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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 divide |
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***************************************************************************** |
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* |
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* Algorithm description: |
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* |
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* if(coefficient_x |
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* p = number_digits(coefficient_y) - number_digits(coefficient_x) |
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* A = coefficient_x*10^p |
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* B = coefficient_y |
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* CA= A*10^(15+j), j=0 for A>=B, 1 otherwise |
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* Q = 0 |
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* else |
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* get Q=(int)(coefficient_x/coefficient_y) |
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* (based on double precision divide) |
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* check for exact divide case |
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* Let R = coefficient_x - Q*coefficient_y |
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* Let m=16-number_digits(Q) |
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* CA=R*10^m, Q=Q*10^m |
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* B = coefficient_y |
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* endif |
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* if (CA<2^64) |
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* Q += CA/B (64-bit unsigned divide) |
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* else |
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* get final Q using double precision divide, followed by 3 integer |
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* iterations |
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* if exact result, eliminate trailing zeros |
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* check for underflow |
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* round coefficient to nearest |
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* |
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****************************************************************************/ |
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#include "bid_internal.h" |
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#include "bid_div_macros.h" |
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#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
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#include |
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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 UINT32 convert_table[5][128][2]; |
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extern SINT8 factors[][2]; |
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extern UINT8 packed_10000_zeros[]; |
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#if DECIMAL_CALL_BY_REFERENCE |
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void |
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bid64_div (UINT64 * pres, UINT64 * px, |
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UINT64 * |
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py _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
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_EXC_INFO_PARAM) { |
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UINT64 x, y; |
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#else |
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UINT64 |
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bid64_div (UINT64 x, |
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UINT64 y _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, sign_y, coefficient_x, coefficient_y, A, B, QX, PD; |
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UINT64 A2, Q, Q2, B2, B4, B5, R, T, DU, res; |
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UINT64 valid_x, valid_y; |
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SINT64 D; |
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int_double t_scale, tempq, temp_b; |
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int_float tempx, tempy; |
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double da, db, dq, da_h, da_l; |
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int exponent_x, exponent_y, bin_expon_cx; |
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int diff_expon, ed1, ed2, bin_index; |
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int rmode, amount; |
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int nzeros, i, j, k, d5; |
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UINT32 QX32, tdigit[3], digit, digit_h, digit_low; |
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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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y = *py; |
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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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// unpack arguments, check for NaN or Infinity |
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if (!valid_x) { |
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// x is Inf. or NaN |
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#ifdef SET_STATUS_FLAGS |
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if ((y & SNAN_MASK64) == SNAN_MASK64) // y is sNaN |
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__set_status_flags (pfpsf, INVALID_EXCEPTION); |
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#endif |
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// test if x is NaN |
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if ((x & NAN_MASK64) == NAN_MASK64) { |
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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 (coefficient_x & QUIET_MASK64); |
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} |
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// x is Infinity? |
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if ((x & INFINITY_MASK64) == INFINITY_MASK64) { |
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// check if y is Inf or NaN |
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if ((y & INFINITY_MASK64) == INFINITY_MASK64) { |
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// y==Inf, return NaN |
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if ((y & NAN_MASK64) == INFINITY_MASK64) { // Inf/Inf |
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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 (NAN_MASK64); |
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} |
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} else { |
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// otherwise return +/-Inf |
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BID_RETURN (((x ^ y) & 0x8000000000000000ull) | |
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INFINITY_MASK64); |
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} |
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} |
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// x==0 |
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if (((y & INFINITY_MASK64) != INFINITY_MASK64) |
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&& !(coefficient_y)) { |
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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 (NAN_MASK64); |
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} |
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if (((y & INFINITY_MASK64) != INFINITY_MASK64)) { |
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if ((y & SPECIAL_ENCODING_MASK64) == SPECIAL_ENCODING_MASK64) |
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exponent_y = ((UINT32) (y >> 51)) & 0x3ff; |
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else |
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exponent_y = ((UINT32) (y >> 53)) & 0x3ff; |
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sign_y = y & 0x8000000000000000ull; |
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exponent_x = 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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BID_RETURN ((sign_x ^ sign_y) | (((UINT64) exponent_x) << 53)); |
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} |
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} |
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if (!valid_y) { |
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// y is Inf. or NaN |
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// test if y is NaN |
