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/* Copyright (C) 2007-2015 Free Software Foundation, Inc. |
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This file is part of GCC. |
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GCC is free software; you can redistribute it and/or modify it under |
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the terms of the GNU General Public License as published by the Free |
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Software Foundation; either version 3, or (at your option) any later |
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version. |
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY |
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WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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for more details. |
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Under Section 7 of GPL version 3, you are granted additional |
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permissions described in the GCC Runtime Library Exception, version |
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3.1, as published by the Free Software Foundation. |
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You should have received a copy of the GNU General Public License and |
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a copy of the GCC Runtime Library Exception along with this program; |
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see |
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. */ |
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#include "bid_internal.h" |
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/***************************************************************************** |
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* BID64_to_uint32_rnint |
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****************************************************************************/ |
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#if DECIMAL_CALL_BY_REFERENCE |
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void |
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bid64_to_uint32_rnint (unsigned int *pres, UINT64 * px |
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_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
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_EXC_INFO_PARAM) { |
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UINT64 x = *px; |
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#else |
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unsigned int |
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bid64_to_uint32_rnint (UINT64 x |
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_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
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_EXC_INFO_PARAM) { |
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#endif |
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unsigned int res; |
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UINT64 x_sign; |
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UINT64 x_exp; |
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int exp; // unbiased exponent |
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// Note: C1 represents x_significand (UINT64) |
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UINT64 tmp64; |
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BID_UI64DOUBLE tmp1; |
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unsigned int x_nr_bits; |
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int q, ind, shift; |
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UINT64 C1; |
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UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
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UINT128 fstar; |
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UINT128 P128; |
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// check for NaN or Infinity |
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if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return Integer Indefinite |
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res = 0x80000000; |
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BID_RETURN (res); |
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} |
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// unpack x |
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x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
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x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
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C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
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if (C1 > 9999999999999999ull) { // non-canonical |
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x_exp = 0; |
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C1 = 0; |
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} |
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} else { |
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x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
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C1 = x & MASK_BINARY_SIG1; |
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} |
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// check for zeros (possibly from non-canonical values) |
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if (C1 == 0x0ull) { |
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// x is 0 |
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res = 0x00000000; |
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BID_RETURN (res); |
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} |
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// x is not special and is not zero |
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// q = nr. of decimal digits in x (1 <= q <= 54) |
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// determine first the nr. of bits in x |
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if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
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// split the 64-bit value in two 32-bit halves to avoid rounding errors |
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if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
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tmp1.d = (double) (C1 >> 32); // exact conversion |
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x_nr_bits = |
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33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
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} else { // x < 2^32 |
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tmp1.d = (double) C1; // exact conversion |
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x_nr_bits = |
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
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} |
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} else { // if x < 2^53 |
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tmp1.d = (double) C1; // exact conversion |
