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Diffstat (limited to 'sysdeps/x86/fpu/powl_helper.c')
| -rw-r--r-- | sysdeps/x86/fpu/powl_helper.c | 211 |
1 files changed, 211 insertions, 0 deletions
diff --git a/sysdeps/x86/fpu/powl_helper.c b/sysdeps/x86/fpu/powl_helper.c new file mode 100644 index 0000000000..3f69b08a1b --- /dev/null +++ b/sysdeps/x86/fpu/powl_helper.c @@ -0,0 +1,211 @@ +/* Implement powl for x86 using extra-precision log. + Copyright (C) 2012 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.h> +#include <math_private.h> + +/* High parts and low parts of -log (k/16), for integer k from 12 to + 24. */ + +static const long double powl_log_table[] = + { + 0x4.9a58844d36e49e1p-4L, -0x1.0522624fd558f574p-68L, + 0x3.527da7915b3c6de4p-4L, 0x1.7d4ef4b901b99b9ep-68L, + 0x2.22f1d044fc8f7bc8p-4L, -0x1.8e97c071a42fc388p-68L, + 0x1.08598b59e3a0688ap-4L, 0x3.fd9bf503372c12fcp-72L, + -0x0p+0L, 0x0p+0L, + -0xf.85186008b15330cp-8L, 0x1.9b47488a6687672cp-72L, + -0x1.e27076e2af2e5e9ep-4L, -0xa.87ffe1fe9e155dcp-72L, + -0x2.bfe60e14f27a791p-4L, 0x1.83bebf1bdb88a032p-68L, + -0x3.91fef8f353443584p-4L, -0xb.b03de5ff734495cp-72L, + -0x4.59d72aeae98380e8p-4L, 0xc.e0aa3be4747dc1p-72L, + -0x5.1862f08717b09f4p-4L, -0x2.decdeccf1cd10578p-68L, + -0x5.ce75fdaef401a738p-4L, -0x9.314feb4fbde5aaep-72L, + -0x6.7cc8fb2fe612fcbp-4L, 0x2.5ca2642feb779f98p-68L, + }; + +/* High 32 bits of log2 (e), and remainder rounded to 64 bits. */ +static const long double log2e_hi = 0x1.71547652p+0L; +static const long double log2e_lo = 0xb.82fe1777d0ffda1p-36L; + +/* Given a number with high part HI and low part LO, add the number X + to it and store the result in *RHI and *RLO. It is given that + either |X| < |0.7 * HI|, or HI == LO == 0, and that the values are + small enough that no overflow occurs. The result does not need to + be exact to 128 bits; 78-bit accuracy of the final accumulated + result suffices. */ + +static inline void +acc_split (long double *rhi, long double *rlo, long double hi, long double lo, + long double x) +{ + long double thi = hi + x; + long double tlo = (hi - thi) + x + lo; + *rhi = thi + tlo; + *rlo = (thi - *rhi) + tlo; +} + +extern long double __powl_helper (long double x, long double y); +libm_hidden_proto (__powl_helper) + +/* Given X a value that is finite and nonzero, or a NaN, and only + negative if Y is not an integer, and Y a finite nonzero value with + 0x1p-79 <= |Y| <= 0x1p78, compute X to the power Y. */ + +long double +__powl_helper (long double x, long double y) +{ + if (isnan (x) || x < 0) + return __ieee754_expl (y * __ieee754_logl (x)); + + /* We need to compute Y * log2 (X) to at least 64 bits after the + point for normal results (that is, to at least 78 bits + precision). */ + int x_int_exponent; + long double x_frac; + x_frac = __frexpl (x, &x_int_exponent); + if (x_frac <= 0x0.aaaaaaaaaaaaaaaap0L) /* 2.0L / 3.0L, rounded down */ + { + x_frac *= 2.0; + x_int_exponent--; + } + + long double log_x_frac_hi, log_x_frac_lo; + /* Determine an initial approximation to log (X_FRAC) using + POWL_LOG_TABLE, and multiply by a value K/16 to reduce to an + interval (24/25, 26/25). */ + int k = (int) ((16.0L / x_frac) + 0.5L); + log_x_frac_hi = powl_log_table[2 * k - 24]; + log_x_frac_lo = powl_log_table[2 * k - 23]; + long double x_frac_low; + if (k == 16) + x_frac_low = 0.0L; + else + { + /* Mask off low 5 bits of X_FRAC so the multiplication by K/16 + is exact. These bits are small enough that they can be + corrected for by adding log2 (e) * X_FRAC_LOW to the final + result. */ + int32_t se; + u_int32_t i0, i1; + GET_LDOUBLE_WORDS (se, i0, i1, x_frac); + x_frac_low = x_frac; + i1 &= 0xffffffe0; + SET_LDOUBLE_WORDS (x_frac, se, i0, i1); + x_frac_low -= x_frac; + x_frac_low /= x_frac; + x_frac *= k / 16.0L; + } + + /* Now compute log (X_FRAC) for X_FRAC in (24/25, 26/25). Separate + W = X_FRAC - 1 into high 16 bits and remaining bits, so that + multiplications for low-order power series terms are exact. The + remaining bits are small enough that adding a 64-bit value of + log2 (1 + W_LO / (1 + W_HI)) will be a sufficient correction for + them. */ + long double w = x_frac - 1; + long double w_hi, w_lo; + int32_t se; + u_int32_t i0, i1; + GET_LDOUBLE_WORDS (se, i0, i1, w); + i0 &= 0xffff0000; + i1 = 0; + SET_LDOUBLE_WORDS (w_hi, se, i0, i1); + w_lo = w - w_hi; + long double wp = w_hi; + acc_split (&log_x_frac_hi, &log_x_frac_lo, log_x_frac_hi, log_x_frac_lo, wp); + wp *= -w_hi; + acc_split (&log_x_frac_hi, &log_x_frac_lo, log_x_frac_hi, log_x_frac_lo, + wp / 2.0L); + wp *= -w_hi; + acc_split (&log_x_frac_hi, &log_x_frac_lo, log_x_frac_hi, log_x_frac_lo, + wp * 0x0.5555p0L); /* -W_HI**3 / 3, high part. */ + acc_split (&log_x_frac_hi, &log_x_frac_lo, log_x_frac_hi, log_x_frac_lo, + wp * 0x0.5555555555555555p-16L); /* -W_HI**3 / 3, low part. */ + wp *= -w_hi; + acc_split (&log_x_frac_hi, &log_x_frac_lo, log_x_frac_hi, log_x_frac_lo, + wp / 4.0L); + /* Subsequent terms are small enough that they only need be computed + to 64 bits. */ + for (int i = 5; i <= 17; i++) + { + wp *= -w_hi; + acc_split (&log_x_frac_hi, &log_x_frac_lo, log_x_frac_hi, log_x_frac_lo, + wp / i); + } + + /* Convert LOG_X_FRAC_HI + LOG_X_FRAC_LO to a base-2 logarithm. */ + long double log2_x_frac_hi, log2_x_frac_lo; + long double log_x_frac_hi32, log_x_frac_lo64; + GET_LDOUBLE_WORDS (se, i0, i1, log_x_frac_hi); + i1 = 0; + SET_LDOUBLE_WORDS (log_x_frac_hi32, se, i0, i1); + log_x_frac_lo64 = (log_x_frac_hi - log_x_frac_hi32) + log_x_frac_lo; + long double log2_x_frac_hi1 = log_x_frac_hi32 * log2e_hi; + long double log2_x_frac_lo1 + = log_x_frac_lo64 * log2e_hi + log_x_frac_hi * log2e_lo; + log2_x_frac_hi = log2_x_frac_hi1 + log2_x_frac_lo1; + log2_x_frac_lo = (log2_x_frac_hi1 - log2_x_frac_hi) + log2_x_frac_lo1; + + /* Correct for the masking off of W_LO. */ + long double log2_1p_w_lo; + asm ("fyl2xp1" + : "=t" (log2_1p_w_lo) + : "0" (w_lo / (1.0L + w_hi)), "u" (1.0L) + : "st(1)"); + acc_split (&log2_x_frac_hi, &log2_x_frac_lo, log2_x_frac_hi, log2_x_frac_lo, + log2_1p_w_lo); + + /* Correct for the masking off of X_FRAC_LOW. */ + acc_split (&log2_x_frac_hi, &log2_x_frac_lo, log2_x_frac_hi, log2_x_frac_lo, + x_frac_low * M_LOG2El); + + /* Add the integer and fractional parts of the base-2 logarithm. */ + long double log2_x_hi, log2_x_lo; + log2_x_hi = x_int_exponent + log2_x_frac_hi; + log2_x_lo = ((x_int_exponent - log2_x_hi) + log2_x_frac_hi) + log2_x_frac_lo; + + /* Compute the base-2 logarithm of the result. */ + long double log2_res_hi, log2_res_lo; + long double log2_x_hi32, log2_x_lo64; + GET_LDOUBLE_WORDS (se, i0, i1, log2_x_hi); + i1 = 0; + SET_LDOUBLE_WORDS (log2_x_hi32, se, i0, i1); + log2_x_lo64 = (log2_x_hi - log2_x_hi32) + log2_x_lo; + long double y_hi32, y_lo32; + GET_LDOUBLE_WORDS (se, i0, i1, y); + i1 = 0; + SET_LDOUBLE_WORDS (y_hi32, se, i0, i1); + y_lo32 = y - y_hi32; + log2_res_hi = log2_x_hi32 * y_hi32; + log2_res_lo = log2_x_hi32 * y_lo32 + log2_x_lo64 * y; + + /* Split the base-2 logarithm of the result into integer and + fractional parts. */ + long double log2_res_int = __roundl (log2_res_hi); + long double log2_res_frac = log2_res_hi - log2_res_int + log2_res_lo; + + /* Compute the final result. */ + long double res; + asm ("f2xm1" : "=t" (res) : "0" (log2_res_frac)); + res += 1.0L; + asm ("fscale" : "=t" (res) : "0" (res), "u" (log2_res_int)); + return res; +} + +libm_hidden_def (__powl_helper) |