clean up powl.c

fix special cases, use multiplication instead of scalbnl

diff --git a/src/math/powl.c b/src/math/powl.c
index a1d2f0769eb550ac39f1cb36f93903c55ebf8e10..2ee0b10b979b02811d964feabdc6d59964f12b35 100644 (file)
--- a/src/math/powl.c
+++ b/src/math/powl.c
@@ -78,8 +78,6 @@ long double powl(long double x, long double y)
 
 /* Table size */
 #define NXT 32
-/* log2(Table size) */
-#define LNXT 5
 
 /* log(1+x) =  x - .5x^2 + x^3 *  P(z)/Q(z)
  * on the domain  2^(-1/32) - 1  <=  x  <=  2^(1/32) - 1
@@ -203,38 +201,35 @@ long double powl(long double x, long double y)
        volatile long double z=0;
        long double w=0, W=0, Wa=0, Wb=0, ya=0, yb=0, u=0;
 
-       if (y == 0.0)
-               return 1.0;
-       if (isnan(x))
+       /* make sure no invalid exception is raised by nan comparision */
+       if (isnan(x)) {
+               if (!isnan(y) && y == 0.0)
+                       return 1.0;
                return x;
-       if (isnan(y))
+       }
+       if (isnan(y)) {
+               if (x == 1.0)
+                       return 1.0;
                return y;
+       }
+       if (x == 1.0)
+               return 1.0; /* 1**y = 1, even if y is nan */
+       if (x == -1.0 && !isfinite(y))
+               return 1.0; /* -1**inf = 1 */
+       if (y == 0.0)
+               return 1.0; /* x**0 = 1, even if x is nan */
        if (y == 1.0)
                return x;
-
-       // FIXME: this is wrong, see pow special cases in c99 F.9.4.4
-       if (!isfinite(y) && (x == -1.0 || x == 1.0) )
-               return y - y;   /* +-1**inf is NaN */
-       if (x == 1.0)
-               return 1.0;
        if (y >= LDBL_MAX) {
-               if (x > 1.0)
+               if (x > 1.0 || x < -1.0)
                        return INFINITY;
-               if (x > 0.0 && x < 1.0)
-                       return 0.0;
-               if (x < -1.0)
-                       return INFINITY;
-               if (x > -1.0 && x < 0.0)
+               if (x != 0.0)
                        return 0.0;
        }
        if (y <= -LDBL_MAX) {
-               if (x > 1.0)
+               if (x > 1.0 || x < -1.0)
                        return 0.0;
-               if (x > 0.0 && x < 1.0)
-                       return INFINITY;
-               if (x < -1.0)
-                       return 0.0;
-               if (x > -1.0 && x < 0.0)
+               if (x != 0.0)
                        return INFINITY;
        }
        if (x >= LDBL_MAX) {
@@ -244,6 +239,7 @@ long double powl(long double x, long double y)
        }
 
        w = floorl(y);
+
        /* Set iyflg to 1 if y is an integer. */
        iyflg = 0;
        if (w == y)
@@ -271,43 +267,33 @@ long double powl(long double x, long double y)
                        return 0.0;
                }
        }
-
-
-       nflg = 0;       /* flag = 1 if x<0 raised to integer power */
+       nflg = 0; /* (x<0)**(odd int) */
        if (x <= 0.0) {
                if (x == 0.0) {
                        if (y < 0.0) {
                                if (signbit(x) && yoddint)
-                                       return -INFINITY;
-                               return INFINITY;
+                                       /* (-0.0)**(-odd int) = -inf, divbyzero */
+                                       return -1.0/0.0;
+                               /* (+-0.0)**(negative) = inf, divbyzero */
+                               return 1.0/0.0;
                        }
-                       if (y > 0.0) {
-                               if (signbit(x) && yoddint)
-                                       return -0.0;
-                               return 0.0;
-                       }
-                       if (y == 0.0)
-                               return 1.0;  /*   0**0   */
-                       return 0.0;  /*   0**y   */
+                       if (signbit(x) && yoddint)
+                               return -0.0;
+                       return 0.0;
                }
                if (iyflg == 0)
                        return (x - x) / (x - x); /* (x<0)**(non-int) is NaN */
-               nflg = 1;
+               /* (x<0)**(integer) */
+               if (yoddint)
+                       nflg = 1; /* negate result */
+               x = -x;
        }
-
-       /* Integer power of an integer.  */
-       if (iyflg) {
-               i = w;
-               w = floorl(x);
-               if (w == x && fabsl(y) < 32768.0) {
-                       w = powil(x, (int)y);
-                       return w;
-               }
+       /* (+integer)**(integer)  */
+       if (iyflg && floorl(x) == x && fabsl(y) < 32768.0) {
+               w = powil(x, (int)y);
+               return nflg ? -w : w;
        }
 
