forked from KolibriOS/kolibrios
553 lines
14 KiB
C
553 lines
14 KiB
C
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/* Copyright (C) 2007-2015 Free Software Foundation, Inc.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 3, or (at your option) any later
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version.
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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/*****************************************************************************
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* BID64 square root
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*****************************************************************************
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*
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* Algorithm description:
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*
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* if(exponent_x is odd)
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* scale coefficient_x by 10, adjust exponent
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* - get lower estimate for number of digits in coefficient_x
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* - scale coefficient x to between 31 and 33 decimal digits
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* - in parallel, check for exact case and return if true
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* - get high part of result coefficient using double precision sqrt
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* - compute remainder and refine coefficient in one iteration (which
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* modifies it by at most 1)
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* - result exponent is easy to compute from the adjusted arg. exponent
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*
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****************************************************************************/
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#include "bid_internal.h"
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#include "bid_sqrt_macros.h"
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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#include <fenv.h>
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#define FE_ALL_FLAGS FE_INVALID|FE_DIVBYZERO|FE_OVERFLOW|FE_UNDERFLOW|FE_INEXACT
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#endif
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extern double sqrt (double);
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#if DECIMAL_CALL_BY_REFERENCE
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void
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bid64_sqrt (UINT64 * pres,
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UINT64 *
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px _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
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_EXC_INFO_PARAM) {
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UINT64 x;
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#else
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UINT64
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bid64_sqrt (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM
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_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
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#endif
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UINT128 CA, CT;
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UINT64 sign_x, coefficient_x;
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UINT64 Q, Q2, A10, C4, R, R2, QE, res;
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SINT64 D;
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int_double t_scale;
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int_float tempx;
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double da, dq, da_h, da_l, dqe;
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int exponent_x, exponent_q, bin_expon_cx;
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int digits_x;
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int scale;
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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fexcept_t binaryflags = 0;
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#endif
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#if DECIMAL_CALL_BY_REFERENCE
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#if !DECIMAL_GLOBAL_ROUNDING
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_IDEC_round rnd_mode = *prnd_mode;
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#endif
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x = *px;
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#endif
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// unpack arguments, check for NaN or Infinity
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if (!unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x)) {
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// x is Inf. or NaN or 0
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if ((x & INFINITY_MASK64) == INFINITY_MASK64) {
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res = coefficient_x;
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if ((coefficient_x & SSNAN_MASK64) == SINFINITY_MASK64) // -Infinity
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{
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res = NAN_MASK64;
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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}
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#ifdef SET_STATUS_FLAGS
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if ((x & SNAN_MASK64) == SNAN_MASK64) // sNaN
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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BID_RETURN (res & QUIET_MASK64);
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}
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// x is 0
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exponent_x = (exponent_x + DECIMAL_EXPONENT_BIAS) >> 1;
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res = sign_x | (((UINT64) exponent_x) << 53);
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BID_RETURN (res);
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}
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// x<0?
