| /* 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_uint32_rnint |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_rnint, x) |
| |
| unsigned int 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in an unsigned 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| if (x_sign) { // if n < 0 and q + exp = 10 |
| // if n < -1/2 then n cannot be converted to uint32 with RN |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 1/2 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x05, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 > 0x05ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 > 0x05 <=> |
| // C > 0x05 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 1/2 up) |
| tmp64 = 0x05ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } else { // if n > 0 and q + exp = 10 |
| // if n >= 2^32 - 1/2 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x9fffffffbull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=> |
| // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32-1/2 up) |
| tmp64 = 0x9fffffffbull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| } |
| // n is not too large to be converted to int32: -1/2 <= n < 2^32 - 1/2 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
| // return 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
| // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) |
| // res = 0 |
| // else if x > 0 |
| // res = +1 |
| // else // if x < 0 |
| // invalid exc |
| ind = q - 1; |
| if (ind <= 18) { // 0 <= ind <= 18 |
| if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { |
| res = 0x00000000; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x80000000; |
| *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 = 0x00000000; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x80000000; |
| *pfpsf |= INVALID_EXCEPTION; |
| } |
| } |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^32-1/2 so x can be rounded |
| // to nearest to a 32-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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 <= 10 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint32_xrnint |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_xrnint, x) |
| |
| unsigned int 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; |
| unsigned int tmp_inexact = 0; |
| |
| // 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in an unsigned 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| if (x_sign) { // if n < 0 and q + exp = 10 |
| // if n < -1/2 then n cannot be converted to uint32 with RN |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 1/2 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x05, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 > 0x05ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 > 0x05 <=> |
| // C > 0x05 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 1/2 up) |
| tmp64 = 0x05ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } else { // if n > 0 and q + exp = 10 |
| // if n >= 2^32 - 1/2 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x9fffffffbull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=> |
| // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32-1/2 up) |
| tmp64 = 0x9fffffffbull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| } |
| // n is not too large to be converted to int32: -1/2 <= n < 2^32 - 1/2 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
| // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) |
| // res = 0 |
| // else if x > 0 |
| // res = +1 |
| // else // if x < 0 |
| // invalid exc |
| ind = q - 1; |
| if (ind <= 18) { // 0 <= ind <= 18 |
| if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { |
| res = 0x00000000; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x80000000; |
| *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 = 0x00000000; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x80000000; |
| *pfpsf |= INVALID_EXCEPTION; |
| BID_RETURN (res); |
| } |
| } |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^32-1/2 so x can be rounded |
| // to nearest to a 32-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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; |
| tmp_inexact = 1; |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| // set the inexact flag |
| // *pfpsf |= INEXACT_EXCEPTION; |
| tmp_inexact = 1; |
| } |
| } 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; |
| tmp_inexact = 1; |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| // set the inexact flag |
| // *pfpsf |= INEXACT_EXCEPTION; |
| tmp_inexact = 1; |
| } |
| } 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; |
| tmp_inexact = 1; |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| // set the inexact flag |
| // *pfpsf |= INEXACT_EXCEPTION; |
| tmp_inexact = 1; |
| } |
| } |
| |
| // 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 |
| if (tmp_inexact) |
| *pfpsf |= INEXACT_EXCEPTION; |
| } else if (exp == 0) { |
| // 1 <= q <= 10 |
| // res = C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint32_floor |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_floor, x) |
| |
| unsigned int 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; |
| int is_inexact_gt_midpoint = 0; |
| int is_midpoint_lt_even = 0; |
| |
| // 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| // x < 0 is invalid |
| if (x_sign) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // x > 0 from this point on |
