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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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#include "bid_internal.h" |
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/***************************************************************************** |
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* BID64_round_integral_exact |
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****************************************************************************/ |
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#if DECIMAL_CALL_BY_REFERENCE |
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void |
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bid64_round_integral_exact (UINT64 * pres, |
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UINT64 * |
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px _RND_MODE_PARAM _EXC_FLAGS_PARAM |
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_EXC_MASKS_PARAM _EXC_INFO_PARAM) { |
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UINT64 x = *px; |
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#if !DECIMAL_GLOBAL_ROUNDING |
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unsigned int rnd_mode = *prnd_mode; |
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#endif |
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#else |
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UINT64 |
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bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM |
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_EXC_MASKS_PARAM _EXC_INFO_PARAM) { |
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#endif |
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UINT64 res = 0xbaddbaddbaddbaddull; |
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UINT64 x_sign; |
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int exp; // unbiased exponent |
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// Note: C1 represents the significand (UINT64) |
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BID_UI64DOUBLE tmp1; |
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int x_nr_bits; |
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int q, ind, shift; |
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UINT64 C1; |
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// UINT64 res is C* at first - represents up to 16 decimal digits <= 54 bits |
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UINT128 fstar = { {0x0ull, 0x0ull} }; |
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UINT128 P128; |
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x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
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// check for NaNs and infinities |
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if ((x & MASK_NAN) == MASK_NAN) { // check for NaN |
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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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else |
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x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
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if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return quiet (SNaN) |
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res = x & 0xfdffffffffffffffull; |
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} else { // QNaN |
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res = x; |
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} |
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BID_RETURN (res); |
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} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
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res = x_sign | 0x7800000000000000ull; |
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BID_RETURN (res); |
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} |
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// unpack x |
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
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// if the steering bits are 11 (condition will be 0), then |
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// the exponent is G[0:w+1] |
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exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; |
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C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
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if (C1 > 9999999999999999ull) { // non-canonical |
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C1 = 0; |
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} |
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} else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) |
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exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; |
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C1 = (x & MASK_BINARY_SIG1); |
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} |
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// if x is 0 or non-canonical return 0 preserving the sign bit and |
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// the preferred exponent of MAX(Q(x), 0) |
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if (C1 == 0) { |
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if (exp < 0) |
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exp = 0; |
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res = x_sign | (((UINT64) exp + 398) << 53); |
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BID_RETURN (res); |
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} |
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// x is a finite non-zero number (not 0, non-canonical, or special) |
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switch (rnd_mode) { |
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case ROUNDING_TO_NEAREST: |
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case ROUNDING_TIES_AWAY: |
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// return 0 if (exp <= -(p+1)) |
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if (exp <= -17) { |
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res = x_sign | 0x31c0000000000000ull; |
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*pfpsf |= INEXACT_EXCEPTION; |
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BID_RETURN (res); |
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} |
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break; |
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case ROUNDING_DOWN: |
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// return 0 if (exp <= -p) |
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if (exp <= -16) { |
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if (x_sign) { |
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res = 0xb1c0000000000001ull; |
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} else { |
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res = 0x31c0000000000000ull; |
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} |
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*pfpsf |= INEXACT_EXCEPTION; |
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BID_RETURN (res); |
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} |
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break; |
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case ROUNDING_UP: |
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// return 0 if (exp <= -p) |
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if (exp <= -16) { |