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if ((y & NAN_MASK64) == NAN_MASK64) { |
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#ifdef SET_STATUS_FLAGS |
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if ((y & 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 (coefficient_y & QUIET_MASK64); |
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} |
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// y is Infinity? |
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if ((y & INFINITY_MASK64) == INFINITY_MASK64) { |
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// return +/-0 |
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BID_RETURN (((x ^ y) & 0x8000000000000000ull)); |
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} |
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// y is 0 |
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#ifdef SET_STATUS_FLAGS |
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__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); |
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#endif |
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BID_RETURN ((sign_x ^ sign_y) | INFINITY_MASK64); |
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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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diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; |
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if (coefficient_x < coefficient_y) { |
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// get number of decimal digits for c_x, c_y |
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//--- get number of bits in the coefficients of x and y --- |
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tempx.d = (float) coefficient_x; |
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tempy.d = (float) coefficient_y; |
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bin_index = (tempy.i - tempx.i) >> 23; |
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A = coefficient_x * power10_index_binexp[bin_index]; |
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B = coefficient_y; |
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temp_b.d = (double) B; |
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// compare A, B |
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DU = (A - B) >> 63; |
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ed1 = 15 + (int) DU; |
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ed2 = estimate_decimal_digits[bin_index] + ed1; |
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T = power10_table_128[ed1].w[0]; |
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__mul_64x64_to_128 (CA, A, T); |
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Q = 0; |
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diff_expon = diff_expon - ed2; |
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// adjust double precision db, to ensure that later A/B - (int)(da/db) > -1 |
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if (coefficient_y < 0x0020000000000000ull) { |
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temp_b.i += 1; |
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db = temp_b.d; |
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} else |
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db = (double) (B + 2 + (B & 1)); |
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} else { |
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// get c_x/c_y |
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// set last bit before conversion to DP |
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A2 = coefficient_x | 1; |
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da = (double) A2; |
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db = (double) coefficient_y; |
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tempq.d = da / db; |
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Q = (UINT64) tempq.d; |
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R = coefficient_x - coefficient_y * Q; |
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// will use to get number of dec. digits of Q |
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bin_expon_cx = (tempq.i >> 52) - 0x3ff; |
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// R<0 ? |
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D = ((SINT64) R) >> 63; |
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Q += D; |
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R += (coefficient_y & D); |
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// exact result ? |
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if (((SINT64) R) <= 0) { |
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// can have R==-1 for coeff_y==1 |
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res = |
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get_BID64 (sign_x ^ sign_y, diff_expon, (Q + R), rnd_mode, |
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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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// get decimal digits of Q |
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DU = power10_index_binexp[bin_expon_cx] - Q - 1; |
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DU >>= 63; |
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ed2 = 16 - estimate_decimal_digits[bin_expon_cx] - (int) DU; |
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T = power10_table_128[ed2].w[0]; |
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__mul_64x64_to_128 (CA, R, T); |
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B = coefficient_y; |
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Q *= power10_table_128[ed2].w[0]; |
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diff_expon -= ed2; |
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} |
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if (!CA.w[1]) { |
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Q2 = CA.w[0] / B; |
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B2 = B + B; |
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B4 = B2 + B2; |
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R = CA.w[0] - Q2 * B; |
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Q += Q2; |
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} else { |
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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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// quotient |
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dq = da / db; |
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Q2 = (UINT64) dq; |
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// get w[0] remainder |
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R = CA.w[0] - Q2 * B; |
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// R<0 ? |
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D = ((SINT64) R) >> 63; |
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Q2 += D; |
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R += (B & D); |
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// now R<6*B |
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// quick divide |
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// 4*B |
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B2 = B + B; |
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B4 = B2 + B2; |
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R = R - B4; |
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// R<0 ? |
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D = ((SINT64) R) >> 63; |
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// restore R if negative |
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R += (B4 & D); |
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Q2 += ((~D) & 4); |
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R = R - B2; |
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// R<0 ? |
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D = ((SINT64) R) >> 63; |
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// restore R if negative |
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R += (B2 & D); |
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Q2 += ((~D) & 2); |
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R = R - B; |
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// R<0 ? |
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D = ((SINT64) R) >> 63; |
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// restore R if negative |
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R += (B & D); |
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Q2 += ((~D) & 1); |
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Q += Q2; |
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} |
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#ifdef SET_STATUS_FLAGS |
