X-Git-Url: https://oss.titaniummirror.com/gitweb?a=blobdiff_plain;f=libgcc%2Fconfig%2Flibbid%2Fbid64_to_int64.c;fp=libgcc%2Fconfig%2Flibbid%2Fbid64_to_int64.c;h=e56bcbac5a854efa664a936152fa376a88b98f22;hb=6fed43773c9b0ce596dca5686f37ac3fc0fa11c0;hp=0000000000000000000000000000000000000000;hpb=27b11d56b743098deb193d510b337ba22dc52e5c;p=msp430-gcc.git diff --git a/libgcc/config/libbid/bid64_to_int64.c b/libgcc/config/libbid/bid64_to_int64.c new file mode 100644 index 00000000..e56bcbac --- /dev/null +++ b/libgcc/config/libbid/bid64_to_int64.c @@ -0,0 +1,2329 @@ +/* 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 +. */ + +#include "bid_internal.h" + +/***************************************************************************** + * BID64_to_int64_rnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_rnint (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_rnint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+1), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000005, 1<=q<=16 + // <=> C * 10^(20-q) > 0x50000000000000005, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] > 0x05ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; // 0 <= ind <= 15 + if (C1 <= midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + 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] + } + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xrnint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xrnint (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xrnint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64+1), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000005, 1<=q<=16 + // <=> C * 10^(20-q) > 0x50000000000000005, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] > 0x05ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1/2 <= n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; // 0 <= ind <= 15 + if (C1 <= midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1/2 <= x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + 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) { + 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] + } + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_floor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_floor (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_floor (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000000, 1<=q<=16 + // <=> C * 10^(20-q) > 0x50000000000000000, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] != 0)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] >= 0x05ull) { + // actually C.w[1] == 0x05ull && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63 <= n < 2^63 + // 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 -1 or 0 + if (x_sign) + res = 0xffffffffffffffffull; + else + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63 <= x <= -1 or 1 <= x < 2^63 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + 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] + if (x_sign) { // negative and inexact + 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] + if (x_sign) { // negative and inexact + Cstar++; + } + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xfloor + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xfloor (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xfloor (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } + // x is not special and is not zero + + // q = nr. of decimal digits in x (1 <= q <= 54) + // determine first the nr. of bits in x + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + // split the 64-bit value in two 32-bit halves to avoid rounding errors + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion + x_nr_bits = + 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion + x_nr_bits = + 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); + } + q = nr_digits[x_nr_bits - 1].digits; + if (q == 0) { + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) + q++; + } + exp = x_exp - 398; // unbiased exponent + + if ((q + exp) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n < -2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 > 0x50000000000000000, 1<=q<=16 + // <=> C * 10^(20-q) > 0x50000000000000000, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] != 0)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] >= 0x05ull) { + // actually C.w[1] == 0x05ull && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63 <= n < 2^63 + // 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 -1 or 0 + if (x_sign) + res = 0xffffffffffffffffull; + else + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63 <= x <= -1 or 1 <= x < 2^63 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + 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] + if (x_sign) { // negative and inexact + 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] + if (x_sign) { // negative and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_ceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_ceil (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_ceil (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n > 2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 - 1 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64-2), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 0x4fffffffffffffff6, 1<=q<=16 + // <=> if C * 10^(20-q) > 0x4fffffffffffffff6, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffff6ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // 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 or 1 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x <= 2^63 - 1 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + 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] + if (!x_sign) { // positive and inexact + 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] + if (!x_sign) { // positive and inexact + Cstar++; + } + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xceil + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xceil (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xceil (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n > 2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) > 2^63 - 1 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 5*(2^64-2), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 > 0x4fffffffffffffff6, 1<=q<=16 + // <=> if C * 10^(20-q) > 0x4fffffffffffffff6, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffff6ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] > 0xfffffffffffffff6ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // 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 or 1 + if (x_sign) + res = 0x00000000; + else + res = 0x00000001; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x <= 2^63 - 1 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + 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] + if (!x_sign) { // positive and inexact + 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] + if (!x_sign) { // positive and inexact + Cstar++; + } + // set the inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } // else the result is exact + } + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_int + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_int (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_int (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] >= 0x05ull) { + // actually C.w[1] == 0x05ull && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x < 2^63 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + 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; + + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xint + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xint (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xint (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) +{ +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+2), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x5000000000000000a, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x5000000000000000a, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x5000000000000000a, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x0aull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*2^64, 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000000, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x50000000000000000, 1<=q<=16 + C.w[1] = 0x0000000000000005ull; + C.w[0] = 0x0000000000000000ull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] >= 0x05ull) { + // actually C.w[1] == 0x05ull && C.w[0] >= 0x0000000000000000ull) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1 < n < 2^63 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) <= 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1 < x <= -1 or 1 <= x < 2^63 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + 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 + } + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_rninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_rninta (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_rninta (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+1), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000005, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x50000000000000005, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x05ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1/2 < n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; // 0 <= ind <= 15 + if (C1 < midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1/2 < x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + // chop off ind digits from the lower part of C1 + // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits + C1 = C1 + midpoint64[ind - 1]; + // calculate C* and f* + // C* is actually floor(C*) in this case + // C* and f* need shifting and masking, as shown by + // shiftright128[] and maskhigh128[] + // 1 <= x <= 15 + // kx = 10^(-x) = ten2mk64[ind - 1] + // C* = (C1 + 1/2 * 10^x) * 10^(-x) + // the approximation of 10^(-x) was rounded up to 54 bits + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); + Cstar = P128.w[1]; + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 + // if (0 < f* < 10^(-x)) then the result is a midpoint + // if floor(C*) is even then C* = floor(C*) - logical right + // shift; C* has p decimal digits, correct by Prop. 1) + // else if floor(C*) is odd C* = floor(C*)-1 (logical right + // shift; C* has p decimal digits, correct by Pr. 1) + // else + // C* = floor(C*) (logical right shift; C has p decimal digits, + // correct by Property 1) + // n = C* * 10^(e+x) + + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 + Cstar = Cstar >> shift; + + // if the result was a midpoint it was rounded away from zero + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +} + +/***************************************************************************** + * BID64_to_int64_xrninta + ****************************************************************************/ + +#if DECIMAL_CALL_BY_REFERENCE +void +bid64_to_int64_xrninta (SINT64 * pres, UINT64 * px + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { + UINT64 x = *px; +#else +SINT64 +bid64_to_int64_xrninta (UINT64 x + _EXC_FLAGS_PARAM _EXC_MASKS_PARAM + _EXC_INFO_PARAM) { +#endif + SINT64 res; + UINT64 x_sign; + UINT64 x_exp; + int exp; // unbiased exponent + // Note: C1 represents x_significand (UINT64) + UINT64 tmp64; + BID_UI64DOUBLE tmp1; + unsigned int x_nr_bits; + int q, ind, shift; + UINT64 C1; + UINT128 C; + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT128 fstar; + UINT128 P128; + + // check for NaN or Infinity + if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // unpack x + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => + if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; + if (C1 > 9999999999999999ull) { // non-canonical + x_exp = 0; + C1 = 0; + } + } else { + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + C1 = x & MASK_BINARY_SIG1; + } + + // check for zeros (possibly from non-canonical values) + if (C1 == 0x0ull) { + // x is 0 + res = 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) > 19) { // x >= 10^19 ~= 2^63.11... (cannot fit in SINT64) + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 19) { // x = c(0)c(1)...c(18).c(19)...c(q-1) + // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... + // so x rounded to an integer may or may not fit in a signed 64-bit int + // the cases that do not fit are identified here; the ones that fit + // fall through and will be handled with other cases further, + // under '1 <= q + exp <= 19' + if (x_sign) { // if n < 0 and q + exp = 19 + // if n <= -2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63+1/2 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64+1), 1<=q<=16 + // <=> 0.c(0)c(1)...c(q-1) * 10^20 >= 0x50000000000000005, 1<=q<=16 + // <=> C * 10^(20-q) >= 0x50000000000000005, 1<=q<=16 + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + // Note: C1 * 10^(11-q) has 19 or 20 digits; 0x50000000000000005, has 20 + if (C.w[1] > 0x05ull || (C.w[1] == 0x05ull && C.w[0] >= 0x05ull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } else { // if n > 0 and q + exp = 19 + // if n >= 2^63 - 1/2 then n is too large + // too large if c(0)c(1)...c(18).c(19)...c(q-1) >= 2^63-1/2 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 5*(2^64-1), 1<=q<=16 + // <=> if 0.c(0)c(1)...c(q-1) * 10^20 >= 0x4fffffffffffffffb, 1<=q<=16 + // <=> if C * 10^(20-q) >= 0x4fffffffffffffffb, 1<=q<=16 + C.w[1] = 0x0000000000000004ull; + C.w[0] = 0xfffffffffffffffbull; + // 1 <= q <= 16 => 4 <= 20-q <= 19 => 10^(20-q) is 64-bit, and so is C1 + __mul_64x64_to_128MACH (C, C1, ten2k64[20 - q]); + if (C.w[1] > 0x04ull || + (C.w[1] == 0x04ull && C.w[0] >= 0xfffffffffffffffbull)) { + // set invalid flag + *pfpsf |= INVALID_EXCEPTION; + // return Integer Indefinite + res = 0x8000000000000000ull; + BID_RETURN (res); + } + // else cases that can be rounded to a 64-bit int fall through + // to '1 <= q + exp <= 19' + } // end else if n > 0 and q + exp = 19 + } // end else if ((q + exp) == 19) + + // n is not too large to be converted to int64: -2^63-1/2 < n < 2^63-1/2 + // Note: some of the cases tested for above fall through to this point + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + // return 0 + res = 0x0000000000000000ull; + BID_RETURN (res); + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) + // res = 0 + // else + // res = +/-1 + ind = q - 1; // 0 <= ind <= 15 + if (C1 < midpoint64[ind]) { + res = 0x0000000000000000ull; // return 0 + } else if (x_sign) { // n < 0 + res = 0xffffffffffffffffull; // return -1 + } else { // n > 0 + res = 0x0000000000000001ull; // return +1 + } + // set inexact flag + *pfpsf |= INEXACT_EXCEPTION; + } else { // if (1 <= q + exp <= 19, 1 <= q <= 16, -15 <= exp <= 18) + // -2^63-1/2 < x <= -1 or 1 <= x < 2^63-1/2 so x can be rounded + // to nearest to a 64-bit signed integer + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 19 + 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) { + 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 + if (x_sign) + res = -Cstar; + else + res = Cstar; + } else if (exp == 0) { + // 1 <= q <= 16 + // res = +/-C (exact) + if (x_sign) + res = -C1; + else + res = C1; + } else { // if (exp > 0) => 1 <= exp <= 18, 1 <= q <= 16, 2 <= q + exp <= 20 + // (the upper limit of 20 on q + exp is due to the fact that + // +/-C * 10^exp is guaranteed to fit in 64 bits) + // res = +/-C * 10^exp (exact) + if (x_sign) + res = -C1 * ten2k64[exp]; + else + res = C1 * ten2k64[exp]; + } + } + BID_RETURN (res); +}