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if (x_sign) { |
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res = 0xb1c0000000000000ull; |
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} else { |
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res = 0x31c0000000000001ull; |
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} |
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*pfpsf |= INEXACT_EXCEPTION; |
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BID_RETURN (res); |
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} |
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break; |
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case ROUNDING_TO_ZERO: |
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// return 0 if (exp <= -p) |
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if (exp <= -16) { |
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res = x_sign | 0x31c0000000000000ull; |
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*pfpsf |= INEXACT_EXCEPTION; |
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BID_RETURN (res); |
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} |
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break; |
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} // end switch () |
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// q = nr. of decimal digits in x (1 <= q <= 54) |
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// determine first the nr. of bits in x |
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if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
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q = 16; |
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} else { // if x < 2^53 |
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tmp1.d = (double) C1; // exact conversion |
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x_nr_bits = |
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
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q = nr_digits[x_nr_bits - 1].digits; |
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if (q == 0) { |
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q = nr_digits[x_nr_bits - 1].digits1; |
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if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
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q++; |
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} |
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} |
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if (exp >= 0) { // -exp <= 0 |
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// the argument is an integer already |
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res = x; |
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BID_RETURN (res); |
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} |
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switch (rnd_mode) { |
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case ROUNDING_TO_NEAREST: |
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if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q |
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// need to shift right -exp digits from the coefficient; exp will be 0 |
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ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
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// chop off ind digits from the lower part of C1 |
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// C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits |
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// FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate |
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C1 = C1 + midpoint64[ind - 1]; |
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// calculate C* and f* |
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// C* is actually floor(C*) in this case |
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// C* and f* need shifting and masking, as shown by |
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// shiftright128[] and maskhigh128[] |
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// 1 <= x <= 16 |
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// kx = 10^(-x) = ten2mk64[ind - 1] |
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// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
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// the approximation of 10^(-x) was rounded up to 64 bits |
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__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
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// if (0 < f* < 10^(-x)) then the result is a midpoint |
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// if floor(C*) is even then C* = floor(C*) - logical right |
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// shift; C* has p decimal digits, correct by Prop. 1) |
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// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
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// shift; C* has p decimal digits, correct by Pr. 1) |
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// else |
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// C* = floor(C*) (logical right shift; C has p decimal digits, |
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// correct by Property 1) |
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// n = C* * 10^(e+x) |
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if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
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res = P128.w[1]; |
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fstar.w[1] = 0; |
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fstar.w[0] = P128.w[0]; |
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} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
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shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
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res = (P128.w[1] >> shift); |
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fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
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fstar.w[0] = P128.w[0]; |
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} |
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// if (0 < f* < 10^(-x)) then the result is a midpoint |
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// since round_to_even, subtract 1 if current result is odd |
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if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0) |
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&& (fstar.w[0] < ten2mk64[ind - 1])) { |
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res--; |
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} |
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// determine inexactness of the rounding of C* |
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// if (0 < f* - 1/2 < 10^(-x)) then |
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// the result is exact |
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// else // if (f* - 1/2 > T*) then |
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// the result is inexact |
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if (ind - 1 <= 2) { |
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if (fstar.w[0] > 0x8000000000000000ull) { |
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// f* > 1/2 and the result may be exact |
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// fstar.w[0] - 0x8000000000000000ull is f* - 1/2 |
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if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) { |
