| /* 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" |
| |
| /***************************************************************************** |
| * BID128_to_uint64_rnint |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, |
| bid128_to_uint64_rnint, x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| UINT64 tmp64; |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 fstar; |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // if n < -1/2 then n cannot be converted to uint64 with RN |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34 |
| // <=> C * 10^(21-q) > 0x05, 1<=q<=34 |
| if (q == 21) { |
| // C > 5 |
| if (C1.w[1] != 0 || C1.w[0] > 0x05ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to 64-bit unsigned int fall through |
| // to '1 <= q + exp <= 20' |
| } else { |
| // if 1 <= q <= 20 |
| // C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10 |
| // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // if n > 0 and q + exp = 20 |
| // if n >= 2^64 - 1/2 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) |
| // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 >= 0x9fffffffffffffffb |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) >= 0x9fffffffffffffffb |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff |
| C.w[0] = C1.w[0] + C1.w[0]; |
| C.w[1] = C1.w[1] + C1.w[1]; |
| if (C.w[0] < C1.w[0]) |
| C.w[1]++; |
| if (C.w[1] > 0x01 || (C.w[1] == 0x01 |
| && C.w[0] >= 0xffffffffffffffffull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C >= 0x9fffffffffffffffb |
| if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 |
| && C1.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits |
| C.w[1] = 0x09; |
| C.w[0] = 0xfffffffffffffffbull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] |
| || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[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 <= 20' |
| } |
| } |
| } |
| // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
| // return 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
| // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) |
| // res = 0 |
| // else if x > 0 |
| // res = +1 |
| // else // if x < 0 |
| // invalid exc |
| ind = q - 1; |
| if (ind <= 18) { // 0 <= ind <= 18 |
| if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { |
| res = 0x0000000000000000ull; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x8000000000000000ull; |
| *pfpsf |= INVALID_EXCEPTION; |
| } |
| } else { // 19 <= ind <= 33 |
| if ((C1.w[1] < midpoint128[ind - 19].w[1]) |
| || ((C1.w[1] == midpoint128[ind - 19].w[1]) |
| && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { |
| res = 0x0000000000000000ull; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x8000000000000000ull; |
| *pfpsf |= INVALID_EXCEPTION; |
| } |
| } |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded |
| // to nearest to a 64-bit unsigned signed integer |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^64-1/2 so x can be rounded |
| // to nearest to a 64-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; 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 127 bits |
| tmp64 = C1.w[0]; |
| if (ind <= 19) { |
| C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
| } else { |
| C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
| C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
| } |
| if (C1.w[0] < tmp64) |
| C1.w[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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = (C1 + 1/2 * 10^x) * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| fstar.w[3] = 0; |
| fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
| fstar.w[2] = P256.w[2]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| // if the result was a midpoint it was rounded away from zero, so |
| // it will need a correction |
| // check for midpoints |
| if ((fstar.w[3] == 0) && (fstar.w[2] == 0) |
| && (fstar.w[1] || fstar.w[0]) |
| && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
| // the result is a midpoint; round to nearest |
| if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
| // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
| Cstar.w[0]--; // Cstar.w[0] is now even |
| } // else MP in [ODD, EVEN] |
| } |
| res = Cstar.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint64_xrnint |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, |
| bid128_to_uint64_xrnint, x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| UINT64 tmp64, tmp64A; |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 fstar; |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // if n < -1/2 then n cannot be converted to uint64 with RN |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34 |
| // <=> C * 10^(21-q) > 0x05, 1<=q<=34 |
| if (q == 21) { |
| // C > 5 |
| if (C1.w[1] != 0 || C1.w[0] > 0x05ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to 64-bit unsigned int fall through |
| // to '1 <= q + exp <= 20' |
| } else { |
| // if 1 <= q <= 20 |
| // C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10 |
| // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // if n > 0 and q + exp = 20 |
| // if n >= 2^64 - 1/2 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) |
| // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 >= 0x9fffffffffffffffb |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) >= 0x9fffffffffffffffb |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff |
| C.w[0] = C1.w[0] + C1.w[0]; |
| C.w[1] = C1.w[1] + C1.w[1]; |
| if (C.w[0] < C1.w[0]) |
| C.w[1]++; |
| if (C.w[1] > 0x01 || (C.w[1] == 0x01 |
