112 lines
3.0 KiB
C
112 lines
3.0 KiB
C
/*
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* Double-precision log(x) function.
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*
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* Copyright (c) 2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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#include "libc/math/math.h"
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#include "libc/math/libm.h"
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#include "libc/math/log_data.h"
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#define T __log_data.tab
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#define T2 __log_data.tab2
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#define B __log_data.poly1
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#define A __log_data.poly
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#define Ln2hi __log_data.ln2hi
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#define Ln2lo __log_data.ln2lo
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#define N (1 << LOG_TABLE_BITS)
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#define OFF 0x3fe6000000000000
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/* Top 16 bits of a double. */
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static inline uint32_t top16(double x)
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{
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return asuint64(x) >> 48;
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}
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double log(double x)
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{
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double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
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uint64_t ix, iz, tmp;
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uint32_t top;
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int k, i;
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ix = asuint64(x);
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top = top16(x);
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#define LO asuint64(1.0 - 0x1p-4)
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#define HI asuint64(1.0 + 0x1.09p-4)
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if (predict_false(ix - LO < HI - LO)) {
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/* Handle close to 1.0 inputs separately. */
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/* Fix sign of zero with downward rounding when x==1. */
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if (WANT_ROUNDING && predict_false(ix == asuint64(1.0)))
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return 0;
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r = x - 1.0;
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r2 = r * r;
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r3 = r * r2;
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y = r3 *
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(B[1] + r * B[2] + r2 * B[3] +
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r3 * (B[4] + r * B[5] + r2 * B[6] +
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r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
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/* Worst-case error is around 0.507 ULP. */
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w = r * 0x1p27;
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double_t rhi = r + w - w;
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double_t rlo = r - rhi;
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w = rhi * rhi * B[0]; /* B[0] == -0.5. */
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hi = r + w;
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lo = r - hi + w;
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lo += B[0] * rlo * (rhi + r);
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y += lo;
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y += hi;
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return eval_as_double(y);
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}
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if (predict_false(top - 0x0010 >= 0x7ff0 - 0x0010)) {
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/* x < 0x1p-1022 or inf or nan. */
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if (ix * 2 == 0)
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return __math_divzero(1);
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if (ix == asuint64(INFINITY)) /* log(inf) == inf. */
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return x;
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if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
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return __math_invalid(x);
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/* x is subnormal, normalize it. */
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ix = asuint64(x * 0x1p52);
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ix -= 52ULL << 52;
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}
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/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
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The range is split into N subintervals.
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The ith subinterval contains z and c is near its center. */
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tmp = ix - OFF;
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i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
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k = (int64_t)tmp >> 52; /* arithmetic shift */
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iz = ix - (tmp & 0xfffULL << 52);
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invc = T[i].invc;
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logc = T[i].logc;
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z = asdouble(iz);
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/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
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/* r ~= z/c - 1, |r| < 1/(2*N). */
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#if __FP_FAST_FMA
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/* rounding error: 0x1p-55/N. */
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r = __builtin_fma(z, invc, -1.0);
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#else
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/* rounding error: 0x1p-55/N + 0x1p-66. */
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r = (z - T2[i].chi - T2[i].clo) * invc;
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#endif
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kd = (double_t)k;
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/* hi + lo = r + log(c) + k*Ln2. */
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w = kd * Ln2hi + logc;
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hi = w + r;
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lo = w - hi + r + kd * Ln2lo;
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/* log(x) = lo + (log1p(r) - r) + hi. */
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r2 = r * r; /* rounding error: 0x1p-54/N^2. */
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/* Worst case error if |y| > 0x1p-5:
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0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma)
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Worst case error if |y| > 0x1p-4:
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0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma). */
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y = lo + r2 * A[0] +
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r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi;
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return eval_as_double(y);
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}
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