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author | Dan Albert <danalbert@google.com> | 2015-06-17 11:09:54 -0700 |
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committer | Dan Albert <danalbert@google.com> | 2015-06-17 14:15:22 -0700 |
commit | f378ebf14df0952eae870c9865bab8326aa8f137 (patch) | |
tree | 31794503eb2a8c64ea5f313b93100f1163afcffb /gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c | |
parent | 2c58169824949d3a597d9fa81931e001ef9b1bd0 (diff) | |
download | toolchain_gcc-f378ebf14df0952eae870c9865bab8326aa8f137.tar.gz toolchain_gcc-f378ebf14df0952eae870c9865bab8326aa8f137.tar.bz2 toolchain_gcc-f378ebf14df0952eae870c9865bab8326aa8f137.zip |
Delete old versions of GCC.
Change-Id: I710f125d905290e1024cbd67f48299861790c66c
Diffstat (limited to 'gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c')
-rw-r--r-- | gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c | 2278 |
1 files changed, 0 insertions, 2278 deletions
diff --git a/gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c b/gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c deleted file mode 100644 index 7b1d31f8d..000000000 --- a/gcc-4.3.1/libgcc/config/libbid/bid64_to_uint64.c +++ /dev/null @@ -1,2278 +0,0 @@ -/* Copyright (C) 2007 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 2, or (at your option) any later -version. - -In addition to the permissions in the GNU General Public License, the -Free Software Foundation gives you unlimited permission to link the -compiled version of this file into combinations with other programs, -and to distribute those combinations without any restriction coming -from the use of this file. (The General Public License restrictions -do apply in other respects; for example, they cover modification of -the file, and distribution when not linked into a combine -executable.) - -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. - -You should have received a copy of the GNU General Public License -along with GCC; see the file COPYING. If not, write to the Free -Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA -02110-1301, USA. */ - -#include "bid_internal.h" - -/***************************************************************************** - * BID64_to_uint64_rnint - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_rnint (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_rnint (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 fstar; - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - // q = nr. of decimal digits in x (1 <= q <= 54) - // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1/2 - // => set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else { // if n > 0 and q + exp = 20 - // if n >= 2^64 - 1/2 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) - // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16 - if (q == 1) { - // C * 10^20 >= 0x9fffffffffffffffb - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - } - // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) - // return 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) - // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) - // res = 0 - // else if x > 0 - // res = +1 - // else // if x < 0 - // invalid exc - ind = q - 1; // 0 <= ind <= 15 - if (C1 <= midpoint64[ind]) { - res = 0x0000000000000000ull; // return 0 - } else if (!x_sign) { // n > 0 - res = 0x0000000000000001ull; // return +1 - } else { // if n < 0 - res = 0x8000000000000000ull; - *pfpsf |= INVALID_EXCEPTION; - BID_RETURN (res); - } - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (x_sign) { // x <= -1 - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // 1 <= x < 2^64-1/2 so x can be rounded - // to nearest to a 64-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' - // chop off ind digits from the lower part of C1 - // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits - 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = (C1 + 1/2 * 10^x) * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; - fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // 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) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - - // if the result was a midpoint it was rounded away from zero, so - // it will need a correction - // check for midpoints - if ((fstar.w[1] == 0) && fstar.w[0] && - (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - // the result is a midpoint; round to nearest - if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] - // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 - Cstar--; // Cstar is now even - } // else MP in [ODD, EVEN] - } - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} - -/***************************************************************************** - * BID64_to_uint64_xrnint - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_xrnint (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_xrnint (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - UINT64 tmp64; - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 fstar; - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - // q = nr. of decimal digits in x (1 <= q <= 54) - // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1/2 - // => set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else { // if n > 0 and q + exp = 20 - // if n >= 2^64 - 1/2 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) - // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16 - if (q == 1) { - // C * 10^20 >= 0x9fffffffffffffffb - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - } - // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) - // set inexact flag - *pfpsf |= INEXACT_EXCEPTION; - // return 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) - // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) - // res = 0 - // else if x > 0 - // res = +1 - // else // if x < 0 - // invalid exc - ind = q - 1; // 0 <= ind <= 15 - if (C1 <= midpoint64[ind]) { - res = 0x0000000000000000ull; // return 0 - } else if (!x_sign) { // n > 0 - res = 0x0000000000000001ull; // return +1 - } else { // if n < 0 - res = 0x8000000000000000ull; - *pfpsf |= INVALID_EXCEPTION; - BID_RETURN (res); - } - // set inexact flag - *pfpsf |= INEXACT_EXCEPTION; - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (x_sign) { // x <= -1 - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // 1 <= x < 2^64-1/2 so x can be rounded - // to nearest to a 64-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' - // chop off ind digits from the lower part of C1 - // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits - 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = (C1 + 1/2 * 10^x) * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; - fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // 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) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - // 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) { // fstar.w[1] is 0 - if (fstar.w[0] > 0x8000000000000000ull) { - // f* > 1/2 and the result may be exact - tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 - if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[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 <= 14 - 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 - tmp64 = fstar.w[1] - onehalf128[ind - 1]; - if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[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; - } - } - - // if the result was a midpoint it was rounded away from zero, so - // it will need a correction - // check for midpoints - if ((fstar.w[1] == 0) && fstar.w[0] && - (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - // the result is a midpoint; round to nearest - if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] - // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 - Cstar--; // Cstar is now even - } // else MP in [ODD, EVEN] - } - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} - -/***************************************************************************** - * BID64_to_uint64_floor - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_floor (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_floor (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - if (x_sign) { // if n < 0 the conversion is invalid - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - 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 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - // n > 0 and q + exp = 20 - // if n >= 2^64 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65) - // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=16 - if (q == 1) { - // C * 10^20 >= 0xa0000000000000000 - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] >= 0x0a) { - // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000 - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] >= 0x0a) { - // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - // n is not too large to be converted to int64 if -1 < n < 2^64 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) - // return 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // 1 <= x < 2^64 so x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = C1 * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // C* = floor(C*) (logical right shift; C has p decimal digits, - // correct by Property 1) - // n = C* * 10^(e+x) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} - -/***************************************************************************** - * BID64_to_uint64_xfloor - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_xfloor (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_xfloor (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 fstar; - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - if (x_sign) { // if n < 0 the conversion is invalid - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - 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 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - // n > 0 and q + exp = 20 - // if n >= 2^64 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65) - // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=16 - if (q == 1) { - // C * 10^20 >= 0xa0000000000000000 - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] >= 0x0a) { - // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000 - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] >= 0x0a) { - // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - // n is not too large to be converted to int64 if -1 < n < 2^64 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) - // set inexact flag - *pfpsf |= INEXACT_EXCEPTION; - // return 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // 1 <= x < 2^64 so x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = C1 * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; - fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // C* = floor(C*) (logical right shift; C has p decimal digits, - // correct by Property 1) - // n = C* * 10^(e+x) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - // determine inexactness of the rounding of C* - // if (0 < f* < 10^(-x)) then - // the result is exact - // else // if (f* > T*) then - // the result is inexact - if (ind - 1 <= 2) { // fstar.w[1] is 0 - if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - // set the inexact flag - *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - // set the inexact flag - *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } - - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} - -/***************************************************************************** - * BID64_to_uint64_ceil - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_ceil (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_ceil (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 fstar; - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - // q = nr. of decimal digits in x (1 <= q <= 54) - // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1 - // => set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else { // if n > 0 and q + exp = 20 - // if n > 2^64 - 1 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65 - 2) - // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=16 - if (q == 1) { - // C * 10^20 > 0x9fffffffffffffff6 - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] > 0xfffffffffffffff6ull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffff6 - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] > 0xfffffffffffffff6ull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - } - // n is not too large to be converted to int64 if -1 < n < 2^64 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) - // return 0 or 1 - if (x_sign) - res = 0x0000000000000000ull; - else - res = 0x0000000000000001ull; - BID_RETURN (res); - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // x <= -1 or 1 <= x <= 2^64 - 1 so if positive x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (x_sign) { // x <= -1 - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // 1 <= x <= 2^64 - 1 so x can be rounded - // to nearest to a 64-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = C1 * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; - fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // C* = floor(C*) (logical right shift; C has p decimal digits, - // correct by Property 1) - // n = C* * 10^(e+x) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - // determine inexactness of the rounding of C* - // if (0 < f* < 10^(-x)) then - // the result is exact - // else // if (f* > T*) then - // the result is inexact - if (ind - 1 <= 2) { // fstar.w[1] is 0 - if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - Cstar++; - } // else the result is exact - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - Cstar++; - } // else the result is exact - } - - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} - -/***************************************************************************** - * BID64_to_uint64_xceil - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_xceil (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_xceil (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 