RFR: JDK-8301396: Port fdlibm expm1 to Java

Raffaello Giulietti rgiulietti at openjdk.org
Fri Feb 3 12:52:49 UTC 2023


On Thu, 2 Feb 2023 22:18:32 GMT, Joe Darcy <darcy at openjdk.org> wrote:

> Next on the FDLIBM C -> Java port, expm1.
> Coming soon, hyperbolic transcendentals (sinh, cosh, tanh)!
> 
> For expm1, the C vs transliteration port show the usual kind of differences, beside formatting of the constants, the use of the __HI macro on the left-hand side needs to be replaced by a method call and an assignment, as seen below:
> 
> 
> < 
> < #include "fdlibm.h"
> < 
> < #ifdef __STDC__
> < static const double
> < #else
> < static double
> < #endif
> < one             = 1.0,
> < huge            = 1.0e+300,
> < tiny            = 1.0e-300,
> < o_threshold     = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
> < ln2_hi          = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
> < ln2_lo          = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
> < invln2          = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
> ---
>>     static class Expm1 {
>>         private static final double one             = 1.0;
>>         private static final double huge            = 1.0e+300;
>>         private static final double tiny            = 1.0e-300;
>>         private static final double o_threshold     = 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
>>         private static final double ln2_hi          = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */
>>         private static final double ln2_lo          = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */
>>         private static final double invln2          = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
> 111,115c104,108
> < Q1  =  -3.33333333333331316428e-02, /* BFA11111 111110F4 */
> < Q2  =   1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
> < Q3  =  -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
> < Q4  =   4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
> < Q5  =  -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
> ---
>>         private static final double Q1  =  -3.33333333333331316428e-02; /* BFA11111 111110F4 */
>>         private static final double Q2  =   1.58730158725481460165e-03; /* 3F5A01A0 19FE5585 */
>>         private static final double Q3  =  -7.93650757867487942473e-05; /* BF14CE19 9EAADBB7 */
>>         private static final double Q4  =   4.00821782732936239552e-06; /* 3ED0CFCA 86E65239 */
>>         private static final double Q5  =  -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
> 117,123c110
> < #ifdef __STDC__
> <         double expm1(double x)
> < #else
> <         double expm1(x)
> <         double x;
> < #endif
> < {
> ---
>>         static double compute(double x) {
> 126c113
> <         unsigned hx;
> ---
>>             /*unsigned*/ int hx;
> 157c144
> <                 k  = invln2*x+((xsb==0)?0.5:-0.5);
> ---
>>                     k  = (int)(invln2*x+((xsb==0)?0.5:-0.5));
> 188c175
> <                 __HI(y) += (k<<20);     /* add k to y's exponent */
> ---
>>                     y = __HI(y,  __HI(y) + (k<<20));     /* add k to y's exponent */
> 193c180
> <                 __HI(t) = 0x3ff00000 - (0x200000>>k);  /* t=1-2^-k */
> ---
>>                     t = __HI(t, 0x3ff00000 - (0x200000>>k));  /* t=1-2^-k */
> 195c182
> <                 __HI(y) += (k<<20);     /* add k to y's exponent */
> ---
>>                     y = __HI(y, __HI(y) + (k<<20));     /* add k to y's exponent */
> 197c184
> <                 __HI(t)  = ((0x3ff-k)<<20);     /* 2^-k */
> ---
>>                     t = __HI(t, ((0x3ff-k)<<20));     /* 2^-k */
> 200c187
> <                 __HI(y) += (k<<20);     /* add k to y's exponent */
> ---
>>                     y = __HI(y, __HI(y) + (k<<20));     /* add k to y's exponent */
> 205c192
> < 
> ---
>>     }
> 
> 
> When comparing the transliteration port and the more idiomatic port, there were no surprising or notable differences:
> 
> 
> $ diff -w Expm1.translit.java Expm1.fdlibm.java  
> 99,102c99,102
> <         private static final double o_threshold     = 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
> <         private static final double ln2_hi          = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */
> <         private static final double ln2_lo          = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */
> <         private static final double invln2          = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
> ---
>>         private static final double o_threshold =  0x1.62e42fefa39efp9;   //  7.09782712893383973096e+02
>>         private static final double ln2_hi      =  0x1.62e42feep-1;       //  6.93147180369123816490e-01
>>         private static final double ln2_lo      =  0x1.a39ef35793c76p-33; //  1.90821492927058770002e-10
>>         private static final double invln2      =  0x1.71547652b82fep0;   //  1.44269504088896338700e+00
> 104,108c104,108
