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-rw-r--r--sysdeps/ieee754/flt-32/e_exp2f.c170
1 files changed, 63 insertions, 107 deletions
diff --git a/sysdeps/ieee754/flt-32/e_exp2f.c b/sysdeps/ieee754/flt-32/e_exp2f.c
index 567d3ff6d0..72b7d8829f 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 +16,73 @@
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)
{
- 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 (__glibc_unlikely (abstop >= top12 (128.0f)))
{
- 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 = math_narrow_eval ((double) (xd + SHIFT)); /* Needs to be double. */
+ 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)