| /* Copyright (C) 2007-2017 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); |
| } |
| } |