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if (R) { |
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// set status flags |
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__set_status_flags (pfpsf, INEXACT_EXCEPTION); |
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} |
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#ifndef LEAVE_TRAILING_ZEROS |
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else |
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#endif |
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#else |
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#ifndef LEAVE_TRAILING_ZEROS |
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if (!R) |
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#endif |
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#endif |
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#ifndef LEAVE_TRAILING_ZEROS |
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{ |
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// eliminate trailing zeros |
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// check whether CX, CY are short |
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if ((coefficient_x <= 1024) && (coefficient_y <= 1024)) { |
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i = (int) coefficient_y - 1; |
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j = (int) coefficient_x - 1; |
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// difference in powers of 2 factors for Y and X |
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nzeros = ed2 - factors[i][0] + factors[j][0]; |
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// difference in powers of 5 factors |
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d5 = ed2 - factors[i][1] + factors[j][1]; |
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if (d5 < nzeros) |
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nzeros = d5; |
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__mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]); |
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// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 |
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amount = short_recip_scale[nzeros]; |
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Q = CT.w[1] >> amount; |
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diff_expon += nzeros; |
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} else { |
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tdigit[0] = Q & 0x3ffffff; |
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tdigit[1] = 0; |
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QX = Q >> 26; |
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QX32 = QX; |
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nzeros = 0; |
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for (j = 0; QX32; j++, QX32 >>= 7) { |
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k = (QX32 & 127); |
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tdigit[0] += convert_table[j][k][0]; |
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tdigit[1] += convert_table[j][k][1]; |
|
|
380 |
if (tdigit[0] >= 100000000) { |
|
|
381 |
tdigit[0] -= 100000000; |
|
|
382 |
tdigit[1]++; |
|
|
383 |
} |
|
|
384 |
} |
|
|
385 |
|
|
|
386 |
digit = tdigit[0]; |
|
|
387 |
if (!digit && !tdigit[1]) |
|
|
388 |
nzeros += 16; |
|
|
389 |
else { |
|
|
390 |
if (!digit) { |
|
|
391 |
nzeros += 8; |
|
|
392 |
digit = tdigit[1]; |
|
|
393 |
} |
|
|
394 |
// decompose digit |
|
|
395 |
PD = (UINT64) digit *0x068DB8BBull; |
|
|
396 |
digit_h = (UINT32) (PD >> 40); |
|
|
397 |
digit_low = digit - digit_h * 10000; |
|
|
398 |
|
|
|
399 |
if (!digit_low) |
|
|
400 |
nzeros += 4; |
|
|
401 |
else |
|
|
402 |
digit_h = digit_low; |
|
|
403 |
|
|
|
404 |
if (!(digit_h & 1)) |
|
|
405 |
nzeros += |
|
|
406 |
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> |
|
|
407 |
(digit_h & 7)); |
|
|
408 |
} |
|
|
409 |
|
|
|
410 |
if (nzeros) { |
|
|
411 |
__mul_64x64_to_128 (CT, Q, reciprocals10_64[nzeros]); |
|
|
412 |
|
|
|
413 |
// now get P/10^extra_digits: shift C64 right by M[extra_digits]-128 |
|
|
414 |
amount = short_recip_scale[nzeros]; |
|
|
415 |
Q = CT.w[1] >> amount; |
|
|
416 |
} |
|
|
417 |
diff_expon += nzeros; |
|
|
418 |
|
|
|
419 |
} |
|
|
420 |
if (diff_expon >= 0) { |
|
|
421 |
res = |
|
|
422 |
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, |
|
|
423 |
rnd_mode, pfpsf); |
|
|
424 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
425 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
426 |
#endif |
|
|
427 |
BID_RETURN (res); |
|
|
428 |
} |
|
|
429 |
} |
|
|
430 |
#endif |
|
|
431 |
|
|
|
432 |
if (diff_expon >= 0) { |
|
|
433 |
#ifdef IEEE_ROUND_NEAREST |
|
|
434 |
// round to nearest code |
|
|
435 |
// R*10 |
|
|
436 |
R += R; |
|
|
437 |
R = (R << 2) + R; |
|
|
438 |
B5 = B4 + B; |
|
|
439 |
|
|
|
440 |
// compare 10*R to 5*B |
|
|
441 |
R = B5 - R; |
|
|
442 |
// correction for (R==0 && (Q&1)) |
|
|
443 |
R -= (Q & 1); |
|
|
444 |
// R<0 ? |
|
|
445 |
D = ((UINT64) R) >> 63; |
|
|
446 |
Q += D; |
|
|
447 |
#else |
|
|
448 |
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
449 |
// round to nearest code |
|
|
450 |
// R*10 |
|
|
451 |
R += R; |
|
|
452 |
R = (R << 2) + R; |
|
|
453 |
B5 = B4 + B; |
|
|
454 |
|
|
|
455 |
// compare 10*R to 5*B |
|
|
456 |
R = B5 - R; |
|
|
457 |
// correction for (R==0 && (Q&1)) |
|
|
458 |
R -= (Q & 1); |
|
|
459 |
// R<0 ? |
|
|
460 |
D = ((UINT64) R) >> 63; |
|
|
461 |
Q += D; |
|
|
462 |
#else |
|
|
463 |
rmode = rnd_mode; |
|
|
464 |
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) |
|
|
465 |
rmode = 3 - rmode; |
|
|
466 |
switch (rmode) { |
|
|
467 |
case 0: // round to nearest code |
|
|
468 |
case ROUNDING_TIES_AWAY: |
|
|
469 |
// R*10 |
|
|
470 |
R += R; |
|
|
471 |
R = (R << 2) + R; |
|
|
472 |
B5 = B4 + B; |
|
|
473 |
// compare 10*R to 5*B |
|
|
474 |
R = B5 - R; |
|
|
475 |
// correction for (R==0 && (Q&1)) |
|
|
476 |
R -= ((Q | (rmode >> 2)) & 1); |
|
|
477 |
// R<0 ? |
|
|
478 |
D = ((UINT64) R) >> 63; |
|
|
479 |
Q += D; |
|
|
480 |
break; |
|
|
481 |
case ROUNDING_DOWN: |
|
|
482 |
case ROUNDING_TO_ZERO: |
|
|
483 |
break; |
|
|
484 |
default: // rounding up |
|
|
485 |
Q++; |
|
|
486 |
break; |
|
|
487 |
} |
|
|
488 |
#endif |
|
|
489 |
#endif |
|
|
490 |
|
|
|
491 |
res = |
|
|
492 |
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, Q, rnd_mode, |
|
|
493 |
pfpsf); |
|
|
494 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
495 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
496 |
#endif |
|
|
497 |
BID_RETURN (res); |
|
|
498 |
} else { |
|
|
499 |
// UF occurs |
|
|
500 |
|
|
|
501 |
#ifdef SET_STATUS_FLAGS |
|
|
502 |
if ((diff_expon + 16 < 0)) { |
|
|
503 |
// set status flags |
|
|
504 |
__set_status_flags (pfpsf, INEXACT_EXCEPTION); |
|
|
505 |
} |
|
|
506 |
#endif |
|
|
507 |
rmode = rnd_mode; |
|
|
508 |
res = |
|
|
509 |
get_BID64_UF (sign_x ^ sign_y, diff_expon, Q, R, rmode, pfpsf); |
|
|
510 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
511 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
512 |
#endif |
|
|
513 |
BID_RETURN (res); |
|
|
514 |
|
|
|
515 |
} |
|
|
516 |
} |
|
|
517 |
|
|
|
518 |
|
|
|
519 |
|
|
|
520 |
TYPE0_FUNCTION_ARGTYPE1_ARG128 (UINT64, bid64dq_div, UINT64, x, y) |
|
|
521 |
UINT256 CA4 = |
|
|
522 |
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; |
|
|
523 |
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Tmp; |
|
|
524 |
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res; |
|
|
525 |
int_float fx, fy, f64; |
|
|
526 |
UINT32 QX32, tdigit[3], digit, digit_h, digit_low; |
|
|
527 |
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, |
|
|
528 |
digits_q, amount; |
|
|
529 |
int nzeros, i, j, k, d5, done = 0; |
|
|
530 |
unsigned rmode; |
|
|
531 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
532 |
fexcept_t binaryflags = 0; |
|
|
533 |
#endif |
|
|
534 |
|
|
|
535 |
valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); |
|
|
536 |
|
|
|
537 |
// unpack arguments, check for NaN or Infinity |
|
|
538 |
CX.w[1] = 0; |
|
|
539 |
if (!unpack_BID64 (&sign_x, &exponent_x, &CX.w[0], (x))) { |
|
|
540 |
#ifdef SET_STATUS_FLAGS |
|
|
541 |
if (((y.w[1] & SNAN_MASK64) == SNAN_MASK64) || // y is sNaN |
|
|
542 |
((x & SNAN_MASK64) == SNAN_MASK64)) |
|
|
543 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
544 |
#endif |
|
|
545 |
// test if x is NaN |
|
|
546 |
if (((x) & 0x7c00000000000000ull) == 0x7c00000000000000ull) { |
|
|
547 |
res = CX.w[0]; |
|
|
548 |
BID_RETURN (res & QUIET_MASK64); |
|
|
549 |
} |
|
|
550 |
// x is Infinity? |
|
|
551 |
if (((x) & 0x7800000000000000ull) == 0x7800000000000000ull) { |
|
|
552 |
// check if y is Inf. |
|
|
553 |
if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) |
|
|
554 |
// return NaN |
|
|
555 |
{ |
|
|
556 |
#ifdef SET_STATUS_FLAGS |
|
|
557 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
