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/* Copyright (C) 2007, 2009 Free Software Foundation, Inc. This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. Under Section 7 of GPL version 3, you are granted additional permissions described in the GCC Runtime Library Exception, version 3.1, as published by the Free Software Foundation. You should have received a copy of the GNU General Public License and a copy of the GCC Runtime Library Exception along with this program; see the files COPYING3 and COPYING.RUNTIME respectively. If not, see <http://www.gnu.org/licenses/>. */ #include "bid_internal.h" /***************************************************************************** * BID64_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); }
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