| && C.w[0] >= 0xffffffffffffffffull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C >= 0x9fffffffffffffffb |
| if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 |
| && C1.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits |
| C.w[1] = 0x09; |
| C.w[0] = 0xfffffffffffffffbull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] |
| || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[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 <= 20' |
| } |
| } |
| } |
| // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
| // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) |
| // res = 0 |
| // else if x > 0 |
| // res = +1 |
| // else // if x < 0 |
| // invalid exc |
| ind = q - 1; |
| if (ind <= 18) { // 0 <= ind <= 18 |
| if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { |
| res = 0x0000000000000000ull; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x8000000000000000ull; |
| *pfpsf |= INVALID_EXCEPTION; |
| BID_RETURN (res); |
| } |
| } else { // 19 <= ind <= 33 |
| if ((C1.w[1] < midpoint128[ind - 19].w[1]) |
| || ((C1.w[1] == midpoint128[ind - 19].w[1]) |
| && (C1.w[0] <= midpoint128[ind - 19].w[0]))) { |
| res = 0x0000000000000000ull; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x8000000000000000ull; |
| *pfpsf |= INVALID_EXCEPTION; |
| BID_RETURN (res); |
| } |
| } |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded |
| // to nearest to a 64-bit unsigned signed integer |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^64-1/2 so x can be rounded |
| // to nearest to a 64-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; 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 127 bits |
| tmp64 = C1.w[0]; |
| if (ind <= 19) { |
| C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
| } else { |
| C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
| C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
| } |
| if (C1.w[0] < tmp64) |
| C1.w[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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = (C1 + 1/2 * 10^x) * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| fstar.w[3] = 0; |
| fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
| fstar.w[2] = P256.w[2]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| // 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[1] > 0x8000000000000000ull || |
| (fstar.w[1] == 0x8000000000000000ull |
| && fstar.w[0] > 0x0ull)) { |
| // f* > 1/2 and the result may be exact |
| tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
| if (tmp64 > ten2mk128trunc[ind - 1].w[1] |
| || (tmp64 == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { |
| // 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 (ind - 1 <= 21) { // if 3 <= ind <= 21 |
| if (fstar.w[3] > 0x0 || |
| (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
| (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
| (fstar.w[1] || fstar.w[0]))) { |
| // f2* > 1/2 and the result may be exact |
| // Calculate f2* - 1/2 |
| tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
| tmp64A = fstar.w[3]; |
| if (tmp64 > fstar.w[2]) |
| tmp64A--; |
| if (tmp64A || tmp64 |
| || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // 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 22 <= ind <= 33 |
| if (fstar.w[3] > onehalf128[ind - 1] || |
| (fstar.w[3] == onehalf128[ind - 1] && |
| (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { |
| // f2* > 1/2 and the result may be exact |
| // Calculate f2* - 1/2 |
| tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
| if (tmp64 || fstar.w[2] |
| || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // 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[3] == 0) && (fstar.w[2] == 0) |
| && (fstar.w[1] || fstar.w[0]) |
| && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
| // the result is a midpoint; round to nearest |
| if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
| // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
| Cstar.w[0]--; // Cstar.w[0] is now even |
| } // else MP in [ODD, EVEN] |
| } |
| res = Cstar.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint64_floor |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, |
| bid128_to_uint64_floor, x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // if n < 0 then n cannot be converted to uint64 with RM |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| // if n > 0 and q + exp = 20 |
| // if n >= 2^64 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65 |
| // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 >= 0xa0000000000000000 |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] >= 0x0a) { |
| // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) >= 0xa0000000000000000 |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] >= 0x0a) { |
| // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C >= 0x10000000000000000 |
| if (C1.w[1] >= 0x01) { |
| // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C >= 0xa0000000000000000 |
| if (C1.w[1] >= 0x0a) { |
| // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits |
| C.w[1] = 0x0a; |
| C.w[0] = 0x0000000000000000ull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[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 <= 20' |
| } |
| } |
| // n is not too large to be converted to int64 if 0 <= n < 2^64 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) |
| // return 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // 1 <= x < 2^64 so x can be rounded |
| // down to a 64-bit unsigned signed integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
| // chop off ind digits from the lower part of C1 |
