98 lines
2.6 KiB
C
98 lines
2.6 KiB
C
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/*
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* Single-precision log10 function.
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*
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* Copyright (c) 2022-2023, Arm Limited.
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* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
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*/
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#include <math.h>
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#include <stdint.h>
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#include "math_config.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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/* Data associated to logf:
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LOGF_TABLE_BITS = 4
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LOGF_POLY_ORDER = 4
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ULP error: 0.818 (nearest rounding.)
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Relative error: 1.957 * 2^-26 (before rounding.). */
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#define T __logf_data.tab
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#define A __logf_data.poly
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#define Ln2 __logf_data.ln2
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#define InvLn10 __logf_data.invln10
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#define N (1 << LOGF_TABLE_BITS)
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#define OFF 0x3f330000
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/* This naive implementation of log10f mimics that of log
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then simply scales the result by 1/log(10) to switch from base e to
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base 10. Hence, most computations are carried out in double precision.
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Scaling before rounding to single precision is both faster and more accurate.
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ULP error: 0.797 ulp (nearest rounding.). */
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float
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log10f (float x)
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{
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/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
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double_t z, r, r2, y, y0, invc, logc;
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uint32_t ix, iz, tmp;
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int k, i;
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ix = asuint (x);
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#if WANT_ROUNDING
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/* Fix sign of zero with downward rounding when x==1. */
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if (unlikely (ix == 0x3f800000))
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return 0;
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#endif
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if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
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{
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/* x < 0x1p-126 or inf or nan. */
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if (ix * 2 == 0)
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return __math_divzerof (1);
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if (ix == 0x7f800000) /* log(inf) == inf. */
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return x;
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if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
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return __math_invalidf (x);
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/* x is subnormal, normalize it. */
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ix = asuint (x * 0x1p23f);
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ix -= 23 << 23;
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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 >> (23 - LOGF_TABLE_BITS)) % N;
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k = (int32_t) tmp >> 23; /* arithmetic shift. */
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iz = ix - (tmp & 0xff800000);
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invc = T[i].invc;
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logc = T[i].logc;
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z = (double_t) asfloat (iz);
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/* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
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r = z * invc - 1;
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y0 = logc + (double_t) k * Ln2;
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/* Pipelined polynomial evaluation to approximate log1p(r). */
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r2 = r * r;
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y = A[1] * r + A[2];
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y = A[0] * r2 + y;
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y = y * r2 + (y0 + r);
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/* Multiply by 1/log(10). */
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y = y * InvLn10;
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return eval_as_float (y);
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}
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PL_SIG (S, F, 1, log10, 0.01, 11.1)
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PL_TEST_ULP (log10f, 0.30)
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PL_TEST_INTERVAL (log10f, 0, 0xffff0000, 10000)
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PL_TEST_INTERVAL (log10f, 0x1p-127, 0x1p-26, 50000)
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PL_TEST_INTERVAL (log10f, 0x1p-26, 0x1p3, 50000)
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PL_TEST_INTERVAL (log10f, 0x1p-4, 0x1p4, 50000)
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PL_TEST_INTERVAL (log10f, 0, inf, 50000)
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