--- /dev/null
+/* Copyright (C) 2007, 2009 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);
+ }
+}
projects / msp430-gcc.git / blobdiff