New generic log2f

Similar to the new logf: double precision arithmetics and a small
lookup table is used. The argument reduction step is the same as in
the new logf.

without wrapper on aarch64:
log2f reciprocal-throughput: 2.3x faster
log2f latency: 2.1x faster
old worst case error: 1.72 ulp
new worst case error: 0.75 ulp
aarch64 .text size: -252 bytes
aarch64 .rodata size: +244 bytes

	* math/Makefile (type-float-routines): Add e_log2f_data.
	* sysdeps/ieee754/flt-32/e_log2f.c: New implementation.
	* sysdeps/ieee754/flt-32/e_log2f_data.c: New file.
	* sysdeps/ieee754/flt-32/math_config.h (__log2f_data): Define.
	(LOG2F_TABLE_BITS, LOG2F_POLY_ORDER): Define.
	* sysdeps/i386/fpu/e_log2f_data.c: New file.
	* sysdeps/ia64/fpu/e_log2f_data.c: New file.
	* sysdeps/m68k/m680x0/fpu/e_log2f_data.c: New file.

3 files changed, 130 insertions, 73 deletions

diff --git a/sysdeps/ieee754/flt-32/e_log2f.c b/sysdeps/ieee754/flt-32/e_log2f.c
index 782d901094..6c42f27843 100644
--- a/sysdeps/ieee754/flt-32/e_log2f.c
+++ b/sysdeps/ieee754/flt-32/e_log2f.c
@@ -1,86 +1,88 @@
-/* e_logf.c -- float version of e_log.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- * adapted for log2 by Ulrich Drepper <drepper@cygnus.com>
- */
+/* Single-precision log2 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 <fix-int-fp-convert-zero.h>
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+LOG2F_TABLE_BITS = 4
+LOG2F_POLY_ORDER = 4
 
-static const float
-ln2 = 0.69314718055994530942,
-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 */
+ULP error: 0.752 (nearest rounding.)
+Relative error: 1.9 * 2^-26 (before rounding.)
+*/
 
-static const float zero   =  0.0;
+#define N (1 << LOG2F_TABLE_BITS)
+#define T __log2f_data.tab
+#define A __log2f_data.poly
+#define OFF 0x3f330000
 
 float
-__ieee754_log2f(float x)
+__ieee754_log2f (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, p, y, y0, invc, logc;
+  uint32_t ix, iz, top, 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) /* log2(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 - LOG2F_TABLE_BITS)) % N;
+  top = tmp & 0xff800000;
+  iz = ix - top;
+  k = (int32_t) tmp >> 23; /* arithmetic shift */
+  invc = T[i].invc;
+  logc = T[i].logc;
+  z = (double_t) asfloat (iz);
 
-	GET_FLOAT_WORD(ix,x);
+  /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
+  r = z * invc - 1;
+  y0 = logc + (double_t) k;
 
-	k=0;
-	if (ix < 0x00800000) {			/* x < 2**-126  */
-	    if (__builtin_expect((ix&0x7fffffff)==0, 0))
-		return -two25/__fabsf (x);	/* 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);
-	dk = (float)k;
-	f = x-(float)1.0;
-	if((0x007fffff&(15+ix))<16) {	/* |f| < 2**-20 */
-	    if(f==zero)
-	      {
-		if (FIX_INT_FP_CONVERT_ZERO && dk == 0.0f)
-		  dk = 0.0f;
-		return dk;
-	      }
-	    R = f*f*((float)0.5-(float)0.33333333333333333*f);
-	    return dk-(R-f)/ln2;
-	}
-	s = f/((float)2.0+f);
-	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;
-	    return dk-((hfsq-(s*(hfsq+R)))-f)/ln2;
-	} else {
-	    return dk-((s*(f-R))-f)/ln2;
-	}
+  /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
+  r2 = r * r;
+  y = A[1] * r + A[2];
+  y = A[0] * r2 + y;
+  p = A[3] * r + y0;
+  y = y * r2 + p;
+  return (float) y;
 }
 strong_alias (__ieee754_log2f, __log2f_finite)
diff --git a/sysdeps/ieee754/flt-32/e_log2f_data.c b/sysdeps/ieee754/flt-32/e_log2f_data.c
new file mode 100644
index 0000000000..e39de3ba56
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/e_log2f_data.c
@@ -0,0 +1,44 @@
+/* Data definition for log2f.
+   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 log2f_data __log2f_data = {
+  .tab = {
+  { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 },
+  { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 },
+  { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 },
+  { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 },
+  { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 },
+  { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 },
+  { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 },
+  { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 },
+  { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 },
+  { 0x1p+0, 0x0p+0 },
+  { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 },
+  { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 },
+  { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 },
+  { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 },
+  { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 },
+  { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 },
+  },
+  .poly = {
+  -0x1.712b6f70a7e4dp-2, 0x1.ecabf496832ep-2, -0x1.715479ffae3dep-1,
+  0x1.715475f35c8b8p0,
+  }
+};
diff --git a/sysdeps/ieee754/flt-32/math_config.h b/sysdeps/ieee754/flt-32/math_config.h
index 953a4bc583..f869fbc66c 100644
--- a/sysdeps/ieee754/flt-32/math_config.h
+++ b/sysdeps/ieee754/flt-32/math_config.h
@@ -123,4 +123,15 @@ extern const struct logf_data
   double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1.  */
 } __logf_data attribute_hidden;
 
+#define LOG2F_TABLE_BITS 4
+#define LOG2F_POLY_ORDER 4
+extern const struct log2f_data
+{
+  struct
+  {
+    double invc, logc;
+  } tab[1 << LOG2F_TABLE_BITS];
+  double poly[LOG2F_POLY_ORDER];
+} __log2f_data attribute_hidden;
+
 #endif