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[PATCH] Optimized generic expf and exp2f
- From: Szabolcs Nagy <szabolcs dot nagy at arm dot com>
- To: GNU C Library <libc-alpha at sourceware dot org>
- Cc: nd at arm dot com
- Date: Tue, 05 Sep 2017 17:54:50 +0100
- Subject: [PATCH] Optimized generic expf and exp2f
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Based on new expf and exp2f code from
https://github.com/ARM-software/optimized-routines/
with https://sourceware.org/ml/libc-alpha/2017-08/msg01126.html
expf reciprocal-throughput: 3.3x faster
expf latency: 1.7x faster
libm.so size: -8byte data, -2140byte text
expf/exp2f worst case nearest rounding ulp error: 0.502
Error checks are inline and actual error handling is
in separate functions that are tail called and expected
to be reusable when other math functions are implemented
without wrappers. (expf, __expf, __ieee754_expf symbols
are aliases, _LIB_VERSION is not checked, errno is set
unconditionally according to POSIX rules.)
Double precision arithmetics is used which is expected
to be faster on most targets (including soft-float) than
using single precision and it is easier to get good
precision result with it.
Const data is kept in a separate translation unit which
complicates maintenance a bit, but is expected to give
good code for literal loads on most targets and allows
sharing data across expf, exp2f and powf.
Some configuration is in a new math_config.h which is
currently kept similar to the one in optimized-routines
repo which had to be self-contained, I expect that this
will need more adjustments for glibc.
Some details may need target specific tweaks:
- best convert and round to int operation in the arg
reduction may be different across targets.
- code was optimized on fma target, optimal polynomial
eval may be different without fma.
- gcc does not always generate good code for fp bit
representation access via unions or it may be inherently
slow on some target.
One issue with the argument reduction is that it only
works right with nearest rounded rint, otherwise the
interval is [0,2c] or [-2c,0] instead of [-c,c]. The
polynomial is optimized for [-c,c] but it has sufficent
extra precision that it gives acceptable results on
[-2c,2c] too assuming users are less interested in
non-nearest rounded precision, however this means some
glibc ulp error limits will need adjustment.
Another issue is with the polynomial evaluation which
causes 1 ulp errors for tiny inputs in some non-nearest
rounding, but i think it is worth the trade off for
better pipelined polynomial.
2017-09-05 Szabolcs Nagy <szabolcs.nagy@arm.com>
* math/Makefile (type-float-routines): Add math_errf and e_exp2f_data.
* sysdeps/ieee754/flt-32/w_expf_compat.c: Move to...
* math/w_expf_compat.c: ... here.
* sysdeps/aarch64/fpu/math_private.h (TOINT_INTRINSICS): Define.
(roundtoint, converttoint): Likewise.
* sysdeps/ieee754/flt-32/e_expf.c: New implementation.
* sysdeps/ieee754/flt-32/e_exp2f.c: New implementation.
* sysdeps/ieee754/flt-32/e_exp2f_data.c: New file.
* sysdeps/ieee754/flt-32/math_config.h: New file.
* sysdeps/ieee754/flt-32/math_errf.c: New file.
* sysdeps/ieee754/flt-32/w_exp2f_compat.c: New file.
* sysdeps/x86_64/fpu/w_expf_compat.c: New file.
diff --git a/math/Makefile b/math/Makefile
index 0601f3ac43..04586156f8 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
+type-float-routines := k_rem_pio2f math_errf e_exp2f_data
# _Float128 support
type-float128-suffix := f128
diff --git a/math/w_expf_compat.c b/math/w_expf_compat.c
new file mode 100644
index 0000000000..8a1fa51e46
--- /dev/null
+++ b/math/w_expf_compat.c
@@ -0,0 +1,35 @@
+/* Copyright (C) 2011-2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Ulrich Drepper <drepper@gmail.com>, 2011.
