RFR: JDK-8302027: Port fdlibm trig functions (sin, cos, tan) to Java

[Joe Darcy]

On Wed, 1 Mar 2023 05:28:34 GMT, Joe Darcy <darcy at openjdk.org> wrote:

> Last and certainly not least in the port of FDLIBM to Java, the transcendental methods for sin, cos, and tan.
> 
> Some more tests are to be written in the StrictMath directory to verify that the StrictMath algorihtm for sin/cos/tan is being used rather than a different one. However, I wanted to get the rest of the change out for review first.
> 
> The sin/cos/tan methods are grouped together since they share the same argument reduction logic. Argument reduction is the process of mapping an argument of a function to an argument in a restricted range (and possibly returning some function of the reduced argument). For sin, cos, and tan, since they are fundamentally periodic with respect to a multiple of pi, argument reduction is done to find the remainder of the original argument with respect to pi/2.

Various diffs to aid the review:


$ diff -w Sin.c Sin.translit.java 
1c1
< /* sin(x)
---
>     /** sin(x)
31,41c31,34
< 
< #include "fdlibm.h"
< 
< #ifdef __STDC__
<         double sin(double x)
< #else
<         double sin(x)
<         double x;
< #endif
< {
<         double y[2],z=0.0;
---
>     static class Sin {
>         static double compute(double x) {
>             double[] y = new double[2];
>             double z=0.0;
56c49
<             n = __ieee754_rem_pio2(x,y);
---
>                 n = RemPio2.__ieee754_rem_pio2(x,y);
58,60c51,53
<                 case 0: return  __kernel_sin(y[0],y[1],1);
<                 case 1: return  __kernel_cos(y[0],y[1]);
<                 case 2: return -__kernel_sin(y[0],y[1],1);
---
>                 case 0: return  Sin.__kernel_sin(y[0],y[1],1);
>                 case 1: return  Cos.__kernel_cos(y[0],y[1]);
>                 case 2: return -Sin.__kernel_sin(y[0],y[1],1);
62c55
<                         return -__kernel_cos(y[0],y[1]);
---
>                     return -Cos.__kernel_cos(y[0],y[1]);
66c59,60
< /* __kernel_sin( x, y, iy)
---
> 
>         /** __kernel_sin( x, y, iy)
93,100c87
< 
< #include "fdlibm.h"
< 
< #ifdef __STDC__
< static const double
< #else
< static double
< #endif
---
>         private static final double
109,115c96
< #ifdef __STDC__
<         double __kernel_sin(double x, double y, int iy)
< #else
<         double __kernel_sin(x, y, iy)
<         double x,y; int iy;             /* iy=0 if y is zero */
< #endif
< {
---
>         static double __kernel_sin(double x, double y, int iy) {
126a108
>     }






$ diff -w Sin.translit.java Sin.fdlibm.java 
31a32,33
>         private Sin() {throw new UnsupportedOperationException();}
> 
37c39
<             /* High word of x. */
---
>             // High word of x.
40,48c42,48
<             /* |x| ~< pi/4 */
<             ix &= 0x7fffffff;
<             if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
< 
<             /* sin(Inf or NaN) is NaN */
<             else if (ix>=0x7ff00000) return x-x;
< 
<             /* argument reduction needed */
<             else {
---
>             // |x| ~< pi/4
>             ix &= 0x7fff_ffff;
>             if (ix <= 0x3fe9_21fb) {
>                 return __kernel_sin(x, z, 0);
>             } else if (ix>=0x7ff0_0000) {  // sin(Inf or NaN) is NaN
>                 return x - x;
>             } else { // argument reduction needed
88,94c88,93
<             half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
<             S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
<             S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
<             S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
<             S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
<             S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
<             S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
---
>             S1  = -0x1.5555555555549p-3,  // -1.66666666666666324348e-01
>             S2  =  0x1.111111110f8a6p-7,  //  8.33333333332248946124e-03
>             S3  = -0x1.a01a019c161d5p-13, // -1.98412698298579493134e-04
>             S4  =  0x1.71de357b1fe7dp-19, //  2.75573137070700676789e-06
>             S5  = -0x1.ae5e68a2b9cebp-26, // -2.50507602534068634195e-08
>             S6  =  0x1.5d93a5acfd57cp-33; //  1.58969099521155010221e-10
99,101c98,102
<             ix = __HI(x)&0x7fffffff;        /* high word of x */
<             if(ix<0x3e400000)                       /* |x| < 2**-27 */
<                 {if((int)x==0) return x;}            /* generate inexact */
---
>             ix = __HI(x) & 0x7fff_ffff;        // high word of x
>             if (ix < 0x3e40_0000) {            // |x| < 2**-27
>                 if ((int)x == 0)               // generate inexact
>                     return x;
>             }
105,106c106,110
<             if(iy==0) return x+v*(S1+z*r);
<             else      return x-((z*(half*y-v*r)-y)-v*S1);
---
>             if (iy == 0) {
>                 return x + v*(S1 + z*r);
>             } else {
>                 return x - ((z*(0.5*y - v*r) - y) - v*S1);
>             }

-------------

PR: https://git.openjdk.org/jdk/pull/12800