fstar; - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - // q = nr. of decimal digits in x (1 <= q <= 54) - // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1 - // => set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else { // if n > 0 and q + exp = 20 - // if n > 2^64 - 1 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65 - 2) - // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=16 - if (q == 1) { - // C * 10^20 > 0x9fffffffffffffff6 - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] > 0xfffffffffffffff6ull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffff6 - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] > 0xfffffffffffffff6ull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - } - // n is not too large to be converted to int64 if -1 < n < 2^64 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) - // set inexact flag - *pfpsf |= INEXACT_EXCEPTION; - // return 0 or 1 - if (x_sign) - res = 0x0000000000000000ull; - else - res = 0x0000000000000001ull; - BID_RETURN (res); - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // x <= -1 or 1 <= x <= 2^64 - 1 so if positive x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (x_sign) { // x <= -1 - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // 1 <= x <= 2^64 - 1 so x can be rounded - // to nearest to a 64-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = C1 * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; - fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // C* = floor(C*) (logical right shift; C has p decimal digits, - // correct by Property 1) - // n = C* * 10^(e+x) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - // determine inexactness of the rounding of C* - // if (0 < f* < 10^(-x)) then - // the result is exact - // else // if (f* > T*) then - // the result is inexact - if (ind - 1 <= 2) { // fstar.w[1] is 0 - if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - Cstar++; - // set the inexact flag - *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - Cstar++; - // set the inexact flag - *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } - - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} - -/***************************************************************************** - * BID64_to_uint64_int - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_int (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) -{ - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_int (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) -{ -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - // q = nr. of decimal digits in x (1 <= q <= 54) - // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1 - // => set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else { // if n > 0 and q + exp = 20 - // if n >= 2^64 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65) - // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=16 - if (q == 1) { - // C * 10^20 >= 0xa0000000000000000 - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] >= 0x0a) { - // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000 - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] >= 0x0a) { - // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - } - // n is not too large to be converted to int64 if -1 < n < 2^64 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) - // return 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (x_sign) { // x <= -1 - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // 1 <= x < 2^64 so x can be rounded - // to nearest to a 64-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = C1 * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // C* = floor(C*) (logical right shift; C has p decimal digits, - // correct by Property 1) - // n = C* * 10^(e+x) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} - -/***************************************************************************** - * BID64_to_uint64_xint - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_xint (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_xint (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 fstar; - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - // q = nr. of decimal digits in x (1 <= q <= 54) - // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1 - // => set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else { // if n > 0 and q + exp = 20 - // if n >= 2^64 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65) - // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=16 - if (q == 1) { - // C * 10^20 >= 0xa0000000000000000 - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] >= 0x0a) { - // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0xa0000000000000000 - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] >= 0x0a) { - // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - } - // n is not too large to be converted to int64 if -1 < n < 2^64 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) - // set inexact flag - *pfpsf |= INEXACT_EXCEPTION; - // return 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (x_sign) { // x <= -1 - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // 1 <= x < 2^64 so x can be rounded - // to nearest to a 64-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = C1 * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; - fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // C* = floor(C*) (logical right shift; C has p decimal digits, - // correct by Property 1) - // n = C* * 10^(e+x) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - // determine inexactness of the rounding of C* - // if (0 < f* < 10^(-x)) then - // the result is exact - // else // if (f* > T*) then - // the result is inexact - if (ind - 1 <= 2) { // fstar.w[1] is 0 - if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - // set the inexact flag - *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[1] - // set the inexact flag - *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } - - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} - -/***************************************************************************** - * BID64_to_uint64_rninta - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_rninta (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_rninta (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - // q = nr. of decimal digits in x (1 <= q <= 54) - // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1/2 - // => set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else { // if n > 0 and q + exp = 20 - // if n >= 2^64 - 1/2 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) - // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16 - if (q == 1) { - // C * 10^20 >= 0x9fffffffffffffffb - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - } - // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) - // return 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) - // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) - // res = 0 - // else if x > 0 - // res = +1 - // else // if x < 0 - // invalid