+
+ 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 <math-svid-compat.h>
+
+/* wrapper expf */
+float
+__expf (float x)
+{
+ float z = __ieee754_expf (x);
+ if (__builtin_expect (!isfinite (z) || z == 0, 0)
+ && isfinite (x) && _LIB_VERSION != _IEEE_)
+ return __kernel_standard_f (x, x, 106 + !!signbit (x));
+
+ return z;
+}
+hidden_def (__expf)
+weak_alias (__expf, expf)
diff --git a/sysdeps/aarch64/fpu/math_private.h b/sysdeps/aarch64/fpu/math_private.h
index 807111ea5a..775237ffb2 100644
--- a/sysdeps/aarch64/fpu/math_private.h
+++ b/sysdeps/aarch64/fpu/math_private.h
@@ -319,6 +319,26 @@ libc_feresetround_noex_aarch64_ctx (struct rm_ctx *ctx)
#define libc_feresetround_noexf_ctx libc_feresetround_noex_aarch64_ctx
#define libc_feresetround_noexl_ctx libc_feresetround_noex_aarch64_ctx
+/* Hack: only include the large arm_neon.h when needed. */
+#ifdef _MATH_CONFIG_H
+#include <arm_neon.h>
+
+/* ACLE intrinsics for frintn and fcvtns instructions. */
+#define TOINT_INTRINSICS 1
+
+static inline double_t
+roundtoint (double_t x)
+{
+ return vget_lane_f64 (vrndn_f64 (vld1_f64 (&x)), 0);
+}
+
+static inline uint64_t
+converttoint (double_t x)
+{
+ return vcvtnd_s64_f64 (x);
+}
+#endif
+
#include_next <math_private.h>
#endif
diff --git a/sysdeps/ieee754/flt-32/e_exp2f.c b/sysdeps/ieee754/flt-32/e_exp2f.c
index 567d3ff6d0..dfadd85f93 100644
--- a/sysdeps/ieee754/flt-32/e_exp2f.c
+++ b/sysdeps/ieee754/flt-32/e_exp2f.c
@@ -1,7 +1,6 @@
-/* Single-precision floating point 2^x.
- Copyright (C) 1997-2017 Free Software Foundation, Inc.
+/* Single-precision 2^x function.
+ Copyright (C) 2017 Free Software Foundation, Inc.
This file is part of the GNU C Library.
- Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
@@ -17,116 +16,75 @@
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
-/* The basic design here is from
- Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical
- Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft.,
- 17 (1), March 1991, pp. 26-45.
- It has been slightly modified to compute 2^x instead of e^x, and for
- single-precision.
- */
-#ifndef _GNU_SOURCE
-# define _GNU_SOURCE
-#endif
-#include <stdlib.h>
-#include <float.h>
-#include <ieee754.h>
#include <math.h>
-#include <fenv.h>
-#include <inttypes.h>
-#include <math_private.h>
-
-#include "t_exp2f.h"
-
-static const float TWOM100 = 7.88860905e-31;
-static const float TWO127 = 1.7014118346e+38;
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+EXP2F_TABLE_BITS = 5
+EXP2F_POLY_ORDER = 3
+
+ULP error: 0.502 (nearest rounding.)
+Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
+Wrong count: 168353 (all nearest rounding wrong results with fma.)
+Non-nearest ULP error: 1 (rounded ULP error)
+*/
+
+#define N (1 << EXP2F_TABLE_BITS)
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly
+#define SHIFT __exp2f_data.shift_scaled
+
+static inline uint32_t
+top12 (float x)
+{
+ return asuint (x) >> 20;
+}
float
-__ieee754_exp2f (float x)
+__exp2f (float x)
{
- static const float himark = (float) FLT_MAX_EXP;
- static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1);
-
- /* Check for usual case. */
- if (isless (x, himark) && isgreaterequal (x, lomark))
+ uint32_t abstop;
+ uint64_t ki, t;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, xd, z, r, r2, y, s;
+
+ xd = (double_t) x;
+ abstop = top12 (x) & 0x7ff;
+ if (__builtin_expect (abstop >= top12 (128.0f), 0))
{
- static const float THREEp14 = 49152.0;
- int tval, unsafe;
- float rx, x22, result;
- union ieee754_float ex2_u, scale_u;
-
- if (fabsf (x) < FLT_EPSILON / 4.0f)
- return 1.0f + x;
-
- {
- SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
-
- /* 1. Argument reduction.
- Choose integers ex, -128 <= t < 128, and some real
- -1/512 <= x1 <= 1/512 so that
- x = ex + t/512 + x1.
-
- First, calculate rx = ex + t/256. */
- rx = x + THREEp14;
- rx -= THREEp14;
- x -= rx; /* Compute x=x1. */
- /* Compute tval = (ex*256 + t)+128.
- Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %;
- and /-round-to-nearest not the usual c integer /]. */
- tval = (int) (rx * 256.0f + 128.0f);
-
- /* 2. Adjust for accurate table entry.
