src/math/log2f.c

   1 /*
   2  * Single-precision log2 function.
   3  *
   4  * Copyright (c) 2017-2018, Arm Limited.
   5  * SPDX-License-Identifier: MIT
   6  */
   7
   8 #include <math.h>
   9 #include <stdint.h>
  10 #include "libm.h"
  11 #include "log2f_data.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 log2f(float x)
  27 {
  28         double_t z, r, r2, p, y, y0, invc, logc;
  29         uint32_t ix, iz, top, tmp;
  30         int k, i;
  31
  32         ix = asuint(x);
  33         /* Fix sign of zero with downward rounding when x==1.  */
  34         if (WANT_ROUNDING && predict_false(ix == 0x3f800000))
  35                 return 0;
  36         if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
  37                 /* x < 0x1p-126 or inf or nan.  */
  38                 if (ix * 2 == 0)
  39                         return __math_divzerof(1);
  40                 if (ix == 0x7f800000) /* log2(inf) == inf.  */
  41                         return x;
  42                 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
  43                         return __math_invalidf(x);
  44                 /* x is subnormal, normalize it.  */
  45                 ix = asuint(x * 0x1p23f);
  46                 ix -= 23 << 23;
  47         }
  48
  49         /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
  50            The range is split into N subintervals.
  51            The ith subinterval contains z and c is near its center.  */
  52         tmp = ix - OFF;
  53         i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
  54         top = tmp & 0xff800000;
  55         iz = ix - top;
  56         k = (int32_t)tmp >> 23; /* arithmetic shift */
  57         invc = T[i].invc;
  58         logc = T[i].logc;
  59         z = (double_t)asfloat(iz);
  60
  61         /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
  62         r = z * invc - 1;
  63         y0 = logc + (double_t)k;
  64
  65         /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
  66         r2 = r * r;
  67         y = A[1] * r + A[2];
  68         y = A[0] * r2 + y;
  69         p = A[3] * r + y0;
  70         y = y * r2 + p;
  71         return eval_as_float(y);
  72 }