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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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. */ |
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/***************************************************************************** |
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* BID64 fma |
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***************************************************************************** |
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* |
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* Algorithm description: |
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* |
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* if multiplication is guranteed exact (short coefficients) |
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* call the unpacked arg. equivalent of bid64_add(x*y, z) |
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* else |
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* get full coefficient_x*coefficient_y product |
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* call subroutine to perform addition of 64-bit argument |
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* to 128-bit product |
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* |
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****************************************************************************/ |
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#include "bid_inline_add.h" |
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#if DECIMAL_CALL_BY_REFERENCE |
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extern void bid64_mul (UINT64 * pres, UINT64 * px, |
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UINT64 * |
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py _RND_MODE_PARAM _EXC_FLAGS_PARAM |
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_EXC_MASKS_PARAM _EXC_INFO_PARAM); |
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#else |
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extern UINT64 bid64_mul (UINT64 x, |
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UINT64 y _RND_MODE_PARAM |
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_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
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_EXC_INFO_PARAM); |
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#endif |
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#if DECIMAL_CALL_BY_REFERENCE |
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void |
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bid64_fma (UINT64 * pres, UINT64 * px, UINT64 * py, |
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UINT64 * |
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pz _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
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_EXC_INFO_PARAM) { |
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UINT64 x, y, z; |
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#else |
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UINT64 |
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bid64_fma (UINT64 x, UINT64 y, |
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UINT64 z _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 P, PU, CT, CZ; |
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UINT64 sign_x, sign_y, coefficient_x, coefficient_y, sign_z, |
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coefficient_z; |
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UINT64 C64, remainder_y, res; |
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UINT64 CYh, CY0L, T, valid_x, valid_y, valid_z; |
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int_double tempx, tempy; |
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int extra_digits, exponent_x, exponent_y, bin_expon_cx, bin_expon_cy, |
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bin_expon_product, rmode; |
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int digits_p, bp, final_exponent, exponent_z, digits_z, ez, ey, |
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scale_z, uf_status; |
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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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y = *py; |
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z = *pz; |
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#endif |
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valid_x = unpack_BID64 (&sign_x, &exponent_x, &coefficient_x, x); |
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valid_y = unpack_BID64 (&sign_y, &exponent_y, &coefficient_y, y); |
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valid_z = unpack_BID64 (&sign_z, &exponent_z, &coefficient_z, z); |
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// unpack arguments, check for NaN, Infinity, or 0 |
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if (!valid_x || !valid_y || !valid_z) { |
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if ((y & MASK_NAN) == MASK_NAN) { // y is NAN |
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// if x = {0, f, inf, NaN}, y = NaN, z = {0, f, inf, NaN} then res = Q (y) |
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// check first for non-canonical NaN payload |
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y = y & 0xfe03ffffffffffffull; // clear G6-G12 |
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if ((y & 0x0003ffffffffffffull) > 999999999999999ull) { |
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y = y & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
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} |
