2  * Double-precision log10(x) function.
4  * Copyright (c) 2020-2024, Arm Limited.
5  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
22 #define LO asuint64 (1.0 - 0x1p-4)
23 #define HI asuint64 (1.0 + 0x1.09p-4)
25 /* Top 16 bits of a double.  */
27 top16 (double x)  in top16()
34    - Polynomials are computed for log10(1+r) with r on same intervals as log.
35    - Lookup parameters are scaled (at runtime) to switch from base e to
36      base 10. Many errors above 1.59 ulp are observed across the whole range of
38      log10(0x1.dc8710333a29bp-1) got -0x1.fee26884905a6p-6
39 				want -0x1.fee26884905a8p-6.  */
40 double
41 log10 (double x)  in log10()
52   if (unlikely (ix - LO < HI - LO))  in log10()
58       r = x - 1.0;  in log10()
66       /* Worst-case error is around 0.507 ULP.  */  in log10()
68       double_t rhi = r + w - w;  in log10()
69       double_t rlo = r - rhi;  in log10()
72       lo = r - hi + w;  in log10()
81   if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))  in log10()
83       /* x < 0x1p-1022 or inf or nan.  */  in log10()
92       ix -= 52ULL << 52;  in log10()
95   /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.  in log10()
96      The range is split into N subintervals.  in log10()
98   tmp = ix - OFF;  in log10()
99   i = (tmp >> (52 - LOG10_TABLE_BITS)) % N;  in log10()
101   iz = ix - (tmp & 0xfffULL << 52);  in log10()
106   /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */  in log10()
107   /* r ~= z/c - 1, |r| < 1/(2*N).  */  in log10()
109   /* rounding error: 0x1p-55/N.  */  in log10()
110   r = fma (z, invc, -1.0);  in log10()
112   /* rounding error: 0x1p-55/N + 0x1p-66.  */  in log10()
113   r = (z - T2[i].chi - T2[i].clo) * invc;  in log10()
120   lo = w - hi + r + kd * Ln2lo;  in log10()
122   /* log10(x) = (w + r)/log(10) + (log10(1+r) - r/log(10)).  */  in log10()
123   r2 = r * r; /* rounding error: 0x1p-54/N^2.  */  in log10()
133 // clang-format off
138 long double  in strong_alias()
139 log10l (long double x)  in strong_alias()
145 // clang-format on
150 TEST_INTERVAL (log10, 0x1p-4, 0x1p4, 40000)