/* 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_uint32_rnint ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_rnint (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_rnint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // if n > 0 and q + exp = 10 // if n >= 2^32 - 1/2 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0x9fffffffbull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0x9fffffffb <=> // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0x9fffffffbull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } } // n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 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 = 0x00000000; 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; if (C1 <= midpoint64[ind]) { res = 0x00000000; // return 0 } else if (x_sign) { // n < 0 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // n > 0 res = 0x00000001; // return +1 } } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // 1 <= x < 2^32-1/2 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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_uint32_xrnint ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_xrnint (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_xrnint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // if n > 0 and q + exp = 10 // if n >= 2^32 - 1/2 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0x9fffffffbull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0x9fffffffb <=> // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0x9fffffffbull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } } // n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 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 = 0x00000000; 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; if (C1 <= midpoint64[ind]) { res = 0x00000000; // return 0 } else if (x_sign) { // n < 0 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // n > 0 res = 0x00000001; // return +1 } // set inexact flag *pfpsf |= INEXACT_EXCEPTION; } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // 1 <= x < 2^32-1/2 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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_uint32_floor ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_floor (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_floor (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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 = 0x80000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' // n > 0 and q + exp = 10 // if n >= 2^32 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0xa00000000ull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0xa00000000 <=> // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0xa00000000ull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } // n is not too large to be converted to int32 if -1 < n < 2^32 // 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 = 0x00000000; BID_RETURN (res); } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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_uint32_xfloor ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_xfloor (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_xfloor (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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 = 0x80000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' // if n > 0 and q + exp = 10 // if n >= 2^32 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0xa00000000ull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0xa00000000 <=> // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0xa00000000ull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } // n is not too large to be converted to int32 if -1 < n < 2^32 // 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 = 0x00000000; BID_RETURN (res); } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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) { 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_uint32_ceil ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_ceil (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_ceil (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // if n > 0 and q + exp = 10 // if n > 2^32 - 1 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16 // <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 > 0x9fffffff6ull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) > 0x9fffffff6 <=> // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1 up) // Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0x9fffffff6ull * ten2k64[q - 11]; if (C1 > tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } } // n is not too large to be converted to int32 if -1 < n < 2^32 // 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 = 0x00000000; else res = 0x00000001; BID_RETURN (res); } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // x <= -1 or 1 <= x <= 2^32 - 1 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // 1 <= x <= 2^32 - 1 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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_uint32_xceil ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_xceil (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_xceil (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // if n > 0 and q + exp = 10 // if n > 2^32 - 1 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16 // <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 > 0x9fffffff6ull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) > 0x9fffffff6 <=> // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1 up) // Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0x9fffffff6ull * ten2k64[q - 11]; if (C1 > tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } } // n is not too large to be converted to int32 if -1 < n < 2^32 // 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 = 0x00000000; else res = 0x00000001; BID_RETURN (res); } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // x <= -1 or 1 <= x < 2^32 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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_uint32_int ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_int (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_int (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // if n > 0 and q + exp = 10 // if n >= 2^32 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0xa00000000ull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0xa00000000 <=> // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0xa00000000ull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } } // n is not too large to be converted to int32 if -1 < n < 2^32 // 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 = 0x00000000; BID_RETURN (res); } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // x <= -1 or 1 <= x < 2^32 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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_uint32_xint ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_xint (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_xint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // if n > 0 and q + exp = 10 // if n >= 2^32 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0xa00000000ull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0xa00000000 <=> // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0xa00000000ull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } } // n is not too large to be converted to int32 if -1 < n < 2^32 // 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 = 0x00000000; BID_RETURN (res); } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // x <= -1 or 1 <= x < 2^32 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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_uint32_rninta ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_rninta (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_rninta (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // if n > 0 and q + exp = 10 // if n >= 2^32 - 1/2 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0x9fffffffbull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0x9fffffffb <=> // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0x9fffffffbull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } } // n is not too large to be converted to int32 if -1/2 < n < 2^32 - 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 = 0x00000000; 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; if (C1 < midpoint64[ind]) { res = 0x00000000; // return 0 } else if (x_sign) { // n < 0 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // n > 0 res = 0x00000001; // return +1 } } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // 1 <= x < 2^32-1/2 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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 // 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_uint32_xrninta ****************************************************************************/ #if DECIMAL_CALL_BY_REFERENCE void bid64_to_uint32_xrninta (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int bid64_to_uint32_xrninta (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int 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; 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 = 0x80000000; 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 = 0x00000000; 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-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 <= 10' if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // if n > 0 and q + exp = 10 // if n >= 2^32 - 1/2 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0x9fffffffbull) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0x9fffffffb <=> // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 tmp64 = 0x9fffffffbull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // else cases that can be rounded to a 32-bit int fall through // to '1 <= q + exp <= 10' } } } // n is not too large to be converted to int32 if -1/2 < n < 2^32 - 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 = 0x00000000; 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; if (C1 < midpoint64[ind]) { res = 0x00000000; // return 0 } else if (x_sign) { // n < 0 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } else { // n > 0 res = 0x00000001; // return +1 } // set inexact flag *pfpsf |= INEXACT_EXCEPTION; } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); } // 1 <= x < 2^32-1/2 so x can be rounded // to nearest to a 32-bit unsigned integer if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 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 // 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); }