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x_nr_bits = |
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
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} |
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q = nr_digits[x_nr_bits - 1].digits; |
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if (q == 0) { |
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q = nr_digits[x_nr_bits - 1].digits1; |
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if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
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q++; |
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} |
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exp = x_exp - 398; // unbiased exponent |
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if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return Integer Indefinite |
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res = 0x80000000; |
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BID_RETURN (res); |
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} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
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// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
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// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
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// the cases that do not fit are identified here; the ones that fit |
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// fall through and will be handled with other cases further, |
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// under '1 <= q + exp <= 10' |
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if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 |
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// => set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return Integer Indefinite |
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res = 0x80000000; |
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BID_RETURN (res); |
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} else { // if n > 0 and q + exp = 10 |
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// if n >= 2^32 - 1/2 then n is too large |
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// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 |
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// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 |
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// <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 |
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if (q <= 11) { |
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// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits |
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tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
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// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
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if (tmp64 >= 0x9fffffffbull) { |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return Integer Indefinite |
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res = 0x80000000; |
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BID_RETURN (res); |
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} |
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// else cases that can be rounded to a 32-bit unsigned int fall through |
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// to '1 <= q + exp <= 10' |
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} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
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// C * 10^(11-q) >= 0x9fffffffb <=> |
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// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 |
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// (scale 2^32-1/2 up) |
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// Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 |
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tmp64 = 0x9fffffffbull * ten2k64[q - 11]; |
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if (C1 >= tmp64) { |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return Integer Indefinite |
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res = 0x80000000; |
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BID_RETURN (res); |
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} |
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// else cases that can be rounded to a 32-bit int fall through |
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// to '1 <= q + exp <= 10' |
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} |
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} |
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} |
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// n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 1/2 |
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// Note: some of the cases tested for above fall through to this point |
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if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
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// return 0 |
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res = 0x00000000; |
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BID_RETURN (res); |
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} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
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// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) |
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// res = 0 |
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// else if x > 0 |
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// res = +1 |
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// else // if x < 0 |
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// invalid exc |
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ind = q - 1; |
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if (C1 <= midpoint64[ind]) { |
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res = 0x00000000; // return 0 |
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} else if (x_sign) { // n < 0 |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return Integer Indefinite |
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res = 0x80000000; |
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BID_RETURN (res); |
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} else { // n > 0 |
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res = 0x00000001; // return +1 |
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} |
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} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
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// -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be |
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// rounded to nearest to a 32-bit unsigned integer |
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if (x_sign) { // x <= -1 |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return Integer Indefinite |
