math: expf.c cleanup

similar to exp.c cleanup: use scalbnf, don't return excess precision,
drop some optimizatoins.
exp.c was changed to be more consistent with expf.c code.

diff --git a/src/math/exp.c b/src/math/exp.c
index 5c0edee..5ec8f8a 100644 (file)
--- a/src/math/exp.c
+++ b/src/math/exp.c
@@ -80,7 +80,7 @@ P5   =  4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
 
 double exp(double x)
 {
 
 double exp(double x)
 {

-       double hi, lo, c, z;
+       double hi, lo, c, xx;

        int k, sign;
        uint32_t hx;
 
        int k, sign;
        uint32_t hx;
 


@@ -92,24 +92,26 @@ double exp(double x)
        if (hx >= 0x40862e42) {  /* if |x| >= 709.78... */
                if (isnan(x))
                        return x;
        if (hx >= 0x40862e42) {  /* if |x| >= 709.78... */
                if (isnan(x))
                        return x;

+               if (hx == 0x7ff00000 && sign) /* -inf */
+                       return 0;

                if (x > 709.782712893383973096) {
                        /* overflow if x!=inf */
                        STRICT_ASSIGN(double, x, 0x1p1023 * x);
                        return x;
                }
                if (x < -745.13321910194110842) {
                if (x > 709.782712893383973096) {
                        /* overflow if x!=inf */
                        STRICT_ASSIGN(double, x, 0x1p1023 * x);
                        return x;
                }
                if (x < -745.13321910194110842) {

-                       /* underflow if x!=-inf */
-                       STRICT_ASSIGN(double, x, 0x1p-1000 / -x * 0x1p-1000);
+                       /* underflow */
+                       STRICT_ASSIGN(double, x, 0x1p-1000 * 0x1p-1000);

                        return x;
                }
        }
 
        /* argument reduction */
        if (hx > 0x3fd62e42) {  /* if |x| > 0.5 ln2 */
                        return x;
                }
        }
 
        /* argument reduction */
        if (hx > 0x3fd62e42) {  /* if |x| > 0.5 ln2 */

-               if (hx < 0x3ff0a2b2)  /* if |x| < 1.5 ln2 */
-                       k = 1 - sign - sign; /* optimization */
-               else
+               if (hx >= 0x3ff0a2b2)  /* if |x| >= 1.5 ln2 */

                        k = (int)(invln2*x + half[sign]);
                        k = (int)(invln2*x + half[sign]);

+               else
+                       k = 1 - sign - sign;

                hi = x - k*ln2hi;  /* k*ln2hi is exact here */
                lo = k*ln2lo;
                STRICT_ASSIGN(double, x, hi - lo);
                hi = x - k*ln2hi;  /* k*ln2hi is exact here */
                lo = k*ln2lo;
                STRICT_ASSIGN(double, x, hi - lo);


@@ -124,9 +126,9 @@ double exp(double x)
        }
 
        /* x is now in primary range */
        }
 
        /* x is now in primary range */

-       z = x*x;
-       c = x - z*(P1+z*(P2+z*(P3+z*(P4+z*P5))));
-       x = 1 + ((x*c/(2-c) - lo) + hi);
+       xx = x*x;
+       c = x - xx*(P1+xx*(P2+xx*(P3+xx*(P4+xx*P5))));
+       x = 1 + (x*c/(2-c) - lo + hi);

        if (k == 0)
                return x;
        return scalbn(x, k);
        if (k == 0)
                return x;
        return scalbn(x, k);

diff --git a/src/math/expf.c b/src/math/expf.c
index 3c3e2ab..8aefc91 100644 (file)
--- a/src/math/expf.c
+++ b/src/math/expf.c
@@ -16,79 +16,69 @@
 #include "libm.h"
 
 static const float
 #include "libm.h"
 
 static const float

-halF[2] = {0.5,-0.5,},
-huge    = 1.0e+30,
-o_threshold =  8.8721679688e+01,  /* 0x42b17180 */
-u_threshold = -1.0397208405e+02,  /* 0xc2cff1b5 */
-ln2HI[2]   = { 6.9314575195e-01,  /* 0x3f317200 */
-              -6.9314575195e-01,},/* 0xbf317200 */
-ln2LO[2]   = { 1.4286067653e-06,  /* 0x35bfbe8e */
-              -1.4286067653e-06,},/* 0xb5bfbe8e */
-invln2 = 1.4426950216e+00,        /* 0x3fb8aa3b */
+half[2] = {0.5,-0.5},
+ln2hi   = 6.9314575195e-1f,  /* 0x3f317200 */
+ln2lo   = 1.4286067653e-6f,  /* 0x35bfbe8e */
+invln2  = 1.4426950216e+0f,  /* 0x3fb8aa3b */