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// set the inexact flag |
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*pfpsf |= INEXACT_EXCEPTION; |
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} // else the result is exact |
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} else { // the result is inexact; f2* <= 1/2 |
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// set the inexact flag |
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*pfpsf |= INEXACT_EXCEPTION; |
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} |
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} else { // if 3 <= ind - 1 <= 21 |
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if (fstar.w[1] > onehalf128[ind - 1] || |
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(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { |
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// f2* > 1/2 and the result may be exact |
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// Calculate f2* - 1/2 |
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if (fstar.w[1] > onehalf128[ind - 1] |
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|| fstar.w[0] > ten2mk64[ind - 1]) { |
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// set the inexact flag |
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*pfpsf |= INEXACT_EXCEPTION; |
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} // else the result is exact |
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} else { // the result is inexact; f2* <= 1/2 |
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// set the inexact flag |
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*pfpsf |= INEXACT_EXCEPTION; |
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} |
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} |
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// set exponent to zero as it was negative before. |
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res = x_sign | 0x31c0000000000000ull | res; |
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BID_RETURN (res); |
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} else { // if exp < 0 and q + exp < 0 |
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// the result is +0 or -0 |
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res = x_sign | 0x31c0000000000000ull; |
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*pfpsf |= INEXACT_EXCEPTION; |
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BID_RETURN (res); |
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} |
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break; |
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case ROUNDING_TIES_AWAY: |
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if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q |
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// need to shift right -exp digits from the coefficient; exp will be 0 |
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ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
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// chop off ind digits from the lower part of C1 |
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// C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits |
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// FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate |
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C1 = C1 + midpoint64[ind - 1]; |
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// calculate C* and f* |
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// C* is actually floor(C*) in this case |
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// C* and f* need shifting and masking, as shown by |
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// shiftright128[] and maskhigh128[] |
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// 1 <= x <= 16 |
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// kx = 10^(-x) = ten2mk64[ind - 1] |
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// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
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// the approximation of 10^(-x) was rounded up to 64 bits |
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__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
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// if (0 < f* < 10^(-x)) then the result is a midpoint |
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// C* = floor(C*) - logical right shift; C* has p decimal digits, |
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// correct by Prop. 1) |
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// else |
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// C* = floor(C*) (logical right shift; C has p decimal digits, |
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// correct by Property 1) |
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// n = C* * 10^(e+x) |
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if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
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res = P128.w[1]; |
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fstar.w[1] = 0; |
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fstar.w[0] = P128.w[0]; |
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} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
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shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
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res = (P128.w[1] >> shift); |
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fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
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fstar.w[0] = P128.w[0]; |
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} |
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// midpoints are already rounded correctly |
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// determine inexactness of the rounding of C* |
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// if (0 < f* - 1/2 < 10^(-x)) then |
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// the result is exact |
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// else // if (f* - 1/2 > T*) then |
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// the result is inexact |
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if (ind - 1 <= 2) { |
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if (fstar.w[0] > 0x8000000000000000ull) { |
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// f* > 1/2 and the result may be exact |
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// fstar.w[0] - 0x8000000000000000ull is f* - 1/2 |
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if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) { |
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// set the inexact flag |
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*pfpsf |= INEXACT_EXCEPTION; |
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} // else the result is exact |
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} else { // the result is inexact; f2* <= 1/2 |
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// set the inexact flag |
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*pfpsf |= INEXACT_EXCEPTION; |
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} |
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} else { // if 3 <= ind - 1 <= 21 |
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if (fstar.w[1] > onehalf128[ind - 1] || |
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(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { |
