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.

8 files changed, 136 insertions, 75 deletions

diff --git a/NEWS b/NEWS
index e346d2afe6..05850f8288 100644
--- a/NEWS
+++ b/NEWS
@@ -14,7 +14,7 @@ Major new features:
 
 * Optimized x86-64 trunc and truncf for processors with SSE4.1.
 
-* Optimized generic expf and exp2f.
+* Optimized generic expf, exp2f, logf.
 
 * In order to support faster and safer process termination the malloc API
   family of functions will no longer print a failure address and stack
diff --git a/math/Makefile b/math/Makefile
index 04586156f8..919fec13ef 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -115,7 +115,7 @@ type-double-routines := branred doasin dosincos halfulp mpa mpatan2	\
 
 # float support
 type-float-suffix := f
-type-float-routines := k_rem_pio2f math_errf e_exp2f_data
+type-float-routines := k_rem_pio2f math_errf e_exp2f_data e_logf_data
 
 # _Float128 support
 type-float128-suffix := f128
diff --git a/sysdeps/i386/fpu/e_logf_data.c b/sysdeps/i386/fpu/e_logf_data.c
new file mode 100644
index 0000000000..1cc8931700
--- /dev/null
+++ b/sysdeps/i386/fpu/e_logf_data.c
@@ -0,0 +1 @@
+/* Not needed.  */
diff --git a/sysdeps/ia64/fpu/e_logf_data.c b/sysdeps/ia64/fpu/e_logf_data.c
new file mode 100644
index 0000000000..1cc8931700
--- /dev/null
+++ b/sysdeps/ia64/fpu/e_logf_data.c
@@ -0,0 +1 @@
+/* Not needed.  */
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)
diff --git a/sysdeps/ieee754/flt-32/e_logf_data.c b/sysdeps/ieee754/flt-32/e_logf_data.c
new file mode 100644
index 0000000000..ce2a0f8a5c
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/e_logf_data.c
@@ -0,0 +1,44 @@
+/* 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,
+  }
+};
diff --git a/sysdeps/ieee754/flt-32/math_config.h b/sysdeps/ieee754/flt-32/math_config.h
index 31f0470612..953a4bc583 100644
--- a/sysdeps/ieee754/flt-32/math_config.h
+++ b/sysdeps/ieee754/flt-32/math_config.h
@@ -111,4 +111,16 @@ extern const struct exp2f_data
   double poly_scaled[EXP2F_POLY_ORDER];
 } __exp2f_data attribute_hidden;
 
+#define LOGF_TABLE_BITS 4
+#define LOGF_POLY_ORDER 4
+extern const struct logf_data
+{
+  struct
+  {
+    double invc, logc;
+  } tab[1 << LOGF_TABLE_BITS];
+  double ln2;
+  double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1.  */
+} __logf_data attribute_hidden;
+
 #endif
diff --git a/sysdeps/m68k/m680x0/fpu/e_logf_data.c b/sysdeps/m68k/m680x0/fpu/e_logf_data.c
new file mode 100644
index 0000000000..1cc8931700
--- /dev/null
+++ b/sysdeps/m68k/m680x0/fpu/e_logf_data.c
@@ -0,0 +1 @@
+/* Not needed.  */