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Diffstat (limited to 'contrib/arm-optimized-routines/pl/math/log10_2u.c')
| -rw-r--r-- | contrib/arm-optimized-routines/pl/math/log10_2u.c | 150 |
1 files changed, 150 insertions, 0 deletions
diff --git a/contrib/arm-optimized-routines/pl/math/log10_2u.c b/contrib/arm-optimized-routines/pl/math/log10_2u.c new file mode 100644 index 000000000000..74828ea9ef3c --- /dev/null +++ b/contrib/arm-optimized-routines/pl/math/log10_2u.c @@ -0,0 +1,150 @@ +/* + * Double-precision log10(x) function. + * + * Copyright (c) 2020-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "math_config.h" +#include "pl_sig.h" +#include "pl_test.h" + +/* Polynomial coefficients and lookup tables. */ +#define T __log10_data.tab +#define T2 __log10_data.tab2 +#define B __log10_data.poly1 +#define A __log10_data.poly +#define Ln2hi __log10_data.ln2hi +#define Ln2lo __log10_data.ln2lo +#define InvLn10 __log10_data.invln10 +#define N (1 << LOG10_TABLE_BITS) +#define OFF 0x3fe6000000000000 +#define LO asuint64 (1.0 - 0x1p-4) +#define HI asuint64 (1.0 + 0x1.09p-4) + +/* Top 16 bits of a double. */ +static inline uint32_t +top16 (double x) +{ + return asuint64 (x) >> 48; +} + +/* Fast and low accuracy implementation of log10. + The implementation is similar to that of math/log, except that: + - Polynomials are computed for log10(1+r) with r on same intervals as log. + - Lookup parameters are scaled (at runtime) to switch from base e to base 10. + Many errors above 1.59 ulp are observed across the whole range of doubles. + The greatest observed error is 1.61 ulp, at around 0.965: + log10(0x1.dc8710333a29bp-1) got -0x1.fee26884905a6p-6 + want -0x1.fee26884905a8p-6. */ +double +log10 (double x) +{ + /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ + double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo; + uint64_t ix, iz, tmp; + uint32_t top; + int k, i; + + ix = asuint64 (x); + top = top16 (x); + + if (unlikely (ix - LO < HI - LO)) + { + /* Handle close to 1.0 inputs separately. */ + /* Fix sign of zero with downward rounding when x==1. */ + if (WANT_ROUNDING && unlikely (ix == asuint64 (1.0))) + return 0; + r = x - 1.0; + r2 = r * r; + r3 = r * r2; + y = r3 + * (B[1] + r * B[2] + r2 * B[3] + + r3 + * (B[4] + r * B[5] + r2 * B[6] + + r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10]))); + /* Worst-case error is around 0.507 ULP. */ + w = r * 0x1p27; + double_t rhi = r + w - w; + double_t rlo = r - rhi; + w = rhi * rhi * B[0]; + hi = r + w; + lo = r - hi + w; + lo += B[0] * rlo * (rhi + r); + y += lo; + y += hi; + /* Scale by 1/ln(10). Polynomial already contains scaling. */ + y = y * InvLn10; + + return eval_as_double (y); + } + if (unlikely (top - 0x0010 >= 0x7ff0 - 0x0010)) + { + /* x < 0x1p-1022 or inf or nan. */ + if (ix * 2 == 0) + return __math_divzero (1); + if (ix == asuint64 (INFINITY)) /* log10(inf) == inf. */ + return x; + if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0) + return __math_invalid (x); + /* x is subnormal, normalize it. */ + ix = asuint64 (x * 0x1p52); + ix -= 52ULL << 52; + } + + /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. + The range is split into N subintervals. + The ith subinterval contains z and c is near its center. */ + tmp = ix - OFF; + i = (tmp >> (52 - LOG10_TABLE_BITS)) % N; + k = (int64_t) tmp >> 52; /* arithmetic shift. */ + iz = ix - (tmp & 0xfffULL << 52); + invc = T[i].invc; + logc = T[i].logc; + z = asdouble (iz); + + /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ + /* r ~= z/c - 1, |r| < 1/(2*N). */ +#if HAVE_FAST_FMA + /* rounding error: 0x1p-55/N. */ + r = fma (z, invc, -1.0); +#else + /* rounding error: 0x1p-55/N + 0x1p-66. */ + r = (z - T2[i].chi - T2[i].clo) * invc; +#endif + kd = (double_t) k; + + /* w = log(c) + k*Ln2hi. */ + w = kd * Ln2hi + logc; + hi = w + r; + lo = w - hi + r + kd * Ln2lo; + + /* log10(x) = (w + r)/log(10) + (log10(1+r) - r/log(10)). */ + r2 = r * r; /* rounding error: 0x1p-54/N^2. */ + + /* Scale by 1/ln(10). Polynomial already contains scaling. */ + y = lo + r2 * A[0] + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi; + y = y * InvLn10; + + return eval_as_double (y); +} + +// clang-format off +#if USE_GLIBC_ABI +strong_alias (log10, __log10_finite) +hidden_alias (log10, __ieee754_log10) +#if LDBL_MANT_DIG == 53 +long double +log10l (long double x) +{ + return log10 (x); +} +#endif +#endif +// clang-format on + +PL_SIG (S, D, 1, log10, 0.01, 11.1) +PL_TEST_ULP (log10, 1.11) +PL_TEST_INTERVAL (log10, 0, 0xffff000000000000, 10000) +PL_TEST_INTERVAL (log10, 0x1p-4, 0x1p4, 40000) +PL_TEST_INTERVAL (log10, 0, inf, 40000) |