///////////////////////////////////////
// Implements:
//   double log(double x);
///////////////////////////////////////
// Notes:
//   This is taken from newlib.
// @nolint

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

#include <stdint.h>

/* __ieee754_log(x)
 * Return the logrithm of x
 *
 * Method :                  
 *   1. Argument Reduction: find k and f such that 
 *      x = 2^k * (1+f), 
 *     where  sqrt(2)/2 < 1+f < sqrt(2) .
 *
 *   2. Approximation of log(1+f).
 *  Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
 *     = 2s + 2/3 s**3 + 2/5 s**5 + .....,
 *         = 2s + s*R
 *      We use a special Reme algorithm on [0,0.1716] to generate 
 *  a polynomial of degree 14 to approximate R The maximum error 
 *  of this polynomial approximation is bounded by 2**-58.45. In
 *  other words,
 *            2      4      6      8      10      12      14
 *      R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
 *    (the values of Lg1 to Lg7 are listed in the program)
 *  and
 *      |      2          14          |     -58.45
 *      | Lg1*s +...+Lg7*s    -  R(z) | <= 2 
 *      |                             |
 *  Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
 *  In order to guarantee error in log below 1ulp, we compute log
 *  by
 *    log(1+f) = f - s*(f - R)  (if f is not too large)
 *    log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
 *  
 *  3. Finally,  log(x) = k*ln2 + log(1+f).  
 *          = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
 *     Here ln2 is split into two floating point number: 
 *      ln2_hi + ln2_lo,
 *     where n*ln2_hi is always exact for |n| < 2000.
 *
 * Special cases:
 *  log(x) is NaN with signal if x < 0 (including -INF) ; 
 *  log(+INF) is +INF; log(0) is -INF with signal;
 *  log(NaN) is that NaN with no signal.
 *
 * Accuracy:
 *  according to an error analysis, the error is always less than
 *  1 ulp (unit in the last place).
 *
 * 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.
 */

static const double
ln2_hi  =  6.93147180369123816490e-01,  /* 3fe62e42 fee00000 */
ln2_lo  =  1.90821492927058770002e-10,  /* 3dea39ef 35793c76 */
two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */

static const double zero   =  0.0;

typedef union
{
  double value;
  struct
  {
    uint32_t lsw;
    uint32_t msw;
  } parts;
} ieee_double_shape_type;

#define EXTRACT_WORDS(ix0,ix1,d)        \
do {                \
  ieee_double_shape_type ew_u;          \
  ew_u.value = (d);           \
  (ix0) = ew_u.parts.msw;         \
  (ix1) = ew_u.parts.lsw;         \
} while (0)

/* Get the more significant 32 bit int from a double.  */

#define GET_HIGH_WORD(i,d)          \
do {                \
  ieee_double_shape_type gh_u;          \
  gh_u.value = (d);           \
  (i) = gh_u.parts.msw;           \
} while (0)

/* Set the more significant 32 bits of a double from an int.  */

#define SET_HIGH_WORD(d,v)          \
do {                \
  ieee_double_shape_type sh_u;          \
  sh_u.value = (d);           \
  sh_u.parts.msw = (v);           \
  (d) = sh_u.value;           \
} while (0)

double log(double x)
{
  double hfsq,f,s,z,R,w,t1,t2,dk;
  int32_t k,hx,i,j;
  uint32_t lx;

  EXTRACT_WORDS(hx,lx,x);

  k=0;
  if (hx < 0x00100000) {      /* x < 2**-1022  */
      if (((hx&0x7fffffff)|lx)==0) 
    return -two54/zero;   /* 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;
  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);
  f = x-1.0;
  if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
          if(f==zero) { if(k==0) return zero;  else {dk=(double)k;
                               return dk*ln2_hi+dk*ln2_lo;}}
      R = f*f*(0.5-0.33333333333333333*f);
      if(k==0) return f-R; else {dk=(double)k;
             return dk*ln2_hi-((R-dk*ln2_lo)-f);}
  }
  s = f/(2.0+f); 
  dk = (double)k;
  z = s*s;
  i = hx-0x6147a;
  w = z*z;
  j = 0x6b851-hx;
  t1= w*(Lg2+w*(Lg4+w*Lg6)); 
  t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 
  i |= j;
  R = t2+t1;
  if(i>0) {
      hfsq=0.5*f*f;
      if(k==0) return f-(hfsq-s*(hfsq+R)); else
         return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
  } else {
      if(k==0) return f-s*(f-R); else
         return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
  }
}
