libc/AOR_v20.02/math/logf.c

   1 /*
   2  * Single-precision log 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 LOGF_TABLE_BITS = 4
  15 LOGF_POLY_ORDER = 4
  16
  17 ULP error: 0.818 (nearest rounding.)
  18 Relative error: 1.957 * 2^-26 (before rounding.)
  19 */
  20
  21 #define T __logf_data.tab
  22 #define A __logf_data.poly
  23 #define Ln2 __logf_data.ln2
  24 #define N (1 << LOGF_TABLE_BITS)
  25 #define OFF 0x3f330000
  26
  27 float
  28 logf (float x)
  29 {
  30   /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  31   double_t z, r, r2, y, y0, invc, logc;
  32   uint32_t ix, iz, tmp;
  33   int k, i;
  34
  35   ix = asuint (x);
  36 #if WANT_ROUNDING
  37   /* Fix sign of zero with downward rounding when x==1.  */
  38   if (unlikely (ix == 0x3f800000))
  39     return 0;
  40 #endif
  41   if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
  42     {
  43       /* x < 0x1p-126 or inf or nan.  */
  44       if (ix * 2 == 0)
  45         return __math_divzerof (1);
  46       if (ix == 0x7f800000) /* log(inf) == inf.  */
  47         return x;
  48       if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
  49         return __math_invalidf (x);
  50       /* x is subnormal, normalize it.  */
  51       ix = asuint (x * 0x1p23f);
  52       ix -= 23 << 23;
  53     }
  54
  55   /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
  56      The range is split into N subintervals.
  57      The ith subinterval contains z and c is near its center.  */
  58   tmp = ix - OFF;
  59   i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
  60   k = (int32_t) tmp >> 23; /* arithmetic shift */
  61   iz = ix - (tmp & 0x1ff << 23);
  62   invc = T[i].invc;
  63   logc = T[i].logc;
  64   z = (double_t) asfloat (iz);
  65
  66   /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
  67   r = z * invc - 1;
  68   y0 = logc + (double_t) k * Ln2;
  69
  70   /* Pipelined polynomial evaluation to approximate log1p(r).  */
  71   r2 = r * r;
  72   y = A[1] * r + A[2];
  73   y = A[0] * r2 + y;
  74   y = y * r2 + (y0 + r);
  75   return eval_as_float (y);
  76 }
  77 #if USE_GLIBC_ABI
  78 strong_alias (logf, __logf_finite)
  79 hidden_alias (logf, __ieee754_logf)
  80 #endif