| // 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in a signed 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| // n > 0 and q + exp = 10 |
| // if n >= 2^32 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0xa00000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=> |
| // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32 up) |
| tmp64 = 0xa00000000ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| // n is not too large to be converted to int32: 0 <= n < 2^31 |
| // 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) or n = +0.c(0)c(1)...c(q-1) |
| // return 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| // 1 <= x < 2^32 so x can be rounded down to a 32-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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])) { |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| is_inexact_gt_midpoint = 1; |
| } |
| } 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])) { |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| is_inexact_gt_midpoint = 1; |
| } |
| } 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])) { |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| is_inexact_gt_midpoint = 1; |
| } |
| } |
| |
| // 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 |
| is_inexact_gt_midpoint = 0; |
| } else { // else MP in [ODD, EVEN] |
| is_midpoint_lt_even = 1; |
| is_inexact_gt_midpoint = 0; |
| } |
| } |
| // general correction for RM |
| if (is_midpoint_lt_even || is_inexact_gt_midpoint) { |
| Cstar.w[0] = Cstar.w[0] - 1; |
| } else { |
| ; // the result is already correct |
| } |
| res = Cstar.w[0]; |
| } else if (exp == 0) { |
| // 1 <= q <= 10 |
| // res = +C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = +C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint32_xfloor |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_xfloor, x) |
| |
| unsigned int 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; |
| int is_inexact_gt_midpoint = 0; |
| int is_midpoint_lt_even = 0; |
| |
| // 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else { // x is not special and is not zero |
| // x < 0 is invalid |
| if (x_sign) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // x > 0 from this point on |
| // 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in a signed 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| // n > 0 and q + exp = 10 |
| // if n >= 2^32 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0xa00000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=> |
| // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32 up) |
| tmp64 = 0xa00000000ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| // n is not too large to be converted to int32: 0 <= n < 2^31 |
| // 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) or n = +0.c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| // 1 <= x < 2^32 so x can be rounded down to a 32-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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; |
| is_inexact_gt_midpoint = 1; |
| } |
| } 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; |
| is_inexact_gt_midpoint = 1; |
| } |
| } 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; |
| is_inexact_gt_midpoint = 1; |
| } |
| } |
| |
| // 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 |
| is_inexact_gt_midpoint = 0; |
| } else { // else MP in [ODD, EVEN] |
| is_midpoint_lt_even = 1; |
| is_inexact_gt_midpoint = 0; |
| } |
| } |
| // general correction for RM |
| if (is_midpoint_lt_even || is_inexact_gt_midpoint) { |
| Cstar.w[0] = Cstar.w[0] - 1; |
| } else { |
| ; // the result is already correct |
| } |
| res = Cstar.w[0]; |
| } else if (exp == 0) { |
| // 1 <= q <= 10 |
| // res = +C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = +C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint32_ceil |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_ceil, x) |
| |
| unsigned int 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; |
| int is_inexact_lt_midpoint = 0; |
| int is_midpoint_gt_even = 0; |
| |
| // 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in a signed 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| if (x_sign) { // if n < 0 and q + exp = 10 |
| // if n <= -1 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x0aull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=> |
| // C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 1 up) |
| tmp64 = 0x0aull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } else { // if n > 0 and q + exp = 10 |
| // if n > 2^32 - 1 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 > 0x9fffffff6ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6 <=> |
| // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32 up) |
| tmp64 = 0x9fffffff6ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| } |
| // n is not too large to be converted to int32: -2^32-1 < n <= 2^32-1 |
| // 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) or n = +/-0.c(0)c(1)...c(q-1) |
| // return 0 |
| if (x_sign) |
| res = 0x00000000; |
| else |
| res = 0x00000001; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| // -2^32-1 < x <= -1 or 1 <= x <= 2^32-1 so x can be rounded |
| // toward positive infinity to a 32-bit signed integer |
| if (x_sign) { // x <= -1 is invalid |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // x > 0 from this point on |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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])) { |