exc - ind = q - 1; // 0 <= ind <= 15 - if (C1 < midpoint64[ind]) { - res = 0x0000000000000000ull; // return 0 - } else if (!x_sign) { // n > 0 - res = 0x0000000000000001ull; // return +1 - } else { // if n < 0 - res = 0x8000000000000000ull; - *pfpsf |= INVALID_EXCEPTION; - BID_RETURN (res); - } - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (x_sign) { // x <= -1 - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // 1 <= x < 2^64-1/2 so x can be rounded - // to nearest to a 64-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' - // chop off ind digits from the lower part of C1 - // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits - 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = (C1 + 1/2 * 10^x) * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // 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) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - - // if the result was a midpoint it was rounded away from zero - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} - -/***************************************************************************** - * BID64_to_uint64_xrninta - ****************************************************************************/ - -#if DECIMAL_CALL_BY_REFERENCE -void -bid64_to_uint64_xrninta (UINT64 * pres, UINT64 * px - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { - UINT64 x = *px; -#else -UINT64 -bid64_to_uint64_xrninta (UINT64 x - _EXC_FLAGS_PARAM _EXC_MASKS_PARAM - _EXC_INFO_PARAM) { -#endif - UINT64 res; - UINT64 x_sign; - UINT64 x_exp; - int exp; // unbiased exponent - // Note: C1 represents x_significand (UINT64) - UINT64 tmp64; - BID_UI64DOUBLE tmp1; - unsigned int x_nr_bits; - int q, ind, shift; - UINT64 C1; - UINT128 C; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits - UINT128 fstar; - UINT128 P128; - - // check for NaN or Infinity - if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative - // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => - if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased - C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical - x_exp = 0; - C1 = 0; - } - } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased - C1 = x & MASK_BINARY_SIG1; - } - - // check for zeros (possibly from non-canonical values) - if (C1 == 0x0ull) { - // x is 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } - // x is not special and is not zero - - // q = nr. of decimal digits in x (1 <= q <= 54) - // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 - // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion - x_nr_bits = - 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion - x_nr_bits = - 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } - } 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++; - } - exp = x_exp - 398; // unbiased exponent - - if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) - // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... - // so x rounded to an integer may or may not fit in an unsigned 64-bit int - // the cases that do not fit are identified here; the ones that fit - // fall through and will be handled with other cases further, - // under '1 <= q + exp <= 20' - if (x_sign) { // if n < 0 and q + exp = 20 then x is much less than -1/2 - // => set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } else { // if n > 0 and q + exp = 20 - // if n >= 2^64 - 1/2 then n is too large - // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 - // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) - // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16 - if (q == 1) { - // C * 10^20 >= 0x9fffffffffffffffb - __mul_128x64_to_128 (C, C1, ten2k128[0]); // 10^20 * C - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } else { // if (2 <= q <= 16) => 5 <= 21 - q <= 19 - // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb - // has 21 digits - __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]); - if (C.w[1] > 0x09 || - (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) { - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // else cases that can be rounded to a 64-bit int fall through - // to '1 <= q + exp <= 20' - } - } - } - // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 - // Note: some of the cases tested for above fall through to this point - if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) - // set inexact flag - *pfpsf |= INEXACT_EXCEPTION; - // return 0 - res = 0x0000000000000000ull; - BID_RETURN (res); - } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) - // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) - // res = 0 - // else if x > 0 - // res = +1 - // else // if x < 0 - // invalid exc - ind = q - 1; // 0 <= ind <= 15 - if (C1 < midpoint64[ind]) { - res = 0x0000000000000000ull; // return 0 - } else if (!x_sign) { // n > 0 - res = 0x0000000000000001ull; // return +1 - } else { // if n < 0 - res = 0x8000000000000000ull; - *pfpsf |= INVALID_EXCEPTION; - BID_RETURN (res); - } - // set inexact flag - *pfpsf |= INEXACT_EXCEPTION; - } else { // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19) - // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded - // to nearest to a 64-bit unsigned signed integer - if (x_sign) { // x <= -1 - // set invalid flag - *pfpsf |= INVALID_EXCEPTION; - // return Integer Indefinite - res = 0x8000000000000000ull; - BID_RETURN (res); - } - // 1 <= x < 2^64-1/2 so x can be rounded - // to nearest to a 64-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' - // chop off ind digits from the lower part of C1 - // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits - 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 <= 15 - // kx = 10^(-x) = ten2mk64[ind - 1] - // C* = (C1 + 1/2 * 10^x) * 10^(-x) - // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); - Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; - fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 - // 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) - - // shift right C* by Ex-64 = shiftright128[ind] - shift = shiftright128[ind - 1]; // 0 <= shift <= 39 - Cstar = Cstar >> shift; - // 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) { // fstar.w[1] is 0 - if (fstar.w[0] > 0x8000000000000000ull) { - // f* > 1/2 and the result may be exact - tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 - if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[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 <= 14 - 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 - tmp64 = fstar.w[1] - onehalf128[ind - 1]; - if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { - // ten2mk128trunc[ind -1].w[1] is identical to - // ten2mk128[ind -1].w[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; - } - } - - // if the result was a midpoint it was rounded away from zero - res = Cstar; // the result is positive - } else if (exp == 0) { - // 1 <= q <= 10 - // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 - // res = +C * 10^exp (exact) - res = C1 * ten2k64[exp]; // the result is positive - } - } - BID_RETURN (res); -} |