-/* origin: FreeBSD /usr/src/lib/msun/src/e_logf.c */
/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * Single-precision log function.
*
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
+ * Copyright (c) 2017-2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
*/
+#include <math.h>
+#include <stdint.h>
#include "libm.h"
+#include "logf_data.h"
+
+/*
+LOGF_TABLE_BITS = 4
+LOGF_POLY_ORDER = 4
+
+ULP error: 0.818 (nearest rounding.)
+Relative error: 1.957 * 2^-26 (before rounding.)
+*/
-static const float
-ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
-ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
-two25 = 3.355443200e+07, /* 0x4c000000 */
-/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
-Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
-Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
-Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
-Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
+#define T __logf_data.tab
+#define A __logf_data.poly
+#define Ln2 __logf_data.ln2
+#define N (1 << LOGF_TABLE_BITS)
+#define OFF 0x3f330000
float logf(float x)
{
- float hfsq,f,s,z,R,w,t1,t2,dk;
- int32_t k,ix,i,j;
-
- GET_FLOAT_WORD(ix, x);
+ double_t z, r, r2, y, y0, invc, logc;
+ uint32_t ix, iz, tmp;
+ int k, i;
- k = 0;
- if (ix < 0x00800000) { /* x < 2**-126 */
- if ((ix & 0x7fffffff) == 0)
- return -two25/0.0f; /* log(+-0)=-inf */
- if (ix < 0)
- return (x-x)/0.0f; /* log(-#) = NaN */
- /* subnormal number, scale up x */
- k -= 25;
- x *= two25;
- GET_FLOAT_WORD(ix, x);
- }
- if (ix >= 0x7f800000)
- return x+x;
- k += (ix>>23) - 127;
- ix &= 0x007fffff;
- i = (ix + (0x95f64<<3)) & 0x800000;
- SET_FLOAT_WORD(x, ix|(i^0x3f800000)); /* normalize x or x/2 */
- k += i>>23;
- f = x - 1.0f;
- if ((0x007fffff & (0x8000 + ix)) < 0xc000) { /* -2**-9 <= f < 2**-9 */
- if (f == 0.0f) {
- if (k == 0)
- return 0.0f;
- dk = (float)k;
- return dk*ln2_hi + dk*ln2_lo;
- }
- R = f*f*(0.5f - 0.33333333333333333f*f);
- if (k == 0)
- return f-R;
- dk = (float)k;
- return dk*ln2_hi - ((R-dk*ln2_lo)-f);
- }
- s = f/(2.0f + f);
- dk = (float)k;
- z = s*s;
- i = ix-(0x6147a<<3);
- w = z*z;
- j = (0x6b851<<3)-ix;
- t1= w*(Lg2+w*Lg4);
- t2= z*(Lg1+w*Lg3);
- i |= j;
- R = t2 + t1;
- if (i > 0) {
- hfsq = 0.5f * f * f;
- if (k == 0)
- return f - (hfsq-s*(hfsq+R));
- return dk*ln2_hi - ((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
- } else {
- if (k == 0)
- return f - s*(f-R);
- return dk*ln2_hi - ((s*(f-R)-dk*ln2_lo)-f);
+ ix = asuint(x);
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (WANT_ROUNDING && predict_false(ix == 0x3f800000))
+ return 0;
+ if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
+ /* x < 0x1p-126 or inf or nan. */
+ if (ix * 2 == 0)
+ return __math_divzerof(1);
+ if (ix == 0x7f800000) /* log(inf) == inf. */
+ return x;
+ if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
+ return __math_invalidf(x);
+ /* x is subnormal, normalize it. */
+ ix = asuint(x * 0x1p23f);
+ ix -= 23 << 23;
}
+
+ /* 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 >> (23 - LOGF_TABLE_BITS)) % N;
+ k = (int32_t)tmp >> 23; /* arithmetic shift */
+ iz = ix - (tmp & 0x1ff << 23);
+ invc = T[i].invc;
+ logc = T[i].logc;
+ z = (double_t)asfloat(iz);
+
+ /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
+ r = z * invc - 1;
+ y0 = logc + (double_t)k * Ln2;
+
+ /* Pipelined polynomial evaluation to approximate log1p(r). */
+ r2 = r * r;
+ y = A[1] * r + A[2];
+ y = A[0] * r2 + y;
+ y = y * r2 + (y0 + r);
+ return eval_as_float(y);
}
projects / musl / blobdiff