| /* Copyright (C) 2007-2021 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); |
| } |