- Find e so that
- x = ex + t/256 + e + x2
- where -7e-4 < e < 7e-4, and
- (float)(2^(t/256+e))
- is accurate to one part in 2^-64. */
-
- /* 'tval & 255' is the same as 'tval%256' except that it's always
- positive.
- Compute x = x2. */
- x -= __exp2f_deltatable[tval & 255];
-
- /* 3. Compute ex2 = 2^(t/255+e+ex). */
- ex2_u.f = __exp2f_atable[tval & 255];
- tval >>= 8;
- /* x2 is an integer multiple of 2^-30; avoid intermediate
- underflow from the calculation of x22 * x. */
- unsafe = abs(tval) >= -FLT_MIN_EXP - 32;
- ex2_u.ieee.exponent += tval >> unsafe;
- scale_u.f = 1.0;
- scale_u.ieee.exponent += tval - (tval >> unsafe);
-
- /* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
- with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
- less than 1.3e-10. */
-
- x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
- }
-
- /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */
- result = x22 * x + ex2_u.f;
-
- if (!unsafe)
- return result;
- else
- {
- result *= scale_u.f;
- math_check_force_underflow_nonneg (result);
- return result;
- }
- }
- /* Exceptional cases: */
- else if (isless (x, himark))
- {
- if (isinf (x))
- /* e^-inf == 0, with no error. */
- return 0;
- else
- /* Underflow */
- return TWOM100 * TWOM100;
+ /* |x| >= 128 or x is nan. */
+ if (asuint (x) == asuint (-INFINITY))
+ return 0.0f;
+ if (abstop >= top12 (INFINITY))
+ return x + x;
+ if (x > 0.0f)
+ return __math_oflowf (0);
+ if (x <= -150.0f)
+ return __math_uflowf (0);
+#if WANT_ERRNO_UFLOW
+ if (x < -149.0f)
+ return __math_may_uflowf (0);
+#endif
}
- else
- /* Return x, if x is a NaN or Inf; or overflow, otherwise. */
- return TWO127*x;
+
+ /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */
+ kd = (double) (xd + SHIFT); /* Rounding to double precision is required. */
+ ki = asuint64 (kd);
+ kd -= SHIFT; /* k/N for int k. */
+ r = xd - kd;
+
+ /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+ t = T[ki % N];
+ t += ki << (52 - EXP2F_TABLE_BITS);
+ s = asdouble (t);
+ z = C[0] * r + C[1];
+ r2 = r * r;
+ y = C[2] * r + 1;
+ y = z * r2 + y;
+ y = y * s;
+ return (float) y;
}
-strong_alias (__ieee754_exp2f, __exp2f_finite)
+weak_alias (__exp2f, exp2f)
+strong_alias (__exp2f, __ieee754_exp2f)
+strong_alias (__exp2f, __exp2f_finite)
diff --git a/sysdeps/ieee754/flt-32/e_exp2f_data.c b/sysdeps/ieee754/flt-32/e_exp2f_data.c
new file mode 100644
index 0000000000..390dcae333
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/e_exp2f_data.c
@@ -0,0 +1,44 @@
+/* Shared data between expf, exp2f and powf.
+ 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"
+
+#define N (1 << EXP2F_TABLE_BITS)
+
+const struct exp2f_data __exp2f_data = {
+ /* tab[i] = uint(2^(i/N)) - (i << 52-BITS)
+ used for computing 2^(k/N) for an int |k| < 150 N as
+ double(tab[k%N] + (k << 52-BITS)) */
+ .tab = {
+0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
+0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
+0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
+0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
+0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
+0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
+0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
+0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
+ },
+ .shift_scaled = 0x1.8p+52 / N,
+ .poly = { 0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1 },
+ .shift = 0x1.8p+52,
+ .invln2_scaled = 0x1.71547652b82fep+0 * N,
+ .poly_scaled = {
+0x1.c6af84b912394p-5/N/N/N, 0x1.ebfce50fac4f3p-3/N/N, 0x1.62e42ff0c52d6p-1/N
+ },
+};
diff --git a/sysdeps/ieee754/flt-32/e_expf.c b/sysdeps/ieee754/flt-32/e_expf.c
index 782072f213..d1eabdae08 100644
--- a/sysdeps/ieee754/flt-32/e_expf.c
+++ b/sysdeps/ieee754/flt-32/e_expf.c
@@ -1,7 +1,6 @@
-/* Single-precision floating point e^x.
