-/* e_logf.c -- float version of e_log.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
+/* Single-precision log function.
+ Copyright (C) 2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * 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.
- * ====================================================
- */
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
#include <math.h>
-#include <math_private.h>
+#include <stdint.h>
+#include "math_config.h"
-static const float
-ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
-ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
-two25 = 3.355443200e+07, /* 0x4c000000 */
-Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
-Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
-Lg3 = 2.8571429849e-01, /* 3E924925 */
-Lg4 = 2.2222198546e-01, /* 3E638E29 */
-Lg5 = 1.8183572590e-01, /* 3E3A3325 */
-Lg6 = 1.5313838422e-01, /* 3E1CD04F */
-Lg7 = 1.4798198640e-01; /* 3E178897 */
+/*
+LOGF_TABLE_BITS = 4
+LOGF_POLY_ORDER = 4
-static const float zero = 0.0;
+ULP error: 0.818 (nearest rounding.)
+Relative error: 1.957 * 2^-26 (before rounding.)
+*/
+
+#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
-__ieee754_logf(float x)
+__ieee754_logf (float x)
{
- float hfsq,f,s,z,R,w,t1,t2,dk;
- int32_t k,ix,i,j;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t z, r, r2, y, y0, invc, logc;
+ uint32_t ix, iz, tmp;
+ int k, i;
+
+ ix = asuint (x);
+#if WANT_ROUNDING
+ /* Fix sign of zero with downward rounding when x==1. */
+ if (__glibc_unlikely (ix == 0x3f800000))
+ return 0;
+#endif
+ if (__glibc_unlikely (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);
- GET_FLOAT_WORD(ix,x);
+ /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
+ r = z * invc - 1;
+ y0 = logc + (double_t) k * Ln2;
- k=0;
- if (ix < 0x00800000) { /* x < 2**-126 */
- if (__builtin_expect((ix&0x7fffffff)==0, 0))
- return -two25/zero; /* log(+-0)=-inf */
- if (__builtin_expect(ix<0, 0))
- return (x-x)/(x-x); /* log(-#) = NaN */
- k -= 25; x *= two25; /* subnormal number, scale up x */
- GET_FLOAT_WORD(ix,x);
- }
- if (__builtin_expect(ix >= 0x7f800000, 0)) 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-(float)1.0;
- if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
- if(f==zero) {
- if(k==0) return zero; else {dk=(float)k;
- return dk*ln2_hi+dk*ln2_lo;}
- }
- R = f*f*((float)0.5-(float)0.33333333333333333*f);
- if(k==0) return f-R; else {dk=(float)k;
- return dk*ln2_hi-((R-dk*ln2_lo)-f);}
- }
- s = f/((float)2.0+f);
- dk = (float)k;
- z = s*s;
- i = ix-(0x6147a<<3);
- w = z*z;
- j = (0x6b851<<3)-ix;
- t1= w*(Lg2+w*(Lg4+w*Lg6));
- t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
- i |= j;
- R = t2+t1;
- if(i>0) {
- hfsq=(float)0.5*f*f;
- if(k==0) return f-(hfsq-s*(hfsq+R)); else
- return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
- } else {
- if(k==0) return f-s*(f-R); else
- return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
- }
+ /* 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 (float) y;
}
strong_alias (__ieee754_logf, __logf_finite)
--- /dev/null
+/* Data definition for logf.
+ Copyright (C) 2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include "math_config.h"
+
+const struct logf_data __logf_data = {
+ .tab = {
+ { 0x1.661ec79f8f3bep+0, -0x1.57bf7808caadep-2 },
+ { 0x1.571ed4aaf883dp+0, -0x1.2bef0a7c06ddbp-2 },
+ { 0x1.49539f0f010bp+0, -0x1.01eae7f513a67p-2 },
+ { 0x1.3c995b0b80385p+0, -0x1.b31d8a68224e9p-3 },
+ { 0x1.30d190c8864a5p+0, -0x1.6574f0ac07758p-3 },
+ { 0x1.25e227b0b8eap+0, -0x1.1aa2bc79c81p-3 },
+ { 0x1.1bb4a4a1a343fp+0, -0x1.a4e76ce8c0e5ep-4 },
+ { 0x1.12358f08ae5bap+0, -0x1.1973c5a611cccp-4 },
+ { 0x1.0953f419900a7p+0, -0x1.252f438e10c1ep-5 },
+ { 0x1p+0, 0x0p+0 },
+ { 0x1.e608cfd9a47acp-1, 0x1.aa5aa5df25984p-5 },
+ { 0x1.ca4b31f026aap-1, 0x1.c5e53aa362eb4p-4 },
+ { 0x1.b2036576afce6p-1, 0x1.526e57720db08p-3 },
+ { 0x1.9c2d163a1aa2dp-1, 0x1.bc2860d22477p-3 },
+ { 0x1.886e6037841edp-1, 0x1.1058bc8a07ee1p-2 },
+ { 0x1.767dcf5534862p-1, 0x1.4043057b6ee09p-2 },
+ },
+ .ln2 = 0x1.62e42fefa39efp-1,
+ .poly = {
+ -0x1.00ea348b88334p-2, 0x1.5575b0be00b6ap-2, -0x1.ffffef20a4123p-2,
+ }
+};
projects / thirdparty / glibc.git / commitdiff
