text: /* Double-precision log(x) function.
     Copyright (c) 2018 Arm Ltd.  All rights reserved.
  
     SPDX-License-Identifier: BSD-3-Clause
  
     Redistribution and use in source and binary forms, with or without
     modification, are permitted provided that the following conditions
     are met:
     1. Redistributions of source code must retain the above copyright
        notice, this list of conditions and the following disclaimer.
     2. Redistributions in binary form must reproduce the above copyright
        notice, this list of conditions and the following disclaimer in the
        documentation and/or other materials provided with the distribution.
     3. The name of the company may not be used to endorse or promote
        products derived from this software without specific prior written
        permission.
  
     THIS SOFTWARE IS PROVIDED BY Arm LTD ``AS IS AND ANY EXPRESS OR IMPLIED
     WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
     MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
     IN NO EVENT SHALL Arm LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
     SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
     TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
     PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
     LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
     NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
     SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
  
  #include "fdlibm.h"
  #if !__OBSOLETE_MATH
  
  #include <math.h>
  #include <stdint.h>
  #include "math_config.h"
  
  #define T __log_data.tab
  #define T2 __log_data.tab2
  #define B __log_data.poly1
  #define A __log_data.poly
  #define Ln2hi __log_data.ln2hi
  #define Ln2lo __log_data.ln2lo
  #define N (1 << LOG_TABLE_BITS)
  #define OFF 0x3fe6000000000000
  
  /* Top 16 bits of a double.  */
  static inline uint32_t
  top16 (double x)
  {
    return asuint64 (x) >> 48;
  }
  
  double
  log (double x)
  {
    /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
    double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
    uint64_t ix, iz, tmp;
    uint32_t top;
    int k, i;
  
    ix = asuint64 (x);
    top = top16 (x);
  
  #if LOG_POLY1_ORDER == 10 || LOG_POLY1_ORDER == 11
  # define LO asuint64 (1.0 - 0x1p-5)
  # define HI asuint64 (1.0 + 0x1.1p-5)
  #elif LOG_POLY1_ORDER == 12
  # define LO asuint64 (1.0 - 0x1p-4)
  # define HI asuint64 (1.0 + 0x1.09p-4)
  #endif
    if (unlikely (ix - LO < HI - LO))
      {
        /* Handle close to 1.0 inputs separately.  */
        /* Fix sign of zero with downward rounding when x==1.  */
        if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
  	return 0;
        r = x - 1.0;
        r2 = r * r;
        r3 = r * r2;
  #if LOG_POLY1_ORDER == 10
        /* Worst-case error is around 0.516 ULP.  */
        y = r3 * (B[1] + r * B[2] + r2 * B[3]
  		+ r3 * (B[4] + r * B[5] + r2 * B[6] + r3 * (B[7] + r * B[8])));
        w = B[0] * r2; /* B[0] == -0.5.  */
        hi = r + w;
        y += r - hi + w;
        y += hi;
  #elif LOG_POLY1_ORDER == 11
        /* Worst-case error is around 0.516 ULP.  */
        y = r3 * (B[1] + r * B[2]
  		+ r2 * (B[3] + r * B[4] + r2 * B[5]
  			+ r3 * (B[6] + r * B[7] + r2 * B[8] + r3 * B[9])));
        w = B[0] * r2; /* B[0] == -0.5.  */
        hi = r + w;
        y += r - hi + w;
        y += hi;
  #elif LOG_POLY1_ORDER == 12
        y = r3 * (B[1] + r * B[2] + r2 * B[3]
  		+ r3 * (B[4] + r * B[5] + r2 * B[6]
  			+ r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
  # if N <= 64
        /* Worst-case error is around 0.532 ULP.  */
        w = B[0] * r2; /* B[0] == -0.5.  */
        hi = r + w;
        y += r - hi + w;
        y += hi;
  # else
        /* Worst-case error is around 0.507 ULP.  */
        w = r * 0x1p27;
        double_t rhi = r + w - w;
        double_t rlo = r - rhi;
        w = rhi * rhi * B[0]; /* B[0] == -0.5.  */
        hi = r + w;
        lo = r - hi + w;
        lo += B[0] * rlo * (rhi + r);
        y += lo;
        y += hi;
  # endif
  #endif
        return y;
      }
    if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
      {
        /* x < 0x1p-1022 or inf or nan.  */
        if (ix * 2 == 0)
  	return __math_divzero (1);
        if (ix == asuint64 (INFINITY)) /* log(inf) == inf.  */
  	return x;
        if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
  	return __math_invalid (x);
        /* x is subnormal, normalize it.  */
        ix = asuint64 (x * 0x1p52);
        ix -= 52ULL << 52;
      }
  
    /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
       The range is split into N subintervals.
       The ith subinterval contains z and c is near its center.  */
    tmp = ix - OFF;
    i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
    k = (int64_t) tmp >> 52; /* arithmetic shift */
    iz = ix - (tmp & 0xfffULL << 52);
    invc = T[i].invc;
    logc = T[i].logc;
    z = asdouble (iz);
  
    /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
    /* r ~= z/c - 1, |r| < 1/(2*N).  */
  #if HAVE_FAST_FMA
    /* rounding error: 0x1p-55/N.  */
    r = fma (z, invc, -1.0);
  #else
    /* rounding error: 0x1p-55/N + 0x1p-66.  */
    r = (z - T2[i].chi - T2[i].clo) * invc;
  #endif
    kd = (double_t) k;
  
    /* hi + lo = r + log(c) + k*Ln2.  */
    w = kd * Ln2hi + logc;
    hi = w + r;
    lo = w - hi + r + kd * Ln2lo;
  
    /* log(x) = lo + (log1p(r) - r) + hi.  */
    r2 = r * r; /* rounding error: 0x1p-54/N^2.  */
    /* Worst case error if |y| > 0x1p-5:
       0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma)
       Worst case error if |y| > 0x1p-4:
       0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma).  */
  #if LOG_POLY_ORDER == 6
    y = lo + r2 * A[0] + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi;
  #elif LOG_POLY_ORDER == 7
    y = lo
        + r2 * (A[0] + r * A[1] + r2 * (A[2] + r * A[3])
  	      + r2 * r2 * (A[4] + r * A[5]))
        + hi;
  #endif
    return y;
  }
  #endif
  