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Diffstat (limited to 'gcc-4.9/libgcc/config/libbid/bid64_round_integral.c')
| -rw-r--r-- | gcc-4.9/libgcc/config/libbid/bid64_round_integral.c | 1221 |
1 files changed, 1221 insertions, 0 deletions
diff --git a/gcc-4.9/libgcc/config/libbid/bid64_round_integral.c b/gcc-4.9/libgcc/config/libbid/bid64_round_integral.c new file mode 100644 index 000000000..c4b0d38b5 --- /dev/null +++ b/gcc-4.9/libgcc/config/libbid/bid64_round_integral.c @@ -0,0 +1,1221 @@ +/* Copyright (C) 2007-2014 Free Software Foundation, Inc. + +This file is part of GCC. + +GCC is free software; you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free +Software Foundation; either version 3, or (at your option) any later +version. + +GCC is distributed in the hope that it will be useful, but WITHOUT ANY +WARRANTY; without even the implied warranty of MERCHANTABILITY or +FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +<http://www.gnu.org/licenses/>. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64_round_integral_exact + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_exact (UINT64 * pres, + UINT64 * + px _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#if !DECIMAL_GLOBAL_ROUNDING + unsigned int rnd_mode = *prnd_mode; +#endif +#else +UINT64 +bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1 represents the significand (UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + // UINT64 res is C* at first - represents up to 16 decimal digits <= 54 bits + UINT128 fstar = { {0x0ull, 0x0ull} }; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical return 0 preserving the sign bit and + // the preferred exponent of MAX(Q(x), 0) + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + switch (rnd_mode) { + case ROUNDING_TO_NEAREST: + case ROUNDING_TIES_AWAY: + // return 0 if (exp <= -(p+1)) + if (exp <= -17) { + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_DOWN: + // return 0 if (exp <= -p) + if (exp <= -16) { + if (x_sign) { + res = 0xb1c0000000000001ull; + } else { + res = 0x31c0000000000000ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_UP: + // return 0 if (exp <= -p) + if (exp <= -16) { + if (x_sign) { + res = 0xb1c0000000000000ull; + } else { + res = 0x31c0000000000001ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_TO_ZERO: + // return 0 if (exp <= -p) + if (exp <= -16) { + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + } // end switch () + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } + + switch (rnd_mode) { + case ROUNDING_TO_NEAREST: + if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (0 < f* < 10^(-x)) then the result is a midpoint + // since round_to_even, subtract 1 if current result is odd + if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0) + && (fstar.w[0] < ten2mk64[ind - 1])) { + res--; + } + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + // fstar.w[0] - 0x8000000000000000ull is f* - 1/2 + if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 21 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + if (fstar.w[1] > onehalf128[ind - 1] + || fstar.w[0] > ten2mk64[ind - 1]) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_TIES_AWAY: + if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // if (0 < f* < 10^(-x)) then the result is a midpoint + // C* = floor(C*) - logical right shift; C* has p decimal digits, + // correct by Prop. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // midpoints are already rounded correctly + // determine inexactness of the rounding of C* + // if (0 < f* - 1/2 < 10^(-x)) then + // the result is exact + // else // if (f* - 1/2 > T*) then + // the result is inexact + if (ind - 1 <= 2) { + if (fstar.w[0] > 0x8000000000000000ull) { + // f* > 1/2 and the result may be exact + // fstar.w[0] - 0x8000000000000000ull is f* - 1/2 + if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } else { // if 3 <= ind - 1 <= 21 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { + // f2* > 1/2 and the result may be exact + // Calculate f2* - 1/2 + if (fstar.w[1] > onehalf128[ind - 1] + || fstar.w[0] > ten2mk64[ind - 1]) { + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_DOWN: + if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) { + if (x_sign) { + // if negative and not exact, increment magnitude + res++; + } + *pfpsf |= INEXACT_EXCEPTION; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + // the result is +0 or -1 + if (x_sign) { + res = 0xb1c0000000000001ull; + } else { + res = 0x31c0000000000000ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_UP: + if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) { + if (!x_sign) { + // if positive and not exact, increment magnitude + res++; + } + *pfpsf |= INEXACT_EXCEPTION; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + // the result is -0 or +1 + if (x_sign) { + res = 0xb1c0000000000000ull; + } else { + res = 0x31c0000000000001ull; + } + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + case ROUNDING_TO_ZERO: + if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) { + *pfpsf |= INEXACT_EXCEPTION; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + *pfpsf |= INEXACT_EXCEPTION; + BID_RETURN (res); + } + break; + } // end switch () + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_round_integral_nearest_even + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_nearest_even (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 fstar; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -(p+1)) + if (exp <= -17) { + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (0 < f* < 10^(-x)) then the result is a midpoint + // since round_to_even, subtract 1 if current result is odd + if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0) + && (fstar.w[0] < ten2mk64[ind - 1])) { + res--; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } +} + +/***************************************************************************** + * BID64_round_integral_negative + *****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_negative (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_negative (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + // UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits + UINT128 fstar; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -p) + if (exp <= -16) { + if (x_sign) { + res = 0xb1c0000000000001ull; + } else { + res = 0x31c0000000000000ull; + } + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if (x_sign + && ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1]))) { + // if negative and not exact, increment magnitude + res++; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + // the result is +0 or -1 + if (x_sign) { + res = 0xb1c0000000000001ull; + } else { + res = 0x31c0000000000000ull; + } + BID_RETURN (res); + } +} + +/***************************************************************************** + * BID64_round_integral_positive + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_positive (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_positive (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + // UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits + UINT128 fstar; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -p) + if (exp <= -16) { + if (x_sign) { + res = 0xb1c0000000000000ull; + } else { + res = 0x31c0000000000001ull; + } + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 64 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + fstar.w[1] = 0; + fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + if (!x_sign + && ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1]))) { + // if positive and not exact, increment magnitude + res++; + } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp <= 0 + // the result is -0 or +1 + if (x_sign) { + res = 0xb1c0000000000000ull; + } else { + res = 0x31c0000000000001ull; + } + BID_RETURN (res); + } +} + +/***************************************************************************** + * BID64_round_integral_zero + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_zero (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_zero (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + // UINT64 res is C* at first - represents up to 34 decimal digits ~ 113 bits + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -p) + if (exp <= -16) { + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 fits in 127 bits + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = C1 * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // if (0 < f* < 10^(-x)) then the result is exact + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + // redundant fstar.w[1] = 0; + // redundant fstar.w[0] = P128.w[0]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + // redundant fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; + // redundant fstar.w[0] = P128.w[0]; + } + // if (f* > 10^(-x)) then the result is inexact + // if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind-1])){ + // // redundant + // } + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } +} + +/***************************************************************************** + * BID64_round_integral_nearest_away + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_round_integral_nearest_away (UINT64 * pres, + UINT64 * + px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +UINT64 +bid64_round_integral_nearest_away (UINT64 x _EXC_FLAGS_PARAM + _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + + UINT64 res = 0xbaddbaddbaddbaddull; + UINT64 x_sign; + int exp; // unbiased exponent + // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) + BID_UI64DOUBLE tmp1; + int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 P128; + + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + + // check for NaNs and infinities + if ((x & MASK_NAN) == MASK_NAN) { // check for NaN + if ((x & 0x0003ffffffffffffull) > 999999999999999ull) + x = x & 0xfe00000000000000ull; // clear G6-G12 and the payload bits + else + x = x & 0xfe03ffffffffffffull; // clear G6-G12 + if ((x & MASK_SNAN) == MASK_SNAN) { // SNaN + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return quiet (SNaN) + res = x & 0xfdffffffffffffffull; + } else { // QNaN + res = x; + } + BID_RETURN (res); + } else if ((x & MASK_INF) == MASK_INF) { // check for Infinity + res = x_sign | 0x7800000000000000ull; + BID_RETURN (res); + } + // unpack x + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + // if the steering bits are 11 (condition will be 0), then + // the exponent is G[0:w+1] + exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398; + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + C1 = 0; + } + } else { // if ((x & MASK_STEERING_BITS) != MASK_STEERING_BITS) + exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398; + C1 = (x & MASK_BINARY_SIG1); + } + + // if x is 0 or non-canonical + if (C1 == 0) { + if (exp < 0) + exp = 0; + res = x_sign | (((UINT64) exp + 398) << 53); + BID_RETURN (res); + } + // x is a finite non-zero number (not 0, non-canonical, or special) + + // return 0 if (exp <= -(p+1)) + if (exp <= -17) { + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + q = 16; + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + } + + if (exp >= 0) { // -exp <= 0 + // the argument is an integer already + res = x; + BID_RETURN (res); + } else if ((q + exp) >= 0) { // exp < 0 and 1 <= -exp <= q + // need to shift right -exp digits from the coefficient; the exp will be 0 + ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits + // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 16 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 64 bits + __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]); + + // if (0 < f* < 10^(-x)) then the result is a midpoint + // C* = floor(C*) - logical right shift; C* has p decimal digits, + // correct by Prop. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0 + res = P128.w[1]; + } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63 + shift = shiftright128[ind - 1]; // 3 <= shift <= 63 + res = (P128.w[1] >> shift); + } + // midpoints are already rounded correctly + // set exponent to zero as it was negative before. + res = x_sign | 0x31c0000000000000ull | res; + BID_RETURN (res); + } else { // if exp < 0 and q + exp < 0 + // the result is +0 or -0 + res = x_sign | 0x31c0000000000000ull; + BID_RETURN (res); + } +} |