-       if (nflg)
-               x = fabsl(x);
-
        /* separate significand from exponent */
        x = frexpl(x, &i);
        e = i;
@@ -354,9 +340,7 @@ long double powl(long double x, long double y)
        z += x;
 
        /* Compute exponent term of the base 2 logarithm. */
-       w = -i;
-       // TODO: use w * 0x1p-5;
-       w = scalbnl(w, -LNXT); /* divide by NXT */
+       w = -i / NXT;
        w += e;
        /* Now base 2 log of x is w + z. */
 
@@ -381,7 +365,7 @@ long double powl(long double x, long double y)
 
        H = Fb + Gb;
        Ha = reducl(H);
-       w = scalbnl( Ga+Ha, LNXT );
+       w = (Ga + Ha) * NXT;
 
        /* Test the power of 2 for overflow */
        if (w > MEXP)
@@ -418,18 +402,8 @@ long double powl(long double x, long double y)
        z = z + w;
        z = scalbnl(z, i);  /* multiply by integer power of 2 */
 
-       if (nflg) {
-               /* For negative x,
-                * find out if the integer exponent
-                * is odd or even.
-                */
-               w = 0.5*y;
-               w = floorl(w);
-               w = 2.0*w;
-               if (w != y)
-                       z = -z;  /* odd exponent */
-       }
-
+       if (nflg)
+               z = -z;
        return z;
 }
 
@@ -439,15 +413,14 @@ static long double reducl(long double x)
 {
        long double t;
 
-       t = scalbnl(x, LNXT);
+       t = x * NXT;
        t = floorl(t);
-       t = scalbnl(t, -LNXT);
+       t = t / NXT;
        return t;
 }
 
-/*                                                      powil.c
- *
- *      Real raised to integer power, long double precision
+/*
+ *      Positive real raised to integer power, long double precision
  *
  *
  * SYNOPSIS:
@@ -460,7 +433,7 @@ static long double reducl(long double x)
  *
  * DESCRIPTION:
  *
- * Returns argument x raised to the nth power.
+ * Returns argument x>0 raised to the nth power.
  * The routine efficiently decomposes n as a sum of powers of
  * two. The desired power is a product of two-to-the-kth
  * powers of x.  Thus to compute the 32767 power of x requires
@@ -482,25 +455,11 @@ static long double powil(long double x, int nn)
 {
        long double ww, y;
        long double s;
-       int n, e, sign, asign, lx;
-
-       if (x == 0.0) {
-               if (nn == 0)
-                       return 1.0;
-               else if (nn < 0)
-                       return LDBL_MAX;
-               return 0.0;
-       }
+       int n, e, sign, lx;
 
        if (nn == 0)
                return 1.0;
 
-       if (x < 0.0) {
-               asign = -1;
-               x = -x;
-       } else
-               asign = 0;
-
        if (nn < 0) {
                sign = -1;
                n = -nn;
@@ -539,10 +498,8 @@ static long double powil(long double x, int nn)
        /* First bit of the power */
        if (n & 1)
                y = x;
-       else {
+       else
                y = 1.0;
-               asign = 0;
-       }
 
        ww = x;
        n >>= 1;
@@ -553,8 +510,6 @@ static long double powil(long double x, int nn)
                n >>= 1;
        }
 
-       if (asign)
-               y = -y;  /* odd power of negative number */
        if (sign < 0)
                y = 1.0/y;
        return y;