| // C1 fits in 127 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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = C1 * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| res = Cstar.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint64_xfloor |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, |
| bid128_to_uint64_xfloor, x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 fstar; |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // if n < 0 then n cannot be converted to uint64 with RM |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| // if n > 0 and q + exp = 20 |
| // if n >= 2^64 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65 |
| // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 >= 0xa0000000000000000 |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] >= 0x0a) { |
| // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) >= 0xa0000000000000000 |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] >= 0x0a) { |
| // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C >= 0x10000000000000000 |
| if (C1.w[1] >= 0x01) { |
| // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C >= 0xa0000000000000000 |
| if (C1.w[1] >= 0x0a) { |
| // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits |
| C.w[1] = 0x0a; |
| C.w[0] = 0x0000000000000000ull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[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 <= 20' |
| } |
| } |
| // n is not too large to be converted to int64 if 0 <= n < 2^64 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // 1 <= x < 2^64 so x can be rounded |
| // down to a 64-bit unsigned signed integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
| // chop off ind digits from the lower part of C1 |
| // C1 fits in 127 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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = C1 * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| fstar.w[3] = 0; |
| fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
| fstar.w[2] = P256.w[2]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| // 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[1] > ten2mk128trunc[ind - 1].w[1] || |
| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] && |
| fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // set the inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } // else the result is exact |
| } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
| if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // set the inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } // else the result is exact |
| } else { // if 22 <= ind <= 33 |
| if (fstar.w[3] || fstar.w[2] |
| || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // set the inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } // else the result is exact |
| } |
| |
| res = Cstar.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint64_ceil |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_ceil, |
| x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 fstar; |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // if n <= -1 then n cannot be converted to uint64 with RZ |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34 |
| // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34 |
| if (q == 21) { |
| // C >= a |
| if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to 64-bit unsigned int fall through |
| // to '1 <= q + exp <= 20' |
| } else { |
| // if 1 <= q <= 20 |
| // C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10 |
| // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // if n > 0 and q + exp = 20 |
| // if n > 2^64 - 1 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1) |
| // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 > 0x9fffffffffffffff6 |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] > 0xfffffffffffffff6ull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) > 0x9fffffffffffffff6 |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] > 0xfffffffffffffff6ull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C > 0xffffffffffffffff |
| if (C1.w[1]) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C > 0x9fffffffffffffff6 |
| if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 |
| && C1.w[0] > 0xfffffffffffffff6ull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits |
| C.w[1] = 0x09; |
| C.w[0] = 0xfffffffffffffff6ull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[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 <= 20' |
| } |
| } |
| } |
| // n is not too large to be converted to int64 if -1 < n <= 2^64 - 1 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) |
| // return 0 or 1 |
| if (x_sign) |
| res = 0x0000000000000000ull; |
| else |
| res = 0x0000000000000001ull; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded |
| // to zero to a 64-bit unsigned signed integer |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // 1 <= x <= 2^64 - 1 so x can be rounded |
| // to zero to a 64-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
| // chop off ind digits from the lower part of C1 |
| // C1 fits in 127 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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = C1 * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| fstar.w[3] = 0; |
| fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
| fstar.w[2] = P256.w[2]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| // if the result is positive and inexact, need to add 1 to it |
| |
| // 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[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| if (!x_sign) { // positive and inexact |
