565 lines
14 KiB
C
565 lines
14 KiB
C
/* Copyright (C) 2007-2020 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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#define BID_128RES
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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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BID128_FUNCTION_ARG1 (bid128_sqrt, x)
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UINT256 M256, C256, C4, C8;
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UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res;
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UINT64 sign_x, Carry;
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SINT64 D;
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int_float fx, f64;
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int exponent_x, bin_expon_cx;
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int digits, scale, exponent_q;
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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.w[1] = CX.w[1];
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res.w[0] = CX.w[0];
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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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res.w[1] = CX.w[1] & QUIET_MASK64;
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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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res.w[1] = CX.w[1];
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if (sign_x) {
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// -Inf, return NaN
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res.w[1] = 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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res.w[1] =
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sign_x |
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((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1) << 49);
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res.w[0] = 0;
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BID_RETURN (res);
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}
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if (sign_x) {
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res.w[1] = 0x7c00000000000000ull;
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res.w[0] = 0;
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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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CS.w[0] = short_sqrt128 (A10);
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CS.w[1] = 0;
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// check for exact result
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if (CS.w[0] * CS.w[0] == A10.w[0]) {
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__mul_64x64_to_128_fast (S2, CS.w[0], 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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get_BID128_very_fast (&res, 0,
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(exponent_x +
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DECIMAL_EXPONENT_BIAS_128) >> 1, CS);
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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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// get number of digits in CX
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D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1];
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if (D > 0
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|| (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0]))
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digits++;
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// if exponent is odd, scale coefficient by 10
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scale = 67 - digits;
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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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if (scale > 38) {
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T128 = power10_table_128[scale - 37];
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__mul_128x128_low (CX1, CX, T128);
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TP128 = power10_table_128[37];
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__mul_128x128_to_256 (C256, CX1, TP128);
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} else {
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T128 = power10_table_128[scale];
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__mul_128x128_to_256 (C256, CX, T128);
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}
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// 4*C256
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C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62);
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C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62);
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C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62);
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C4.w[0] = C256.w[0] << 2;
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long_sqrt128 (&CS, C256);
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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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// compare to midpoints
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CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
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CSM.w[0] = (CS.w[0] + CS.w[0]) | 1;
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// CSM^2
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//__mul_128x128_to_256(M256, CSM, CSM);
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__sqr128_to_256 (M256, CSM);
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if (C4.w[3] > M256.w[3]
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|| (C4.w[3] == M256.w[3]
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&& (C4.w[2] > M256.w[2]
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|| (C4.w[2] == M256.w[2]
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&& (C4.w[1] > M256.w[1]
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|| (C4.w[1] == M256.w[1]
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&& C4.w[0] > M256.w[0])))))) {
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// round up
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CS.w[0]++;
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if (!CS.w[0])
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CS.w[1]++;
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} else {
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C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61);
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C8.w[0] = CS.w[0] << 3;
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// M256 - 8*CSM
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__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
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__sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
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__sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
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M256.w[3] = M256.w[3] - Carry;
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// if CSM' > C256, round up
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if (M256.w[3] > C4.w[3]
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|| (M256.w[3] == C4.w[3]
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&& (M256.w[2] > C4.w[2]
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|| (M256.w[2] == C4.w[2]
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&& (M256.w[1] > C4.w[1]
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|| (M256.w[1] == C4.w[1]
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&& M256.w[0] > C4.w[0])))))) {
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// round down
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if (!CS.w[0])
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CS.w[1]--;
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CS.w[0]--;
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}
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}
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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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__sqr128_to_256 (M256, CS);
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C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
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C8.w[0] = CS.w[0] << 1;
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if (M256.w[3] > C256.w[3]
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|| (M256.w[3] == C256.w[3]
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&& (M256.w[2] > C256.w[2]
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|| (M256.w[2] == C256.w[2]
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&& (M256.w[1] > C256.w[1]
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|| (M256.w[1] == C256.w[1]
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&& M256.w[0] > C256.w[0])))))) {
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__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
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__sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
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__sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
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M256.w[3] = M256.w[3] - Carry;
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M256.w[0]++;
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if (!M256.w[0]) {
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M256.w[1]++;
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if (!M256.w[1]) {
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M256.w[2]++;
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if (!M256.w[2])
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M256.w[3]++;
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}
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}
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if (!CS.w[0])
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CS.w[1]--;
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CS.w[0]--;
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if (M256.w[3] > C256.w[3]
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|| (M256.w[3] == C256.w[3]
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&& (M256.w[2] > C256.w[2]
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|| (M256.w[2] == C256.w[2]
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&& (M256.w[1] > C256.w[1]
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|| (M256.w[1] == C256.w[1]
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&& M256.w[0] > C256.w[0])))))) {
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if (!CS.w[0])
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CS.w[1]--;
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CS.w[0]--;
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}
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}
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else {
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__add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
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__add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
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__add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
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M256.w[3] = M256.w[3] + Carry;
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M256.w[0]++;
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if (!M256.w[0]) {
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M256.w[1]++;
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if (!M256.w[1]) {
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M256.w[2]++;
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if (!M256.w[2])
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M256.w[3]++;
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}
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}
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if (M256.w[3] < C256.w[3]
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|| (M256.w[3] == C256.w[3]
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&& (M256.w[2] < C256.w[2]
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|| (M256.w[2] == C256.w[2]
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&& (M256.w[1] < C256.w[1]
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|| (M256.w[1] == C256.w[1]
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&& M256.w[0] <= C256.w[0])))))) {
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CS.w[0]++;
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if (!CS.w[0])
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CS.w[1]++;
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}
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}
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// RU?
