libc/AOR_v20.02/math/log.c

   1 /*
   2  * Double-precision 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 <float.h>
  10 #include <math.h>
  11 #include <stdint.h>
  12 #include "math_config.h"
  13
  14 #define T __log_data.tab
  15 #define T2 __log_data.tab2
  16 #define B __log_data.poly1
  17 #define A __log_data.poly
  18 #define Ln2hi __log_data.ln2hi
  19 #define Ln2lo __log_data.ln2lo
  20 #define N (1 << LOG_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 log (double x)
  32 {
  33   /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  34   double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
  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 LOG_POLY1_ORDER == 10 || LOG_POLY1_ORDER == 11
  43 # define LO asuint64 (1.0 - 0x1p-5)
  44 # define HI asuint64 (1.0 + 0x1.1p-5)
  45 #elif LOG_POLY1_ORDER == 12
  46 # define LO asuint64 (1.0 - 0x1p-4)
  47 # define HI asuint64 (1.0 + 0x1.09p-4)
  48 #endif
  49   if (unlikely (ix - LO < HI - LO))
  50     {
  51       /* Handle close to 1.0 inputs separately.  */
  52       /* Fix sign of zero with downward rounding when x==1.  */
  53       if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0)))
  54         return 0;
  55       r = x - 1.0;
  56       r2 = r * r;
  57       r3 = r * r2;
  58 #if LOG_POLY1_ORDER == 10
  59       /* Worst-case error is around 0.516 ULP.  */
  60       y = r3 * (B[1] + r * B[2] + r2 * B[3]
  61                 + r3 * (B[4] + r * B[5] + r2 * B[6] + r3 * (B[7] + r * B[8])));
  62       w = B[0] * r2; /* B[0] == -0.5.  */
  63       hi = r + w;
  64       y += r - hi + w;
  65       y += hi;
  66 #elif LOG_POLY1_ORDER == 11
  67       /* Worst-case error is around 0.516 ULP.  */
  68       y = r3 * (B[1] + r * B[2]
  69                 + r2 * (B[3] + r * B[4] + r2 * B[5]
  70                         + r3 * (B[6] + r * B[7] + r2 * B[8] + r3 * B[9])));
  71       w = B[0] * r2; /* B[0] == -0.5.  */
  72       hi = r + w;
  73       y += r - hi + w;
  74       y += hi;
  75 #elif LOG_POLY1_ORDER == 12
  76       y = r3 * (B[1] + r * B[2] + r2 * B[3]
  77                 + r3 * (B[4] + r * B[5] + r2 * B[6]
  78                         + r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
  79 # if N <= 64
  80       /* Worst-case error is around 0.532 ULP.  */
  81       w = B[0] * r2; /* B[0] == -0.5.  */
  82       hi = r + w;
  83       y += r - hi + w;
  84       y += hi;
  85 # else
  86       /* Worst-case error is around 0.507 ULP.  */
  87       w = r * 0x1p27;
  88       double_t rhi = r + w - w;
  89       double_t rlo = r - rhi;
  90       w = rhi * rhi * B[0]; /* B[0] == -0.5.  */
  91       hi = r + w;
  92       lo = r - hi + w;
  93       lo += B[0] * rlo * (rhi + r);
  94       y += lo;
  95       y += hi;
  96 # endif
  97 #endif
  98       return eval_as_double (y);
  99     }
 100   if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
 101     {
 102       /* x < 0x1p-1022 or inf or nan.  */
 103       if (ix * 2 == 0)
 104         return __math_divzero (1);
 105       if (ix == asuint64 (INFINITY)) /* log(inf) == inf.  */
 106         return x;
 107       if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
 108         return __math_invalid (x);
 109       /* x is subnormal, normalize it.  */
 110       ix = asuint64 (x * 0x1p52);
 111       ix -= 52ULL << 52;
 112     }
 113
 114   /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
 115      The range is split into N subintervals.
 116      The ith subinterval contains z and c is near its center.  */
 117   tmp = ix - OFF;
 118   i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
 119   k = (int64_t) tmp >> 52; /* arithmetic shift */
 120   iz = ix - (tmp & 0xfffULL << 52);
 121   invc = T[i].invc;
 122   logc = T[i].logc;
 123   z = asdouble (iz);
 124
 125   /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
 126   /* r ~= z/c - 1, |r| < 1/(2*N).  */
 127 #if HAVE_FAST_FMA
 128   /* rounding error: 0x1p-55/N.  */
 129   r = fma (z, invc, -1.0);
 130 #else
 131   /* rounding error: 0x1p-55/N + 0x1p-66.  */
 132   r = (z - T2[i].chi - T2[i].clo) * invc;
 133 #endif
 134   kd = (double_t) k;
 135
 136   /* hi + lo = r + log(c) + k*Ln2.  */
 137   w = kd * Ln2hi + logc;
 138   hi = w + r;
 139   lo = w - hi + r + kd * Ln2lo;
 140
 141   /* log(x) = lo + (log1p(r) - r) + hi.  */
 142   r2 = r * r; /* rounding error: 0x1p-54/N^2.  */
 143   /* Worst case error if |y| > 0x1p-5:
 144      0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma)
 145      Worst case error if |y| > 0x1p-4:
 146      0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma).  */
 147 #if LOG_POLY_ORDER == 6
 148   y = lo + r2 * A[0] + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi;
 149 #elif LOG_POLY_ORDER == 7
 150   y = lo
 151       + r2 * (A[0] + r * A[1] + r2 * (A[2] + r * A[3])
 152               + r2 * r2 * (A[4] + r * A[5]))
 153       + hi;
 154 #endif
 155   return eval_as_double (y);
 156 }
 157 #if USE_GLIBC_ABI
 158 strong_alias (log, __log_finite)
 159 hidden_alias (log, __ieee754_log)
 160 # if LDBL_MANT_DIG == 53
 161 long double logl (long double x) { return log (x); }
 162 # endif
 163 #endif