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// f2* > 1/2 and the result may be exact |
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// Calculate f2* - 1/2 |
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if (fstar.w[1] > onehalf128[ind - 1] |
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|| fstar.w[0] > ten2mk64[ind - 1]) { |
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// set the inexact flag |
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*pfpsf |= INEXACT_EXCEPTION; |
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} // else the result is exact |
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} else { // the result is inexact; f2* <= 1/2 |
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// set the inexact flag |
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*pfpsf |= INEXACT_EXCEPTION; |
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} |
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} |
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// set exponent to zero as it was negative before. |
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res = x_sign | 0x31c0000000000000ull | res; |
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BID_RETURN (res); |
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} else { // if exp < 0 and q + exp < 0 |
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// the result is +0 or -0 |
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res = x_sign | 0x31c0000000000000ull; |
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*pfpsf |= INEXACT_EXCEPTION; |
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BID_RETURN (res); |
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} |
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break; |
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case ROUNDING_DOWN: |
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if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q |
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// need to shift right -exp digits from the coefficient; exp will be 0 |
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ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
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// chop off ind digits from the lower part of C1 |
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// C1 fits in 64 bits |
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// calculate C* and f* |
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// C* is actually floor(C*) in this case |
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|
343 |
// C* and f* need shifting and masking, as shown by |
|
|
344 |
// shiftright128[] and maskhigh128[] |
|
|
345 |
// 1 <= x <= 16 |
|
|
346 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
347 |
// C* = C1 * 10^(-x) |
|
|
348 |
// the approximation of 10^(-x) was rounded up to 64 bits |
|
|
349 |
__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
|
|
350 |
|
|
|
351 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
352 |
// correct by Property 1) |
|
|
353 |
// if (0 < f* < 10^(-x)) then the result is exact |
|
|
354 |
// n = C* * 10^(e+x) |
|
|
355 |
|
|
|
356 |
if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
|
|
357 |
res = P128.w[1]; |
|
|
358 |
fstar.w[1] = 0; |
|
|
359 |
fstar.w[0] = P128.w[0]; |
|
|
360 |
} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
|
|
361 |
shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
|
|
362 |
res = (P128.w[1] >> shift); |
|
|
363 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
364 |
fstar.w[0] = P128.w[0]; |
|
|
365 |
} |
|
|
366 |
// if (f* > 10^(-x)) then the result is inexact |
|
|
367 |
if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) { |
|
|
368 |
if (x_sign) { |
|
|
369 |
// if negative and not exact, increment magnitude |
|
|
370 |
res++; |
|
|
371 |
} |
|
|
372 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
373 |
} |
|
|
374 |
// set exponent to zero as it was negative before. |
|
|
375 |
res = x_sign | 0x31c0000000000000ull | res; |
|
|
376 |
BID_RETURN (res); |
|
|
377 |
} else { // if exp < 0 and q + exp <= 0 |
|
|
378 |
// the result is +0 or -1 |
|
|
379 |
if (x_sign) { |
|
|
380 |
res = 0xb1c0000000000001ull; |
|
|
381 |
} else { |
|
|
382 |
res = 0x31c0000000000000ull; |
|
|
383 |
} |
|
|
384 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
385 |
BID_RETURN (res); |
|
|
386 |
} |
|
|
387 |
break; |
|
|
388 |
case ROUNDING_UP: |
|
|
389 |
if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q |
|
|
390 |
// need to shift right -exp digits from the coefficient; exp will be 0 |
|
|
391 |
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
|
|
392 |
// chop off ind digits from the lower part of C1 |
|
|
393 |
// C1 fits in 64 bits |
|
|
394 |
// calculate C* and f* |
|
|
395 |
// C* is actually floor(C*) in this case |
|
|
396 |
// C* and f* need shifting and masking, as shown by |
|
|
397 |
// shiftright128[] and maskhigh128[] |
|
|
398 |
// 1 <= x <= 16 |
|
|
399 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
400 |
// C* = C1 * 10^(-x) |
|
|
401 |
// the approximation of 10^(-x) was rounded up to 64 bits |
|
|
402 |
__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
|
|
403 |
|
|
|
404 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
405 |
// correct by Property 1) |
|
|
406 |
// if (0 < f* < 10^(-x)) then the result is exact |
|
|
407 |
// n = C* * 10^(e+x) |
|
|
408 |
|
|
|
409 |
if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
|
|
410 |
res = P128.w[1]; |
|
|
411 |
fstar.w[1] = 0; |
|
|
412 |
fstar.w[0] = P128.w[0]; |
|
|
413 |
} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
|
|
414 |
shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
|
|
415 |
res = (P128.w[1] >> shift); |
|
|
416 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
417 |
fstar.w[0] = P128.w[0]; |
|
|
418 |
} |
|
|
419 |
// if (f* > 10^(-x)) then the result is inexact |
|
|
420 |
if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) { |
|
|
421 |
if (!x_sign) { |
|
|
422 |
// if positive and not exact, increment magnitude |
|
|
423 |
res++; |
|
|
424 |
} |
|
|
425 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
426 |
} |
|
|
427 |
// set exponent to zero as it was negative before. |
|
|
428 |
res = x_sign | 0x31c0000000000000ull | res; |
|
|
429 |
BID_RETURN (res); |
|
|
430 |
} else { // if exp < 0 and q + exp <= 0 |
|
|
431 |
// the result is -0 or +1 |
|
|
432 |
if (x_sign) { |
|
|
433 |
res = 0xb1c0000000000000ull; |
|
|
434 |
} else { |
|
|
435 |
res = 0x31c0000000000001ull; |
|
|
436 |
} |
|
|
437 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
438 |
BID_RETURN (res); |
|
|
439 |
} |
|
|
440 |
break; |
|
|
441 |
case ROUNDING_TO_ZERO: |
|
|
442 |
if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q |
|
|
443 |
// need to shift right -exp digits from the coefficient; exp will be 0 |
|
|
444 |
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
|
|
445 |
// chop off ind digits from the lower part of C1 |
|
|
446 |
// C1 fits in 127 bits |
|
|
447 |
// calculate C* and f* |
|
|
448 |
// C* is actually floor(C*) in this case |
|
|
449 |
// C* and f* need shifting and masking, as shown by |
|
|
450 |
// shiftright128[] and maskhigh128[] |
|
|
451 |
// 1 <= x <= 16 |
|
|
452 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
453 |
// C* = C1 * 10^(-x) |
|
|
454 |
// the approximation of 10^(-x) was rounded up to 64 bits |
|
|
455 |
__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
|
|
456 |
|
|
|
457 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
458 |
// correct by Property 1) |
|
|
459 |
// if (0 < f* < 10^(-x)) then the result is exact |
|
|
460 |
// n = C* * 10^(e+x) |
|
|
461 |
|
|
|
462 |
if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
