New generic logf

without wrapper on aarch64:
logf reciprocal-throughput: 2.2x faster
logf latency: 1.9x faster
old worst case error: 0.89 ulp
new worst case error: 0.82 ulp
aarch64 .text size: -356 bytes
aarch64 .rodata size: +240 bytes

Uses double precision arithmetics and a lookup table to allow smaller
polynomial and avoid the use of division.

Data is in a separate translation unit with fixed layout to prevent the
compiler generating suboptimal literal access.

Errors are handled inline according to POSIX rules, but this patch
keeps the wrapper with SVID compatible error handling.

Needs libm-test-ulps adjustment for clogf in non-nearest rounding mode.

	* math/Makefile (type-float-routines): Add e_logf_data.
	* sysdeps/ieee754/flt-32/e_logf.c: New implementation.
	* sysdeps/ieee754/flt-32/e_logf_data.c: New file.
	* sysdeps/ieee754/flt-32/math_config.h (__logf_data): Define.
	(LOGF_TABLE_BITS, LOGF_POLY_ORDER): Define.
	* sysdeps/i386/fpu/e_logf_data.c: New file.
	* sysdeps/ia64/fpu/e_logf_data.c: New file.
	* sysdeps/m68k/m680x0/fpu/e_logf_data.c: New file.

1 files changed, 75 insertions, 73 deletions

diff --git a/sysdeps/ieee754/flt-32/e_logf.c b/sysdeps/ieee754/flt-32/e_logf.c
index cf75e11781..b8d262441f 100644
--- a/sysdeps/ieee754/flt-32/e_logf.c
+++ b/sysdeps/ieee754/flt-32/e_logf.c
@@ -1,85 +1,87 @@
-/* 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)