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if (sign_x && coefficient_x) {
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res = NAN_MASK64;
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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BID_RETURN (res);
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}
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
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#endif
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//--- get number of bits in the coefficient of x ---
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tempx.d = (float) coefficient_x;
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bin_expon_cx = ((tempx.i >> 23) & 0xff) - 0x7f;
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digits_x = estimate_decimal_digits[bin_expon_cx];
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// add test for range
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if (coefficient_x >= power10_index_binexp[bin_expon_cx])
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digits_x++;
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A10 = coefficient_x;
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if (exponent_x & 1) {
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A10 = (A10 << 2) + A10;
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A10 += A10;
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}
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dqe = sqrt ((double) A10);
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QE = (UINT32) dqe;
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if (QE * QE == A10) {
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res =
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very_fast_get_BID64 (0, (exponent_x + DECIMAL_EXPONENT_BIAS) >> 1,
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QE);
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
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#endif
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BID_RETURN (res);
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}
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// if exponent is odd, scale coefficient by 10
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scale = 31 - digits_x;
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exponent_q = exponent_x - scale;
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scale += (exponent_q & 1); // exp. bias is even
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CT = power10_table_128[scale];
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__mul_64x128_short (CA, coefficient_x, CT);
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// 2^64
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t_scale.i = 0x43f0000000000000ull;
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// convert CA to DP
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da_h = CA.w[1];
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da_l = CA.w[0];
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da = da_h * t_scale.d + da_l;
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dq = sqrt (da);
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Q = (UINT64) dq;
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// get sign(sqrt(CA)-Q)
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R = CA.w[0] - Q * Q;
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R = ((SINT64) R) >> 63;
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D = R + R + 1;
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exponent_q = (exponent_q + DECIMAL_EXPONENT_BIAS) >> 1;
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INEXACT_EXCEPTION);
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#endif
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#ifndef IEEE_ROUND_NEAREST
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#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
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if (!((rnd_mode) & 3)) {
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#endif
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#endif
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// midpoint to check
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Q2 = Q + Q + D;
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C4 = CA.w[0] << 2;
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// get sign(-sqrt(CA)+Midpoint)
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R2 = Q2 * Q2 - C4;
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R2 = ((SINT64) R2) >> 63;
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// adjust Q if R!=R2
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Q += (D & (R ^ R2));
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#ifndef IEEE_ROUND_NEAREST
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#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
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} else {
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C4 = CA.w[0];
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Q += D;
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if ((SINT64) (Q * Q - C4) > 0)
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Q--;
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if (rnd_mode == ROUNDING_UP)
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Q++;
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}
