libc/AOR_v20.02/math/log2f.c

   1 /*
   2  * Single-precision log2 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 <math.h>
  10 #include <stdint.h>
  11 #include "math_config.h"
  12
  13 /*
  14 LOG2F_TABLE_BITS = 4
  15 LOG2F_POLY_ORDER = 4
  16
  17 ULP error: 0.752 (nearest rounding.)
  18 Relative error: 1.9 * 2^-26 (before rounding.)
  19 */
  20
  21 #define N (1 << LOG2F_TABLE_BITS)
  22 #define T __log2f_data.tab
  23 #define A __log2f_data.poly
  24 #define OFF 0x3f330000
  25
  26 float
  27 log2f (float x)
  28 {
  29   /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  30   double_t z, r, r2, p, y, y0, invc, logc;
  31   uint32_t ix, iz, top, tmp;
  32   int k, i;
  33
  34   ix = asuint (x);
  35 #if WANT_ROUNDING
  36   /* Fix sign of zero with downward rounding when x==1.  */
  37   if (unlikely (ix == 0x3f800000))
  38     return 0;
  39 #endif
  40   if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
  41     {
  42       /* x < 0x1p-126 or inf or nan.  */
  43       if (ix * 2 == 0)
  44         return __math_divzerof (1);
  45       if (ix == 0x7f800000) /* log2(inf) == inf.  */
  46         return x;
  47       if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
  48         return __math_invalidf (x);
  49       /* x is subnormal, normalize it.  */
  50       ix = asuint (x * 0x1p23f);
  51       ix -= 23 << 23;
  52     }
  53
  54   /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
  55      The range is split into N subintervals.
  56      The ith subinterval contains z and c is near its center.  */
  57   tmp = ix - OFF;
  58   i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
  59   top = tmp & 0xff800000;
  60   iz = ix - top;
  61   k = (int32_t) tmp >> 23; /* arithmetic shift */
  62   invc = T[i].invc;
  63   logc = T[i].logc;
  64   z = (double_t) asfloat (iz);
  65
  66   /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
  67   r = z * invc - 1;
  68   y0 = logc + (double_t) k;
  69
  70   /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
  71   r2 = r * r;
  72   y = A[1] * r + A[2];
  73   y = A[0] * r2 + y;
  74   p = A[3] * r + y0;
  75   y = y * r2 + p;
  76   return eval_as_float (y);
  77 }
  78 #if USE_GLIBC_ABI
  79 strong_alias (log2f, __log2f_finite)
  80 hidden_alias (log2f, __ieee754_log2f)
  81 #endif