diff options
Diffstat (limited to 'sysdeps/ieee754/flt-32/e_exp2f.c')
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_exp2f.c | 170 |
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) |