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if ((y & MASK_SNAN) == MASK_SNAN) { // y is SNAN |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return quiet (y) |
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res = y & 0xfdffffffffffffffull; |
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} else { // y is QNaN |
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// return y |
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res = y; |
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// if z = SNaN or x = SNaN signal invalid exception |
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if ((z & MASK_SNAN) == MASK_SNAN |
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|| (x & MASK_SNAN) == MASK_SNAN) { |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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} |
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} |
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BID_RETURN (res) |
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} else if ((z & MASK_NAN) == MASK_NAN) { // z is NAN |
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// if x = {0, f, inf, NaN}, y = {0, f, inf}, z = NaN then res = Q (z) |
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// check first for non-canonical NaN payload |
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z = z & 0xfe03ffffffffffffull; // clear G6-G12 |
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if ((z & 0x0003ffffffffffffull) > 999999999999999ull) { |
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z = z & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
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} |
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if ((z & MASK_SNAN) == MASK_SNAN) { // z is SNAN |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return quiet (z) |
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res = z & 0xfdffffffffffffffull; |
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} else { // z is QNaN |
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// return z |
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res = z; |
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// if x = SNaN signal invalid exception |
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if ((x & MASK_SNAN) == MASK_SNAN) { |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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} |
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} |
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BID_RETURN (res) |
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} else if ((x & MASK_NAN) == MASK_NAN) { // x is NAN |
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// if x = NaN, y = {0, f, inf}, z = {0, f, inf} then res = Q (x) |
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// check first for non-canonical NaN payload |
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x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
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if ((x & 0x0003ffffffffffffull) > 999999999999999ull) { |
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x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
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} |
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if ((x & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return quiet (x) |
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res = x & 0xfdffffffffffffffull; |
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} else { // x is QNaN |
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// return x |
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res = x; // clear out G[6]-G[16] |
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} |
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BID_RETURN (res) |
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} |
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if (!valid_x) { |
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// x is Inf. or 0 |
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// x is Infinity? |
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if ((x & 0x7800000000000000ull) == 0x7800000000000000ull) { |
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// check if y is 0 |
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if (!coefficient_y) { |
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// y==0, return NaN |
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#ifdef SET_STATUS_FLAGS |
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if ((z & 0x7e00000000000000ull) != 0x7c00000000000000ull) |
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__set_status_flags (pfpsf, INVALID_EXCEPTION); |
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#endif |
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BID_RETURN (0x7c00000000000000ull); |
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} |
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// test if z is Inf of oposite sign |
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if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull) |
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&& (((x ^ y) ^ z) & 0x8000000000000000ull)) { |
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// return NaN |
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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 (0x7c00000000000000ull); |
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} |
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// otherwise return +/-Inf |
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BID_RETURN (((x ^ y) & 0x8000000000000000ull) | |
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0x7800000000000000ull); |
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} |
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// x is 0 |
