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89 lines
2.2 KiB
C
89 lines
2.2 KiB
C
/*
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* Single-precision log function.
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*
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* Copyright (c) 2017-2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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#include <math.h>
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#include <stdint.h>
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#include "logf_data.h"
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float __math_invalidf(float);
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float __math_divzerof(uint32_t);
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/*
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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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*/
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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 N (1 << LOGF_TABLE_BITS)
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#define OFF 0x3f330000
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#define WANT_ROUNDING 1
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#define asuint(f) ((union{float _f; uint32_t _i;}){f})._i
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#define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f
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/* Evaluate an expression as the specified type. With standard excess
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precision handling a type cast or assignment is enough (with
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-ffloat-store an assignment is required, in old compilers argument
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passing and return statement may not drop excess precision). */
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static inline float eval_as_float(float x)
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{
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float y = x;
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return y;
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}
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float logf(float x)
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{
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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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/* Fix sign of zero with downward rounding when x==1. */
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if (WANT_ROUNDING && __builtin_expect(ix == 0x3f800000, 0))
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return 0;
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if (__builtin_expect(ix - 0x00800000 >= 0x7f800000 - 0x00800000, 0)) {
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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 & 0x1ff << 23);
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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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return eval_as_float(y);
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}
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