/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/*
 * Return the base 2 logarithm of x.  See e_log.c and k_log.h for most
 * comments.
 *
 * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel,
 * then does the combining and scaling steps
 *    log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k
 * in not-quite-routine extra precision.
 */

#include <float.h>

#include "math.h"
#include "math_private.h"
#include "k_log.h"

static const double
two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln2hi    =  1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */
ivln2lo    =  1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */

static const double zero   =  0.0;
static volatile double vzero = 0.0;

double
log2(double x)
{
        double f,hfsq,hi,lo,r,val_hi,val_lo,w,y;
        int32_t i,k,hx;
        u_int32_t lx;

        EXTRACT_WORDS(hx,lx,x);

        k=0;
        if (hx < 0x00100000) {                  /* x < 2**-1022  */
            if (((hx&0x7fffffff)|lx)==0)
                return -two54/vzero;            /* log(+-0)=-inf */
            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
            k -= 54; x *= two54; /* subnormal number, scale up x */
            GET_HIGH_WORD(hx,x);
        }
        if (hx >= 0x7ff00000) return x+x;
        if (hx == 0x3ff00000 && lx == 0)
            return zero;                        /* log(1) = +0 */
        k += (hx>>20)-1023;
        hx &= 0x000fffff;
        i = (hx+0x95f64)&0x100000;
        SET_HIGH_WORD(x,hx|(i^0x3ff00000));     /* normalize x or x/2 */
        k += (i>>20);
        y = (double)k;
        f = x - 1.0;
        hfsq = 0.5*f*f;
        r = k_log1p(f);

        /*
         * f-hfsq must (for args near 1) be evaluated in extra precision
         * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
         * This is fairly efficient since f-hfsq only depends on f, so can
         * be evaluated in parallel with R.  Not combining hfsq with R also
         * keeps R small (though not as small as a true `lo' term would be),
         * so that extra precision is not needed for terms involving R.
         *
         * Compiler bugs involving extra precision used to break Dekker's
         * theorem for spitting f-hfsq as hi+lo, unless double_t was used
         * or the multi-precision calculations were avoided when double_t
         * has extra precision.  These problems are now automatically
         * avoided as a side effect of the optimization of combining the
         * Dekker splitting step with the clear-low-bits step.
         *
         * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
         * precision to avoid a very large cancellation when x is very near
         * these values.  Unlike the above cancellations, this problem is
         * specific to base 2.  It is strange that adding +-1 is so much
         * harder than adding +-ln2 or +-log10_2.
         *
         * This uses Dekker's theorem to normalize y+val_hi, so the
         * compiler bugs are back in some configurations, sigh.  And I
         * don't want to used double_t to avoid them, since that gives a
         * pessimization and the support for avoiding the pessimization
         * is not yet available.
         *
         * The multi-precision calculations for the multiplications are
         * routine.
         */
        hi = f - hfsq;
        SET_LOW_WORD(hi,0);
        lo = (f - hi) - hfsq + r;
        val_hi = hi*ivln2hi;
        val_lo = (lo+hi)*ivln2lo + lo*ivln2hi;

        /* spadd(val_hi, val_lo, y), except for not using double_t: */
        w = y + val_hi;
        val_lo += (y - w) + val_hi;
        val_hi = w;

        return val_lo + val_hi;
}

#if (LDBL_MANT_DIG == 53)
__weak_reference(log2, log2l);
#endif