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#endif
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#endif
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res = fast_get_BID64 (0, exponent_q, Q);
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
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#endif
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BID_RETURN (res);
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}
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TYPE0_FUNCTION_ARG1 (UINT64, bid64q_sqrt, x)
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UINT256 M256, C4, C8;
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UINT128 CX, CX2, A10, S2, T128, CS, CSM, CS2, C256, CS1,
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mul_factor2_long = { {0x0ull, 0x0ull} }, QH, Tmp, TP128, Qh, Ql;
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UINT64 sign_x, Carry, B10, res, mul_factor, mul_factor2 = 0x0ull, CS0;
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SINT64 D;
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int_float fx, f64;
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int exponent_x, bin_expon_cx, done = 0;
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int digits, scale, exponent_q = 0, exact = 1, amount, extra_digits;
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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fexcept_t binaryflags = 0;
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#endif
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// unpack arguments, check for NaN or Infinity
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if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) {
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res = CX.w[1];
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// NaN ?
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if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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#ifdef SET_STATUS_FLAGS
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if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull);
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Tmp.w[0] = CX.w[0];
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TP128 = reciprocals10_128[18];
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__mul_128x128_full (Qh, Ql, Tmp, TP128);
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amount = recip_scale[18];
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__shr_128 (Tmp, Qh, amount);
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res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0];
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BID_RETURN (res);
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}
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// x is Infinity?
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if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) {
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if (sign_x) {
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// -Inf, return NaN
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res = 0x7c00000000000000ull;
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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}
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BID_RETURN (res);
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}
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// x is 0 otherwise
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exponent_x =
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((exponent_x - DECIMAL_EXPONENT_BIAS_128) >> 1) +
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DECIMAL_EXPONENT_BIAS;
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if (exponent_x < 0)
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exponent_x = 0;
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if (exponent_x > DECIMAL_MAX_EXPON_64)
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exponent_x = DECIMAL_MAX_EXPON_64;
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//res= sign_x | (((UINT64)exponent_x)<<53);
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res = get_BID64 (sign_x, exponent_x, 0, rnd_mode, pfpsf);
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BID_RETURN (res);
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}
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if (sign_x) {
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res = 0x7c00000000000000ull;
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INVALID_EXCEPTION);
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#endif
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BID_RETURN (res);
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}
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS);
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#endif
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// 2^64
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f64.i = 0x5f800000;
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// fx ~ CX
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fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0];
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bin_expon_cx = ((fx.i >> 23) & 0xff) - 0x7f;
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digits = estimate_decimal_digits[bin_expon_cx];
