From e931f4585585e39ccb5f1f3a29debe670eb53629 Mon Sep 17 00:00:00 2001
From: Szabolcs Nagy <szabolcs.nagy@arm.com>
Date: Mon, 4 Sep 2017 17:53:47 +0100
Subject: [PATCH 3/7] 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
2017-09-19 Szabolcs Nagy <szabolcs.nagy@arm.com>
* 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.
---
math/Makefile | 3 +-
sysdeps/i386/fpu/e_log2f_data.c | 1 +
sysdeps/ia64/fpu/e_log2f_data.c | 1 +
sysdeps/ieee754/flt-32/e_log2f.c | 148 +++++++++++++++++----------------
sysdeps/ieee754/flt-32/e_log2f_data.c | 44 ++++++++++
sysdeps/ieee754/flt-32/math_config.h | 11 +++
sysdeps/m68k/m680x0/fpu/e_log2f_data.c | 1 +
7 files changed, 135 insertions(+), 74 deletions(-)
create mode 100644 sysdeps/i386/fpu/e_log2f_data.c
create mode 100644 sysdeps/ia64/fpu/e_log2f_data.c
create mode 100644 sysdeps/ieee754/flt-32/e_log2f_data.c
create mode 100644 sysdeps/m68k/m680x0/fpu/e_log2f_data.c
@@ -115,7 +115,8 @@ 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 e_logf_data
+type-float-routines := k_rem_pio2f math_errf e_exp2f_data e_logf_data \
+ e_log2f_data
# _Float128 support
type-float128-suffix := f128
new file mode 100644
@@ -0,0 +1 @@
+/* Not needed. */
new file mode 100644
@@ -0,0 +1 @@
+/* Not needed. */
@@ -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)
new file mode 100644
@@ -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,
+ }
+};
@@ -123,4 +123,15 @@ extern const struct logf_data
double poly[LOGF_POLY_ORDER];
} __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
new file mode 100644
@@ -0,0 +1 @@
+/* Not needed. */
--
2.11.0