libc/AOR_v20.02/math/log2.c

   1 /*
   2  * Double-precision log2(x) function.
   3  *
   4  * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   5  * See https://llvm.org/LICENSE.txt for license information.
   6  * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   7  */
   8
   9 #include <float.h>
  10 #include <math.h>
  11 #include <stdint.h>
  12 #include "math_config.h"
  13
  14 #define T __log2_data.tab
  15 #define T2 __log2_data.tab2
  16 #define B __log2_data.poly1
  17 #define A __log2_data.poly
  18 #define InvLn2hi __log2_data.invln2hi
  19 #define InvLn2lo __log2_data.invln2lo
  20 #define N (1 << LOG2_TABLE_BITS)
  21 #define OFF 0x3fe6000000000000
  22
  23 /* Top 16 bits of a double.  */
  24 static inline uint32_t
  25 top16 (double x)
  26 {
  27   return asuint64 (x) >> 48;
  28 }
  29
  30 double
  31 log2 (double x)
  32 {
  33   /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  34   double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
  35   uint64_t ix, iz, tmp;
  36   uint32_t top;
  37   int k, i;
  38
  39   ix = asuint64 (x);
  40   top = top16 (x);
  41
  42 #if LOG2_POLY1_ORDER == 11
  43 # define LO asuint64 (1.0 - 0x1.5b51p-5)
  44 # define HI asuint64 (1.0 + 0x1.6ab2p-5)
  45 #endif
  46   if (unlikely (ix - LO < HI - LO))
  47     {
  48       /* Handle close to 1.0 inputs separately.  */
  49       /* Fix sign of zero with downward rounding when x==1.  */
  50       if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
  51         return 0;
  52       r = x - 1.0;
  53 #if HAVE_FAST_FMA
  54       hi = r * InvLn2hi;
  55       lo = r * InvLn2lo + fma (r, InvLn2hi, -hi);
  56 #else
  57       double_t rhi, rlo;
  58       rhi = asdouble (asuint64 (r) & -1ULL << 32);
  59       rlo = r - rhi;
  60       hi = rhi * InvLn2hi;
  61       lo = rlo * InvLn2hi + r * InvLn2lo;
  62 #endif
  63       r2 = r * r; /* rounding error: 0x1p-62.  */
  64       r4 = r2 * r2;
  65 #if LOG2_POLY1_ORDER == 11
  66       /* Worst-case error is less than 0.54 ULP (0.55 ULP without fma).  */
  67       p = r2 * (B[0] + r * B[1]);
  68       y = hi + p;
  69       lo += hi - y + p;
  70       lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5])
  71                   + r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9])));
  72       y += lo;
  73 #endif
  74       return eval_as_double (y);
  75     }
  76   if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
  77     {
  78       /* x < 0x1p-1022 or inf or nan.  */
  79       if (ix * 2 == 0)
  80         return __math_divzero (1);
  81       if (ix == asuint64 (INFINITY)) /* log(inf) == inf.  */
  82         return x;
  83       if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
  84         return __math_invalid (x);
  85       /* x is subnormal, normalize it.  */
  86       ix = asuint64 (x * 0x1p52);
  87       ix -= 52ULL << 52;
  88     }
  89
  90   /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
  91      The range is split into N subintervals.
  92      The ith subinterval contains z and c is near its center.  */
  93   tmp = ix - OFF;
  94   i = (tmp >> (52 - LOG2_TABLE_BITS)) % N;
  95   k = (int64_t) tmp >> 52; /* arithmetic shift */
  96   iz = ix - (tmp & 0xfffULL << 52);
  97   invc = T[i].invc;
  98   logc = T[i].logc;
  99   z = asdouble (iz);
 100   kd = (double_t) k;
 101
 102   /* log2(x) = log2(z/c) + log2(c) + k.  */
 103   /* r ~= z/c - 1, |r| < 1/(2*N).  */
 104 #if HAVE_FAST_FMA
 105   /* rounding error: 0x1p-55/N.  */
 106   r = fma (z, invc, -1.0);
 107   t1 = r * InvLn2hi;
 108   t2 = r * InvLn2lo + fma (r, InvLn2hi, -t1);
 109 #else
 110   double_t rhi, rlo;
 111   /* rounding error: 0x1p-55/N + 0x1p-65.  */
 112   r = (z - T2[i].chi - T2[i].clo) * invc;
 113   rhi = asdouble (asuint64 (r) & -1ULL << 32);
 114   rlo = r - rhi;
 115   t1 = rhi * InvLn2hi;
 116   t2 = rlo * InvLn2hi + r * InvLn2lo;
 117 #endif
 118
 119   /* hi + lo = r/ln2 + log2(c) + k.  */
 120   t3 = kd + logc;
 121   hi = t3 + t1;
 122   lo = t3 - hi + t1 + t2;
 123
 124   /* log2(r+1) = r/ln2 + r^2*poly(r).  */
 125   /* Evaluation is optimized assuming superscalar pipelined execution.  */
 126   r2 = r * r; /* rounding error: 0x1p-54/N^2.  */
 127   r4 = r2 * r2;
 128 #if LOG2_POLY_ORDER == 7
 129   /* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
 130      ~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma).  */
 131   p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]);
 132   y = lo + r2 * p + hi;
 133 #endif
 134   return eval_as_double (y);
 135 }
 136 #if USE_GLIBC_ABI
 137 strong_alias (log2, __log2_finite)
 138 hidden_alias (log2, __ieee754_log2)
 139 # if LDBL_MANT_DIG == 53
 140 long double log2l (long double x) { return log2 (x); }
 141 # endif
 142 #endif