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if (((y & 0x7800000000000000ull) != 0x7800000000000000ull) |
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&& ((z & 0x7800000000000000ull) != 0x7800000000000000ull)) { |
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if (coefficient_z) { |
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exponent_y = exponent_x - DECIMAL_EXPONENT_BIAS + exponent_y; |
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sign_z = z & 0x8000000000000000ull; |
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if (exponent_y >= exponent_z) |
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BID_RETURN (z); |
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res = |
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add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z, |
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&rnd_mode, pfpsf); |
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BID_RETURN (res); |
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} |
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} |
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} |
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if (!valid_y) { |
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// y is Inf. or 0 |
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// y is Infinity? |
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if ((y & 0x7800000000000000ull) == 0x7800000000000000ull) { |
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// check if x is 0 |
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if (!coefficient_x) { |
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// y==0, return NaN |
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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 (0x7c00000000000000ull); |
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} |
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// test if z is Inf of oposite sign |
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if (((z & 0x7c00000000000000ull) == 0x7800000000000000ull) |
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&& (((x ^ y) ^ z) & 0x8000000000000000ull)) { |
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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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// return NaN |
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BID_RETURN (0x7c00000000000000ull); |
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} |
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// otherwise return +/-Inf |
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BID_RETURN (((x ^ y) & 0x8000000000000000ull) | |
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0x7800000000000000ull); |
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} |
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// y is 0 |
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if (((z & 0x7800000000000000ull) != 0x7800000000000000ull)) { |
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if (coefficient_z) { |
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exponent_y += exponent_x - DECIMAL_EXPONENT_BIAS; |
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sign_z = z & 0x8000000000000000ull; |
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if (exponent_y >= exponent_z) |
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BID_RETURN (z); |
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res = |
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add_zero64 (exponent_y, sign_z, exponent_z, coefficient_z, |
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&rnd_mode, pfpsf); |
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BID_RETURN (res); |
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} |
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} |
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} |
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if (!valid_z) { |
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// y is Inf. or 0 |
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// test if y is NaN/Inf |
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if ((z & 0x7800000000000000ull) == 0x7800000000000000ull) { |
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BID_RETURN (coefficient_z & QUIET_MASK64); |
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} |
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// z is 0, return x*y |
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if ((!coefficient_x) || (!coefficient_y)) { |
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//0+/-0 |
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exponent_x += exponent_y - DECIMAL_EXPONENT_BIAS; |
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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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else if (exponent_x < 0) |
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exponent_x = 0; |
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if (exponent_x <= exponent_z) |
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res = ((UINT64) exponent_x) << 53; |
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else |
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res = ((UINT64) exponent_z) << 53; |
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if ((sign_x ^ sign_y) == sign_z) |
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res |= sign_z; |
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#ifndef IEEE_ROUND_NEAREST_TIES_AWAY |
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#ifndef IEEE_ROUND_NEAREST |
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else if (rnd_mode == ROUNDING_DOWN) |
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res |= 0x8000000000000000ull; |
