0/>
>>
>> As before with pow, this isn't necessarily the end state of the code 
>> we'd like to stop at, but it should be sufficiently idiomatic Java 
>> for an initial port.
>>
>> To make comparison against the original C algorithm easier, I listed 
>> the C version of hypot as the base file to compare FdLibm.java against.
>