|
|
463 |
res = P128.w[1]; |
|
|
464 |
fstar.w[1] = 0; |
|
|
465 |
fstar.w[0] = P128.w[0]; |
|
|
466 |
} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
|
|
467 |
shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
|
|
468 |
res = (P128.w[1] >> shift); |
|
|
469 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
470 |
fstar.w[0] = P128.w[0]; |
|
|
471 |
} |
|
|
472 |
// if (f* > 10^(-x)) then the result is inexact |
|
|
473 |
if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) { |
|
|
474 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
475 |
} |
|
|
476 |
// set exponent to zero as it was negative before. |
|
|
477 |
res = x_sign | 0x31c0000000000000ull | res; |
|
|
478 |
BID_RETURN (res); |
|
|
479 |
} else { // if exp < 0 and q + exp < 0 |
|
|
480 |
// the result is +0 or -0 |
|
|
481 |
res = x_sign | 0x31c0000000000000ull; |
|
|
482 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
483 |
BID_RETURN (res); |
|
|
484 |
} |
|
|
485 |
break; |
|
|
486 |
} // end switch () |
|
|
487 |
BID_RETURN (res); |
|
|
488 |
} |
|
|
489 |
|
|
|
490 |
/***************************************************************************** |
|
|
491 |
* BID64_round_integral_nearest_even |
|
|
492 |
****************************************************************************/ |
|
|
493 |
|
|
|
494 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
495 |
void |
|
|
496 |
bid64_round_integral_nearest_even (UINT64 * pres, |
|
|
497 |
UINT64 * |
|
|
498 |
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
499 |
_EXC_INFO_PARAM) { |
|
|
500 |
UINT64 x = *px; |
|
|
501 |
#else |
|
|
502 |
UINT64 |
|
|
503 |
bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM |
|
|
504 |
_EXC_MASKS_PARAM _EXC_INFO_PARAM) { |
|
|
505 |
#endif |
|
|
506 |
|
|
|
507 |
UINT64 res = 0xbaddbaddbaddbaddull; |
|
|
508 |
UINT64 x_sign; |
|
|
509 |
int exp; // unbiased exponent |
|
|
510 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
511 |
BID_UI64DOUBLE tmp1; |
|
|
512 |
int x_nr_bits; |
|
|
513 |
int q, ind, shift; |
|
|
514 |
UINT64 C1; |
|
|
515 |
UINT128 fstar; |
|
|
516 |
UINT128 P128; |
|
|
517 |
|
|
|
518 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
519 |
|
|
|
520 |
// check for NaNs and infinities |
|
|
521 |
if ((x & MASK_NAN) == MASK_NAN) { // check for NaN |
|
|
522 |
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) |
|
|
523 |
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
|
|
524 |
else |
|
|
525 |
x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
|
|
526 |
if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN |
|
|
527 |
// set invalid flag |
|
|
528 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
529 |
// return quiet (SNaN) |
|
|
530 |
res = x & 0xfdffffffffffffffull; |
|
|
531 |
} else { // QNaN |
|
|
532 |
res = x; |
|
|
533 |
} |
|
|
534 |
BID_RETURN (res); |
|
|
535 |
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
|
|
536 |
res = x_sign | 0x7800000000000000ull; |
|
|
537 |
BID_RETURN (res); |
|
|
538 |
} |
|
|
539 |
// unpack x |
|
|
540 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
541 |
// if the steering bits are 11 (condition will be 0), then |
|
|
542 |
// the exponent is G[0:w+1] |
|
|
543 |
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; |
|
|
544 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
545 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
546 |
C1 = 0; |
|
|
547 |
} |
|
|
548 |
} else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) |
|
|
549 |
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; |
|
|
550 |
C1 = (x & MASK_BINARY_SIG1); |
|
|
551 |
} |
|
|
552 |
|
|
|
553 |
// if x is 0 or non-canonical |
|
|
554 |
if (C1 == 0) { |
|
|
555 |
if (exp < 0) |
|
|
556 |
exp = 0; |
|
|
557 |
res = x_sign | (((UINT64) exp + 398) << 53); |
|
|
558 |
BID_RETURN (res); |
|
|
559 |
} |
|
|
560 |
// x is a finite non-zero number (not 0, non-canonical, or special) |
|
|
561 |
|
|
|
562 |
// return 0 if (exp <= -(p+1)) |
|
|
563 |
if (exp <= -17) { |
|
|
564 |
res = x_sign | 0x31c0000000000000ull; |
|
|
565 |
BID_RETURN (res); |
|
|
566 |
} |
|
|
567 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
568 |
// determine first the nr. of bits in x |
|
|
569 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
570 |
q = 16; |
|
|
571 |
} else { // if x < 2^53 |
|
|
572 |
tmp1.d = (double) C1; // exact conversion |
|
|
573 |
x_nr_bits = |
|
|
574 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
575 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
576 |
if (q == 0) { |
|
|
577 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
578 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
579 |
q++; |
|
|
580 |
} |
|
|
581 |
} |
|
|
582 |
|
|
|
583 |
if (exp >= 0) { // -exp <= 0 |
|
|
584 |
// the argument is an integer already |
|
|
585 |
res = x; |
|
|
586 |
BID_RETURN (res); |
|
|
587 |
} else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q |
|
|
588 |
// need to shift right -exp digits from the coefficient; the exp will be 0 |
|
|
589 |
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
|
|
590 |
// chop off ind digits from the lower part of C1 |
|
|
591 |
// C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits |
|
|
592 |
// FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate |
|
|
593 |
C1 = C1 + midpoint64[ind - 1]; |
|
|
594 |
// calculate C* and f* |
|
|
595 |
// C* is actually floor(C*) in this case |
|
|
596 |
// C* and f* need shifting and masking, as shown by |
|
|
597 |
// shiftright128[] and maskhigh128[] |
|
|
598 |
// 1 <= x <= 16 |
|
|
599 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
600 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
601 |
// the approximation of 10^(-x) was rounded up to 64 bits |
|
|
602 |
__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
|
|
603 |
|
|
|
604 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
605 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
606 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
607 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
608 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
609 |
// else |
|
|
610 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
611 |
// correct by Property 1) |
|
|
612 |
// n = C* * 10^(e+x) |
|
|
613 |
|
|
|
614 |
if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
|
|
615 |
res = P128.w[1]; |
|
|
616 |
fstar.w[1] = 0; |
|
|
617 |
fstar.w[0] = P128.w[0]; |
|
|
618 |
} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
|
|
619 |
shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
|
|
620 |
res = (P128.w[1] >> shift); |
|
|
621 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
622 |
fstar.w[0] = P128.w[0]; |
|
|
623 |
} |
|
|
624 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
625 |
// since round_to_even, subtract 1 if current result is odd |
|
|
626 |
if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0) |
|
|
627 |
&& (fstar.w[0] < ten2mk64[ind - 1])) { |
|
|
628 |
res--; |
|
|
629 |
} |
|
|
630 |
// set exponent to zero as it was negative before. |
|
|
631 |
res = x_sign | 0x31c0000000000000ull | res; |
|
|
632 |
BID_RETURN (res); |
|
|
633 |
} else { // if exp < 0 and q + exp < 0 |
|
|
634 |
// the result is +0 or -0 |
|
|
635 |
res = x_sign | 0x31c0000000000000ull; |
|
|
636 |
BID_RETURN (res); |
|
|
637 |
} |
|
|
638 |
} |
|
|
639 |
|
|
|
640 |
/***************************************************************************** |
|
|
641 |
* BID64_round_integral_negative |
|
|
642 |
*****************************************************************************/ |
|
|
643 |
|
|
|
644 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
645 |
void |
|
|
646 |
bid64_round_integral_negative (UINT64 * pres, |
|
|
647 |
UINT64 * |
|
|
648 |
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
649 |