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res = 0x80000000; |
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BID_RETURN (res); |
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} |
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// 1 <= x < 2^32-1/2 so x can be rounded |
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// to nearest to a 32-bit unsigned integer |
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if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
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ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
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// chop off ind digits from the lower part of C1 |
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// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits |
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C1 = C1 + midpoint64[ind - 1]; |
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// calculate C* and f* |
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// C* is actually floor(C*) in this case |
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// C* and f* need shifting and masking, as shown by |
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// shiftright128[] and maskhigh128[] |
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// 1 <= x <= 15 |
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// kx = 10^(-x) = ten2mk64[ind - 1] |
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// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
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// the approximation of 10^(-x) was rounded up to 54 bits |
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__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
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Cstar = P128.w[1]; |
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fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
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fstar.w[0] = P128.w[0]; |
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// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
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// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
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// if (0 < f* < 10^(-x)) then the result is a midpoint |
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// if floor(C*) is even then C* = floor(C*) - logical right |
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// shift; C* has p decimal digits, correct by Prop. 1) |
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// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
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// shift; C* has p decimal digits, correct by Pr. 1) |
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// else |
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// C* = floor(C*) (logical right shift; C has p decimal digits, |
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// correct by Property 1) |
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// n = C* * 10^(e+x) |
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// shift right C* by Ex-64 = shiftright128[ind] |
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shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
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Cstar = Cstar >> shift; |
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// if the result was a midpoint it was rounded away from zero, so |
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// it will need a correction |
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// check for midpoints |
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if ((fstar.w[1] == 0) && fstar.w[0] && |
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(fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { |
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// ten2mk128trunc[ind -1].w[1] is identical to |
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// ten2mk128[ind -1].w[1] |
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// the result is a midpoint; round to nearest |
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if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] |
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// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
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Cstar--; // Cstar is now even |
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} // else MP in [ODD, EVEN] |
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} |
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res = Cstar; // the result is positive |
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} else if (exp == 0) { |
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// 1 <= q <= 10 |
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// res = +C (exact) |
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res = C1; // the result is positive |
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} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
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// res = +C * 10^exp (exact) |
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res = C1 * ten2k64[exp]; // the result is positive |
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} |
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} |
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BID_RETURN (res); |
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} |
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/***************************************************************************** |
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* BID64_to_uint32_xrnint |
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****************************************************************************/ |
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#if DECIMAL_CALL_BY_REFERENCE |
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void |
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bid64_to_uint32_xrnint (unsigned int *pres, UINT64 * px |
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_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
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_EXC_INFO_PARAM) { |
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UINT64 x = *px; |
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#else |
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unsigned int |
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bid64_to_uint32_xrnint (UINT64 x |
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_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
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_EXC_INFO_PARAM) { |
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#endif |
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unsigned int res; |
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UINT64 x_sign; |
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UINT64 x_exp; |
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int exp; // unbiased exponent |
