initial check-in, version 0.5.0v0.5.0

1 files changed, 300 insertions, 0 deletions

diff --git a/src/math/e_pow.c b/src/math/e_pow.c
new file mode 100644
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+++ b/src/math/e_pow.c
@@ -0,0 +1,300 @@
+/* @(#)e_pow.c 1.5 04/04/22 SMI */
+/*
+ * ====================================================
+ * 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 
+ * is preserved.
+ * ====================================================
+ */
+
+/* pow(x,y) return x**y
+ *
+ *                    n
+ * Method:  Let x =  2   * (1+f)
+ *      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 muti-precision 
+ *         arithmetic, where |y'|<=0.5.
+ *      3. Return x**y = 2**n*exp(y'*log2)
+ *
+ * Special cases:
+ *      1.  (anything) ** 0  is 1
+ *      2.  (anything) ** 1  is itself
+ *      3.  (anything) ** NAN is NAN
+ *      4.  NAN ** (anything except 0) is NAN
+ *      5.  +-(|x| > 1) **  +INF is +INF
+ *      6.  +-(|x| > 1) **  -INF is +0
+ *      7.  +-(|x| < 1) **  +INF is +0
+ *      8.  +-(|x| < 1) **  -INF is +INF
+ *      9.  +-1         ** +-INF is NAN
+ *      10. +0 ** (+anything except 0, NAN)               is +0
+ *      11. -0 ** (+anything except 0, NAN, odd integer)  is +0
+ *      12. +0 ** (-anything except 0, NAN)               is +INF
+ *      13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
+ *      14. -0 ** (odd integer) = -( +0 ** (odd integer) )
+ *      15. +INF ** (+anything except 0,NAN) is +INF
+ *      16. +INF ** (-anything except 0,NAN) is +0
+ *      17. -INF ** (anything)  = -0 ** (-anything)
+ *      18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
+ *      19. (-anything except 0 and inf) ** (non-integer) is NAN
+ *
+ * Accuracy:
+ *      pow(x,y) returns x**y nearly rounded. In particular
+ *                      pow(integer,integer)
+ *      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 
+ * to produce the hexadecimal values shown.
+ */
+
+#include <math.h>
+#include "math_private.h"
+
+static const double
+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,
+one     =  1.0,
+two     =  2.0,
+two53   =  9007199254740992.0,  /* 0x43400000, 0x00000000 */
+huge    =  1.0e300,
+tiny    =  1.0e-300,
+        /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
+L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
+L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
+L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
+L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
+L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
+P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
+P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
+P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
+P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
+P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
+lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
+lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
+lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
+ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
+cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
+cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
+cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
+ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
+ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
+ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
+
+double
+pow(double x, double y)
+{
+        double z,ax,z_h,z_l,p_h,p_l;
+        double y1,t1,t2,r,s,t,u,v,w;
+        int32_t i,j,k,yisint,n;
+        int32_t hx,hy,ix,iy;
+        uint32_t lx,ly;
+
+        EXTRACT_WORDS(hx,lx,x);
+        EXTRACT_WORDS(hy,ly,y);
+        ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
+
+    /* y==zero: x**0 = 1 */
+        if((iy|ly)==0) return one;      
+
+    /* +-NaN return x+y */
+        if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
+           iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) 
+                return x+y;     
+
+    /* determine if y is an odd int when x < 0
+     * yisint = 0       ... y is not an integer
+     * yisint = 1       ... y is an odd int
+     * yisint = 2       ... y is an even int
+     */
+        yisint  = 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);
+                } 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 (iy==0x7ff00000) {       /* y is +-inf */
+                if(((ix-0x3ff00000)|lx)==0)
+                    return  y - y;      /* inf**+-1 is NaN */
+                else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
+                    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;
+            }
+            if(hy==0x40000000) return x*x; /* y is  2 */
+            if(hy==0x3fe00000) {        /* y is  0.5 */
+                if(hx>=0)       /* x >= +0 */