 /*
  * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
  * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
  */
 /*
  * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
  * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
  */

-P1 =  1.6666625440e-1, /*  0xaaaa8f.0p-26 */
-P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
-
-static const volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
+P1 =  1.6666625440e-1f, /*  0xaaaa8f.0p-26 */
+P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */

 
 float expf(float x)
 {
 
 float expf(float x)
 {

-       float y,hi=0.0,lo=0.0,c,t,twopk;
-       int32_t k=0,xsb;
+       float hi, lo, c, xx;
+       int k, sign;

        uint32_t hx;
 
        GET_FLOAT_WORD(hx, x);
        uint32_t hx;
 
        GET_FLOAT_WORD(hx, x);

-       xsb = (hx>>31)&1;  /* sign bit of x */
+       sign = hx >> 31;   /* sign bit of x */

        hx &= 0x7fffffff;  /* high word of |x| */
 
        hx &= 0x7fffffff;  /* high word of |x| */
 

-       /* filter out non-finite argument */
-       if (hx >= 0x42b17218) {  /* if |x|>=88.721... */
+       /* special cases */
+       if (hx >= 0x42b17218) {  /* if |x| >= 88.722839f or NaN */

                if (hx > 0x7f800000)  /* NaN */
                if (hx > 0x7f800000)  /* NaN */

-                       return x+x;
-               if (hx == 0x7f800000)  /* exp(+-inf)={inf,0} */
-                       return xsb==0 ? x : 0.0;
-               if (x > o_threshold)
-                       return huge*huge; /* overflow */
-               if (x < u_threshold)
-                       return twom100*twom100; /* underflow */
+                       return x;
+               if (!sign) {
+                       /* overflow if x!=inf */
+                       STRICT_ASSIGN(float, x, x * 0x1p127f);
+                       return x;
+               }
+               if (hx == 0x7f800000)  /* -inf */
+                       return 0;
+               if (hx >= 0x42cff1b5) { /* x <= -103.972084f */
+                       /* underflow */
+                       STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f);
+                       return x;
+               }

        }
 
        /* argument reduction */
        }
 
        /* argument reduction */

-       if (hx > 0x3eb17218) {  /* if  |x| > 0.5 ln2 */
-               if (hx < 0x3F851592) {  /* and |x| < 1.5 ln2 */
-                       hi = x-ln2HI[xsb];
-                       lo = ln2LO[xsb];
-                       k = 1 - xsb - xsb;
-               } else {
-                       k  = invln2*x + halF[xsb];
-                       t  = k;
-                       hi = x - t*ln2HI[0];  /* t*ln2HI is exact here */
-                       lo = t*ln2LO[0];
-               }
+       if (hx > 0x3eb17218) {  /* if |x| > 0.5 ln2 */
+               if (hx > 0x3f851592)  /* if |x| > 1.5 ln2 */
+                       k = invln2*x + half[sign];
+               else
+                       k = 1 - sign - sign;
+               hi = x - k*ln2hi;  /* k*ln2hi is exact here */
+               lo = k*ln2lo;

                STRICT_ASSIGN(float, x, hi - lo);
                STRICT_ASSIGN(float, x, hi - lo);

-       } else if(hx < 0x39000000)  {  /* |x|<2**-14 */
-               /* raise inexact */
-               if (huge+x > 1.0f)
-                       return 1.0f + x;
-       } else
+       } else if (hx > 0x39000000) {  /* |x| > 2**-14 */

                k = 0;
                k = 0;

+               hi = x;
+               lo = 0;
+       } else {
+               /* raise inexact */
+               FORCE_EVAL(0x1p127f + x);
+               return 1 + x;
+       }

 
        /* x is now in primary range */
 
        /* x is now in primary range */

-       t = x*x;
-       if (k >= -125)
-               SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));
-       else
-               SET_FLOAT_WORD(twopk, 0x3f800000+((k+100)<<23));
-       c  = x - t*(P1+t*P2);
+       xx = x*x;
+       c = x - xx*(P1+xx*P2);
+       x = 1 + (x*c/(2-c) - lo + hi);

        if (k == 0)
        if (k == 0)

-               return 1.0f - ((x*c)/(c - 2.0f) - x);
-       y = 1.0f - ((lo - (x*c)/(2.0f - c)) - hi);
-       if (k < -125)
-               return y*twopk*twom100;
-       if (k == 128)
-               return y*2.0f*0x1p127f;
-       return y*twopk;
+               return x;
+       return scalbnf(x, k);

 }
 }