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if ((rnd_mode) == ROUNDING_UP) {
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CS.w[0]++;
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if (!CS.w[0])
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CS.w[1]++;
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}
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}
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#endif
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#endif
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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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get_BID128_fast (&res, 0,
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(exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1, CS);
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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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BID128_FUNCTION_ARGTYPE1 (bid128d_sqrt, UINT64, x)
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UINT256 M256, C256, C4, C8;
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UINT128 CX, CX1, CX2, A10, S2, T128, TP128, CS, CSM, res;
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UINT64 sign_x, Carry;
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SINT64 D;
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int_float fx, f64;
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int exponent_x, bin_expon_cx;
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int digits, scale, exponent_q;
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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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// unpack arguments, check for NaN or Infinity
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CX.w[1] = 0;
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if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], x)) {
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res.w[1] = CX.w[0];
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res.w[0] = 0;
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// NaN ?
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if ((x & 0x7c00000000000000ull) == 0x7c00000000000000ull) {
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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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res.w[0] = (CX.w[0] & 0x0003ffffffffffffull);
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__mul_64x64_to_128 (res, res.w[0], power10_table_128[18].w[0]);
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res.w[1] |= ((CX.w[0]) & 0xfc00000000000000ull);
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BID_RETURN (res);
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}
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// x is Infinity?
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if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) {
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if (sign_x) {
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// -Inf, return NaN
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res.w[1] = 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 + DECIMAL_EXPONENT_BIAS_128;
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res.w[1] =
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sign_x | ((((UINT64) (exponent_x + DECIMAL_EXPONENT_BIAS_128)) >> 1)
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<< 49);
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res.w[0] = 0;
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BID_RETURN (res);
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}
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if (sign_x) {
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res.w[1] = 0x7c00000000000000ull;
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res.w[0] = 0;
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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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exponent_x =
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exponent_x - DECIMAL_EXPONENT_BIAS + DECIMAL_EXPONENT_BIAS_128;
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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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CS.w[0] = short_sqrt128 (A10);
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CS.w[1] = 0;
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// check for exact result
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if (CS.w[0] * CS.w[0] == A10.w[0]) {
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__mul_64x64_to_128_fast (S2, CS.w[0], CS.w[0]);
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if (S2.w[1] == A10.w[1]) {
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get_BID128_very_fast (&res, 0,
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(exponent_x + DECIMAL_EXPONENT_BIAS_128) >> 1,
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CS);
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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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// get number of digits in CX