558 |
#endif |
|
|
559 |
res = 0x7c00000000000000ull; |
|
|
560 |
BID_RETURN (res); |
|
|
561 |
} |
|
|
562 |
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { |
|
|
563 |
// otherwise return +/-Inf |
|
|
564 |
res = |
|
|
565 |
(((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; |
|
|
566 |
BID_RETURN (res); |
|
|
567 |
} |
|
|
568 |
} |
|
|
569 |
// x is 0 |
|
|
570 |
if ((y.w[1] & INFINITY_MASK64) != INFINITY_MASK64) { |
|
|
571 |
if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { |
|
|
572 |
#ifdef SET_STATUS_FLAGS |
|
|
573 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
574 |
#endif |
|
|
575 |
// x=y=0, return NaN |
|
|
576 |
res = 0x7c00000000000000ull; |
|
|
577 |
BID_RETURN (res); |
|
|
578 |
} |
|
|
579 |
// return 0 |
|
|
580 |
res = ((x) ^ y.w[1]) & 0x8000000000000000ull; |
|
|
581 |
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS_128; |
|
|
582 |
if (exponent_x > DECIMAL_MAX_EXPON_64) |
|
|
583 |
exponent_x = DECIMAL_MAX_EXPON_64; |
|
|
584 |
else if (exponent_x < 0) |
|
|
585 |
exponent_x = 0; |
|
|
586 |
res |= (((UINT64) exponent_x) << 53); |
|
|
587 |
BID_RETURN (res); |
|
|
588 |
} |
|
|
589 |
} |
|
|
590 |
exponent_x += (DECIMAL_EXPONENT_BIAS_128 - DECIMAL_EXPONENT_BIAS); |
|
|
591 |
if (!valid_y) { |
|
|
592 |
// y is Inf. or NaN |
|
|
593 |
|
|
|
594 |
// test if y is NaN |
|
|
595 |
if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { |
|
|
596 |
#ifdef SET_STATUS_FLAGS |
|
|
597 |
if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN |
|
|
598 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
599 |
#endif |
|
|
600 |
Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull); |
|
|
601 |
Tmp.w[0] = CY.w[0]; |
|
|
602 |
TP128 = reciprocals10_128[18]; |
|
|
603 |
__mul_128x128_high (Qh, Tmp, TP128); |
|
|
604 |
amount = recip_scale[18]; |
|
|
605 |
__shr_128 (Tmp, Qh, amount); |
|
|
606 |
res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; |
|
|
607 |
BID_RETURN (res); |
|
|
608 |
} |
|
|
609 |
// y is Infinity? |
|
|
610 |
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { |
|
|
611 |
// return +/-0 |
|
|
612 |
res = sign_x ^ sign_y; |
|
|
613 |
BID_RETURN (res); |
|
|
614 |
} |
|
|
615 |
// y is 0, return +/-Inf |
|
|
616 |
res = |
|
|
617 |
(((x) ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; |
|
|
618 |
#ifdef SET_STATUS_FLAGS |
|
|
619 |
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); |
|
|
620 |
#endif |
|
|
621 |
BID_RETURN (res); |
|
|
622 |
} |
|
|
623 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
624 |
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
625 |
#endif |
|
|
626 |
diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; |
|
|
627 |
|
|
|
628 |
if (__unsigned_compare_gt_128 (CY, CX)) { |
|
|
629 |
// CX < CY |
|
|
630 |
|
|
|
631 |
// 2^64 |
|
|
632 |
f64.i = 0x5f800000; |
|
|
633 |
|
|
|
634 |
// fx ~ CX, fy ~ CY |
|
|
635 |
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; |
|
|
636 |
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; |
|
|
637 |
// expon_cy - expon_cx |
|
|
638 |
bin_index = (fy.i - fx.i) >> 23; |
|
|
639 |
|
|
|
640 |
if (CX.w[1]) { |
|
|
641 |
T = power10_index_binexp_128[bin_index].w[0]; |
|
|
642 |
__mul_64x128_short (CA, T, CX); |
|
|
643 |
} else { |
|
|
644 |
T128 = power10_index_binexp_128[bin_index]; |
|
|
645 |
__mul_64x128_short (CA, CX.w[0], T128); |
|
|
646 |
} |
|
|
647 |
|
|
|
648 |
ed2 = 15; |
|
|
649 |
if (__unsigned_compare_gt_128 (CY, CA)) |
|
|
650 |
ed2++; |
|
|
651 |
|
|
|
652 |
T128 = power10_table_128[ed2]; |
|
|
653 |
__mul_128x128_to_256 (CA4, CA, T128); |
|
|
654 |
|
|
|
655 |
ed2 += estimate_decimal_digits[bin_index]; |
|
|
656 |
CQ.w[0] = CQ.w[1] = 0; |
|
|
657 |
diff_expon = diff_expon - ed2; |
|
|
658 |
|
|
|
659 |
} else { |
|
|
660 |
// get CQ = CX/CY |
|
|
661 |
__div_128_by_128 (&CQ, &CR, CX, CY); |
|
|
662 |
|
|
|
663 |
// get number of decimal digits in CQ |
|
|
664 |
// 2^64 |
|
|
665 |
f64.i = 0x5f800000; |
|
|
666 |
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; |
|
|
667 |
// binary expon. of CQ |
|
|
668 |
bin_expon = (fx.i - 0x3f800000) >> 23; |
|
|
669 |
|
|
|
670 |
digits_q = estimate_decimal_digits[bin_expon]; |
|
|
671 |
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; |
|
|
672 |
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; |
|
|
673 |
if (__unsigned_compare_ge_128 (CQ, TP128)) |
|
|
674 |
digits_q++; |
|
|
675 |
|
|
|
676 |
if (digits_q <= 16) { |
|
|
677 |
if (!CR.w[1] && !CR.w[0]) { |
|
|
678 |
res = get_BID64 (sign_x ^ sign_y, diff_expon, |
|
|
679 |
CQ.w[0], rnd_mode, pfpsf); |
|
|
680 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
681 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
682 |
#endif |
|
|
683 |
BID_RETURN (res); |
|
|
684 |
} |
|
|
685 |
|
|
|
686 |
ed2 = 16 - digits_q; |
|
|
687 |
T128.w[0] = power10_table_128[ed2].w[0]; |
|
|
688 |
__mul_64x128_to_192 (CA4, (T128.w[0]), CR); |
|
|
689 |
diff_expon = diff_expon - ed2; |
|
|
690 |
CQ.w[0] *= T128.w[0]; |
|
|
691 |
} else { |
|
|
692 |
ed2 = digits_q - 16; |
|
|
693 |
diff_expon += ed2; |
|
|
694 |
T128 = reciprocals10_128[ed2]; |
|
|
695 |
__mul_128x128_to_256 (P256, CQ, T128); |
|
|
696 |
amount = recip_scale[ed2]; |
|
|
697 |
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); |
|
|
698 |
CQ.w[1] = 0; |
|
|
699 |
|
|
|
700 |
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); |
|
|
701 |
|
|
|
702 |
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); |
|
|
703 |
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; |
|
|
704 |
|
|
|
705 |
CA4.w[1] = CX.w[1] - QB256.w[1]; |
|
|
706 |
CA4.w[0] = CX.w[0] - QB256.w[0]; |
|
|
707 |
if (CX.w[0] < QB256.w[0]) |
|
|
708 |
CA4.w[1]--; |
|
|
709 |
if (CR.w[0] || CR.w[1]) |
|
|
710 |
CA4.w[0] |= 1; |
|
|
711 |
done = 1; |
|
|
712 |
|
|
|
713 |
} |
|
|
714 |
|
|
|
715 |
} |
|
|
716 |
if (!done) { |
|
|
717 |
__div_256_by_128 (&CQ, &CA4, CY); |
|
|
718 |
} |
|
|
719 |
|
|
|
720 |
|
|
|
721 |
|
|
|
722 |
#ifdef SET_STATUS_FLAGS |
|
|
723 |
if (CA4.w[0] || CA4.w[1]) { |
|
|
724 |
// set status flags |
|
|
725 |
__set_status_flags (pfpsf, INEXACT_EXCEPTION); |
|
|
726 |
} |
|
|
727 |
#ifndef LEAVE_TRAILING_ZEROS |
|
|
728 |
else |
|
|
729 |
#endif |
|
|
730 |
#else |
|
|
731 |
#ifndef LEAVE_TRAILING_ZEROS |
|
|
732 |
if (!CA4.w[0] && !CA4.w[1]) |
|
|
733 |
#endif |
|
|
734 |
#endif |
|
|
735 |
#ifndef LEAVE_TRAILING_ZEROS |
|
|
736 |
// check whether result is exact |
|
|
737 |
{ |
|
|
738 |
// check whether CX, CY are short |
|
|
739 |
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { |
|
|
740 |
i = (int) CY.w[0] - 1; |
|
|
741 |
j = (int) CX.w[0] - 1; |
|
|
742 |
// difference in powers of 2 factors for Y and X |
|
|
743 |
nzeros = ed2 - factors[i][0] + factors[j][0]; |
|
|
744 |
// difference in powers of 5 factors |
|
|
745 |
d5 = ed2 - factors[i][1] + factors[j][1]; |
|
|
746 |
if (d5 < nzeros) |
|
|
747 |
nzeros = d5; |
|
|
748 |
// get P*(2^M[extra_digits])/10^extra_digits |
|
|
749 |
__mul_128x128_high (Qh, CQ, reciprocals10_128[nzeros]); |
|
|
750 |
|
|
|
751 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
752 |
amount = recip_scale[nzeros]; |
|
|
753 |
__shr_128_long (CQ, Qh, amount); |
|
|
754 |
|
|
|
755 |
diff_expon += nzeros; |
|
|
756 |
} else { |
|
|
757 |
// decompose Q as Qh*10^17 + Ql |
|
|
758 |
Q_low = CQ.w[0]; |
|
|
759 |
|
|
|
760 |
{ |
|
|
761 |
tdigit[0] = Q_low & 0x3ffffff; |
|
|
762 |
tdigit[1] = 0; |
|
|
763 |
QX = Q_low >> 26; |
|
|
764 |
QX32 = QX; |
|
|
765 |
nzeros = 0; |
|
|
766 |
|
|
|
767 |
for (j = 0; QX32; j++, QX32 >>= 7) { |
|
|
768 |
k = (QX32 & 127); |
|
|
769 |
tdigit[0] += convert_table[j][k][0]; |
|
|
770 |
tdigit[1] += convert_table[j][k][1]; |
|
|
771 |
if (tdigit[0] >= 100000000) { |
|
|
772 |
tdigit[0] -= 100000000; |
|
|
773 |
tdigit[1]++; |
|
|
774 |
} |
|
|
775 |
} |
|
|
776 |
|
|
|
777 |
if (tdigit[1] >= 100000000) { |
|
|
778 |
tdigit[1] -= 100000000; |
|
|
779 |
if (tdigit[1] >= 100000000) |
|
|
780 |
tdigit[1] -= 100000000; |
|
|
781 |
} |
|
|
782 |
|
|
|
783 |
digit = tdigit[0]; |
|
|
784 |
if (!digit && !tdigit[1]) |
|
|
785 |
nzeros += 16; |
|
|
786 |
else { |
|
|
787 |
if (!digit) { |
|
|
788 |
nzeros += 8; |
|
|
789 |
digit = tdigit[1]; |
|
|
790 |
} |
|
|
791 |
// decompose digit |
|
|
792 |
PD = (UINT64) digit *0x068DB8BBull; |
|
|
793 |
digit_h = (UINT32) (PD >> 40); |
|
|
794 |
digit_low = digit - digit_h * 10000; |
|
|
795 |
|
|
|
796 |
if (!digit_low) |
|
|
797 |
nzeros += 4; |
|
|
798 |
else |
|
|
799 |
digit_h = digit_low; |
|
|
800 |
|
|
|
801 |
if (!(digit_h & 1)) |
|
|
802 |
nzeros += |
|
|
803 |
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> |
|
|
804 |
(digit_h & 7)); |
|
|
805 |
} |
|
|
806 |
|
|
|
807 |
if (nzeros) { |
|
|
808 |
// get P*(2^M[extra_digits])/10^extra_digits |
|
|
809 |
__mul_128x128_high (Qh, CQ, reciprocals10_128[nzeros]); |
|
|
810 |
|
|
|
811 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
812 |
amount = recip_scale[nzeros]; |
|
|
813 |
__shr_128 (CQ, Qh, amount); |
|
|
814 |
} |
|
|
815 |
diff_expon += nzeros; |