| Cstar.w[0]++; |
| if (Cstar.w[0] == 0x0) |
| Cstar.w[1]++; |
| } |
| } // else the result is exact |
| } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
| if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| if (!x_sign) { // positive and inexact |
| Cstar.w[0]++; |
| if (Cstar.w[0] == 0x0) |
| Cstar.w[1]++; |
| } |
| } // else the result is exact |
| } else { // if 22 <= ind <= 33 |
| if (fstar.w[3] || fstar.w[2] |
| || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| if (!x_sign) { // positive and inexact |
| Cstar.w[0]++; |
| if (Cstar.w[0] == 0x0) |
| Cstar.w[1]++; |
| } |
| } // else the result is exact |
| } |
| |
| res = Cstar.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint64_xceil |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, |
| bid128_to_uint64_xceil, x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 fstar; |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // if n <= -1 then n cannot be converted to uint64 with RZ |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34 |
| // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34 |
| if (q == 21) { |
| // C >= a |
| if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to 64-bit unsigned int fall through |
| // to '1 <= q + exp <= 20' |
| } else { |
| // if 1 <= q <= 20 |
| // C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10 |
| // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // if n > 0 and q + exp = 20 |
| // if n > 2^64 - 1 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1) |
| // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 > 0x9fffffffffffffff6 |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] > 0xfffffffffffffff6ull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) > 0x9fffffffffffffff6 |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] > 0xfffffffffffffff6ull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C > 0xffffffffffffffff |
| if (C1.w[1]) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C > 0x9fffffffffffffff6 |
| if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 |
| && C1.w[0] > 0xfffffffffffffff6ull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits |
| C.w[1] = 0x09; |
| C.w[0] = 0xfffffffffffffff6ull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[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 <= 20' |
| } |
| } |
| } |
| // n is not too large to be converted to int64 if -1 < n <= 2^64 - 1 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 or 1 |
| if (x_sign) |
| res = 0x0000000000000000ull; |
| else |
| res = 0x0000000000000001ull; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded |
| // to zero to a 64-bit unsigned signed integer |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // 1 <= x <= 2^64 - 1 so x can be rounded |
| // to zero to a 64-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
| // chop off ind digits from the lower part of C1 |
| // C1 fits in 127 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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = C1 * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| fstar.w[3] = 0; |
| fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
| fstar.w[2] = P256.w[2]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| // if the result is positive and inexact, need to add 1 to it |
| |
| // 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[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| if (!x_sign) { // positive and inexact |
| Cstar.w[0]++; |
| if (Cstar.w[0] == 0x0) |
| Cstar.w[1]++; |
| } |
| // set the inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } // else the result is exact |
| } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
| if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| if (!x_sign) { // positive and inexact |
| Cstar.w[0]++; |
| if (Cstar.w[0] == 0x0) |
| Cstar.w[1]++; |
| } |
| // set the inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } // else the result is exact |
| } else { // if 22 <= ind <= 33 |
| if (fstar.w[3] || fstar.w[2] |
| || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| if (!x_sign) { // positive and inexact |
| Cstar.w[0]++; |
| if (Cstar.w[0] == 0x0) |
| Cstar.w[1]++; |
| } |
| // set the inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } // else the result is exact |
| } |
| |
| res = Cstar.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint64_int |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_int, |
| x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // if n <= -1 then n cannot be converted to uint64 with RZ |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34 |
| // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34 |
| if (q == 21) { |
| // C >= a |
| if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to 64-bit unsigned int fall through |
| // to '1 <= q + exp <= 20' |
| } else { |
| // if 1 <= q <= 20 |
| // C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10 |
| // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // if n > 0 and q + exp = 20 |
| // if n >= 2^64 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65 |
| // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 >= 0xa0000000000000000 |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] >= 0x0a) { |
| // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) >= 0xa0000000000000000 |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] >= 0x0a) { |
| // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C >= 0x10000000000000000 |
| if (C1.w[1] >= 0x01) { |
| // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C >= 0xa0000000000000000 |
| if (C1.w[1] >= 0x0a) { |
| // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits |
| C.w[1] = 0x0a; |
| C.w[0] = 0x0000000000000000ull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] |
| || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[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 <= 20' |
| } |
| } |
| } |
| // n is not too large to be converted to int64 if -1 < n < 2^64 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) |
| // return 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded |
| // to zero to a 64-bit unsigned signed integer |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^64 so x can be rounded |
| // to zero to a 64-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
| // chop off ind digits from the lower part of C1 |
| // C1 fits in 127 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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = C1 * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| res = Cstar.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint64_xint |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_xint, |
| x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 fstar; |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // if n <= -1 then n cannot be converted to uint64 with RZ |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34 |
| // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34 |
| if (q == 21) { |
| // C >= a |
| if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to 64-bit unsigned int fall through |
| // to '1 <= q + exp <= 20' |
| } else { |
| // if 1 <= q <= 20 |
| // C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10 |
| // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // if n > 0 and q + exp = 20 |
| // if n >= 2^64 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65 |
| // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 >= 0xa0000000000000000 |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] >= 0x0a) { |
| // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) >= 0xa0000000000000000 |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] >= 0x0a) { |
| // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C >= 0x10000000000000000 |
| if (C1.w[1] >= 0x01) { |
| // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C >= 0xa0000000000000000 |
| if (C1.w[1] >= 0x0a) { |
| // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits |
| C.w[1] = 0x0a; |
| C.w[0] = 0x0000000000000000ull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] |
| || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[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 <= 20' |
| } |
| } |
| } |
| // n is not too large to be converted to int64 if -1 < n < 2^64 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded |
| // to zero to a 64-bit unsigned signed integer |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^64 so x can be rounded |
| // to zero to a 64-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
| // chop off ind digits from the lower part of C1 |
| // C1 fits in 127 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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = C1 * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| fstar.w[3] = 0; |
| fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
| fstar.w[2] = P256.w[2]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| // 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[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // set the inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } // else the result is exact |
| } else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
| if (fstar.w[2] || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // set the inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } // else the result is exact |
| } else { // if 22 <= ind <= 33 |
| if (fstar.w[3] || fstar.w[2] |
| || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // set the inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } // else the result is exact |
| } |
| |
| res = Cstar.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint64_rninta |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, |
| bid128_to_uint64_rninta, x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| UINT64 tmp64; |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // if n <= -1/2 then n cannot be converted to uint64 with RN |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34 |
| // <=> C * 10^(21-q) >= 0x05, 1<=q<=34 |
| if (q == 21) { |
| // C >= 5 |
| if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to 64-bit unsigned int fall through |
| // to '1 <= q + exp <= 20' |
| } else { |
| // if 1 <= q <= 20 |
| // C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10 |
| // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // if n > 0 and q + exp = 20 |
| // if n >= 2^64 - 1/2 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) |
| // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 >= 0x9fffffffffffffffb |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) >= 0x9fffffffffffffffb |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff |
| C.w[0] = C1.w[0] + C1.w[0]; |
| C.w[1] = C1.w[1] + C1.w[1]; |
| if (C.w[0] < C1.w[0]) |
| C.w[1]++; |
| if (C.w[1] > 0x01 || (C.w[1] == 0x01 |
| && C.w[0] >= 0xffffffffffffffffull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C >= 0x9fffffffffffffffb |
| if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 |
| && C1.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits |
| C.w[1] = 0x09; |
