diff options
Diffstat (limited to 'libc-top-half/musl/src/math/log.c')
| -rw-r--r-- | libc-top-half/musl/src/math/log.c | 112 |
1 files changed, 112 insertions, 0 deletions
diff --git a/libc-top-half/musl/src/math/log.c b/libc-top-half/musl/src/math/log.c new file mode 100644 index 0000000..cc52585 --- /dev/null +++ b/libc-top-half/musl/src/math/log.c @@ -0,0 +1,112 @@ +/* + * Double-precision log(x) function. + * + * Copyright (c) 2018, Arm Limited. + * SPDX-License-Identifier: MIT + */ + +#include <math.h> +#include <stdint.h> +#include "libm.h" +#include "log_data.h" + +#define T __log_data.tab +#define T2 __log_data.tab2 +#define B __log_data.poly1 +#define A __log_data.poly +#define Ln2hi __log_data.ln2hi +#define Ln2lo __log_data.ln2lo +#define N (1 << LOG_TABLE_BITS) +#define OFF 0x3fe6000000000000 + +/* Top 16 bits of a double. */ +static inline uint32_t top16(double x) +{ + return asuint64(x) >> 48; +} + +double log(double x) +{ + 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); +#define LO asuint64(1.0 - 0x1p-4) +#define HI asuint64(1.0 + 0x1.09p-4) + if (predict_false(ix - LO < HI - LO)) { + /* Handle close to 1.0 inputs separately. */ + /* Fix sign of zero with downward rounding when x==1. */ + if (WANT_ROUNDING && predict_false(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]; /* B[0] == -0.5. */ + hi = r + w; + lo = r - hi + w; + lo += B[0] * rlo * (rhi + r); + y += lo; + y += hi; + return eval_as_double(y); + } + if (predict_false(top - 0x0010 >= 0x7ff0 - 0x0010)) { + /* x < 0x1p-1022 or inf or nan. */ + if (ix * 2 == 0) + return __math_divzero(1); + if (ix == asuint64(INFINITY)) /* log(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 - LOG_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 __FP_FAST_FMA + /* rounding error: 0x1p-55/N. */ + r = __builtin_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; + + /* hi + lo = r + log(c) + k*Ln2. */ + w = kd * Ln2hi + logc; + hi = w + r; + lo = w - hi + r + kd * Ln2lo; + + /* log(x) = lo + (log1p(r) - r) + hi. */ + r2 = r * r; /* rounding error: 0x1p-54/N^2. */ + /* Worst case error if |y| > 0x1p-5: + 0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma) + Worst case error if |y| > 0x1p-4: + 0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma). */ + y = lo + r2 * A[0] + + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi; + return eval_as_double(y); +} |