|
|
816 |
|
|
|
817 |
} |
|
|
818 |
} |
|
|
819 |
if(diff_expon>=0){ |
|
|
820 |
res = |
|
|
821 |
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], |
|
|
822 |
rnd_mode, pfpsf); |
|
|
823 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
824 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
825 |
#endif |
|
|
826 |
BID_RETURN (res); |
|
|
827 |
} |
|
|
828 |
} |
|
|
829 |
#endif |
|
|
830 |
|
|
|
831 |
if (diff_expon >= 0) { |
|
|
832 |
#ifdef IEEE_ROUND_NEAREST |
|
|
833 |
// rounding |
|
|
834 |
// 2*CA4 - CY |
|
|
835 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
836 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
837 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
838 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
839 |
|
|
|
840 |
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; |
|
|
841 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); |
|
|
842 |
|
|
|
843 |
CQ.w[0] += carry64; |
|
|
844 |
#else |
|
|
845 |
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
846 |
// rounding |
|
|
847 |
// 2*CA4 - CY |
|
|
848 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
849 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
850 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
851 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
852 |
|
|
|
853 |
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; |
|
|
854 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; |
|
|
855 |
|
|
|
856 |
CQ.w[0] += carry64; |
|
|
857 |
if (CQ.w[0] < carry64) |
|
|
858 |
CQ.w[1]++; |
|
|
859 |
#else |
|
|
860 |
rmode = rnd_mode; |
|
|
861 |
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) |
|
|
862 |
rmode = 3 - rmode; |
|
|
863 |
switch (rmode) { |
|
|
864 |
case ROUNDING_TO_NEAREST: // round to nearest code |
|
|
865 |
// rounding |
|
|
866 |
// 2*CA4 - CY |
|
|
867 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
868 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
869 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
870 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
871 |
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; |
|
|
872 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); |
|
|
873 |
CQ.w[0] += carry64; |
|
|
874 |
if (CQ.w[0] < carry64) |
|
|
875 |
CQ.w[1]++; |
|
|
876 |
break; |
|
|
877 |
case ROUNDING_TIES_AWAY: |
|
|
878 |
// rounding |
|
|
879 |
// 2*CA4 - CY |
|
|
880 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
881 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
882 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
883 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
884 |
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; |
|
|
885 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; |
|
|
886 |
CQ.w[0] += carry64; |
|
|
887 |
if (CQ.w[0] < carry64) |
|
|
888 |
CQ.w[1]++; |
|
|
889 |
break; |
|
|
890 |
case ROUNDING_DOWN: |
|
|
891 |
case ROUNDING_TO_ZERO: |
|
|
892 |
break; |
|
|
893 |
default: // rounding up |
|
|
894 |
CQ.w[0]++; |
|
|
895 |
if (!CQ.w[0]) |
|
|
896 |
CQ.w[1]++; |
|
|
897 |
break; |
|
|
898 |
} |
|
|
899 |
#endif |
|
|
900 |
#endif |
|
|
901 |
|
|
|
902 |
res = |
|
|
903 |
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, |
|
|
904 |
pfpsf); |
|
|
905 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
906 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
907 |
#endif |
|
|
908 |
BID_RETURN (res); |
|
|
909 |
} else { |
|
|
910 |
// UF occurs |
|
|
911 |
|
|
|
912 |
#ifdef SET_STATUS_FLAGS |
|
|
913 |
if ((diff_expon + 16 < 0)) { |
|
|
914 |
// set status flags |
|
|
915 |
__set_status_flags (pfpsf, INEXACT_EXCEPTION); |
|
|
916 |
} |
|
|
917 |
#endif |
|
|
918 |
rmode = rnd_mode; |
|
|
919 |
res = |
|
|
920 |
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); |
|
|
921 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
922 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
923 |
#endif |
|
|
924 |
BID_RETURN (res); |
|
|
925 |
|
|
|
926 |
} |
|
|
927 |
|
|
|
928 |
} |
|
|
929 |
|
|
|
930 |
|
|
|
931 |
//#define LEAVE_TRAILING_ZEROS |
|
|
932 |
|
|
|
933 |
TYPE0_FUNCTION_ARG128_ARGTYPE2 (UINT64, bid64qd_div, x, UINT64, y) |
|
|
934 |
|
|
|
935 |
UINT256 CA4 = |
|
|
936 |
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; |
|
|
937 |
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Tmp; |
|
|
938 |
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, PD, res, valid_y; |
|
|
939 |
int_float fx, fy, f64; |
|
|
940 |
UINT32 QX32, tdigit[3], digit, digit_h, digit_low; |
|
|
941 |
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, |
|
|
942 |
digits_q, amount; |
|
|
943 |
int nzeros, i, j, k, d5, done = 0; |
|
|
944 |
unsigned rmode; |
|
|
945 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
946 |
fexcept_t binaryflags = 0; |
|
|
947 |
#endif |
|
|
948 |
|
|
|
949 |
valid_y = unpack_BID64 (&sign_y, &exponent_y, &CY.w[0], (y)); |
|
|
950 |
|
|
|
951 |
// unpack arguments, check for NaN or Infinity |
|
|
952 |
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { |
|
|
953 |
// test if x is NaN |
|
|
954 |
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { |
|
|
955 |
#ifdef SET_STATUS_FLAGS |
|
|
956 |
if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN |
|
|
957 |
(y & 0x7e00000000000000ull) == 0x7e00000000000000ull) |
|
|
958 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
959 |
#endif |
|
|
960 |
Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); |
|
|
961 |
Tmp.w[0] = CX.w[0]; |
|
|
962 |
TP128 = reciprocals10_128[18]; |
|
|
963 |
__mul_128x128_high (Qh, Tmp, TP128); |
|
|
964 |
amount = recip_scale[18]; |
|
|
965 |
__shr_128 (Tmp, Qh, amount); |
|
|
966 |
res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; |
|
|
967 |
BID_RETURN (res); |
|
|
968 |
} |
|
|
969 |
// x is Infinity? |
|
|
970 |
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { |
|
|
971 |
// check if y is Inf. |
|
|
972 |
if (((y & 0x7c00000000000000ull) == 0x7800000000000000ull)) |
|
|
973 |
// return NaN |
|
|
974 |
{ |
|
|
975 |
#ifdef SET_STATUS_FLAGS |
|
|
976 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
977 |
#endif |
|
|
978 |
res = 0x7c00000000000000ull; |
|
|
979 |
BID_RETURN (res); |
|
|
980 |
} |
|
|
981 |
if (((y & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { |
|
|
982 |
// otherwise return +/-Inf |
|
|
983 |
res = |
|
|
984 |
((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; |
|
|
985 |
BID_RETURN (res); |
|
|
986 |
} |
|
|
987 |
} |
|
|
988 |
// x is 0 |
|
|
989 |
if (((y & INFINITY_MASK64) != INFINITY_MASK64) && |
|
|
990 |
!(CY.w[0])) { |
|
|
991 |
#ifdef SET_STATUS_FLAGS |
|
|
992 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
993 |
#endif |
|
|
994 |
// x=y=0, return NaN |
|
|
995 |
res = 0x7c00000000000000ull; |
|
|
996 |
BID_RETURN (res); |
|
|
997 |
} |
|
|
998 |
// return 0 |
|
|
999 |
if (((y & 0x7800000000000000ull) != 0x7800000000000000ull)) { |
|
|
1000 |
if (!CY.w[0]) { |
|
|
1001 |
#ifdef SET_STATUS_FLAGS |
|
|
1002 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
1003 |
#endif |
|
|
1004 |
res = 0x7c00000000000000ull; |
|
|
1005 |
BID_RETURN (res); |
|
|
1006 |
} |
|
|
1007 |
exponent_x = |
|
|
1008 |
exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 + |
|
|
1009 |
(DECIMAL_EXPONENT_BIAS << 1); |
|
|
1010 |
if (exponent_x > DECIMAL_MAX_EXPON_64) |
|
|
1011 |
exponent_x = DECIMAL_MAX_EXPON_64; |
|
|
1012 |
else if (exponent_x < 0) |
|
|
1013 |
exponent_x = 0; |
|
|
1014 |
res = (sign_x ^ sign_y) | (((UINT64) exponent_x) << 53); |
|
|
1015 |
BID_RETURN (res); |
|
|
1016 |
} |
|
|
1017 |
} |
|
|
1018 |
CY.w[1] = 0; |
|
|
1019 |
if (!valid_y) { |
|
|
1020 |
// y is Inf. or NaN |
|
|
1021 |
|
|
|
1022 |
// test if y is NaN |
|
|
1023 |
if ((y & NAN_MASK64) == NAN_MASK64) { |
|
|
1024 |
#ifdef SET_STATUS_FLAGS |
|
|
1025 |
if ((y & SNAN_MASK64) == SNAN_MASK64) // sNaN |
|
|
1026 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
1027 |
#endif |
|
|
1028 |
BID_RETURN (CY.w[0] & QUIET_MASK64); |
|
|
1029 |
} |
|
|
1030 |
// y is Infinity? |
|
|
1031 |
if (((y) & 0x7800000000000000ull) == 0x7800000000000000ull) { |
|
|
1032 |
// return +/-0 |
|
|
1033 |
res = sign_x ^ sign_y; |
|
|
1034 |
BID_RETURN (res); |
|
|
1035 |
} |
|
|
1036 |
// y is 0, return +/-Inf |
|
|
1037 |
res = |
|
|
1038 |
((x.w[1] ^ (y)) & 0x8000000000000000ull) | 0x7800000000000000ull; |
|
|
1039 |
#ifdef SET_STATUS_FLAGS |
|
|
1040 |
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); |
|
|
1041 |
#endif |
|
|
1042 |
BID_RETURN (res); |
|
|
1043 |
} |
|
|
1044 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1045 |
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1046 |
#endif |
|
|
1047 |
diff_expon = |
|
|
1048 |
exponent_x - exponent_y - DECIMAL_EXPONENT_BIAS_128 + |
|
|
1049 |
(DECIMAL_EXPONENT_BIAS << 1); |
|
|
1050 |
|
|
|
1051 |
if (__unsigned_compare_gt_128 (CY, CX)) { |
|
|
1052 |
// CX < CY |
|
|
1053 |
|
|
|
1054 |
// 2^64 |
|
|
1055 |
f64.i = 0x5f800000; |
|
|
1056 |
|
|
|
1057 |
// fx ~ CX, fy ~ CY |
|
|
1058 |