| is_inexact_lt_midpoint = 1; |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| ; |
| } |
| } 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])) { |
| is_inexact_lt_midpoint = 1; |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| } |
| } 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])) { |
| is_inexact_lt_midpoint = 1; |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| ; |
| } |
| } |
| |
| // 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 |
| is_midpoint_gt_even = 1; |
| is_inexact_lt_midpoint = 0; |
| } else { // else MP in [ODD, EVEN] |
| is_inexact_lt_midpoint = 0; |
| } |
| } |
| // general correction for RM |
| if (is_midpoint_gt_even || is_inexact_lt_midpoint) { |
| Cstar.w[0] = Cstar.w[0] + 1; |
| } else { |
| ; // the result is already correct |
| } |
| res = Cstar.w[0]; |
| } else if (exp == 0) { |
| // 1 <= q <= 10 |
| // res = +C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = +C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint32_xceil |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_xceil, x) |
| |
| unsigned int 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; |
| int is_inexact_lt_midpoint = 0; |
| int is_midpoint_gt_even = 0; |
| |
| // 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in a signed 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| if (x_sign) { // if n < 0 and q + exp = 10 |
| // if n <= -1 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x0aull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=> |
| // C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 1 up) |
| tmp64 = 0x0aull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } else { // if n > 0 and q + exp = 10 |
| // if n > 2^32 - 1 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 > 0x9fffffff6ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6 <=> |
| // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32 up) |
| tmp64 = 0x9fffffff6ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| } |
| // n is not too large to be converted to int32: -2^32-1 < n <= 2^32-1 |
| // 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) or n = +/-0.c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 |
| if (x_sign) |
| res = 0x00000000; |
| else |
| res = 0x00000001; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| // -2^32-1 < x <= -1 or 1 <= x <= 2^32-1 so x can be rounded |
| // toward positive infinity to a 32-bit signed integer |
| if (x_sign) { // x <= -1 is invalid |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // x > 0 from this point on |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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; |
| is_inexact_lt_midpoint = 1; |
| } // 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; |
| is_inexact_lt_midpoint = 1; |
| } // 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; |
| is_inexact_lt_midpoint = 1; |
| } // 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 |
| is_midpoint_gt_even = 1; |
| is_inexact_lt_midpoint = 0; |
| } else { // else MP in [ODD, EVEN] |
| is_inexact_lt_midpoint = 0; |
| } |
| } |
| // general correction for RM |
| if (is_midpoint_gt_even || is_inexact_lt_midpoint) { |
| Cstar.w[0] = Cstar.w[0] + 1; |
| } else { |
| ; // the result is already correct |
| } |
| res = Cstar.w[0]; |
| } else if (exp == 0) { |
| // 1 <= q <= 10 |
| // res = +C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = +C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint32_int |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_int, x) |
| |
| int 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; |
| int is_inexact_gt_midpoint = 0; |
| int is_midpoint_lt_even = 0; |
| |
| // 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in a signed 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| if (x_sign) { // if n < 0 and q + exp = 10 |
| // if n <= -1 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x0aull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit uint fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=> |
| // C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 1 up) |
| tmp64 = 0x0aull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } else { // if n > 0 and q + exp = 10 |
| // if n >= 2^32 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0xa00000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit uint fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=> |
| // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32 up) |
| tmp64 = 0xa00000000ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| } |
| // n is not too large to be converted to uint32: -2^32 < n < 2^32 |
| // 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) or n = +/-0.c(0)c(1)...c(q-1) |
| // return 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| // x = d(0)...d(k).d(k+1)..., k >= 0, d(0) != 0 |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // x > 0 from this point on |
| // 1 <= x < 2^32 so x can be rounded to zero to a 32-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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])) { |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| is_inexact_gt_midpoint = 1; |
| } |
| } 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])) { |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| is_inexact_gt_midpoint = 1; |