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// Note: C1 represents x_significand (UINT64) |
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UINT64 tmp64; |
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BID_UI64DOUBLE tmp1; |
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unsigned int x_nr_bits; |
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int q, ind, shift; |
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UINT64 C1; |
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UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
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UINT128 fstar; |
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UINT128 P128; |
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// check for NaN or Infinity |
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if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
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// set invalid flag |
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*pfpsf |= INVALID_EXCEPTION; |
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// return Integer Indefinite |
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res = 0x80000000; |
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BID_RETURN (res); |
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} |
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// unpack x |
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x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
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// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
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if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
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x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
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C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
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if (C1 > 9999999999999999ull) { // non-canonical |
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x_exp = 0; |
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C1 = 0; |
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} |
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} else { |
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x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
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C1 = x & MASK_BINARY_SIG1; |
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} |
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// check for zeros (possibly from non-canonical values) |
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if (C1 == 0x0ull) { |
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// x is 0 |
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res = 0x00000000; |
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BID_RETURN (res); |
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} |
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// x is not special and is not zero |
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// q = nr. of decimal digits in x (1 <= q <= 54) |
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// determine first the nr. of bits in x |
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if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
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// split the 64-bit value in two 32-bit halves to avoid rounding errors |
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if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
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tmp1.d = (double) (C1 >> 32); // exact conversion |
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x_nr_bits = |
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33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
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} else { // x < 2^32 |
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tmp1.d = (double) C1; // exact conversion |
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x_nr_bits = |
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1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
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} |
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|
337 |
} else { // if x < 2^53 |
|
|
338 |
tmp1.d = (double) C1; // exact conversion |
|
|
339 |
x_nr_bits = |
|
|
340 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
341 |
} |
|
|
342 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
343 |
if (q == 0) { |
|
|
344 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
345 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
346 |
q++; |
|
|
347 |
} |
|
|
348 |
exp = x_exp - 398; // unbiased exponent |
|
|
349 |
|
|
|
350 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
351 |
// set invalid flag |
|
|
352 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
353 |
// return Integer Indefinite |
|
|
354 |
res = 0x80000000; |
|
|
355 |
BID_RETURN (res); |
|
|
356 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
357 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
358 |
// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
|
|
359 |
// the cases that do not fit are identified here; the ones that fit |
|
|
360 |
// fall through and will be handled with other cases further, |
|
|
361 |
// under '1 <= q + exp <= 10' |
|
|
362 |
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 |
|
|
363 |
// => set invalid flag |
|
|
364 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
365 |
// return Integer Indefinite |
|
|
366 |
res = 0x80000000; |
|
|
367 |
BID_RETURN (res); |
|
|
368 |
} else { // if n > 0 and q + exp = 10 |
|
|
369 |
// if n >= 2^32 - 1/2 then n is too large |
|
|
370 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 |
|
|
371 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 |
|
|
372 |
// <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 |
|
|
373 |
if (q <= 11) { |
|
|
374 |
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits |
|
|
375 |
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
376 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
377 |
if (tmp64 >= 0x9fffffffbull) { |
|
|
378 |
// set invalid flag |
|
|
379 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
380 |
// return Integer Indefinite |
|
|
381 |
res = 0x80000000; |
|
|
382 |
BID_RETURN (res); |
|
|
383 |
} |
|
|
384 |
// else cases that can be rounded to a 32-bit unsigned int fall through |
|
|
385 |
// to '1 <= q + exp <= 10' |
|
|
386 |
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
|
|
387 |
// C * 10^(11-q) >= 0x9fffffffb <=> |
|
|
388 |
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 |
|
|
389 |
// (scale 2^32-1/2 up) |
|
|
390 |
// Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 |
|
|
391 |
tmp64 = 0x9fffffffbull * ten2k64[q - 11]; |
|
|
392 |
if (C1 >= tmp64) { |
|
|
393 |
// set invalid flag |
|
|
394 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
395 |
// return Integer Indefinite |
|
|
396 |
res = 0x80000000; |
|
|
397 |
BID_RETURN (res); |
|
|
398 |
} |
|
|
399 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
400 |
// to '1 <= q + exp <= 10' |
|
|
401 |
} |
