libc/AOR_v20.02/math/v_log.c

   1 /*
   2  * Double-precision vector log(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 "mathlib.h"
  10 #include "v_math.h"
  11 #include "v_log.h"
  12 #if V_SUPPORTED
  13
  14 /* Worst-case error: 1.17 + 0.5 ulp.  */
  15
  16 static const f64_t Poly[] = {
  17   /* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ].  */
  18   -0x1.ffffffffffff7p-2,
  19    0x1.55555555170d4p-2,
  20   -0x1.0000000399c27p-2,
  21    0x1.999b2e90e94cap-3,
  22   -0x1.554e550bd501ep-3,
  23 };
  24
  25 #define A0 v_f64 (Poly[0])
  26 #define A1 v_f64 (Poly[1])
  27 #define A2 v_f64 (Poly[2])
  28 #define A3 v_f64 (Poly[3])
  29 #define A4 v_f64 (Poly[4])
  30 #define Ln2 v_f64 (0x1.62e42fefa39efp-1)
  31 #define N (1 << V_LOG_TABLE_BITS)
  32 #define OFF v_u64 (0x3fe6900900000000)
  33
  34 struct entry
  35 {
  36   v_f64_t invc;
  37   v_f64_t logc;
  38 };
  39
  40 static inline struct entry
  41 lookup (v_u64_t i)
  42 {
  43   struct entry e;
  44 #ifdef SCALAR
  45   e.invc = __v_log_data[i].invc;
  46   e.logc = __v_log_data[i].logc;
  47 #else
  48   e.invc[0] = __v_log_data[i[0]].invc;
  49   e.logc[0] = __v_log_data[i[0]].logc;
  50   e.invc[1] = __v_log_data[i[1]].invc;
  51   e.logc[1] = __v_log_data[i[1]].logc;
  52 #endif
  53   return e;
  54 }
  55
  56 VPCS_ATTR
  57 __attribute__ ((noinline)) static v_f64_t
  58 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
  59 {
  60   return v_call_f64 (log, x, y, cmp);
  61 }
  62
  63 VPCS_ATTR
  64 v_f64_t
  65 V_NAME(log) (v_f64_t x)
  66 {
  67   v_f64_t z, r, r2, p, y, kd, hi;
  68   v_u64_t ix, iz, tmp, top, i, cmp;
  69   v_s64_t k;
  70   struct entry e;
  71
  72   ix = v_as_u64_f64 (x);
  73   top = ix >> 48;
  74   cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010));
  75
  76   /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
  77      The range is split into N subintervals.
  78      The ith subinterval contains z and c is near its center.  */
  79   tmp = ix - OFF;
  80   i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N;
  81   k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */
  82   iz = ix - (tmp & v_u64 (0xfffULL << 52));
  83   z = v_as_f64_u64 (iz);
  84   e = lookup (i);
  85
  86   /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
  87   r = v_fma_f64 (z, e.invc, v_f64 (-1.0));
  88   kd = v_to_f64_s64 (k);
  89
  90   /* hi = r + log(c) + k*Ln2.  */
  91   hi = v_fma_f64 (kd, Ln2, e.logc + r);
  92   /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi.  */
  93   r2 = r * r;
  94   y = v_fma_f64 (A3, r, A2);
  95   p = v_fma_f64 (A1, r, A0);
  96   y = v_fma_f64 (A4, r2, y);
  97   y = v_fma_f64 (y, r2, p);
  98   y = v_fma_f64 (y, r2, hi);
  99
 100   if (unlikely (v_any_u64 (cmp)))
 101     return specialcase (x, y, cmp);
 102   return y;
 103 }
 104 VPCS_ALIAS
 105 #endif