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D = CX.w[1] - power10_index_binexp_128[bin_expon_cx].w[1];
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if (D > 0
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|| (!D && CX.w[0] >= power10_index_binexp_128[bin_expon_cx].w[0]))
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digits++;
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// if exponent is odd, scale coefficient by 10
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scale = 67 - digits;
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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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if (scale > 38) {
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T128 = power10_table_128[scale - 37];
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__mul_128x128_low (CX1, CX, T128);
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TP128 = power10_table_128[37];
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__mul_128x128_to_256 (C256, CX1, TP128);
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} else {
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T128 = power10_table_128[scale];
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__mul_128x128_to_256 (C256, CX, T128);
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}
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// 4*C256
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C4.w[3] = (C256.w[3] << 2) | (C256.w[2] >> 62);
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C4.w[2] = (C256.w[2] << 2) | (C256.w[1] >> 62);
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C4.w[1] = (C256.w[1] << 2) | (C256.w[0] >> 62);
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C4.w[0] = C256.w[0] << 2;
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long_sqrt128 (&CS, C256);
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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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// compare to midpoints
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CSM.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
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CSM.w[0] = (CS.w[0] + CS.w[0]) | 1;
|
|
// CSM^2
|
|
//__mul_128x128_to_256(M256, CSM, CSM);
|
|
__sqr128_to_256 (M256, CSM);
|
|
|
|
if (C4.w[3] > M256.w[3]
|
|
|| (C4.w[3] == M256.w[3]
|
|
&& (C4.w[2] > M256.w[2]
|
|
|| (C4.w[2] == M256.w[2]
|
|
&& (C4.w[1] > M256.w[1]
|
|
|| (C4.w[1] == M256.w[1]
|
|
&& C4.w[0] > M256.w[0])))))) {
|
|
// round up
|
|
CS.w[0]++;
|
|
if (!CS.w[0])
|
|
CS.w[1]++;
|
|
} else {
|
|
C8.w[1] = (CS.w[1] << 3) | (CS.w[0] >> 61);
|
|
C8.w[0] = CS.w[0] << 3;
|
|
// M256 - 8*CSM
|
|
__sub_borrow_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
|
|
__sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
|
|
__sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
|
|
M256.w[3] = M256.w[3] - Carry;
|
|
|
|
// if CSM' > C256, round up
|
|
if (M256.w[3] > C4.w[3]
|
|
|| (M256.w[3] == C4.w[3]
|
|
&& (M256.w[2] > C4.w[2]
|
|
|| (M256.w[2] == C4.w[2]
|
|
&& (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[1]--;
|
|
CS.w[0]--;
|
|
}
|
|
}
|
|
#ifndef IEEE_ROUND_NEAREST
|
|
#ifndef IEEE_ROUND_NEAREST_TIES_AWAY
|
|
} else {
|
|
__sqr128_to_256 (M256, CS);
|
|
C8.w[1] = (CS.w[1] << 1) | (CS.w[0] >> 63);
|
|
C8.w[0] = CS.w[0] << 1;
|
|
if (M256.w[3] > C256.w[3]
|
|
|| (M256.w[3] == C256.w[3]
|
|
&& (M256.w[2] > C256.w[2]
|
|
|| (M256.w[2] == C256.w[2]
|
|
&& (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]);
|
|
__sub_borrow_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
|
|
__sub_borrow_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
|
|
M256.w[3] = M256.w[3] - Carry;
|
|
M256.w[0]++;
|
|
if (!M256.w[0]) {
|
|
M256.w[1]++;
|
|
if (!M256.w[1]) {
|
|
M256.w[2]++;
|
|
if (!M256.w[2])
|
|
M256.w[3]++;
|
|
}
|
|
}
|
|
|
|
if (!CS.w[0])
|
|
CS.w[1]--;
|
|
CS.w[0]--;
|
|
|
|
if (M256.w[3] > C256.w[3]
|
|
|| (M256.w[3] == C256.w[3]
|
|
&& (M256.w[2] > C256.w[2]
|
|
|| (M256.w[2] == C256.w[2]
|
|
&& (M256.w[1] > C256.w[1]
|
|
|| (M256.w[1] == C256.w[1]
|
|
&& M256.w[0] > C256.w[0])))))) {
|
|
|
|
if (!CS.w[0])
|
|
CS.w[1]--;
|
|
CS.w[0]--;
|
|
}
|
|
}
|
|
|
|
else {
|
|
__add_carry_out (M256.w[0], Carry, M256.w[0], C8.w[0]);
|
|
__add_carry_in_out (M256.w[1], Carry, M256.w[1], C8.w[1], Carry);
|
|
__add_carry_in_out (M256.w[2], Carry, M256.w[2], 0, Carry);
|
|
M256.w[3] = M256.w[3] + Carry;
|
|
M256.w[0]++;
|
|
if (!M256.w[0]) {
|
|
M256.w[1]++;
|
|
if (!M256.w[1]) {
|
|
M256.w[2]++;
|
|
if (!M256.w[2])
|
|
M256.w[3]++;
|
|
}
|
|
}
|
|
if (M256.w[3] < C256.w[3]
|
|
|| (M256.w[3] == C256.w[3]
|
|
&& (M256.w[2] < C256.w[2]
|
|
|| (M256.w[2] == C256.w[2]
|
|
&& (M256.w[1] < C256.w[1]
|
|
|| (M256.w[1] == C256.w[1]
|
|
&& M256.w[0] <= C256.w[0])))))) {
|
|
|
|
CS.w[0]++;
|
|
if (!CS.w[0])
|
|
CS.w[1]++;
|
|
}
|
|
}
|
|
// RU?
|
|
if ((rnd_mode) == ROUNDING_UP) {
|
|
CS.w[0]++;
|
|
if (!CS.w[0])
|
|
CS.w[1]++;
|
|
}
|
|
|
|
}
|
|
#endif
|
|
#endif
|
|
|
|
#ifdef SET_STATUS_FLAGS
|
|
__set_status_flags (pfpsf, INEXACT_EXCEPTION);
|
|
#endif
|
|
get_BID128_fast (&res, 0, (exponent_q + DECIMAL_EXPONENT_BIAS_128) >> 1,
|
|
CS);
|
|
#ifdef UNCHANGED_BINARY_STATUS_FLAGS
|
|
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS);
|
|
#endif
|
|
BID_RETURN (res);
|
|
|
|
|
|
}
|