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; |
|
|
1059 |
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; |
|
|
1060 |
// expon_cy - expon_cx |
|
|
1061 |
bin_index = (fy.i - fx.i) >> 23; |
|
|
1062 |
|
|
|
1063 |
if (CX.w[1]) { |
|
|
1064 |
T = power10_index_binexp_128[bin_index].w[0]; |
|
|
1065 |
__mul_64x128_short (CA, T, CX); |
|
|
1066 |
} else { |
|
|
1067 |
T128 = power10_index_binexp_128[bin_index]; |
|
|
1068 |
__mul_64x128_short (CA, CX.w[0], T128); |
|
|
1069 |
} |
|
|
1070 |
|
|
|
1071 |
ed2 = 15; |
|
|
1072 |
if (__unsigned_compare_gt_128 (CY, CA)) |
|
|
1073 |
ed2++; |
|
|
1074 |
|
|
|
1075 |
T128 = power10_table_128[ed2]; |
|
|
1076 |
__mul_128x128_to_256 (CA4, CA, T128); |
|
|
1077 |
|
|
|
1078 |
ed2 += estimate_decimal_digits[bin_index]; |
|
|
1079 |
CQ.w[0] = CQ.w[1] = 0; |
|
|
1080 |
diff_expon = diff_expon - ed2; |
|
|
1081 |
|
|
|
1082 |
} else { |
|
|
1083 |
// get CQ = CX/CY |
|
|
1084 |
__div_128_by_128 (&CQ, &CR, CX, CY); |
|
|
1085 |
|
|
|
1086 |
// get number of decimal digits in CQ |
|
|
1087 |
// 2^64 |
|
|
1088 |
f64.i = 0x5f800000; |
|
|
1089 |
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; |
|
|
1090 |
// binary expon. of CQ |
|
|
1091 |
bin_expon = (fx.i - 0x3f800000) >> 23; |
|
|
1092 |
|
|
|
1093 |
digits_q = estimate_decimal_digits[bin_expon]; |
|
|
1094 |
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; |
|
|
1095 |
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; |
|
|
1096 |
if (__unsigned_compare_ge_128 (CQ, TP128)) |
|
|
1097 |
digits_q++; |
|
|
1098 |
|
|
|
1099 |
if (digits_q <= 16) { |
|
|
1100 |
if (!CR.w[1] && !CR.w[0]) { |
|
|
1101 |
res = get_BID64 (sign_x ^ sign_y, diff_expon, |
|
|
1102 |
CQ.w[0], rnd_mode, pfpsf); |
|
|
1103 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1104 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1105 |
#endif |
|
|
1106 |
BID_RETURN (res); |
|
|
1107 |
} |
|
|
1108 |
|
|
|
1109 |
ed2 = 16 - digits_q; |
|
|
1110 |
T128.w[0] = power10_table_128[ed2].w[0]; |
|
|
1111 |
__mul_64x128_to_192 (CA4, (T128.w[0]), CR); |
|
|
1112 |
diff_expon = diff_expon - ed2; |
|
|
1113 |
CQ.w[0] *= T128.w[0]; |
|
|
1114 |
} else { |
|
|
1115 |
ed2 = digits_q - 16; |
|
|
1116 |
diff_expon += ed2; |
|
|
1117 |
T128 = reciprocals10_128[ed2]; |
|
|
1118 |
__mul_128x128_to_256 (P256, CQ, T128); |
|
|
1119 |
amount = recip_scale[ed2]; |
|
|
1120 |
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); |
|
|
1121 |
CQ.w[1] = 0; |
|
|
1122 |
|
|
|
1123 |
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); |
|
|
1124 |
|
|
|
1125 |
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); |
|
|
1126 |
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; |
|
|
1127 |
|
|
|
1128 |
CA4.w[1] = CX.w[1] - QB256.w[1]; |
|
|
1129 |
CA4.w[0] = CX.w[0] - QB256.w[0]; |
|
|
1130 |
if (CX.w[0] < QB256.w[0]) |
|
|
1131 |
CA4.w[1]--; |
|
|
1132 |
if (CR.w[0] || CR.w[1]) |
|
|
1133 |
CA4.w[0] |= 1; |
|
|
1134 |
done = 1; |
|
|
1135 |
if(CA4.w[1]|CA4.w[0]) { |
|
|
1136 |
__mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY); |
|
|
1137 |
} |
|
|
1138 |
|
|
|
1139 |
} |
|
|
1140 |
|
|
|
1141 |
} |
|
|
1142 |
|
|
|
1143 |
if (!done) { |
|
|
1144 |
__div_256_by_128 (&CQ, &CA4, CY); |
|
|
1145 |
} |
|
|
1146 |
|
|
|
1147 |
#ifdef SET_STATUS_FLAGS |
|
|
1148 |
if (CA4.w[0] || CA4.w[1]) { |
|
|
1149 |
// set status flags |
|
|
1150 |
__set_status_flags (pfpsf, INEXACT_EXCEPTION); |
|
|
1151 |
} |
|
|
1152 |
#ifndef LEAVE_TRAILING_ZEROS |
|
|
1153 |
else |
|
|
1154 |
#endif |
|
|
1155 |
#else |
|
|
1156 |
#ifndef LEAVE_TRAILING_ZEROS |
|
|
1157 |
if (!CA4.w[0] && !CA4.w[1]) |
|
|
1158 |
#endif |
|
|
1159 |
#endif |
|
|
1160 |
#ifndef LEAVE_TRAILING_ZEROS |
|
|
1161 |
// check whether result is exact |
|
|
1162 |
{ |
|
|
1163 |
if(!done) { |
|
|
1164 |
// check whether CX, CY are short |
|
|
1165 |
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { |
|
|
1166 |
i = (int) CY.w[0] - 1; |
|
|
1167 |
j = (int) CX.w[0] - 1; |
|
|
1168 |
// difference in powers of 2 factors for Y and X |
|
|
1169 |
nzeros = ed2 - factors[i][0] + factors[j][0]; |
|
|
1170 |
// difference in powers of 5 factors |
|
|
1171 |
d5 = ed2 - factors[i][1] + factors[j][1]; |
|
|
1172 |
if (d5 < nzeros) |
|
|
1173 |
nzeros = d5; |
|
|
1174 |
// get P*(2^M[extra_digits])/10^extra_digits |
|
|
1175 |
__mul_128x128_high (Qh, CQ, reciprocals10_128[nzeros]); |
|
|
1176 |
//__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; |
|
|
1177 |
|
|
|
1178 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
1179 |
amount = recip_scale[nzeros]; |
|
|
1180 |
__shr_128_long (CQ, Qh, amount); |
|
|
1181 |
|
|
|
1182 |
diff_expon += nzeros; |
|
|
1183 |
} else { |
|
|
1184 |
// decompose Q as Qh*10^17 + Ql |
|
|
1185 |
//T128 = reciprocals10_128[17]; |
|
|
1186 |
Q_low = CQ.w[0]; |
|
|
1187 |
|
|
|
1188 |
{ |
|
|
1189 |
tdigit[0] = Q_low & 0x3ffffff; |
|
|
1190 |
tdigit[1] = 0; |
|
|
1191 |
QX = Q_low >> 26; |
|
|
1192 |
QX32 = QX; |
|
|
1193 |
nzeros = 0; |
|
|
1194 |
|
|
|
1195 |
for (j = 0; QX32; j++, QX32 >>= 7) { |
|
|
1196 |
k = (QX32 & 127); |
|
|
1197 |
tdigit[0] += convert_table[j][k][0]; |
|
|
1198 |
tdigit[1] += convert_table[j][k][1]; |
|
|
1199 |
if (tdigit[0] >= 100000000) { |
|
|
1200 |
tdigit[0] -= 100000000; |
|
|
1201 |
tdigit[1]++; |
|
|
1202 |
} |
|
|
1203 |
} |
|
|
1204 |
|
|
|
1205 |
if (tdigit[1] >= 100000000) { |
|
|
1206 |
tdigit[1] -= 100000000; |
|
|
1207 |
if (tdigit[1] >= 100000000) |
|
|
1208 |
tdigit[1] -= 100000000; |
|
|
1209 |
} |
|
|
1210 |
|
|
|
1211 |
digit = tdigit[0]; |
|
|
1212 |
if (!digit && !tdigit[1]) |
|
|
1213 |
nzeros += 16; |
|
|
1214 |
else { |
|
|
1215 |
if (!digit) { |
|
|
1216 |
nzeros += 8; |
|
|
1217 |
digit = tdigit[1]; |
|
|
1218 |
} |
|
|
1219 |
// decompose digit |
|
|
1220 |
PD = (UINT64) digit *0x068DB8BBull; |
|
|
1221 |
digit_h = (UINT32) (PD >> 40); |
|
|
1222 |
digit_low = digit - digit_h * 10000; |
|
|
1223 |
|
|
|
1224 |
if (!digit_low) |
|
|
1225 |
nzeros += 4; |
|
|
1226 |
else |
|
|
1227 |
digit_h = digit_low; |
|
|
1228 |
|
|
|
1229 |
if (!(digit_h & 1)) |
|
|
1230 |
nzeros += |
|
|
1231 |
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> |
|
|
1232 |
(digit_h & 7)); |
|
|
1233 |
} |
|
|
1234 |
|
|
|
1235 |
if (nzeros) { |
|
|
1236 |
// get P*(2^M[extra_digits])/10^extra_digits |
|
|
1237 |
__mul_128x128_high (Qh, CQ, reciprocals10_128[nzeros]); |
|
|
1238 |
|
|
|
1239 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
1240 |
amount = recip_scale[nzeros]; |
|
|
1241 |
__shr_128 (CQ, Qh, amount); |
|
|
1242 |
} |
|
|
1243 |
diff_expon += nzeros; |
|
|
1244 |
|
|
|
1245 |
} |
|
|
1246 |
} |
|
|
1247 |
} |
|
|
1248 |
if(diff_expon>=0){ |
|
|
1249 |
res = |
|
|
1250 |
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], |
|
|
1251 |
rnd_mode, pfpsf); |
|
|
1252 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1253 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1254 |
#endif |
|
|
1255 |
BID_RETURN (res); |
|
|
1256 |
} |
|
|
1257 |
} |
|
|
1258 |
#endif |
|
|
1259 |
|
|
|
1260 |
if (diff_expon >= 0) { |
|
|
1261 |
#ifdef IEEE_ROUND_NEAREST |
|
|
1262 |
// rounding |
|
|
1263 |
// 2*CA4 - CY |
|
|
1264 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
1265 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
1266 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
1267 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
1268 |
|
|
|
1269 |
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; |
|
|
1270 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); |
|
|
1271 |
|
|
|
1272 |
CQ.w[0] += carry64; |
|
|
1273 |
//if(CQ.w[0] |
|
|
1274 |
//CQ.w[1] ++; |
|
|
1275 |
#else |
|
|
1276 |
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1277 |
// rounding |
|
|
1278 |
// 2*CA4 - CY |
|
|
1279 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
1280 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
1281 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
1282 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
1283 |
|
|
|
1284 |
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; |
|
|
1285 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; |
|
|
1286 |
|
|
|
1287 |
CQ.w[0] += carry64; |
|
|
1288 |
if (CQ.w[0] < carry64) |
|
|
1289 |
CQ.w[1]++; |
|
|
1290 |
#else |
|
|
1291 |
rmode = rnd_mode; |
|
|
1292 |
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) |
|
|
1293 |
rmode = 3 - rmode; |
|
|
1294 |
switch (rmode) { |
|
|
1295 |
case ROUNDING_TO_NEAREST: // round to nearest code |
|
|
1296 |
// rounding |
|
|
1297 |
// 2*CA4 - CY |
|
|
1298 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
1299 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
1300 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
1301 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
1302 |
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; |
|
|
1303 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); |
|
|
1304 |
CQ.w[0] += carry64; |
|
|
1305 |
if (CQ.w[0] < carry64) |
|
|
1306 |
CQ.w[1]++; |
|
|
1307 |
break; |
|
|
1308 |