| } |
| } 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])) { |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| is_inexact_gt_midpoint = 1; |
| } |
| } |
| |
| // 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 |
| is_inexact_gt_midpoint = 0; |
| } else { // else MP in [ODD, EVEN] |
| is_midpoint_lt_even = 1; |
| is_inexact_gt_midpoint = 0; |
| } |
| } |
| // general correction for RZ |
| if (is_midpoint_lt_even || is_inexact_gt_midpoint) { |
| Cstar.w[0] = Cstar.w[0] - 1; |
| } else { |
| ; // exact, the result is already correct |
| } |
| res = Cstar.w[0]; |
| } else if (exp == 0) { |
| // 1 <= q <= 10 |
| // res = +C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = +C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint32_xint |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_xint, x) |
| |
| int 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; |
| int is_inexact_gt_midpoint = 0; |
| int is_midpoint_lt_even = 0; |
| |
| // 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in a signed 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| if (x_sign) { // if n < 0 and q + exp = 10 |
| // if n <= -1 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x0aull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit uint fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x0a <=> |
| // C >= 0x0a * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 1 up) |
| tmp64 = 0x0aull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } else { // if n > 0 and q + exp = 10 |
| // if n >= 2^32 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0xa00000000ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit uint fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000 <=> |
| // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32 up) |
| tmp64 = 0xa00000000ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| } |
| // n is not too large to be converted to uint32: -2^32 < n < 2^32 |
| // 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) or n = +/-0.c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| // x = d(0)...d(k).d(k+1)..., k >= 0, d(0) != 0 |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // x > 0 from this point on |
| // 1 <= x < 2^32 so x can be rounded to zero to a 32-bit unsigned integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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; |
| is_inexact_gt_midpoint = 1; |
| } |
| } 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; |
| is_inexact_gt_midpoint = 1; |
| } |
| } 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; |
| is_inexact_gt_midpoint = 1; |
| } |
| } |
| |
| // 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 |
| is_inexact_gt_midpoint = 0; |
| } else { // else MP in [ODD, EVEN] |
| is_midpoint_lt_even = 1; |
| is_inexact_gt_midpoint = 0; |
| } |
| } |
| // general correction for RZ |
| if (is_midpoint_lt_even || is_inexact_gt_midpoint) { |
| Cstar.w[0] = Cstar.w[0] - 1; |
| } else { |
| ; // exact, the result is already correct |
| } |
| res = Cstar.w[0]; |
| } else if (exp == 0) { |
| // 1 <= q <= 10 |
| // res = +C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = +C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint32_rninta |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_rninta, x) |
| |
| unsigned int 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in a signed 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| if (x_sign) { // if n < 0 and q + exp = 10 |
| // if n <= -1/2 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1/2 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x05ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05 <=> |
| // C >= 0x05 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 1/2 up) |
| tmp64 = 0x05ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } else { // if n > 0 and q + exp = 10 |
| // if n >= 2^32 - 1/2 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x9fffffffbull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=> |
| // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32-1/2 up) |
| tmp64 = 0x9fffffffbull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| } |
| // n is not too large to be converted to int32: -1/2 < n < 2^32 - 1/2 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
| // return 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
| // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) |
| // res = 0 |
| // else if x > 0 |
| // res = +1 |
| // else // if x < 0 |
| // invalid exc |
| ind = q - 1; |
| if (ind <= 18) { // 0 <= ind <= 18 |
| if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { |
| res = 0x00000000; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x80000000; |
| *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 = 0x00000000; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x80000000; |
| *pfpsf |= INVALID_EXCEPTION; |
| } |
| } |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^31-1/2 so x can be rounded |
| // to nearest-away to a 32-bit signed integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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 already rounded away from zero |
| res = Cstar.w[0]; // always positive |
| // no need to check for midpoints - already rounded away from zero! |
| } else if (exp == 0) { |
| // 1 <= q <= 10 |
| // res = +C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = +C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