_EXC_INFO_PARAM) { |
|
|
650 |
UINT64 x = *px; |
|
|
651 |
#else |
|
|
652 |
UINT64 |
|
|
653 |
bid64_round_integral_negative (UINT64 x _EXC_FLAGS_PARAM |
|
|
654 |
_EXC_MASKS_PARAM _EXC_INFO_PARAM) { |
|
|
655 |
#endif |
|
|
656 |
|
|
|
657 |
UINT64 res = 0xbaddbaddbaddbaddull; |
|
|
658 |
UINT64 x_sign; |
|
|
659 |
int exp; // unbiased exponent |
|
|
660 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
661 |
BID_UI64DOUBLE tmp1; |
|
|
662 |
int x_nr_bits; |
|
|
663 |
int q, ind, shift; |
|
|
664 |
UINT64 C1; |
|
|
665 |
// UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits |
|
|
666 |
UINT128 fstar; |
|
|
667 |
UINT128 P128; |
|
|
668 |
|
|
|
669 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
670 |
|
|
|
671 |
// check for NaNs and infinities |
|
|
672 |
if ((x & MASK_NAN) == MASK_NAN) { // check for NaN |
|
|
673 |
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) |
|
|
674 |
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
|
|
675 |
else |
|
|
676 |
x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
|
|
677 |
if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN |
|
|
678 |
// set invalid flag |
|
|
679 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
680 |
// return quiet (SNaN) |
|
|
681 |
res = x & 0xfdffffffffffffffull; |
|
|
682 |
} else { // QNaN |
|
|
683 |
res = x; |
|
|
684 |
} |
|
|
685 |
BID_RETURN (res); |
|
|
686 |
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
|
|
687 |
res = x_sign | 0x7800000000000000ull; |
|
|
688 |
BID_RETURN (res); |
|
|
689 |
} |
|
|
690 |
// unpack x |
|
|
691 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
692 |
// if the steering bits are 11 (condition will be 0), then |
|
|
693 |
// the exponent is G[0:w+1] |
|
|
694 |
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; |
|
|
695 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
696 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
697 |
C1 = 0; |
|
|
698 |
} |
|
|
699 |
} else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) |
|
|
700 |
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; |
|
|
701 |
C1 = (x & MASK_BINARY_SIG1); |
|
|
702 |
} |
|
|
703 |
|
|
|
704 |
// if x is 0 or non-canonical |
|
|
705 |
if (C1 == 0) { |
|
|
706 |
if (exp < 0) |
|
|
707 |
exp = 0; |
|
|
708 |
res = x_sign | (((UINT64) exp + 398) << 53); |
|
|
709 |
BID_RETURN (res); |
|
|
710 |
} |
|
|
711 |
// x is a finite non-zero number (not 0, non-canonical, or special) |
|
|
712 |
|
|
|
713 |
// return 0 if (exp <= -p) |
|
|
714 |
if (exp <= -16) { |
|
|
715 |
if (x_sign) { |
|
|
716 |
res = 0xb1c0000000000001ull; |
|
|
717 |
} else { |
|
|
718 |
res = 0x31c0000000000000ull; |
|
|
719 |
} |
|
|
720 |
BID_RETURN (res); |
|
|
721 |
} |
|
|
722 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
723 |
// determine first the nr. of bits in x |
|
|
724 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
725 |
q = 16; |
|
|
726 |
} else { // if x < 2^53 |
|
|
727 |
tmp1.d = (double) C1; // exact conversion |
|
|
728 |
x_nr_bits = |
|
|
729 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
730 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
731 |
if (q == 0) { |
|
|
732 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
733 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
734 |
q++; |
|
|
735 |
} |
|
|
736 |
} |
|
|
737 |
|
|
|
738 |
if (exp >= 0) { // -exp <= 0 |
|
|
739 |
// the argument is an integer already |
|
|
740 |
res = x; |
|
|
741 |
BID_RETURN (res); |
|
|
742 |
} else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q |
|
|
743 |
// need to shift right -exp digits from the coefficient; the exp will be 0 |
|
|
744 |
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
|
|
745 |
// chop off ind digits from the lower part of C1 |
|
|
746 |
// C1 fits in 64 bits |
|
|
747 |
// calculate C* and f* |
|
|
748 |
// C* is actually floor(C*) in this case |
|
|
749 |
// C* and f* need shifting and masking, as shown by |
|
|
750 |
// shiftright128[] and maskhigh128[] |
|
|
751 |
// 1 <= x <= 16 |
|
|
752 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
753 |
// C* = C1 * 10^(-x) |
|
|
754 |
// the approximation of 10^(-x) was rounded up to 64 bits |
|
|
755 |
__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
|
|
756 |
|
|
|
757 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
758 |
// correct by Property 1) |
|
|
759 |
// if (0 < f* < 10^(-x)) then the result is exact |
|
|
760 |
// n = C* * 10^(e+x) |
|
|
761 |
|
|
|
762 |
if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
|
|
763 |
res = P128.w[1]; |
|
|
764 |
fstar.w[1] = 0; |
|
|
765 |
fstar.w[0] = P128.w[0]; |
|
|
766 |
} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
|
|
767 |
shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
|
|
768 |
res = (P128.w[1] >> shift); |
|
|
769 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
770 |
fstar.w[0] = P128.w[0]; |
|
|
771 |
} |
|
|
772 |
// if (f* > 10^(-x)) then the result is inexact |
|
|
773 |
if (x_sign |
|
|
774 |
&& ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1]))) { |
|
|
775 |
// if negative and not exact, increment magnitude |
|
|
776 |
res++; |
|
|
777 |
} |
|
|
778 |
// set exponent to zero as it was negative before. |
|
|
779 |
res = x_sign | 0x31c0000000000000ull | res; |
|
|
780 |
BID_RETURN (res); |
|
|
781 |
} else { // if exp < 0 and q + exp <= 0 |
|
|
782 |
// the result is +0 or -1 |
|
|
783 |
if (x_sign) { |
|
|
784 |
res = 0xb1c0000000000001ull; |
|
|
785 |
} else { |
|
|
786 |
res = 0x31c0000000000000ull; |
|
|
787 |
} |
|
|
788 |
BID_RETURN (res); |
|
|
789 |
} |
|
|
790 |
} |
|
|
791 |
|
|
|
792 |
/***************************************************************************** |
|
|
793 |
* BID64_round_integral_positive |
|
|
794 |
****************************************************************************/ |
|
|
795 |
|
|
|
796 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
797 |
void |
|
|
798 |
bid64_round_integral_positive (UINT64 * pres, |
|
|
799 |
UINT64 * |
|
|
800 |
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
801 |
_EXC_INFO_PARAM) { |
|
|
802 |
UINT64 x = *px; |
|
|
803 |
#else |
|
|
804 |
UINT64 |
|
|
805 |
bid64_round_integral_positive (UINT64 x _EXC_FLAGS_PARAM |
|
|
806 |
_EXC_MASKS_PARAM _EXC_INFO_PARAM) { |
|
|
807 |
#endif |
|
|
808 |
|
|
|
809 |
UINT64 res = 0xbaddbaddbaddbaddull; |
|
|
810 |
UINT64 x_sign; |
|
|
811 |
int exp; // unbiased exponent |
|
|
812 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
813 |
BID_UI64DOUBLE tmp1; |
|
|
814 |
int x_nr_bits; |
|
|
815 |
int q, ind, shift; |
|
|
816 |
UINT64 C1; |
|
|
817 |
// UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits |
|
|
818 |
UINT128 fstar; |
|
|
819 |
UINT128 P128; |
|
|
820 |
|
|
|
821 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
822 |
|
|
|
823 |
// check for NaNs and infinities |
|
|
824 |
if ((x & MASK_NAN) == MASK_NAN) { // check for NaN |
|
|
825 |
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) |
|
|
826 |
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
|
|
827 |
else |
|
|
828 |
x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
|
|
829 |
if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN |
|
|
830 |
// set invalid flag |
|
|
831 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
832 |
// return quiet (SNaN) |
|
|
833 |
res = x & 0xfdffffffffffffffull; |
|
|
834 |
} else { // QNaN |
|
|
835 |
res = x; |
|
|
836 |
} |
|
|
837 |
BID_RETURN (res); |
|
|
838 |
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
|
|
839 |
res = x_sign | 0x7800000000000000ull; |
|
|
840 |
BID_RETURN (res); |
|
|
841 |
} |
|
|
842 |
// unpack x |
|
|
843 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
844 |
// if the steering bits are 11 (condition will be 0), then |
|
|
845 |
// the exponent is G[0:w+1] |
|
|
846 |