case ROUNDING_TIES_AWAY: |
|
|
1309 |
// rounding |
|
|
1310 |
// 2*CA4 - CY |
|
|
1311 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
1312 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
1313 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
1314 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
1315 |
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; |
|
|
1316 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; |
|
|
1317 |
CQ.w[0] += carry64; |
|
|
1318 |
if (CQ.w[0] < carry64) |
|
|
1319 |
CQ.w[1]++; |
|
|
1320 |
break; |
|
|
1321 |
case ROUNDING_DOWN: |
|
|
1322 |
case ROUNDING_TO_ZERO: |
|
|
1323 |
break; |
|
|
1324 |
default: // rounding up |
|
|
1325 |
CQ.w[0]++; |
|
|
1326 |
if (!CQ.w[0]) |
|
|
1327 |
CQ.w[1]++; |
|
|
1328 |
break; |
|
|
1329 |
} |
|
|
1330 |
#endif |
|
|
1331 |
#endif |
|
|
1332 |
|
|
|
1333 |
|
|
|
1334 |
res = |
|
|
1335 |
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, |
|
|
1336 |
pfpsf); |
|
|
1337 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1338 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1339 |
#endif |
|
|
1340 |
BID_RETURN (res); |
|
|
1341 |
} else { |
|
|
1342 |
// UF occurs |
|
|
1343 |
|
|
|
1344 |
#ifdef SET_STATUS_FLAGS |
|
|
1345 |
if ((diff_expon + 16 < 0)) { |
|
|
1346 |
// set status flags |
|
|
1347 |
__set_status_flags (pfpsf, INEXACT_EXCEPTION); |
|
|
1348 |
} |
|
|
1349 |
#endif |
|
|
1350 |
rmode = rnd_mode; |
|
|
1351 |
res = |
|
|
1352 |
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); |
|
|
1353 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1354 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1355 |
#endif |
|
|
1356 |
BID_RETURN (res); |
|
|
1357 |
|
|
|
1358 |
} |
|
|
1359 |
|
|
|
1360 |
} |
|
|
1361 |
|
|
|
1362 |
//#define LEAVE_TRAILING_ZEROS |
|
|
1363 |
|
|
|
1364 |
extern UINT32 convert_table[5][128][2]; |
|
|
1365 |
extern SINT8 factors[][2]; |
|
|
1366 |
extern UINT8 packed_10000_zeros[]; |
|
|
1367 |
|
|
|
1368 |
|
|
|
1369 |
//UINT64* bid64_div128x128(UINT64 res, UINT128 *px, UINT128 *py, unsigned rnd_mode, unsigned *pfpsf) |
|
|
1370 |
|
|
|
1371 |
TYPE0_FUNCTION_ARG128_ARG128 (UINT64, bid64qq_div, x, y) |
|
|
1372 |
UINT256 CA4 = |
|
|
1373 |
{ {0x0ull, 0x0ull, 0x0ull, 0x0ull} }, CA4r, P256, QB256; |
|
|
1374 |
UINT128 CX, CY, T128, CQ, CQ2, CR, CA, TP128, Qh, Tmp; |
|
|
1375 |
UINT64 sign_x, sign_y, T, carry64, D, Q_low, QX, valid_y, PD, res; |
|
|
1376 |
int_float fx, fy, f64; |
|
|
1377 |
UINT32 QX32, tdigit[3], digit, digit_h, digit_low; |
|
|
1378 |
int exponent_x, exponent_y, bin_index, bin_expon, diff_expon, ed2, |
|
|
1379 |
digits_q, amount; |
|
|
1380 |
int nzeros, i, j, k, d5, done = 0; |
|
|
1381 |
unsigned rmode; |
|
|
1382 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1383 |
fexcept_t binaryflags = 0; |
|
|
1384 |
#endif |
|
|
1385 |
|
|
|
1386 |
valid_y = unpack_BID128_value (&sign_y, &exponent_y, &CY, y); |
|
|
1387 |
|
|
|
1388 |
// unpack arguments, check for NaN or Infinity |
|
|
1389 |
if (!unpack_BID128_value (&sign_x, &exponent_x, &CX, x)) { |
|
|
1390 |
// test if x is NaN |
|
|
1391 |
if ((x.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { |
|
|
1392 |
#ifdef SET_STATUS_FLAGS |
|
|
1393 |
if ((x.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull || // sNaN |
|
|
1394 |
(y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) |
|
|
1395 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
1396 |
#endif |
|
|
1397 |
Tmp.w[1] = (CX.w[1] & 0x00003fffffffffffull); |
|
|
1398 |
Tmp.w[0] = CX.w[0]; |
|
|
1399 |
TP128 = reciprocals10_128[18]; |
|
|
1400 |
__mul_128x128_high (Qh, Tmp, TP128); |
|
|
1401 |
amount = recip_scale[18]; |
|
|
1402 |
__shr_128 (Tmp, Qh, amount); |
|
|
1403 |
res = (CX.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; |
|
|
1404 |
BID_RETURN (res); |
|
|
1405 |
} |
|
|
1406 |
// x is Infinity? |
|
|
1407 |
if ((x.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { |
|
|
1408 |
// check if y is Inf. |
|
|
1409 |
if (((y.w[1] & 0x7c00000000000000ull) == 0x7800000000000000ull)) |
|
|
1410 |
// return NaN |
|
|
1411 |
{ |
|
|
1412 |
#ifdef SET_STATUS_FLAGS |
|
|
1413 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
1414 |
#endif |
|
|
1415 |
res = 0x7c00000000000000ull; |
|
|
1416 |
BID_RETURN (res); |
|
|
1417 |
} |
|
|
1418 |
if (((y.w[1] & 0x7c00000000000000ull) != 0x7c00000000000000ull)) { |
|
|
1419 |
// otherwise return +/-Inf |
|
|
1420 |
res = |
|
|
1421 |
((x.w[1] ^ y. |
|
|
1422 |
w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; |
|
|
1423 |
BID_RETURN (res); |
|
|
1424 |
} |
|
|
1425 |
} |
|
|
1426 |
// x is 0 |
|
|
1427 |
if (((y.w[1] & 0x7800000000000000ull) != 0x7800000000000000ull)) { |
|
|
1428 |
if ((!CY.w[0]) && !(CY.w[1] & 0x0001ffffffffffffull)) { |
|
|
1429 |
#ifdef SET_STATUS_FLAGS |
|
|
1430 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
1431 |
#endif |
|
|
1432 |
// x=y=0, return NaN |
|
|
1433 |
res = 0x7c00000000000000ull; |
|
|
1434 |
BID_RETURN (res); |
|
|
1435 |
} |
|
|
1436 |
// return 0 |
|
|
1437 |
res = (x.w[1] ^ y.w[1]) & 0x8000000000000000ull; |
|
|
1438 |
exponent_x = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; |
|
|
1439 |
if (exponent_x > DECIMAL_MAX_EXPON_64) |
|
|
1440 |
exponent_x = DECIMAL_MAX_EXPON_64; |
|
|
1441 |
else if (exponent_x < 0) |
|
|
1442 |
exponent_x = 0; |
|
|
1443 |
res |= (((UINT64) exponent_x) << 53); |
|
|
1444 |
BID_RETURN (res); |
|
|
1445 |
} |
|
|
1446 |
} |
|
|
1447 |
if (!valid_y) { |
|
|
1448 |
// y is Inf. or NaN |
|
|
1449 |
|
|
|
1450 |
// test if y is NaN |
|
|
1451 |
if ((y.w[1] & 0x7c00000000000000ull) == 0x7c00000000000000ull) { |
|
|
1452 |
#ifdef SET_STATUS_FLAGS |
|
|
1453 |
if ((y.w[1] & 0x7e00000000000000ull) == 0x7e00000000000000ull) // sNaN |
|
|
1454 |
__set_status_flags (pfpsf, INVALID_EXCEPTION); |
|
|
1455 |
#endif |
|
|
1456 |
Tmp.w[1] = (CY.w[1] & 0x00003fffffffffffull); |
|
|
1457 |
Tmp.w[0] = CY.w[0]; |
|
|
1458 |
TP128 = reciprocals10_128[18]; |
|
|
1459 |
__mul_128x128_high (Qh, Tmp, TP128); |
|
|
1460 |
amount = recip_scale[18]; |
|
|
1461 |
__shr_128 (Tmp, Qh, amount); |
|
|
1462 |
res = (CY.w[1] & 0xfc00000000000000ull) | Tmp.w[0]; |
|
|
1463 |
BID_RETURN (res); |
|
|
1464 |
} |
|
|
1465 |
// y is Infinity? |
|
|
1466 |
if ((y.w[1] & 0x7800000000000000ull) == 0x7800000000000000ull) { |
|
|
1467 |
// return +/-0 |
|
|
1468 |
res = sign_x ^ sign_y; |
|
|
1469 |
BID_RETURN (res); |
|
|
1470 |
} |
|
|
1471 |
// y is 0, return +/-Inf |
|
|
1472 |
res = |
|
|
1473 |
((x.w[1] ^ y.w[1]) & 0x8000000000000000ull) | 0x7800000000000000ull; |
|
|
1474 |
#ifdef SET_STATUS_FLAGS |
|
|
1475 |
__set_status_flags (pfpsf, ZERO_DIVIDE_EXCEPTION); |
|
|
1476 |
#endif |
|
|
1477 |
BID_RETURN (res); |
|
|
1478 |
} |
|
|
1479 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1480 |
(void) fegetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1481 |
#endif |
|
|
1482 |
diff_expon = exponent_x - exponent_y + DECIMAL_EXPONENT_BIAS; |
|
|
1483 |
|
|
|
1484 |
if (__unsigned_compare_gt_128 (CY, CX)) { |
|
|
1485 |
// CX < CY |
|
|
1486 |
|
|
|
1487 |
// 2^64 |
|
|
1488 |
f64.i = 0x5f800000; |
|
|
1489 |
|
|
|
1490 |
// fx ~ CX, fy ~ CY |
|
|
1491 |
fx.d = (float) CX.w[1] * f64.d + (float) CX.w[0]; |
|
|
1492 |
fy.d = (float) CY.w[1] * f64.d + (float) CY.w[0]; |
|
|
1493 |
// expon_cy - expon_cx |
|
|
1494 |
bin_index = (fy.i - fx.i) >> 23; |
|
|
1495 |
|
|
|
1496 |
if (CX.w[1]) { |
|
|
1497 |
T = power10_index_binexp_128[bin_index].w[0]; |
|
|
1498 |
__mul_64x128_short (CA, T, CX); |
|
|
1499 |
} else { |
|
|
1500 |
T128 = power10_index_binexp_128[bin_index]; |
|
|
1501 |
__mul_64x128_short (CA, CX.w[0], T128); |
|
|
1502 |
} |
|
|
1503 |
|
|
|
1504 |
ed2 = 15; |
|
|
1505 |
if (__unsigned_compare_gt_128 (CY, CA)) |
|
|
1506 |
ed2++; |
|
|
1507 |
|
|
|
1508 |
T128 = power10_table_128[ed2]; |
|
|
1509 |
__mul_128x128_to_256 (CA4, CA, T128); |
|
|
1510 |
|
|
|
1511 |
ed2 += estimate_decimal_digits[bin_index]; |
|
|
1512 |
CQ.w[0] = CQ.w[1] = 0; |
|
|
1513 |
diff_expon = diff_expon - ed2; |
|
|
1514 |
|
|
|
1515 |
} else { |
|
|
1516 |
// get CQ = CX/CY |
|
|
1517 |
__div_128_by_128 (&CQ, &CR, CX, CY); |
|
|
1518 |
|
|
|
1519 |
// get number of decimal digits in CQ |
|
|
1520 |
// 2^64 |
|
|
1521 |
f64.i = 0x5f800000; |
|
|
1522 |
fx.d = (float) CQ.w[1] * f64.d + (float) CQ.w[0]; |
|
|
1523 |
// binary expon. of CQ |
|
|
1524 |
bin_expon = (fx.i - 0x3f800000) >> 23; |
|
|
1525 |
|
|
|
1526 |
digits_q = estimate_decimal_digits[bin_expon]; |
|
|
1527 |
TP128.w[0] = power10_index_binexp_128[bin_expon].w[0]; |
|
|
1528 |
TP128.w[1] = power10_index_binexp_128[bin_expon].w[1]; |
|
|
1529 |
if (__unsigned_compare_ge_128 (CQ, TP128)) |
|
|
1530 |
digits_q++; |
|
|
1531 |
|
|
|
1532 |
if (digits_q <= 16) { |
|
|
1533 |
if (!CR.w[1] && !CR.w[0]) { |
|
|
1534 |
res = get_BID64 (sign_x ^ sign_y, diff_expon, |
|
|
1535 |
CQ.w[0], rnd_mode, pfpsf); |
|
|
1536 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1537 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1538 |
#endif |
|
