Issue #1291 - Part 3: Update fdlibm to Sept 2019 version

1 files changed, 27 insertions, 23 deletions

diff --git a/modules/fdlibm/src/e_pow.cpp b/modules/fdlibm/src/e_pow.cpp
index 7f22afce8..c18226b8a 100644
--- a/modules/fdlibm/src/e_pow.cpp
+++ b/modules/fdlibm/src/e_pow.cpp
@@ -4,7 +4,7 @@
  * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
  *
  * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice 
+ * software is freely granted, provided that this notice
  * is preserved.
  * ====================================================
  */
@@ -19,7 +19,7 @@
  *	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 multi-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)
  *
@@ -47,18 +47,19 @@
  * Accuracy:
  *	pow(x,y) returns x**y nearly rounded. In particular
  *			pow(integer,integer)
- *	always returns the correct integer provided it is 
+ *	always returns the correct integer provided it is
  *	representable.
  *
  * Constants :
- * The hexadecimal values are the intended ones for the following 
- * constants. The decimal values may be used, provided that the 
- * compiler will convert from decimal to binary accurately enough 
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
  * to produce the hexadecimal values shown.
  */
 
 #include <cmath>
 
+#include <float.h>
 #include "math_private.h"
 
 static const double
@@ -66,6 +67,9 @@ bp[] = {1.0, 1.5,},
 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
 zero    =  0.0,
+half    =  0.5,
+qrtr    =  0.25,
+thrd    =  3.3333333333333331e-01, /* 0x3fd55555, 0x55555555 */
 one	=  1.0,
 two	=  2.0,
 two53	=  9007199254740992.0,	/* 0x43400000, 0x00000000 */
@@ -108,15 +112,15 @@ __ieee754_pow(double x, double y)
 	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
 
     /* y==zero: x**0 = 1 */
-	if((iy|ly)==0) return one; 	
+	if((iy|ly)==0) return one;
 
     /* x==1: 1**y = 1, even if y is NaN */
 	if (hx==0x3ff00000 && lx == 0) return one;
 
     /* y!=zero: result is NaN if either arg is NaN */
 	if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
-	   iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) 
-		return (x+0.0)+(y+0.0);
+	   iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
+	    return nan_mix(x, y);
 
     /* determine if y is an odd int when x < 0
      * yisint = 0	... y is not an integer
@@ -124,22 +128,22 @@ __ieee754_pow(double x, double y)
      * yisint = 2	... y is an even int
      */
 	yisint  = 0;
-	if(hx<0) {	
+	if(hx<0) {
 	    if(iy>=0x43400000) yisint = 2; /* even integer y */
 	    else if(iy>=0x3ff00000) {
 		k = (iy>>20)-0x3ff;	   /* exponent */
 		if(k>20) {
 		    j = ly>>(52-k);
-		    if((j<<(52-k))==ly) yisint = 2-(j&1);
+		    if(((u_int32_t)j<<(52-k))==ly) yisint = 2-(j&1);
 		} else if(ly==0) {
 		    j = iy>>(20-k);
 		    if((j<<(20-k))==iy) yisint = 2-(j&1);
 		}
-	    }		
-	} 
+	    }
+	}
 
     /* special value of y */
-	if(ly==0) { 	
+	if(ly==0) {
 	    if (iy==0x7ff00000) {	/* y is +-inf */
 	        if(((ix-0x3ff00000)|lx)==0)
 		    return  one;	/* (-1)**+-inf is 1 */
@@ -147,7 +151,7 @@ __ieee754_pow(double x, double y)
 		    return (hy>=0)? y: zero;
 	        else			/* (|x|<1)**-,+inf = inf,0 */
 		    return (hy<0)?-y: zero;
-	    } 
+	    }
 	    if(iy==0x3ff00000) {	/* y is  +-1 */
 		if(hy<0) return one/x; else return x;
 	    }
@@ -167,13 +171,13 @@ __ieee754_pow(double x, double y)
 		if(hx<0) {
 		    if(((ix-0x3ff00000)|yisint)==0) {
 			z = (z-z)/(z-z); /* (-1)**non-int is NaN */
-		    } else if(yisint==1) 
+		    } else if(yisint==1)
 			z = -z;		/* (x<0)**odd = -(|x|**odd) */
 		}
 		return z;
 	    }
 	}
-    
+
     /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be
 	n = (hx>>31)+1;
        but ANSI C says a right shift of a signed negative quantity is
@@ -195,10 +199,10 @@ __ieee754_pow(double x, double y)
 	/* over/underflow if x is not close to one */
 	    if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
 	    if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
-	/* now |1-x| is tiny <= 2**-20, suffice to compute 
+	/* now |1-x| is tiny <= 2**-20, suffice to compute
 	   log(x) by x-x^2/2+x^3/3-x^4/4 */
 	    t = ax-one;		/* t has 20 trailing zeros */
-	    w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
+	    w = (t*t)*(half-t*(thrd-t*qrtr));
 	    u = ivln2_h*t;	/* ivln2_h has 21 sig. bits */
 	    v = t*ivln2_l-w*ivln2;
 	    t1 = u+v;
@@ -235,9 +239,9 @@ __ieee754_pow(double x, double y)
 	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
 	    r += s_l*(s_h+ss);
 	    s2  = s_h*s_h;
-	    t_h = 3.0+s2+r;
+	    t_h = 3+s2+r;
 	    SET_LOW_WORD(t_h,0);
-	    t_l = r-((t_h-3.0)-s2);
+	    t_l = r-((t_h-3)-s2);
 	/* u+v = ss*(1+...) */
 	    u = s_h*t_h;
 	    v = s_l*t_h+t_l*ss;
@@ -248,7 +252,7 @@ __ieee754_pow(double x, double y)
 	    z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
 	    z_l = cp_l*p_h+p_l*cp+dp_l[k];
 	/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
-	    t = (double)n;
+	    t = n;
 	    t1 = (((z_h+z_l)+dp_h[k])+t);
 	    SET_LOW_WORD(t1,0);
 	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
@@ -288,7 +292,7 @@ __ieee754_pow(double x, double y)
 	    n = ((n&0x000fffff)|0x00100000)>>(20-k);
 	    if(j<0) n = -n;
 	    p_h -= t;
-	} 
+	}
 	t = p_l+p_h;
 	SET_LOW_WORD(t,0);
 	u = t*lg2_h;