> <         private static final double Q1  =  -3.33333333333331316428e-02; /* BFA11111 111110F4 */
> <         private static final double Q2  =   1.58730158725481460165e-03; /* 3F5A01A0 19FE5585 */
> <         private static final double Q3  =  -7.93650757867487942473e-05; /* BF14CE19 9EAADBB7 */
> <         private static final double Q4  =   4.00821782732936239552e-06; /* 3ED0CFCA 86E65239 */
> <         private static final double Q5  =  -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
> ---
>>         private static final double Q1          = -0x1.11111111110f4p-5;  // -3.33333333333331316428e-02
>>         private static final double Q2          =  0x1.a01a019fe5585p-10; //  1.58730158725481460165e-03
>>         private static final double Q3          = -0x1.4ce199eaadbb7p-14; // -7.93650757867487942473e-05
>>         private static final double Q4          =  0x1.0cfca86e65239p-18; //  4.00821782732936239552e-06
>>         private static final double Q5          = -0x1.afdb76e09c32dp-23; // -2.01099218183624371326e-07
> 116,118c116,118
> <             xsb = hx&0x80000000;            /* sign bit of x */
> <             if(xsb==0) y=x; else y= -x;     /* y = |x| */
> <             hx &= 0x7fffffff;               /* high word of |x| */
> ---
>>             xsb = hx & 0x8000_0000;            /* sign bit of x */
>>             y = Math.abs(x);
>>             hx &= 0x7fff_ffff;               /* high word of |x| */
> 121,124c121,124
> <             if(hx >= 0x4043687A) {                  /* if |x|>=56*ln2 */
> <                 if(hx >= 0x40862E42) {              /* if |x|>=709.78... */
> <                     if(hx>=0x7ff00000) {
> <                         if(((hx&0xfffff)|__LO(x))!=0)
> ---
>>             if (hx >= 0x4043_687A) {                  /* if |x| >= 56*ln2 */
>>                 if (hx >= 0x4086_2E42) {              /* if |x| >= 709.78... */
>>                     if (hx >= 0x7ff_00000) {
>>                         if (((hx & 0xf_ffff) | __LO(x)) != 0) {
> 126c126,131
> <                         else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
> ---
>>                         } else {
>>                             return (xsb == 0)? x : -1.0; /* exp(+-inf)={inf,-1} */
>>                         }
>>                     }
>>                     if (x > o_threshold) {
>>                         return huge*huge; /* overflow */
> 128d132
> <                     if(x > o_threshold) return huge*huge; /* overflow */
> 131c135
> <                     if(x+tiny<0.0)          /* raise inexact */
> ---
>>                     if (x + tiny < 0.0) {         /* raise inexact */
> 134a139
>>             }
> 137,142c142,152
> <             if(hx > 0x3fd62e42) {           /* if  |x| > 0.5 ln2 */
> <                 if(hx < 0x3FF0A2B2) {       /* and |x| < 1.5 ln2 */
> <                     if(xsb==0)
> <                         {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
> <                     else
> <                         {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
> ---
>>             if (hx > 0x3fd6_2e42) {           /* if  |x| > 0.5 ln2 */
>>                 if (hx < 0x3FF0_A2B2) {       /* and |x| < 1.5 ln2 */
>>                     if (xsb == 0) {
>>                         hi = x - ln2_hi;
>>                         lo =  ln2_lo;
>>                         k =  1;}
>>                     else {
>>                         hi = x + ln2_hi;
>>                         lo = -ln2_lo;
>>                         k = -1;
>>                     }
> 151,152c161
> <             }
> <             else if(hx < 0x3c900000) {      /* when |x|<2**-54, return x */
> ---
>>             } else if (hx < 0x3c90_0000) {      /* when |x|<2**-54, return x */
> 154a164,165
>>             } else {
>>                 k = 0;
> 156d166
> <             else k = 0;
> 164,165c174,176
> <             if(k==0) return x - (x*e-hxs);          /* c is 0 */
> <             else {
> ---
>>             if (k == 0) {
>>                 return x - (x*e - hxs);          /* c is 0 */
>>             } else {
> 168c179,181
> <                 if(k== -1) return 0.5*(x-e)-0.5;
> ---
>>                 if (k == -1) {
>>                     return 0.5*(x - e) - 0.5;
>>                 }
> 170,171c183,187
> <                     if(x < -0.25) return -2.0*(e-(x+0.5));
> <                     else          return  one+2.0*(x-e);
> ---
>>                     if(x < -0.25) {
>>                         return -2.0*(e - (x + 0.5));
>>                     } else {
>>                         return  one + 2.0*(x - e);
>>                     }
> 180c196
> <                     t = __HI(t, 0x3ff00000 - (0x200000>>k));  /* t=1-2^-k */
> ---
>>                     t = __HI(t, 0x3ff0_0000 - (0x2_00000 >> k));  /* t=1-2^-k */

With the corrections by @turbanoff LGTM.

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

PR: https://git.openjdk.org/jdk/pull/12394


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