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#endif |
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#endif |
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BID_RETURN (res); |
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} |
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} |
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} |
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/* get binary coefficients of x and y */ |
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//--- get number of bits in the coefficients of x and y --- |
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// version 2 (original) |
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tempx.d = (double) coefficient_x; |
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bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52); |
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tempy.d = (double) coefficient_y; |
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bin_expon_cy = ((tempy.i & MASK_BINARY_EXPONENT) >> 52); |
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// magnitude estimate for coefficient_x*coefficient_y is |
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// 2^(unbiased_bin_expon_cx + unbiased_bin_expon_cx) |
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bin_expon_product = bin_expon_cx + bin_expon_cy; |
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// check if coefficient_x*coefficient_y<2^(10*k+3) |
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// equivalent to unbiased_bin_expon_cx + unbiased_bin_expon_cx < 10*k+1 |
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if (bin_expon_product < UPPER_EXPON_LIMIT + 2 * BINARY_EXPONENT_BIAS) { |
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// easy multiply |
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C64 = coefficient_x * coefficient_y; |
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final_exponent = exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS; |
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if ((final_exponent > 0) || (!coefficient_z)) { |
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res = |
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get_add64 (sign_x ^ sign_y, |
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final_exponent, C64, sign_z, exponent_z, coefficient_z, rnd_mode, pfpsf); |
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BID_RETURN (res); |
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} else { |
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P.w[0] = C64; |
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P.w[1] = 0; |
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extra_digits = 0; |
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} |
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} else { |
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if (!coefficient_z) { |
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#if DECIMAL_CALL_BY_REFERENCE |
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bid64_mul (&res, px, |
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py _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG |
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_EXC_INFO_ARG); |
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#else |
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res = |
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bid64_mul (x, |
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y _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG |
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_EXC_INFO_ARG); |
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#endif |
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BID_RETURN (res); |
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} |
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// get 128-bit product: coefficient_x*coefficient_y |
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__mul_64x64_to_128 (P, coefficient_x, coefficient_y); |
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// tighten binary range of P: leading bit is 2^bp |
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// unbiased_bin_expon_product <= bp <= unbiased_bin_expon_product+1 |
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bin_expon_product -= 2 * BINARY_EXPONENT_BIAS; |
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__tight_bin_range_128 (bp, P, bin_expon_product); |
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// get number of decimal digits in the product |
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digits_p = estimate_decimal_digits[bp]; |
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if (!(__unsigned_compare_gt_128 (power10_table_128[digits_p], P))) |
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digits_p++; // if power10_table_128[digits_p] <= P |
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// determine number of decimal digits to be rounded out |
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extra_digits = digits_p - MAX_FORMAT_DIGITS; |
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final_exponent = |
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exponent_x + exponent_y + extra_digits - DECIMAL_EXPONENT_BIAS; |
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} |
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if (((unsigned) final_exponent) >= 3 * 256) { |
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if (final_exponent < 0) { |
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//--- get number of bits in the coefficients of z --- |
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tempx.d = (double) coefficient_z; |
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bin_expon_cx = ((tempx.i & MASK_BINARY_EXPONENT) >> 52) - 0x3ff; |
