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authorwolfbeast <mcwerewolf@wolfbeast.com>2019-11-15 15:17:01 +0100
committerwolfbeast <mcwerewolf@wolfbeast.com>2019-11-15 15:17:01 +0100
commit5e902a4a9a25a9e151b5d3945c68517bc0c73139 (patch)
treea2e314bc193f4bdd52bb45adfc12f2803c265469 /modules/fdlibm/src/e_pow.cpp
parent6ca0b4704367f8804e0373cb439e6e17e5146e4a (diff)
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Issue #1291 - Part 3: Update fdlibm to Sept 2019 version
Diffstat (limited to 'modules/fdlibm/src/e_pow.cpp')
-rw-r--r--modules/fdlibm/src/e_pow.cpp50
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;