- Copyright (C) 1997-2017 Free Software Foundation, Inc.
+/* Single-precision e^x function.
+ Copyright (C) 2017 Free Software Foundation, Inc.
This file is part of the GNU C Library.
- Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
@@ -17,117 +16,90 @@
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
-/* How this works:
-
- The input value, x, is written as
-
- x = n * ln(2) + t/512 + delta[t] + x;
-
- where:
- - n is an integer, 127 >= n >= -150;
- - t is an integer, 177 >= t >= -177
- - delta is based on a table entry, delta[t] < 2^-28
- - x is whatever is left, |x| < 2^-10
-
- Then e^x is approximated as
-
- e^x = 2^n ( e^(t/512 + delta[t])
- + ( e^(t/512 + delta[t])
- * ( p(x + delta[t] + n * ln(2)) - delta ) ) )
-
- where
- - p(x) is a polynomial approximating e(x)-1;
- - e^(t/512 + delta[t]) is obtained from a table.
-
- The table used is the same one as for the double precision version;
- since we have the table, we might as well use it.
-
- It turns out to be faster to do calculations in double precision than
- to perform an 'accurate table method' expf, because of the range reduction
- overhead (compare exp2f).
- */
-#include <float.h>
-#include <ieee754.h>
#include <math.h>
-#include <fenv.h>
-#include <inttypes.h>
-#include <math_private.h>
-
-extern const float __exp_deltatable[178];
-extern const double __exp_atable[355] /* __attribute__((mode(DF))) */;
-
-static const float TWOM100 = 7.88860905e-31;
-static const float TWO127 = 1.7014118346e+38;
+#include <stdint.h>
+#include "math_config.h"
+
+/*
+EXP2F_TABLE_BITS = 5
+EXP2F_POLY_ORDER = 3
+
+ULP error: 0.502 (nearest rounding.)
+Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
+Wrong count: 170635 (all nearest rounding wrong results with fma.)
+Non-nearest ULP error: 1 (rounded ULP error)
+*/
+
+#define N (1 << EXP2F_TABLE_BITS)
+#define InvLn2N __exp2f_data.invln2_scaled
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly_scaled
+
+static inline uint32_t
+top12 (float x)
+{
+ return asuint (x) >> 20;
+}
float
-__ieee754_expf (float x)
+__expf (float x)
{
- static const float himark = 88.72283935546875;
- static const float lomark = -103.972084045410;
- /* Check for usual case. */
- if (isless (x, himark) && isgreater (x, lomark))
+ uint32_t abstop;
+ uint64_t ki, t;
+ /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
+ double_t kd, xd, z, r, r2, y, s;
+
+ xd = (double_t) x;
+ abstop = top12 (x) & 0x7ff;
+ if (__builtin_expect (abstop >= top12 (88.0f), 0))
{
- static const float THREEp42 = 13194139533312.0;
- static const float THREEp22 = 12582912.0;
- /* 1/ln(2). */
-#undef M_1_LN2
- static const float M_1_LN2 = 1.44269502163f;
- /* ln(2) */
-#undef M_LN2
- static const double M_LN2 = .6931471805599452862;
-
- int tval;
- double x22, t, result, dx;
- float n, delta;
- union ieee754_double ex2_u;
-
- {
- SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
-
- /* Calculate n. */
- n = x * M_1_LN2 + THREEp22;
- n -= THREEp22;
- dx = x - n*M_LN2;
-
- /* Calculate t/512. */
- t = dx + THREEp42;
- t -= THREEp42;
- dx -= t;
-
- /* Compute tval = t. */
- tval = (int) (t * 512.0);
-
- if (t >= 0)
- delta = - __exp_deltatable[tval];
- else
- delta = __exp_deltatable[-tval];
-
- /* Compute ex2 = 2^n e^(t/512+delta[t]). */
- ex2_u.d = __exp_atable[tval+177];
- ex2_u.ieee.exponent += (int) n;
-
- /* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
- with maximum error in [-2^-10-2^-28,2^-10+2^-28]
- less than 5e-11. */
- x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
- }
-
- /* Return result. */
- result = x22 * ex2_u.d + ex2_u.d;
- return (float) result;
+ /* |x| >= 88 or x is nan. */
+ if (asuint (x) == asuint (-INFINITY))
+ return 0.0f;
+ if (abstop >= top12 (INFINITY))
+ return x + x;
+ if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
+ return __math_oflowf (0);
+ if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
+ return __math_uflowf (0);
+#if WANT_ERRNO_UFLOW
+ if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