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; |
|
|
847 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
848 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
849 |
C1 = 0; |
|
|
850 |
} |
|
|
851 |
} else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) |
|
|
852 |
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; |
|
|
853 |
C1 = (x & MASK_BINARY_SIG1); |
|
|
854 |
} |
|
|
855 |
|
|
|
856 |
// if x is 0 or non-canonical |
|
|
857 |
if (C1 == 0) { |
|
|
858 |
if (exp < 0) |
|
|
859 |
exp = 0; |
|
|
860 |
res = x_sign | (((UINT64) exp + 398) << 53); |
|
|
861 |
BID_RETURN (res); |
|
|
862 |
} |
|
|
863 |
// x is a finite non-zero number (not 0, non-canonical, or special) |
|
|
864 |
|
|
|
865 |
// return 0 if (exp <= -p) |
|
|
866 |
if (exp <= -16) { |
|
|
867 |
if (x_sign) { |
|
|
868 |
res = 0xb1c0000000000000ull; |
|
|
869 |
} else { |
|
|
870 |
res = 0x31c0000000000001ull; |
|
|
871 |
} |
|
|
872 |
BID_RETURN (res); |
|
|
873 |
} |
|
|
874 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
875 |
// determine first the nr. of bits in x |
|
|
876 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
877 |
q = 16; |
|
|
878 |
} else { // if x < 2^53 |
|
|
879 |
tmp1.d = (double) C1; // exact conversion |
|
|
880 |
x_nr_bits = |
|
|
881 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
882 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
883 |
if (q == 0) { |
|
|
884 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
885 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
886 |
q++; |
|
|
887 |
} |
|
|
888 |
} |
|
|
889 |
|
|
|
890 |
if (exp >= 0) { // -exp <= 0 |
|
|
891 |
// the argument is an integer already |
|
|
892 |
res = x; |
|
|
893 |
BID_RETURN (res); |
|
|
894 |
} else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q |
|
|
895 |
// need to shift right -exp digits from the coefficient; the exp will be 0 |
|
|
896 |
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
|
|
897 |
// chop off ind digits from the lower part of C1 |
|
|
898 |
// C1 fits in 64 bits |
|
|
899 |
// calculate C* and f* |
|
|
900 |
// C* is actually floor(C*) in this case |
|
|
901 |
// C* and f* need shifting and masking, as shown by |
|
|
902 |
// shiftright128[] and maskhigh128[] |
|
|
903 |
// 1 <= x <= 16 |
|
|
904 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
905 |
// C* = C1 * 10^(-x) |
|
|
906 |
// the approximation of 10^(-x) was rounded up to 64 bits |
|
|
907 |
__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
|
|
908 |
|
|
|
909 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
910 |
// correct by Property 1) |
|
|
911 |
// if (0 < f* < 10^(-x)) then the result is exact |
|
|
912 |
// n = C* * 10^(e+x) |
|
|
913 |
|
|
|
914 |
if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
|
|
915 |
res = P128.w[1]; |
|
|
916 |
fstar.w[1] = 0; |
|
|
917 |
fstar.w[0] = P128.w[0]; |
|
|
918 |
} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
|
|
919 |
shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
|
|
920 |
res = (P128.w[1] >> shift); |
|
|
921 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
922 |
fstar.w[0] = P128.w[0]; |
|
|
923 |
} |
|
|
924 |
// if (f* > 10^(-x)) then the result is inexact |
|
|
925 |
if (!x_sign |
|
|
926 |
&& ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1]))) { |
|
|
927 |
// if positive and not exact, increment magnitude |
|
|
928 |
res++; |
|
|
929 |
} |
|
|
930 |
// set exponent to zero as it was negative before. |
|
|
931 |
res = x_sign | 0x31c0000000000000ull | res; |
|
|
932 |
BID_RETURN (res); |
|
|
933 |
} else { // if exp < 0 and q + exp <= 0 |
|
|
934 |
// the result is -0 or +1 |
|
|
935 |
if (x_sign) { |
|
|
936 |
res = 0xb1c0000000000000ull; |
|
|
937 |
} else { |
|
|
938 |
res = 0x31c0000000000001ull; |
|
|
939 |
} |
|
|
940 |
BID_RETURN (res); |
|
|
941 |
} |
|
|
942 |
} |
|
|
943 |
|
|
|
944 |
/***************************************************************************** |
|
|
945 |
* BID64_round_integral_zero |
|
|
946 |
****************************************************************************/ |
|
|
947 |
|
|
|
948 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
949 |
void |
|
|
950 |
bid64_round_integral_zero (UINT64 * pres, |
|
|
951 |
UINT64 * |
|
|
952 |
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
953 |
_EXC_INFO_PARAM) { |
|
|
954 |
UINT64 x = *px; |
|
|
955 |
#else |
|
|
956 |
UINT64 |
|
|
957 |
bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
958 |
_EXC_INFO_PARAM) { |
|
|
959 |
#endif |
|
|
960 |
|
|
|
961 |
UINT64 res = 0xbaddbaddbaddbaddull; |
|
|
962 |
UINT64 x_sign; |
|
|
963 |
int exp; // unbiased exponent |
|
|
964 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
965 |
BID_UI64DOUBLE tmp1; |
|
|
966 |
int x_nr_bits; |
|
|
967 |
int q, ind, shift; |
|
|
968 |
UINT64 C1; |
|
|
969 |
// UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits |
|
|
970 |
UINT128 P128; |
|
|
971 |
|
|
|
972 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
973 |
|
|
|
974 |
// check for NaNs and infinities |
|
|
975 |
if ((x & MASK_NAN) == MASK_NAN) { // check for NaN |
|
|
976 |
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) |
|
|
977 |
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
|
|
978 |
else |
|
|
979 |
x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
|
|
980 |
if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN |
|
|
981 |
// set invalid flag |
|
|
982 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
983 |
// return quiet (SNaN) |
|
|
984 |
res = x & 0xfdffffffffffffffull; |
|
|
985 |
} else { // QNaN |
|
|
986 |
res = x; |
|
|
987 |
} |
|
|
988 |
BID_RETURN (res); |
|
|
989 |
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
|
|
990 |
res = x_sign | 0x7800000000000000ull; |
|
|
991 |
BID_RETURN (res); |
|
|
992 |
} |
|
|
993 |
// unpack x |
|
|
994 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
995 |
// if the steering bits are 11 (condition will be 0), then |
|
|
996 |
// the exponent is G[0:w+1] |
|
|
997 |
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; |
|
|
998 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
999 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
1000 |
C1 = 0; |
|
|
1001 |
} |
|
|
1002 |
} else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) |
|
|
1003 |
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; |
|
|
1004 |
C1 = (x & MASK_BINARY_SIG1); |
|
|
1005 |
} |
|
|
1006 |
|
|
|
1007 |
// if x is 0 or non-canonical |
|
|
1008 |
if (C1 == 0) { |
|
|
1009 |
if (exp < 0) |
|
|
1010 |
exp = 0; |
|
|
1011 |
res = x_sign | (((UINT64) exp + 398) << 53); |
|
|
1012 |
BID_RETURN (res); |
|
|
1013 |
} |
|
|
1014 |
// x is a finite non-zero number (not 0, non-canonical, or special) |
|
|
1015 |
|
|
|
1016 |
// return 0 if (exp <= -p) |
|
|
1017 |
if (exp <= -16) { |
|
|
1018 |
res = x_sign | 0x31c0000000000000ull; |
|
|
1019 |
BID_RETURN (res); |
|
|
1020 |
} |
|
|
1021 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
1022 |
// determine first the nr. of bits in x |
|
|
1023 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1024 |
q = 16; |
|
|
1025 |
} else { // if x < 2^53 |
|
|
1026 |
tmp1.d = (double) C1; // exact conversion |
|
|
1027 |
x_nr_bits = |
|
|
1028 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1029 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1030 |
if (q == 0) { |
|
|
1031 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1032 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
1033 |
q++; |
|
|
1034 |
} |
|
|
1035 |
} |
|
|
1036 |
|
|
|
1037 |
if (exp >= 0) { // -exp <= 0 |
|
|
1038 |
// the argument is an integer already |
|
|
1039 |
res = x; |
|
|
1040 |
BID_RETURN (res); |
|
|
1041 |
} else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q |
|
|
1042 |
// need to shift right -exp digits from the coefficient; the exp will be 0 |