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A10 = CX;
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if (exponent_x & 1) {
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A10.w[1] = (CX.w[1] << 3) | (CX.w[0] >> 61);
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A10.w[0] = CX.w[0] << 3;
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CX2.w[1] = (CX.w[1] << 1) | (CX.w[0] >> 63);
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CX2.w[0] = CX.w[0] << 1;
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__add_128_128 (A10, A10, CX2);
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}
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C256.w[1] = A10.w[1];
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C256.w[0] = A10.w[0];
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CS.w[0] = short_sqrt128 (A10);
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CS.w[1] = 0;
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mul_factor = 0;
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// check for exact result
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if (CS.w[0] < 10000000000000000ull) {
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if (CS.w[0] * CS.w[0] == A10.w[0]) {
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__sqr64_fast (S2, CS.w[0]);
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if (S2.w[1] == A10.w[1]) // && S2.w[0]==A10.w[0])
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{
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res =
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get_BID64 (0,
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((exponent_x - DECIMAL_EXPONENT_BIAS_128) >> 1) +
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DECIMAL_EXPONENT_BIAS, CS.w[0], rnd_mode, pfpsf);
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS
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(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
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#endif
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BID_RETURN (res);
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}
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}
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if (CS.w[0] >= 1000000000000000ull) {
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done = 1;
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exponent_q = exponent_x;
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C256.w[1] = A10.w[1];
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C256.w[0] = A10.w[0];
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}
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INEXACT_EXCEPTION);
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#endif
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exact = 0;
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} else {
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B10 = 0x3333333333333334ull;
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__mul_64x64_to_128_full (CS2, CS.w[0], B10);
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CS0 = CS2.w[1] >> 1;
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if (CS.w[0] != ((CS0 << 3) + (CS0 << 1))) {
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INEXACT_EXCEPTION);
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#endif
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exact = 0;
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}
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done = 1;
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CS.w[0] = CS0;
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exponent_q = exponent_x + 2;
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mul_factor = 10;
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mul_factor2 = 100;
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if (CS.w[0] >= 10000000000000000ull) {
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__mul_64x64_to_128_full (CS2, CS.w[0], B10);
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CS0 = CS2.w[1] >> 1;
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if (CS.w[0] != ((CS0 << 3) + (CS0 << 1))) {
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#ifdef SET_STATUS_FLAGS
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__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
||
|
|
#endif
|
||
|
|
exact = 0;
|
||
|
|
}
|
||
|
|
exponent_q += 2;
|
||
|
|
CS.w[0] = CS0;
|
||
|
|
mul_factor = 100;
|
||
|
|
mul_factor2 = 10000;
|
||
|
|
}
|
||
|
|
if (exact) {
|
||
|
|
CS0 = CS.w[0] * mul_factor;
|
||
|
|
__sqr64_fast (CS1, CS0)
|
||
|
|
if ((CS1.w[0] != A10.w[0]) || (CS1.w[1] != A10.w[1])) {
|
||
|
|
#ifdef SET_STATUS_FLAGS
|
||
|
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
||
|
|
#endif
|
||
|
|
exact = 0;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if (!done) {
|
||
|
|
// get number of digits in CX
|
||
|
|
D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1];
|
||
|
|
if (D > 0
|
||
|
|
|| (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0]))
|
||
|
|
digits++;
|
||
|
|
|
||
|
|
// if exponent is odd, scale coefficient by 10
|
||
|
|
scale = 31 - digits;
|
||
|
|
exponent_q = exponent_x - scale;
|
||
|
|
scale += (exponent_q & 1); // exp. bias is even
|
||
|
|
|
||
|
|
T128 = power10_table_128[scale];
|
||
|
|
__mul_128x128_low (C256, CX, T128);
|
||
|
|
|
||
|
|
|
||
|
|
CS.w[0] = short_sqrt128 (C256);
|