+ return __math_may_uflowf (0);
+#endif
}
- /* Exceptional cases: */
- else if (isless (x, himark))
- {
- if (isinf (x))
- /* e^-inf == 0, with no error. */
- return 0;
- else
- /* Underflow */
- return TWOM100 * TWOM100;
- }
- else
- /* Return x, if x is a NaN or Inf; or overflow, otherwise. */
- return TWO127*x;
+
+ /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
+ z = InvLn2N * xd;
+
+ /* Round and convert z to int, the result is in [-150*N, 128*N] and
+ ideally ties-to-even rule is used, otherwise the magnitude of r
+ can be bigger which gives larger approximation error. */
+#if TOINT_INTRINSICS
+ kd = roundtoint (z);
+ ki = converttoint (z);
+#elif TOINT_RINT
+ kd = rint (z);
+ ki = (long) kd;
+#elif TOINT_SHIFT
+# define SHIFT __exp2f_data.shift
+ kd = (double) (z + SHIFT); /* Rounding to double precision is required. */
+ ki = asuint64 (kd);
+ kd -= SHIFT;
+#endif
+ r = z - kd;
+
+ /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+ t = T[ki % N];
+ t += ki << (52 - EXP2F_TABLE_BITS);
+ s = asdouble (t);
+ z = C[0] * r + C[1];
+ r2 = r * r;
+ y = C[2] * r + 1;
+ y = z * r2 + y;
+ y = y * s;
+ return (float) y;
}
-strong_alias (__ieee754_expf, __expf_finite)
+hidden_def (__expf)
+weak_alias (__expf, expf)
+strong_alias (__expf, __ieee754_expf)
+strong_alias (__expf, __expf_finite)
diff --git a/sysdeps/ieee754/flt-32/math_config.h b/sysdeps/ieee754/flt-32/math_config.h
new file mode 100644
index 0000000000..aaaa90067d
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/math_config.h
@@ -0,0 +1,128 @@
+/* Configuration for math routines.
+ 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/>. */
+
+#ifndef _MATH_CONFIG_H
+#define _MATH_CONFIG_H
+
+#include <math.h>
+#include <math_private.h>
+#include <stdint.h>
+
+#ifndef WANT_ROUNDING
+/* Correct special case results in non-nearest rounding modes. */
+#define WANT_ROUNDING 1
+#endif
+#ifndef WANT_ERRNO
+/* Set errno according to ISO C with (math_errhandling & MATH_ERRNO) != 0. */
+#define WANT_ERRNO 1
+#endif
+#ifndef WANT_ERRNO_UFLOW
+/* Set errno to ERANGE if result underflows to 0 (in all rounding modes). */
+#define WANT_ERRNO_UFLOW (WANT_ROUNDING && WANT_ERRNO)
+#endif
+
+#ifndef TOINT_INTRINSICS
+#define TOINT_INTRINSICS 0
+#endif
+#ifndef TOINT_RINT
+#define TOINT_RINT 0
+#endif
+#ifndef TOINT_SHIFT
+#define TOINT_SHIFT 1
+#endif
+
+static inline uint32_t
+asuint (float f)
+{
+ union
+ {
+ float f;
+ uint32_t i;
+ } u = {f};
+ return u.i;
+}
+
+static inline float
+asfloat (uint32_t i)
+{
+ union
+ {
+ uint32_t i;
+ float f;
+ } u = {i};
+ return u.f;
+}
+
+static inline uint64_t
+asuint64 (double f)
+{
+ union
+ {
+ double f;
+ uint64_t i;
+ } u = {f};
+ return u.i;
+}
+
+static inline double
+asdouble (uint64_t i)
+{
+ union
+ {
+ uint64_t i;
+ double f;
+ } u = {i};
+ return u.f;
+}
+
+static inline int
+ieee_2008_issignaling (float x)
+{
+ uint32_t ix = asuint (x);
+ ix ^= 0x00400000; /* IEEE 754-2008 snan bit. */
+ return 2 * ix > 2u * 0x7fc00000;
+}
+
+#ifdef __GNUC__
+#define HIDDEN __attribute__ ((__visibility__ ("hidden")))
+#define NOINLINE __attribute__ ((noinline))
+#else
+#define HIDDEN
+#define NOINLINE
+#endif
+
+HIDDEN float __math_oflowf (unsigned long);
+HIDDEN float __math_uflowf (unsigned long);
+HIDDEN float __math_may_uflowf (unsigned long);
+HIDDEN float __math_divzerof (unsigned long);
+HIDDEN float __math_invalidf (float);
+
+/* Shared between expf, exp2f and powf. */
+#define EXP2F_TABLE_BITS 5
+#define EXP2F_POLY_ORDER 3
+extern const struct exp2f_data
+{
+ uint64_t tab[1 << EXP2F_TABLE_BITS];
+ double shift_scaled;
+ double poly[EXP2F_POLY_ORDER];
+ double shift;
+ double invln2_scaled;
+ double poly_scaled[EXP2F_POLY_ORDER];
+} __exp2f_data;
+
+#endif
diff --git a/sysdeps/ieee754/flt-32/math_errf.c b/sysdeps/ieee754/flt-32/math_errf.c
new file mode 100644
index 0000000000..11fbdc0b92
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/math_errf.c
@@ -0,0 +1,77 @@
+/* Single-precision math error handling.