|
|
1043 |
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
|
|
1044 |
// chop off ind digits from the lower part of C1 |
|
|
1045 |
// C1 fits in 127 bits |
|
|
1046 |
// calculate C* and f* |
|
|
1047 |
// C* is actually floor(C*) in this case |
|
|
1048 |
// C* and f* need shifting and masking, as shown by |
|
|
1049 |
// shiftright128[] and maskhigh128[] |
|
|
1050 |
// 1 <= x <= 16 |
|
|
1051 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
1052 |
// C* = C1 * 10^(-x) |
|
|
1053 |
// the approximation of 10^(-x) was rounded up to 64 bits |
|
|
1054 |
__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
|
|
1055 |
|
|
|
1056 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
1057 |
// correct by Property 1) |
|
|
1058 |
// if (0 < f* < 10^(-x)) then the result is exact |
|
|
1059 |
// n = C* * 10^(e+x) |
|
|
1060 |
|
|
|
1061 |
if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
|
|
1062 |
res = P128.w[1]; |
|
|
1063 |
// redundant fstar.w[1] = 0; |
|
|
1064 |
// redundant fstar.w[0] = P128.w[0]; |
|
|
1065 |
} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
|
|
1066 |
shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
|
|
1067 |
res = (P128.w[1] >> shift); |
|
|
1068 |
// redundant fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
1069 |
// redundant fstar.w[0] = P128.w[0]; |
|
|
1070 |
} |
|
|
1071 |
// if (f* > 10^(-x)) then the result is inexact |
|
|
1072 |
// if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind-1])){ |
|
|
1073 |
// // redundant |
|
|
1074 |
// } |
|
|
1075 |
// set exponent to zero as it was negative before. |
|
|
1076 |
res = x_sign | 0x31c0000000000000ull | res; |
|
|
1077 |
BID_RETURN (res); |
|
|
1078 |
} else { // if exp < 0 and q + exp < 0 |
|
|
1079 |
// the result is +0 or -0 |
|
|
1080 |
res = x_sign | 0x31c0000000000000ull; |
|
|
1081 |
BID_RETURN (res); |
|
|
1082 |
} |
|
|
1083 |
} |
|
|
1084 |
|
|
|
1085 |
/***************************************************************************** |
|
|
1086 |
* BID64_round_integral_nearest_away |
|
|
1087 |
****************************************************************************/ |
|
|
1088 |
|
|
|
1089 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
1090 |
void |
|
|
1091 |
bid64_round_integral_nearest_away (UINT64 * pres, |
|
|
1092 |
UINT64 * |
|
|
1093 |
px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
1094 |
_EXC_INFO_PARAM) { |
|
|
1095 |
UINT64 x = *px; |
|
|
1096 |
#else |
|
|
1097 |
UINT64 |
|
|
1098 |
bid64_round_integral_nearest_away (UINT64 x _EXC_FLAGS_PARAM |
|
|
1099 |
_EXC_MASKS_PARAM _EXC_INFO_PARAM) { |
|
|
1100 |
#endif |
|
|
1101 |
|
|
|
1102 |
UINT64 res = 0xbaddbaddbaddbaddull; |
|
|
1103 |
UINT64 x_sign; |
|
|
1104 |
int exp; // unbiased exponent |
|
|
1105 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
1106 |
BID_UI64DOUBLE tmp1; |
|
|
1107 |
int x_nr_bits; |
|
|
1108 |
int q, ind, shift; |
|
|
1109 |
UINT64 C1; |
|
|
1110 |
UINT128 P128; |
|
|
1111 |
|
|
|
1112 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
1113 |
|
|
|
1114 |
// check for NaNs and infinities |
|
|
1115 |
if ((x & MASK_NAN) == MASK_NAN) { // check for NaN |
|
|
1116 |
if ((x & 0x0003ffffffffffffull) > 999999999999999ull) |
|
|
1117 |
x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits |
|
|
1118 |
else |
|
|
1119 |
x = x & 0xfe03ffffffffffffull; // clear G6-G12 |
|
|
1120 |
if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN |
|
|
1121 |
// set invalid flag |
|
|
1122 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1123 |
// return quiet (SNaN) |
|
|
1124 |
res = x & 0xfdffffffffffffffull; |
|
|
1125 |
} else { // QNaN |
|
|
1126 |
res = x; |
|
|
1127 |
} |
|
|
1128 |
BID_RETURN (res); |
|
|
1129 |
} else if ((x & MASK_INF) == MASK_INF) { // check for Infinity |
|
|
1130 |
res = x_sign | 0x7800000000000000ull; |
|
|
1131 |
BID_RETURN (res); |
|
|
1132 |
} |
|
|
1133 |
// unpack x |
|
|
1134 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
1135 |
// if the steering bits are 11 (condition will be 0), then |
|
|
1136 |
// the exponent is G[0:w+1] |
|
|
1137 |
exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; |
|
|
1138 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
1139 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
1140 |
C1 = 0; |
|
|
1141 |
} |
|
|
1142 |
} else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) |
|
|
1143 |
exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; |
|
|
1144 |
C1 = (x & MASK_BINARY_SIG1); |
|
|
1145 |
} |
|
|
1146 |
|
|
|
1147 |
// if x is 0 or non-canonical |
|
|
1148 |
if (C1 == 0) { |
|
|
1149 |
if (exp < 0) |
|
|
1150 |
exp = 0; |
|
|
1151 |
res = x_sign | (((UINT64) exp + 398) << 53); |
|
|
1152 |
BID_RETURN (res); |
|
|
1153 |
} |
|
|
1154 |
// x is a finite non-zero number (not 0, non-canonical, or special) |
|
|
1155 |
|
|
|
1156 |
// return 0 if (exp <= -(p+1)) |
|
|
1157 |
if (exp <= -17) { |
|
|
1158 |
res = x_sign | 0x31c0000000000000ull; |
|
|
1159 |
BID_RETURN (res); |
|
|
1160 |
} |
|
|
1161 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
1162 |
// determine first the nr. of bits in x |
|
|
1163 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1164 |
q = 16; |
|
|
1165 |
} else { // if x < 2^53 |
|
|
1166 |
tmp1.d = (double) C1; // exact conversion |
|
|
1167 |
x_nr_bits = |
|
|
1168 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1169 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1170 |
if (q == 0) { |
|
|
1171 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1172 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
1173 |
q++; |
|
|
1174 |
} |
|
|
1175 |
} |
|
|
1176 |
|
|
|
1177 |
if (exp >= 0) { // -exp <= 0 |
|
|
1178 |
// the argument is an integer already |
|
|
1179 |
res = x; |
|
|
1180 |
BID_RETURN (res); |
|
|
1181 |
} else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q |
|
|
1182 |
// need to shift right -exp digits from the coefficient; the exp will be 0 |
|
|
1183 |
ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' |
|
|
1184 |
// chop off ind digits from the lower part of C1 |
|
|
1185 |
// C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits |
|
|
1186 |
// FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate |
|
|
1187 |
C1 = C1 + midpoint64[ind - 1]; |
|
|
1188 |
// calculate C* and f* |
|
|
1189 |
// C* is actually floor(C*) in this case |
|
|
1190 |
// C* and f* need shifting and masking, as shown by |
|
|
1191 |
// shiftright128[] and maskhigh128[] |
|
|
1192 |
// 1 <= x <= 16 |
|
|
1193 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
1194 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
1195 |
// the approximation of 10^(-x) was rounded up to 64 bits |
|
|
1196 |
__mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); |
|
|
1197 |
|
|
|
1198 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
1199 |
// C* = floor(C*) - logical right shift; C* has p decimal digits, |
|
|
1200 |
// correct by Prop. 1) |
|
|
1201 |
// else |
|
|
1202 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
1203 |
// correct by Property 1) |
|
|
1204 |
// n = C* * 10^(e+x) |
|
|
1205 |
|
|
|
1206 |
if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 |
|
|
1207 |
res = P128.w[1]; |
|
|
1208 |
} else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 |
|
|
1209 |
shift = shiftright128[ind - 1]; // 3 <= shift <= 63 |
|
|
1210 |
res = (P128.w[1] >> shift); |
|
|
1211 |
} |
|
|
1212 |
// midpoints are already rounded correctly |
|
|
1213 |
// set exponent to zero as it was negative before. |
|
|
1214 |
res = x_sign | 0x31c0000000000000ull | res; |
|
|
1215 |
BID_RETURN (res); |
|
|
1216 |
} else { // if exp < 0 and q + exp < 0 |
|
|
1217 |
// the result is +0 or -0 |
|
|
1218 |
res = x_sign | 0x31c0000000000000ull; |
|
|
1219 |
BID_RETURN (res); |
|
|
1220 |
} |
|
|
1221 |
} |