||
|
|
}
|
||
|
|
//printf("CS=%016I64x\n",CS.w[0]);
|
||
|
|
|
||
|
|
exponent_q =
|
||
|
|
((exponent_q - DECIMAL_EXPONENT_BIAS_128) >> 1) +
|
||
|
|
DECIMAL_EXPONENT_BIAS;
|
||
|
|
if ((exponent_q < 0) && (exponent_q + MAX_FORMAT_DIGITS >= 0)) {
|
||
|
|
extra_digits = -exponent_q;
|
||
|
|
exponent_q = 0;
|
||
|
|
|
||
|
|
// get coeff*(2^M[extra_digits])/10^extra_digits
|
||
|
|
__mul_64x64_to_128 (QH, CS.w[0], reciprocals10_64[extra_digits]);
|
||
|
|
|
||
|
|
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128
|
||
|
|
amount = short_recip_scale[extra_digits];
|
||
|
|
|
||
|
|
CS0 = QH.w[1] >> amount;
|
||
|
|
|
||
|
|
#ifdef SET_STATUS_FLAGS
|
||
|
|
if (exact) {
|
||
|
|
if (CS.w[0] != CS0 * power10_table_128[extra_digits].w[0])
|
||
|
|
exact = 0;
|
||
|
|
}
|
||
|
|
if (!exact)
|
||
|
|
__set_status_flags (pfpsf, UNDERFLOW_EXCEPTION | INEXACT_EXCEPTION);
|
||
|
|
#endif
|
||
|
|
|
||
|
|
CS.w[0] = CS0;
|
||
|
|
if (!mul_factor)
|
||
|
|
mul_factor = 1;
|
||
|
|
mul_factor *= power10_table_128[extra_digits].w[0];
|
||
|
|
__mul_64x64_to_128 (mul_factor2_long, mul_factor, mul_factor);
|
||
|
|
if (mul_factor2_long.w[1])
|
||
|
|
mul_factor2 = 0;
|
||
|
|
else
|
||
|
|
mul_factor2 = mul_factor2_long.w[1];
|
||
|
|
}
|
||
|
|
// 4*C256
|
||
|
|
C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62);
|
||
|
|
C4.w[0] = C256.w[0] << 2;
|
||
|
|
|
||
|
|
#ifndef IEEE_ROUND_NEAREST
|
||
|
|
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
|
||
|
|
if (!((rnd_mode) & 3)) {
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
// compare to midpoints
|
||
|
|
CSM.w[0] = (CS.w[0] + CS.w[0]) | 1;
|
||
|
|
//printf("C256=%016I64x %016I64x, CSM=%016I64x %016I64x %016I64x\n",C4.w[1],C4.w[0],CSM.w[1],CSM.w[0], CS.w[0]);
|
||
|
|
if (mul_factor)
|
||
|
|
CSM.w[0] *= mul_factor;
|
||
|
|
// CSM^2
|
||
|
|
__mul_64x64_to_128 (M256, CSM.w[0], CSM.w[0]);
|
||
|
|
//__mul_128x128_to_256(M256, CSM, CSM);
|
||
|
|
|
||
|
|
if (C4.w[1] > M256.w[1] ||
|
||
|
|
(C4.w[1] == M256.w[1] && C4.w[0] > M256.w[0])) {
|
||
|
|
// round up
|
||
|
|
CS.w[0]++;
|
||
|
|
} else {
|
||
|
|
C8.w[0] = CS.w[0] << 3;
|
||
|
|
C8.w[1] = 0;
|
||
|
|
if (mul_factor) {
|
||
|
|
if (mul_factor2) {
|
||
|
|
__mul_64x64_to_128 (C8, C8.w[0], mul_factor2);
|
||
|
|
} else {
|
||
|
|
__mul_64x128_low (C8, C8.w[0], mul_factor2_long);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// M256 - 8*CSM
|
||
|
|
__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
|
||
|
|
M256.w[1] = M256.w[1] - C8.w[1] - Carry;
|
||
|
|
|
||
|
|
// if CSM' > C256, round up
|
||
|
|
if (M256.w[1] > C4.w[1] ||
|
||
|
|
(M256.w[1] == C4.w[1] && M256.w[0] > C4.w[0])) {
|
||
|
|
// round down
|
||
|
|
if (CS.w[0])
|
||
|
|
CS.w[0]--;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
#ifndef IEEE_ROUND_NEAREST
|
||
|
|
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
|
||
|
|
} else {
|
||
|
|
CS.w[0]++;
|
||
|
|
CSM.w[0] = CS.w[0];
|
||
|
|
C8.w[0] = CSM.w[0] << 1;
|
||
|
|
if (mul_factor)
|
||
|
|
CSM.w[0] *= mul_factor;
|
||
|
|
__mul_64x64_to_128 (M256, CSM.w[0], CSM.w[0]);
|
||
|
|
C8.w[1] = 0;
|
||
|
|
if (mul_factor) {
|
||
|
|
if (mul_factor2) {
|
||
|
|
__mul_64x64_to_128 (C8, C8.w[0], mul_factor2);
|
||
|
|
} else {
|
||
|
|
__mul_64x128_low (C8, C8.w[0], mul_factor2_long);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//printf("C256=%016I64x %016I64x, CSM=%016I64x %016I64x %016I64x\n",C256.w[1],C256.w[0],M256.w[1],M256.w[0], CS.w[0]);
|
||
|
|
|
||
|
|
if (M256.w[1] > C256.w[1] ||
|
||
|
|
(M256.w[1] == C256.w[1] && M256.w[0] > C256.w[0])) {
|
||
|
|
__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
|
||
|
|
M256.w[1] = M256.w[1] - Carry - C8.w[1];
|
||
|
|
M256.w[0]++;
|
||
|
|
if (!M256.w[0]) {
|
||
|
|
M256.w[1]++;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
if ((M256.w[1] > C256.w[1] ||
|
||
|
|
(M256.w[1] == C256.w[1] && M256.w[0] > C256.w[0]))
|
||
|
|
&& (CS.w[0] > 1)) {
|
||
|
|
|
||
|
|
CS.w[0]--;
|
||
|
|
|
||
|
|
if (CS.w[0] > 1) {
|
||
|
|
__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
|
||
|
|
M256.w[1] = M256.w[1] - Carry - C8.w[1];
|
||
|
|
M256.w[0]++;
|
||
|
|
if (!M256.w[0]) {
|
||
|
|
M256.w[1]++;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (M256.w[1] > C256.w[1] ||
|
||
|
|
(M256.w[1] == C256.w[1] && M256.w[0] > C256.w[0]))
|
||
|
|
CS.w[0]--;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
else {
|
||
|
|
/*__add_carry_out(M256.w[0], Carry, M256.w[0], C8.w[0]);
|
||
|
|
M256.w[1] = M256.w[1] + Carry + C8.w[1];
|
||
|
|
M256.w[0]++;
|
||
|
|
if(!M256.w[0])
|
||
|
|
{
|
||
|
|
M256.w[1]++;
|
||
|
|
}
|
||
|
|
CS.w[0]++;
|
||
|
|
if(M256.w[1]<C256.w[1] ||
|
||
|
|
(M256.w[1]==C256.w[1] && M256.w[0]<=C256.w[0]))
|
||
|
|
{
|
||
|
|
CS.w[0]++;
|
||
|
|
}*/
|
||
|
|
CS.w[0]++;
|
||
|
|
}
|
||
|
|
//printf("C256=%016I64x %016I64x, CSM=%016I64x %016I64x %016I64x %d\n",C4.w[1],C4.w[0],M256.w[1],M256.w[0], CS.w[0], exact);
|
||
|
|
// RU?
|
||
|
|
if (((rnd_mode) != ROUNDING_UP) || exact) {
|
||
|
|
if (CS.w[0])
|
||
|
|
CS.w[0]--;
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
//printf("C256=%016I64x %016I64x, CSM=%016I64x %016I64x %016I64x %d\n",C4.w[1],C4.w[0],M256.w[1],M256.w[0], CS.w[0], exact);
|
||
|
|
|
||
|
|
res = get_BID64 (0, exponent_q, CS.w[0], rnd_mode, pfpsf);
|
||
|
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
||
|
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
||
|
|
#endif
|
||
|
|
BID_RETURN (res);
|
||
|
|
|
||
|
|
|
||
|
|
}
|