+ 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"
+
+#if WANT_ERRNO
+#include <errno.h>
+/* NOINLINE reduces code size and avoids making math functions non-leaf
+ when the error handling is inlined. */
+NOINLINE static float
+with_errnof (float y, int e)
+{
+ errno = e;
+ return y;
+}
+#else
+#define with_errnof(x, e) (x)
+#endif
+
+/* NOINLINE prevents fenv semantics breaking optimizations. */
+NOINLINE static float
+xflowf (unsigned long sign, float y)
+{
+ y = (sign ? -y : y) * y;
+ return with_errnof (y, ERANGE);
+}
+
+HIDDEN float
+__math_uflowf (unsigned long sign)
+{
+ return xflowf (sign, 0x1p-95f);
+}
+
+#if WANT_ERRNO_UFLOW
+/* Underflows to zero in some non-nearest rounding mode, setting errno
+ is valid even if the result is non-zero, but in the subnormal range. */
+HIDDEN float
+__math_may_uflowf (unsigned long sign)
+{
+ return xflowf (sign, 0x1.4p-75f);
+}
+#endif
+
+HIDDEN float
+__math_oflowf (unsigned long sign)
+{
+ return xflowf (sign, 0x1p97f);
+}
+
+HIDDEN float
+__math_divzerof (unsigned long sign)
+{
+ float y = 0;
+ return with_errnof ((sign ? -1 : 1) / y, ERANGE);
+}
+
+HIDDEN float
+__math_invalidf (float x)
+{
+ float y = (x - x) / (x - x);
+ return isnan (x) ? y : with_errnof (y, EDOM);
+}
diff --git a/sysdeps/ieee754/flt-32/w_exp2f_compat.c b/sysdeps/ieee754/flt-32/w_exp2f_compat.c
new file mode 100644
index 0000000000..c37de4df43
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/w_exp2f_compat.c
@@ -0,0 +1 @@
+/* Empty file to disable the exp2f wrapper. */
diff --git a/sysdeps/ieee754/flt-32/w_expf_compat.c b/sysdeps/ieee754/flt-32/w_expf_compat.c
index 8a1fa51e46..578cf4d4a7 100644
--- a/sysdeps/ieee754/flt-32/w_expf_compat.c
+++ b/sysdeps/ieee754/flt-32/w_expf_compat.c
@@ -1,35 +1 @@
-/* Copyright (C) 2011-2017 Free Software Foundation, Inc.
- This file is part of the GNU C Library.
- Contributed by Ulrich Drepper <drepper@gmail.com>, 2011.
-
- 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 <math-svid-compat.h>
-
-/* wrapper expf */
-float
-__expf (float x)
-{
- float z = __ieee754_expf (x);
- if (__builtin_expect (!isfinite (z) || z == 0, 0)
- && isfinite (x) && _LIB_VERSION != _IEEE_)
- return __kernel_standard_f (x, x, 106 + !!signbit (x));
-
- return z;
-}
-hidden_def (__expf)
-weak_alias (__expf, expf)
+/* Empty file to disable the expf wrapper. */
diff --git a/sysdeps/x86_64/fpu/w_expf_compat.c b/sysdeps/x86_64/fpu/w_expf_compat.c
new file mode 100644
index 0000000000..dc454638c3
--- /dev/null
+++ b/sysdeps/x86_64/fpu/w_expf_compat.c
@@ -0,0 +1 @@
+#include <math/w_expf_compat.c>