| C.w[0] = 0xfffffffffffffffbull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] |
| || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[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 <= 20' |
| } |
| } |
| } |
| // n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
| // return 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
| // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) |
| // res = 0 |
| // else if x > 0 |
| // res = +1 |
| // else // if x < 0 |
| // invalid exc |
| ind = q - 1; |
| if (ind <= 18) { // 0 <= ind <= 18 |
| if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { |
| res = 0x0000000000000000ull; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // 19 <= ind <= 33 |
| if ((C1.w[1] < midpoint128[ind - 19].w[1]) |
| || ((C1.w[1] == midpoint128[ind - 19].w[1]) |
| && (C1.w[0] < midpoint128[ind - 19].w[0]))) { |
| res = 0x0000000000000000ull; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded |
| // to nearest to a 64-bit unsigned signed integer |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^64-1/2 so x can be rounded |
| // to nearest to a 64-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; 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 127 bits |
| tmp64 = C1.w[0]; |
| if (ind <= 19) { |
| C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
| } else { |
| C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
| C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
| } |
| if (C1.w[0] < tmp64) |
| C1.w[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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = (C1 + 1/2 * 10^x) * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| |
| // if the result was a midpoint it was rounded away from zero |
| res = Cstar.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint64_xrninta |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, |
| bid128_to_uint64_xrninta, x) |
| |
| UINT64 res; |
| UINT64 x_sign; |
| UINT64 x_exp; |
| int exp; // unbiased exponent |
| // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
| UINT64 tmp64, tmp64A; |
| BID_UI64DOUBLE tmp1; |
| unsigned int x_nr_bits; |
| int q, ind, shift; |
| UINT128 C1, C; |
| UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
| UINT256 fstar; |
| UINT256 P256; |
| |
| // unpack x |
| x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
| x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
| C1.w[1] = x.w[1] & MASK_COEFF; |
| C1.w[0] = x.w[0]; |
| |
| // check for NaN or Infinity |
| if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
| // x is special |
| if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
| if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } else { // x is not a NaN, so it must be infinity |
| if (!x_sign) { // x is +inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| } |
| BID_RETURN (res); |
| } |
| } |
| // check for non-canonical values (after the check for special values) |
| if ((C1.w[1] > 0x0001ed09bead87c0ull) |
| || (C1.w[1] == 0x0001ed09bead87c0ull |
| && (C1.w[0] > 0x378d8e63ffffffffull)) |
| || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| |
| // q = nr. of decimal digits in x |
| // determine first the nr. of bits in x |
| if (C1.w[1] == 0) { |
| if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
| // split the 64-bit value in two 32-bit halves to avoid rounding errors |
| if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
| tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
| x_nr_bits = |
| 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } else { // x < 2^32 |
| tmp1.d = (double) (C1.w[0]); // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // if x < 2^53 |
| tmp1.d = (double) C1.w[0]; // exact conversion |
| x_nr_bits = |
| 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
| } |
| } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
| tmp1.d = (double) C1.w[1]; // exact conversion |
| x_nr_bits = |
| 65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
| || (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
| && C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
| q++; |
| } |
| exp = (x_exp >> 49) - 6176; |
| |
| if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1) |
| // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43... |
| // so x rounded to an integer may or may not fit in an unsigned 64-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 20' |
| if (x_sign) { // if n < 0 and q + exp = 20 |
| // if n <= -1/2 then n cannot be converted to uint64 with RN |
| // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34 |
| // <=> C * 10^(21-q) >= 0x05, 1<=q<=34 |
| if (q == 21) { |
| // C >= 5 |
| if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to 64-bit unsigned int fall through |
| // to '1 <= q + exp <= 20' |
| } else { |
| // if 1 <= q <= 20 |
| // C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10 |
| // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // if n > 0 and q + exp = 20 |
| // if n >= 2^64 - 1/2 then n is too large |
| // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2 |
| // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1) |
| // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34 |
| if (q == 1) { |
| // C * 10^20 >= 0x9fffffffffffffffb |
| __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]); // 10^20 * C |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q <= 19) { |
| // C * 10^(21-q) >= 0x9fffffffffffffffb |
| __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]); |
| if (C.w[1] > 0x09 || (C.w[1] == 0x09 |
| && C.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 20) { |
| // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff |
| C.w[0] = C1.w[0] + C1.w[0]; |
| C.w[1] = C1.w[1] + C1.w[1]; |
| if (C.w[0] < C1.w[0]) |
| C.w[1]++; |
| if (C.w[1] > 0x01 || (C.w[1] == 0x01 |
| && C.w[0] >= 0xffffffffffffffffull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else if (q == 21) { |
| // C >= 0x9fffffffffffffffb |
| if (C1.w[1] > 0x09 || (C1.w[1] == 0x09 |
| && C1.w[0] >= 0xfffffffffffffffbull)) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 64-bit int fall through |
| // to '1 <= q + exp <= 20' |
| } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13 |
| // C >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits |
| C.w[1] = 0x09; |
| C.w[0] = 0xfffffffffffffffbull; |
| __mul_128x64_to_128 (C, ten2k64[q - 21], C); |
| if (C1.w[1] > C.w[1] |
| || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[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 <= 20' |
| } |
| } |
| } |
| // n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 |
| res = 0x0000000000000000ull; |
| BID_RETURN (res); |
| } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
| // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) |
| // res = 0 |
| // else if x > 0 |
| // res = +1 |
| // else // if x < 0 |
| // invalid exc |
| ind = q - 1; |
| if (ind <= 18) { // 0 <= ind <= 18 |
| if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { |
| res = 0x0000000000000000ull; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x8000000000000000ull; |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } else { // 19 <= ind <= 33 |
| if ((C1.w[1] < midpoint128[ind - 19].w[1]) |
| || ((C1.w[1] == midpoint128[ind - 19].w[1]) |
| && (C1.w[0] < midpoint128[ind - 19].w[0]))) { |
| res = 0x0000000000000000ull; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x8000000000000000ull; |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| } |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19) |
| // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded |
| // to nearest to a 64-bit unsigned signed integer |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x8000000000000000ull; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^64-1/2 so x can be rounded |
| // to nearest to a 64-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20 |
| ind = -exp; // 1 <= ind <= 33; 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 127 bits |
| tmp64 = C1.w[0]; |
| if (ind <= 19) { |
| C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
| } else { |
| C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
| C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
| } |
| if (C1.w[0] < tmp64) |
| C1.w[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 <= 33 |
| // kx = 10^(-x) = ten2mk128[ind - 1] |
| // C* = (C1 + 1/2 * 10^x) * 10^(-x) |
| // the approximation of 10^(-x) was rounded up to 118 bits |
| __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[1] = P256.w[3]; |
| Cstar.w[0] = P256.w[2]; |
| fstar.w[3] = 0; |
| fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[1] = 0; |
| Cstar.w[0] = P256.w[3]; |
| fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
| fstar.w[2] = P256.w[2]; |
| fstar.w[1] = P256.w[1]; |
| fstar.w[0] = P256.w[0]; |
| } |
| // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
| // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
| // 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-128 = shiftright128[ind] |
| shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
| if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
| Cstar.w[0] = |
| (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
| // redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
| } else { // 22 <= ind - 1 <= 33 |
| Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
| } |
| // 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[1] > 0x8000000000000000ull || |
| (fstar.w[1] == 0x8000000000000000ull |
| && fstar.w[0] > 0x0ull)) { |
| // f* > 1/2 and the result may be exact |
| tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
| if (tmp64 > ten2mk128trunc[ind - 1].w[1] |
| || (tmp64 == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { |
| // 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 (ind - 1 <= 21) { // if 3 <= ind <= 21 |
| if (fstar.w[3] > 0x0 || |
| (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
| (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
| (fstar.w[1] || fstar.w[0]))) { |
| // f2* > 1/2 and the result may be exact |
| // Calculate f2* - 1/2 |
| tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
| tmp64A = fstar.w[3]; |
| if (tmp64 > fstar.w[2]) |
| tmp64A--; |
| if (tmp64A || tmp64 |
| || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // 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 22 <= ind <= 33 |
| if (fstar.w[3] > onehalf128[ind - 1] || |
| (fstar.w[3] == onehalf128[ind - 1] && |
| (fstar.w[2] || fstar.w[1] || fstar.w[0]))) { |
| // f2* > 1/2 and the result may be exact |
| // Calculate f2* - 1/2 |
| tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
| if (tmp64 || fstar.w[2] |
| || fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
| || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
| && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
| // 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.w[0]; // the result is positive |
| } else if (exp == 0) { |
| // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { |
| // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20 |
| // res = C * 10^exp (exact) - must fit in 64 bits |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