+                return sqrt(x); 
+            }
+        }
+
+        ax   = fabs(x);
+    /* special value of x */
+        if(lx==0) {
+            if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
+                z = ax;                 /*x is +-0,+-inf,+-1*/
+                if(hy<0) z = one/z;     /* z = (1/|x|) */
+                if(hx<0) {
+                    if(((ix-0x3ff00000)|yisint)==0) {
+                        z = (z-z)/(z-z); /* (-1)**non-int is NaN */
+                    } 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
+       implementation defined.  */
+        n = ((uint32_t)hx>>31)-1;
+
+    /* (x<0)**(non-int) is NaN */
+        if((n|yisint)==0) return (x-x)/(x-x);
+
+        s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+        if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
+
+    /* |y| is huge */
+        if(iy>0x41e00000) { /* if |y| > 2**31 */
+            if(iy>0x43f00000){  /* if |y| > 2**64, must o/uflow */
+                if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
+                if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
+            }
+        /* 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 
+           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));
+            u = ivln2_h*t;      /* ivln2_h has 21 sig. bits */
+            v = t*ivln2_l-w*ivln2;
+            t1 = u+v;
+            SET_LOW_WORD(t1,0);
+            t2 = v-(t1-u);
+        } else {
+            double ss,s2,s_h,s_l,t_h,t_l;
+            n = 0;
+        /* take care subnormal number */
+            if(ix<0x00100000)
+                {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
+            n  += ((ix)>>20)-0x3ff;
+            j  = ix&0x000fffff;
+        /* determine interval */
+            ix = j|0x3ff00000;          /* normalize ix */
+            if(j<=0x3988E) k=0;         /* |x|<sqrt(3/2) */
+            else if(j<0xBB67A) k=1;     /* |x|<sqrt(3)   */
+            else {k=0;n+=1;ix -= 0x00100000;}
+            SET_HIGH_WORD(ax,ix);
+
+        /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+            u = ax-bp[k];               /* bp[0]=1.0, bp[1]=1.5 */
+            v = one/(ax+bp[k]);
+            ss = u*v;
+            s_h = ss;
+            SET_LOW_WORD(s_h,0);
+        /* t_h=ax+bp[k] High */
+            t_h = zero;
+            SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
+            t_l = ax - (t_h-bp[k]);
+            s_l = v*((u-s_h*t_h)-s_h*t_l);
+        /* compute log(ax) */
+            s2 = ss*ss;
+            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;
+            SET_LOW_WORD(t_h,0);
+            t_l = r-((t_h-3.0)-s2);
+        /* u+v = ss*(1+...) */
+            u = s_h*t_h;
+            v = s_l*t_h+t_l*ss;
+        /* 2/(3log2)*(ss+...) */
+            p_h = u+v;
+            SET_LOW_WORD(p_h,0);
+            p_l = v-(p_h-u);
+            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;
+            t1 = (((z_h+z_l)+dp_h[k])+t);
+            SET_LOW_WORD(t1,0);
+            t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+        }
+
+    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+        y1  = y;
+        SET_LOW_WORD(y1,0);
+        p_l = (y-y1)*t1+y*t2;
+        p_h = y1*t1;
+        z = p_l+p_h;
+        EXTRACT_WORDS(j,i,z);
+        if (j>=0x40900000) {                            /* z >= 1024 */
+            if(((j-0x40900000)|i)!=0)                   /* if z > 1024 */
+                return s*huge*huge;                     /* overflow */
+            else {
+                if(p_l+ovt>z-p_h) return s*huge*huge;   /* overflow */
+            }
+        } else if((j&0x7fffffff)>=0x4090cc00 ) {        /* z <= -1075 */
+            if(((j-0xc090cc00)|i)!=0)           /* z < -1075 */
+                return s*tiny*tiny;             /* underflow */
+            else {
+                if(p_l<=z-p_h) return s*tiny*tiny;      /* underflow */
+            }
+        }
+    /*
+     * compute 2**(p_h+p_l)
+     */
+        i = j&0x7fffffff;
+        k = (i>>20)-0x3ff;
+        n = 0;
+        if(i>0x3fe00000) {              /* if |z| > 0.5, set n = [z+0.5] */
+            n = j+(0x00100000>>(k+1));
+            k = ((n&0x7fffffff)>>20)-0x3ff;     /* new k for n */
+            t = zero;
+            SET_HIGH_WORD(t,n&~(0x000fffff>>k));
+            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;
+        v = (p_l-(t-p_h))*lg2+t*lg2_l;
+        z = u+v;
+        w = v-(z-u);
+        t  = z*z;
+        t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+        r  = (z*t1)/(t1-two)-(w+z*w);
+        z  = one-(r-z);
+        GET_HIGH_WORD(j,z);
+        j += (n<<20);
+        if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
+        else SET_HIGH_WORD(z,j);
+        return s*z;
+}