| |
| /***************************************************************************** |
| * BID128_to_uint32_xrninta |
| ****************************************************************************/ |
| |
| BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (unsigned int, |
| bid128_to_uint32_xrninta, x) |
| |
| unsigned int 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; |
| unsigned int tmp_inexact = 0; |
| |
| // 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 = 0x80000000; |
| } else { // x is QNaN |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x80000000; |
| } else { // x is -inf |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| } |
| 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 = 0x00000000; |
| BID_RETURN (res); |
| } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
| // x is 0 |
| res = 0x00000000; |
| 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) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
| // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
| // so x rounded to an integer may or may not fit in a signed 32-bit int |
| // the cases that do not fit are identified here; the ones that fit |
| // fall through and will be handled with other cases further, |
| // under '1 <= q + exp <= 10' |
| if (x_sign) { // if n < 0 and q + exp = 10 |
| // if n <= -1/2 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 1/2 |
| // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x05ull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x05 <=> |
| // C >= 0x05 * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 1/2 up) |
| tmp64 = 0x05ull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } else { // if n > 0 and q + exp = 10 |
| // if n >= 2^32 - 1/2 then n is too large |
| // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 |
| // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=34 |
| if (q <= 11) { |
| tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
| // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
| if (tmp64 >= 0x9fffffffbull) { |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
| // 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb <=> |
| // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 |
| // (scale 2^32-1/2 up) |
| tmp64 = 0x9fffffffbull; |
| if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
| __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
| } else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
| __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
| } |
| 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 = 0x80000000; |
| BID_RETURN (res); |
| } |
| // else cases that can be rounded to a 32-bit int fall through |
| // to '1 <= q + exp <= 10' |
| } |
| } |
| } |
| // n is not too large to be converted to int32: -1/2 < n < 2^32 - 1/2 |
| // Note: some of the cases tested for above fall through to this point |
| if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| // return 0 |
| res = 0x00000000; |
| BID_RETURN (res); |
| } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
| // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) |
| // res = 0 |
| // else if x > 0 |
| // res = +1 |
| // else // if x < 0 |
| // invalid exc |
| ind = q - 1; |
| if (ind <= 18) { // 0 <= ind <= 18 |
| if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { |
| res = 0x00000000; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x80000000; |
| *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 = 0x00000000; // return 0 |
| } else if (!x_sign) { // n > 0 |
| res = 0x00000001; // return +1 |
| } else { |
| res = 0x80000000; |
| *pfpsf |= INVALID_EXCEPTION; |
| BID_RETURN (res); |
| } |
| } |
| // set inexact flag |
| *pfpsf |= INEXACT_EXCEPTION; |
| } else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
| if (x_sign) { // x <= -1 |
| // set invalid flag |
| *pfpsf |= INVALID_EXCEPTION; |
| // return Integer Indefinite |
| res = 0x80000000; |
| BID_RETURN (res); |
| } |
| // 1 <= x < 2^31-1/2 so x can be rounded |
| // to nearest-away to a 32-bit signed integer |
| if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
| 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 already rounded away from zero |
| // 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; |
| tmp_inexact = 1; |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| // set the inexact flag |
| // *pfpsf |= INEXACT_EXCEPTION; |
| tmp_inexact = 1; |
| } |
| } 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; |
| tmp_inexact = 1; |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| // set the inexact flag |
| // *pfpsf |= INEXACT_EXCEPTION; |
| tmp_inexact = 1; |
| } |
| } 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; |
| tmp_inexact = 1; |
| } // else the result is exact |
| } else { // the result is inexact; f2* <= 1/2 |
| // set the inexact flag |
| // *pfpsf |= INEXACT_EXCEPTION; |
| tmp_inexact = 1; |
| } |
| } |
| // no need to check for midpoints - already rounded away from zero! |
| res = Cstar.w[0]; // the result is positive |
| if (tmp_inexact) |
| *pfpsf |= INEXACT_EXCEPTION; |
| } else if (exp == 0) { |
| // 1 <= q <= 10 |
| // res = +C (exact) |
| res = C1.w[0]; |
| } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
| // res = +C * 10^exp (exact) |
| res = C1.w[0] * ten2k64[exp]; |
| } |
| } |
| } |
| |
| BID_RETURN (res); |
| } |