|
1539 |
BID_RETURN (res); |
|
|
1540 |
} |
|
|
1541 |
|
|
|
1542 |
ed2 = 16 - digits_q; |
|
|
1543 |
T128.w[0] = power10_table_128[ed2].w[0]; |
|
|
1544 |
__mul_64x128_to_192 (CA4, (T128.w[0]), CR); |
|
|
1545 |
diff_expon = diff_expon - ed2; |
|
|
1546 |
CQ.w[0] *= T128.w[0]; |
|
|
1547 |
} else { |
|
|
1548 |
ed2 = digits_q - 16; |
|
|
1549 |
diff_expon += ed2; |
|
|
1550 |
T128 = reciprocals10_128[ed2]; |
|
|
1551 |
__mul_128x128_to_256 (P256, CQ, T128); |
|
|
1552 |
amount = recip_scale[ed2]; |
|
|
1553 |
CQ.w[0] = (P256.w[2] >> amount) | (P256.w[3] << (64 - amount)); |
|
|
1554 |
CQ.w[1] = 0; |
|
|
1555 |
|
|
|
1556 |
__mul_64x64_to_128 (CQ2, CQ.w[0], (power10_table_128[ed2].w[0])); |
|
|
1557 |
|
|
|
1558 |
__mul_64x64_to_128 (QB256, CQ2.w[0], CY.w[0]); |
|
|
1559 |
QB256.w[1] += CQ2.w[0] * CY.w[1] + CQ2.w[1] * CY.w[0]; |
|
|
1560 |
|
|
|
1561 |
CA4.w[1] = CX.w[1] - QB256.w[1]; |
|
|
1562 |
CA4.w[0] = CX.w[0] - QB256.w[0]; |
|
|
1563 |
if (CX.w[0] < QB256.w[0]) |
|
|
1564 |
CA4.w[1]--; |
|
|
1565 |
if (CR.w[0] || CR.w[1]) |
|
|
1566 |
CA4.w[0] |= 1; |
|
|
1567 |
done = 1; |
|
|
1568 |
if(CA4.w[1]|CA4.w[0]) { |
|
|
1569 |
__mul_64x128_low(CY, (power10_table_128[ed2].w[0]),CY); |
|
|
1570 |
} |
|
|
1571 |
} |
|
|
1572 |
|
|
|
1573 |
} |
|
|
1574 |
|
|
|
1575 |
if (!done) { |
|
|
1576 |
__div_256_by_128 (&CQ, &CA4, CY); |
|
|
1577 |
} |
|
|
1578 |
|
|
|
1579 |
|
|
|
1580 |
|
|
|
1581 |
#ifdef SET_STATUS_FLAGS |
|
|
1582 |
if (CA4.w[0] || CA4.w[1]) { |
|
|
1583 |
// set status flags |
|
|
1584 |
__set_status_flags (pfpsf, INEXACT_EXCEPTION); |
|
|
1585 |
} |
|
|
1586 |
#ifndef LEAVE_TRAILING_ZEROS |
|
|
1587 |
else |
|
|
1588 |
#endif |
|
|
1589 |
#else |
|
|
1590 |
#ifndef LEAVE_TRAILING_ZEROS |
|
|
1591 |
if (!CA4.w[0] && !CA4.w[1]) |
|
|
1592 |
#endif |
|
|
1593 |
#endif |
|
|
1594 |
#ifndef LEAVE_TRAILING_ZEROS |
|
|
1595 |
// check whether result is exact |
|
|
1596 |
{ |
|
|
1597 |
if(!done) { |
|
|
1598 |
// check whether CX, CY are short |
|
|
1599 |
if (!CX.w[1] && !CY.w[1] && (CX.w[0] <= 1024) && (CY.w[0] <= 1024)) { |
|
|
1600 |
i = (int) CY.w[0] - 1; |
|
|
1601 |
j = (int) CX.w[0] - 1; |
|
|
1602 |
// difference in powers of 2 factors for Y and X |
|
|
1603 |
nzeros = ed2 - factors[i][0] + factors[j][0]; |
|
|
1604 |
// difference in powers of 5 factors |
|
|
1605 |
d5 = ed2 - factors[i][1] + factors[j][1]; |
|
|
1606 |
if (d5 < nzeros) |
|
|
1607 |
nzeros = d5; |
|
|
1608 |
// get P*(2^M[extra_digits])/10^extra_digits |
|
|
1609 |
__mul_128x128_high (Qh, CQ, reciprocals10_128[nzeros]); |
|
|
1610 |
//__mul_128x128_to_256(P256, CQ, reciprocals10_128[nzeros]);Qh.w[1]=P256.w[3];Qh.w[0]=P256.w[2]; |
|
|
1611 |
|
|
|
1612 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
1613 |
amount = recip_scale[nzeros]; |
|
|
1614 |
__shr_128_long (CQ, Qh, amount); |
|
|
1615 |
|
|
|
1616 |
diff_expon += nzeros; |
|
|
1617 |
} else { |
|
|
1618 |
// decompose Q as Qh*10^17 + Ql |
|
|
1619 |
//T128 = reciprocals10_128[17]; |
|
|
1620 |
Q_low = CQ.w[0]; |
|
|
1621 |
|
|
|
1622 |
{ |
|
|
1623 |
tdigit[0] = Q_low & 0x3ffffff; |
|
|
1624 |
tdigit[1] = 0; |
|
|
1625 |
QX = Q_low >> 26; |
|
|
1626 |
QX32 = QX; |
|
|
1627 |
nzeros = 0; |
|
|
1628 |
|
|
|
1629 |
for (j = 0; QX32; j++, QX32 >>= 7) { |
|
|
1630 |
k = (QX32 & 127); |
|
|
1631 |
tdigit[0] += convert_table[j][k][0]; |
|
|
1632 |
tdigit[1] += convert_table[j][k][1]; |
|
|
1633 |
if (tdigit[0] >= 100000000) { |
|
|
1634 |
tdigit[0] -= 100000000; |
|
|
1635 |
tdigit[1]++; |
|
|
1636 |
} |
|
|
1637 |
} |
|
|
1638 |
|
|
|
1639 |
if (tdigit[1] >= 100000000) { |
|
|
1640 |
tdigit[1] -= 100000000; |
|
|
1641 |
if (tdigit[1] >= 100000000) |
|
|
1642 |
tdigit[1] -= 100000000; |
|
|
1643 |
} |
|
|
1644 |
|
|
|
1645 |
digit = tdigit[0]; |
|
|
1646 |
if (!digit && !tdigit[1]) |
|
|
1647 |
nzeros += 16; |
|
|
1648 |
else { |
|
|
1649 |
if (!digit) { |
|
|
1650 |
nzeros += 8; |
|
|
1651 |
digit = tdigit[1]; |
|
|
1652 |
} |
|
|
1653 |
// decompose digit |
|
|
1654 |
PD = (UINT64) digit *0x068DB8BBull; |
|
|
1655 |
digit_h = (UINT32) (PD >> 40); |
|
|
1656 |
digit_low = digit - digit_h * 10000; |
|
|
1657 |
|
|
|
1658 |
if (!digit_low) |
|
|
1659 |
nzeros += 4; |
|
|
1660 |
else |
|
|
1661 |
digit_h = digit_low; |
|
|
1662 |
|
|
|
1663 |
if (!(digit_h & 1)) |
|
|
1664 |
nzeros += |
|
|
1665 |
3 & (UINT32) (packed_10000_zeros[digit_h >> 3] >> |
|
|
1666 |
(digit_h & 7)); |
|
|
1667 |
} |
|
|
1668 |
|
|
|
1669 |
if (nzeros) { |
|
|
1670 |
// get P*(2^M[extra_digits])/10^extra_digits |
|
|
1671 |
__mul_128x128_high (Qh, CQ, reciprocals10_128[nzeros]); |
|
|
1672 |
|
|
|
1673 |
// now get P/10^extra_digits: shift Q_high right by M[extra_digits]-128 |
|
|
1674 |
amount = recip_scale[nzeros]; |
|
|
1675 |
__shr_128 (CQ, Qh, amount); |
|
|
1676 |
} |
|
|
1677 |
diff_expon += nzeros; |
|
|
1678 |
|
|
|
1679 |
} |
|
|
1680 |
} |
|
|
1681 |
} |
|
|
1682 |
if(diff_expon>=0){ |
|
|
1683 |
res = |
|
|
1684 |
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], |
|
|
1685 |
rnd_mode, pfpsf); |
|
|
1686 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1687 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1688 |
#endif |
|
|
1689 |
BID_RETURN (res); |
|
|
1690 |
} |
|
|
1691 |
} |
|
|
1692 |
#endif |
|
|
1693 |
|
|
|
1694 |
if(diff_expon>=0) { |
|
|
1695 |
|
|
|
1696 |
#ifdef IEEE_ROUND_NEAREST |
|
|
1697 |
// rounding |
|
|
1698 |
// 2*CA4 - CY |
|
|
1699 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
1700 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
1701 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
1702 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
1703 |
|
|
|
1704 |
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; |
|
|
1705 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); |
|
|
1706 |
|
|
|
1707 |
CQ.w[0] += carry64; |
|
|
1708 |
//if(CQ.w[0] |
|
|
1709 |
//CQ.w[1] ++; |
|
|
1710 |
#else |
|
|
1711 |
#ifdef IEEE_ROUND_NEAREST_TIES_AWAY |
|
|
1712 |
// rounding |
|
|
1713 |
// 2*CA4 - CY |
|
|
1714 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
1715 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
1716 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
1717 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
1718 |
|
|
|
1719 |
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; |
|
|
1720 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; |
|
|
1721 |
|
|
|
1722 |
CQ.w[0] += carry64; |
|
|
1723 |
if (CQ.w[0] < carry64) |
|
|
1724 |
CQ.w[1]++; |
|
|
1725 |
#else |
|
|
1726 |
rmode = rnd_mode; |
|
|
1727 |
if (sign_x ^ sign_y && (unsigned) (rmode - 1) < 2) |
|
|
1728 |
rmode = 3 - rmode; |
|
|
1729 |
switch (rmode) { |
|
|
1730 |
case ROUNDING_TO_NEAREST: // round to nearest code |
|
|
1731 |
// rounding |
|
|
1732 |
// 2*CA4 - CY |
|
|
1733 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
1734 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
1735 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
1736 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
1737 |
D = (CA4r.w[1] | CA4r.w[0]) ? 1 : 0; |
|
|
1738 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) & ((CQ.w[0]) | D); |
|
|
1739 |
CQ.w[0] += carry64; |
|
|
1740 |
if (CQ.w[0] < carry64) |
|
|
1741 |
CQ.w[1]++; |
|
|
1742 |
break; |
|
|
1743 |
case ROUNDING_TIES_AWAY: |
|
|
1744 |
// rounding |
|
|
1745 |
// 2*CA4 - CY |
|
|
1746 |
CA4r.w[1] = (CA4.w[1] + CA4.w[1]) | (CA4.w[0] >> 63); |
|
|
1747 |
CA4r.w[0] = CA4.w[0] + CA4.w[0]; |
|
|
1748 |
__sub_borrow_out (CA4r.w[0], carry64, CA4r.w[0], CY.w[0]); |
|
|
1749 |
CA4r.w[1] = CA4r.w[1] - CY.w[1] - carry64; |
|
|
1750 |
D = (CA4r.w[1] | CA4r.w[0]) ? 0 : 1; |
|
|
1751 |
carry64 = (1 + (((SINT64) CA4r.w[1]) >> 63)) | D; |
|
|
1752 |
CQ.w[0] += carry64; |
|
|
1753 |
if (CQ.w[0] < carry64) |
|
|
1754 |
CQ.w[1]++; |
|
|
1755 |
break; |
|
|
1756 |
case ROUNDING_DOWN: |
|
|
1757 |
case ROUNDING_TO_ZERO: |
|
|
1758 |
break; |
|
|
1759 |
default: // rounding up |
|
|
1760 |
CQ.w[0]++; |
|
|
1761 |
if (!CQ.w[0]) |
|
|
1762 |
CQ.w[1]++; |
|
|
1763 |
break; |
|
|
1764 |
} |
|
|
1765 |
#endif |
|
|
1766 |
#endif |
|
|
1767 |
|
|
|
1768 |
|
|
|
1769 |
res = |
|
|
1770 |
fast_get_BID64_check_OF (sign_x ^ sign_y, diff_expon, CQ.w[0], rnd_mode, |
|
|
1771 |
pfpsf); |
|
|
1772 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1773 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1774 |
#endif |
|
|
1775 |
BID_RETURN (res); |
|
|
1776 |
} else { |
|
|
1777 |
// UF occurs |
|
|
1778 |
|
|
|
1779 |
#ifdef SET_STATUS_FLAGS |
|
|
1780 |
if ((diff_expon + 16 < 0)) { |
|
|
1781 |
// set status flags |
|
|
1782 |
__set_status_flags (pfpsf, INEXACT_EXCEPTION); |
|
|
1783 |
} |
|
|
1784 |
#endif |
|
|
1785 |
rmode = rnd_mode; |
|
|
1786 |
res = |
|
|
1787 |
get_BID64_UF (sign_x ^ sign_y, diff_expon, CQ.w[0], CA4.w[1] | CA4.w[0], rmode, pfpsf); |
|
|
1788 |
#ifdef UNCHANGED_BINARY_STATUS_FLAGS |
|
|
1789 |
(void) fesetexceptflag (&binaryflags, FE_ALL_FLAGS); |
|
|
1790 |
#endif |
|
|
1791 |
BID_RETURN (res); |
|
|
1792 |
|
|
|
1793 |
} |
|
|
1794 |
|
|
|
1795 |
} |