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// get number of decimal digits in the coeff_x |
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digits_z = estimate_decimal_digits[bin_expon_cx]; |
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if (coefficient_z >= power10_table_128[digits_z].w[0]) |
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digits_z++; |
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// underflow |
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if ((final_exponent + 16 < 0) |
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|| (exponent_z + digits_z > 33 + final_exponent)) { |
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356 |
res = |
|
|
357 |
BID_normalize (sign_z, exponent_z, coefficient_z, |
|
|
358 |
sign_x ^ sign_y, 1, rnd_mode, pfpsf); |
|
|
359 |
BID_RETURN (res); |
|
|
360 |
} |
|
|
361 |
|
|
|
362 |
ez = exponent_z + digits_z - 16; |
|
|
363 |
if (ez < 0) |
|
|
364 |
ez = 0; |
|
|
365 |
scale_z = exponent_z - ez; |
|
|
366 |
coefficient_z *= power10_table_128[scale_z].w[0]; |
|
|
367 |
ey = final_exponent - extra_digits; |
|
|
368 |
extra_digits = ez - ey; |
|
|
369 |
if (extra_digits > 33) { |
|
|
370 |
res = |
|
|
371 |
BID_normalize (sign_z, exponent_z, coefficient_z, |
|
|
372 |
sign_x ^ sign_y, 1, rnd_mode, pfpsf); |
|
|
373 |
BID_RETURN (res); |
|
|
374 |
} |
|
|
375 |
//else // extra_digits<=32 |
|
|
376 |
|
|
|
377 |
if (extra_digits > 17) { |
|
|
378 |
CYh = __truncate (P, 16); |
|
|
379 |
// get remainder |
|
|
380 |
T = power10_table_128[16].w[0]; |
|
|
381 |
__mul_64x64_to_64 (CY0L, CYh, T); |
|
|
382 |
remainder_y = P.w[0] - CY0L; |
|
|
383 |
|
|
|
384 |
extra_digits -= 16; |
|
|
385 |
P.w[0] = CYh; |
|
|
386 |
P.w[1] = 0; |
|
|
387 |
} else |
|
|
388 |
remainder_y = 0; |
|
|
389 |
|
|
|
390 |
// align coeff_x, CYh |
|
|
391 |
__mul_64x64_to_128 (CZ, coefficient_z, |
|
|
392 |
power10_table_128[extra_digits].w[0]); |
|
|
393 |
|
|
|
394 |
if (sign_z == (sign_y ^ sign_x)) { |
|
|
395 |
__add_128_128 (CT, CZ, P); |
|
|
396 |
if (__unsigned_compare_ge_128 |
|
|
397 |
(CT, power10_table_128[16 + extra_digits])) { |
|
|
398 |
extra_digits++; |
|
|
399 |
ez++; |
|
|
400 |
} |
|
|
401 |
} else { |
|
|
402 |
if (remainder_y && (__unsigned_compare_ge_128 (CZ, P))) { |
|
|
403 |
P.w[0]++; |
|
|
404 |
if (!P.w[0]) |
|
|
405 |
P.w[1]++; |
|
|
406 |
} |
|
|
407 |
__sub_128_128 (CT, CZ, P); |
|
|
408 |
if (((SINT64) CT.w[1]) < 0) { |
|
|
409 |
sign_z = sign_y ^ sign_x; |
|
|
410 |
CT.w[0] = 0 - CT.w[0]; |
|
|
411 |
CT.w[1] = 0 - CT.w[1]; |
|
|
412 |
if (CT.w[0]) |
|
|
413 |
CT.w[1]--; |
|
|
414 |
} else if(!(CT.w[1]|CT.w[0])) |
|
|
415 |
sign_z = (rnd_mode!=ROUNDING_DOWN)? 0: 0x8000000000000000ull; |
|
|
416 |
if (ez |
|
|
417 |
&& |
|
|
418 |
(__unsigned_compare_gt_128 |
|
|
419 |
(power10_table_128[15 + extra_digits], CT))) { |
|
|
420 |
extra_digits--; |
|
|
421 |
ez--; |
|
|
422 |
} |
|
|
423 |
} |
|
|
424 |
|
|
|
425 |
#ifdef SET_STATUS_FLAGS |
|
|
426 |
uf_status = 0; |
|
|
427 |
if ((!ez) |
|
|
428 |
&& |
|
|
429 |
__unsigned_compare_gt_128 (power10_table_128 |
|
|
430 |
[extra_digits + 15], CT)) { |
|
|
431 |
rmode = rnd_mode; |
|
|
432 |
if (sign_z && (unsigned) (rmode - 1) < 2) |
|
|
433 |
rmode = 3 - rmode; |
|
|
434 |
//__add_128_64(PU, CT, round_const_table[rmode][extra_digits]); |
|
|
435 |
PU = power10_table_128[extra_digits + 15]; |
|
|
436 |
PU.w[0]--; |
|
|
437 |
if (__unsigned_compare_gt_128 (PU, CT) |
|
|
438 |
|| (rmode == ROUNDING_DOWN) |
|
|
439 |
|| (rmode == ROUNDING_TO_ZERO)) |
|
|
440 |
uf_status = UNDERFLOW_EXCEPTION; |
|
|
441 |
else if (extra_digits < 2) { |
|
|
442 |
if ((rmode == ROUNDING_UP)) { |
|
|
443 |
if (!extra_digits) |
|
|
444 |
uf_status = UNDERFLOW_EXCEPTION; |
|
|
445 |
else { |
|
|
446 |
if (remainder_y && (sign_z != (sign_y ^ sign_x))) |
|
|
447 |
remainder_y = power10_table_128[16].w[0] - remainder_y; |
|
|
448 |
|
|
|
449 |
if (power10_table_128[15].w[0] > remainder_y) |
|
|
450 |
uf_status = UNDERFLOW_EXCEPTION; |
|
|
451 |
} |
|
|
452 |
} else // RN or RN_away |
|
|
453 |
{ |
|
|
454 |
if (remainder_y && (sign_z != (sign_y ^ sign_x))) |
|
|
455 |
remainder_y = power10_table_128[16].w[0] - remainder_y; |
|
|
456 |
|
|
|
457 |
if (!extra_digits) { |
|
|
458 |
remainder_y += round_const_table[rmode][15]; |
|
|
459 |
if (remainder_y < power10_table_128[16].w[0]) |
|
|
460 |
uf_status = UNDERFLOW_EXCEPTION; |
|
|
461 |
} else { |
|
|
462 |
if (remainder_y < round_const_table[rmode][16]) |
|
|
463 |
uf_status = UNDERFLOW_EXCEPTION; |
|
|
464 |
} |
|
|
465 |
} |
|
|
466 |
//__set_status_flags (pfpsf, uf_status); |
|
|
467 |
} |
|
|
468 |
} |
|
|
469 |
#endif |
|
|
470 |
res = |
|
|
471 |
__bid_full_round64_remainder (sign_z, ez - extra_digits, CT, |
|
|
472 |
extra_digits, remainder_y, |
|
|
473 |
rnd_mode, pfpsf, uf_status); |
|
|
474 |
BID_RETURN (res); |
|
|
475 |
|
|
|
476 |
} else { |
|
|
477 |
if ((sign_z == (sign_x ^ sign_y)) |
|
|
478 |
|| (final_exponent > 3 * 256 + 15)) { |
|
|
479 |
res = |
|
|
480 |
fast_get_BID64_check_OF (sign_x ^ sign_y, final_exponent, |
|
|
481 |
1000000000000000ull, rnd_mode, |
|
|
482 |
pfpsf); |
|
|
483 |
BID_RETURN (res); |
|
|
484 |
} |
|
|
485 |
} |
|
|
486 |
} |
|
|
487 |
|
|
|
488 |
|
|
|
489 |
if (extra_digits > 0) { |
|
|
490 |
res = |
|
|
491 |
get_add128 (sign_z, exponent_z, coefficient_z, sign_x ^ sign_y, |
|
|
492 |
final_exponent, P, extra_digits, rnd_mode, pfpsf); |
|
|
493 |
BID_RETURN (res); |
|
|
494 |
} |
|
|
495 |
// go to convert_format and exit |
|
|
496 |
else { |
|
|
497 |
C64 = __low_64 (P); |
|
|
498 |
|
|
|
499 |
res = |
|
|
500 |
get_add64 (sign_x ^ sign_y, |
|
|
501 |
exponent_x + exponent_y - DECIMAL_EXPONENT_BIAS, C64, |
|
|
502 |
sign_z, exponent_z, coefficient_z, |
|
|
503 |
rnd_mode, pfpsf); |
|
|
504 |
BID_RETURN (res); |
|
|
505 |
} |
|
|
506 |
} |