|
|
402 |
} |
|
|
403 |
} |
|
|
404 |
// n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 1/2 |
|
|
405 |
// Note: some of the cases tested for above fall through to this point |
|
|
406 |
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
|
|
407 |
// set inexact flag |
|
|
408 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
409 |
// return 0 |
|
|
410 |
res = 0x00000000; |
|
|
411 |
BID_RETURN (res); |
|
|
412 |
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
|
|
413 |
// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) |
|
|
414 |
// res = 0 |
|
|
415 |
// else if x > 0 |
|
|
416 |
// res = +1 |
|
|
417 |
// else // if x < 0 |
|
|
418 |
// invalid exc |
|
|
419 |
ind = q - 1; |
|
|
420 |
if (C1 <= midpoint64[ind]) { |
|
|
421 |
res = 0x00000000; // return 0 |
|
|
422 |
} else if (x_sign) { // n < 0 |
|
|
423 |
// set invalid flag |
|
|
424 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
425 |
// return Integer Indefinite |
|
|
426 |
res = 0x80000000; |
|
|
427 |
BID_RETURN (res); |
|
|
428 |
} else { // n > 0 |
|
|
429 |
res = 0x00000001; // return +1 |
|
|
430 |
} |
|
|
431 |
// set inexact flag |
|
|
432 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
433 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
|
|
434 |
// -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be |
|
|
435 |
// rounded to nearest to a 32-bit unsigned integer |
|
|
436 |
if (x_sign) { // x <= -1 |
|
|
437 |
// set invalid flag |
|
|
438 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
439 |
// return Integer Indefinite |
|
|
440 |
res = 0x80000000; |
|
|
441 |
BID_RETURN (res); |
|
|
442 |
} |
|
|
443 |
// 1 <= x < 2^32-1/2 so x can be rounded |
|
|
444 |
// to nearest to a 32-bit unsigned integer |
|
|
445 |
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
446 |
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
|
|
447 |
// chop off ind digits from the lower part of C1 |
|
|
448 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits |
|
|
449 |
C1 = C1 + midpoint64[ind - 1]; |
|
|
450 |
// calculate C* and f* |
|
|
451 |
// C* is actually floor(C*) in this case |
|
|
452 |
// C* and f* need shifting and masking, as shown by |
|
|
453 |
// shiftright128[] and maskhigh128[] |
|
|
454 |
// 1 <= x <= 15 |
|
|
455 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
456 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
457 |
// the approximation of 10^(-x) was rounded up to 54 bits |
|
|
458 |
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
|
|
459 |
Cstar = P128.w[1]; |
|
|
460 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
461 |
fstar.w[0] = P128.w[0]; |
|
|
462 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
|
|
463 |
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
|
|
464 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
465 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
466 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
467 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
468 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
469 |
// else |
|
|
470 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
471 |
// correct by Property 1) |
|
|
472 |
// n = C* * 10^(e+x) |
|
|
473 |
|
|
|
474 |
// shift right C* by Ex-64 = shiftright128[ind] |
|
|
475 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
|
|
476 |
Cstar = Cstar >> shift; |
|
|
477 |
// determine inexactness of the rounding of C* |
|
|
478 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
479 |
// the result is exact |
|
|
480 |
// else // if (f* - 1/2 > T*) then |
|
|
481 |
// the result is inexact |
|
|
482 |
if (ind - 1 <= 2) { // fstar.w[1] is 0 |
|
|
483 |
if (fstar.w[0] > 0x8000000000000000ull) { |
|
|
484 |
// f* > 1/2 and the result may be exact |
|
|
485 |
tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 |
|
|
486 |
if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { |
|
|
487 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
488 |
// ten2mk128[ind -1].w[1] |
|
|
489 |
// set the inexact flag |
|
|
490 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
491 |
} // else the result is exact |
|
|
492 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
493 |
// set the inexact flag |
|
|
494 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
495 |
} |
|
|
496 |
} else { // if 3 <= ind - 1 <= 14 |
|
|
497 |
if (fstar.w[1] > onehalf128[ind - 1] || |
|
|
498 |
(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { |
|
|
499 |
// f2* > 1/2 and the result may be exact |
|
|
500 |
// Calculate f2* - 1/2 |
|
|
501 |
tmp64 = fstar.w[1] - onehalf128[ind - 1]; |
|
|
502 |
if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
503 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
504 |
// ten2mk128[ind -1].w[1] |
|
|
505 |
// set the inexact flag |
|
|
506 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
507 |
} // else the result is exact |
|
|
508 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
509 |
// set the inexact flag |
|
|
510 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
511 |
} |
|
|
512 |
} |
|
|
513 |
|
|
|
514 |
// if the result was a midpoint it was rounded away from zero, so |
|
|
515 |
// it will need a correction |
|
|
516 |
// check for midpoints |
|
|
517 |
if ((fstar.w[1] == 0) && fstar.w[0] && |
|
|
518 |
(fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { |
|
|
519 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
520 |
// ten2mk128[ind -1].w[1] |
|
|
521 |
// the result is a midpoint; round to nearest |
|
|
522 |
if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] |
|
|
523 |
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
|
|
524 |
Cstar--; // Cstar is now even |
|
|
525 |
} // else MP in [ODD, EVEN] |
|
|
526 |
} |
|
|
527 |
res = Cstar; // the result is positive |
|
|
528 |
} else if (exp == 0) { |
|
|
529 |
// 1 <= q <= 10 |
|
|
530 |
// res = +C (exact) |
|
|
531 |
res = C1; // the result is positive |
|
|
532 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
533 |
// res = +C * 10^exp (exact) |
|
|
534 |
res = C1 * ten2k64[exp]; // the result is positive |
|
|
535 |
} |
|
|
536 |
} |
|
|
537 |
BID_RETURN (res); |
|
|
538 |
} |
|
|
539 |
|
|
|
540 |
/***************************************************************************** |
|
|
541 |
* BID64_to_uint32_floor |
|
|
542 |
****************************************************************************/ |
|
|
543 |
|
|
|
544 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
545 |
void |
|
|
546 |
bid64_to_uint32_floor (unsigned int *pres, UINT64 * px |
|
|
547 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
548 |
_EXC_INFO_PARAM) { |
|
|
549 |
UINT64 x = *px; |
|
|
550 |
#else |
|
|
551 |
unsigned int |
|
|
552 |
bid64_to_uint32_floor (UINT64 x |
|
|
553 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
554 |
_EXC_INFO_PARAM) { |
|
|
555 |
#endif |
|
|
556 |
unsigned int res; |
|
|
557 |
UINT64 x_sign; |
|
|
558 |
UINT64 x_exp; |
|
|
559 |
int exp; // unbiased exponent |
|
|
560 |
// Note: C1 represents x_significand (UINT64) |
|
|
561 |
UINT64 tmp64; |
|
|
562 |
BID_UI64DOUBLE tmp1; |
|
|
563 |
unsigned int x_nr_bits; |
|
|
564 |
int q, ind, shift; |
|
|
565 |
UINT64 C1; |
|
|
566 |
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
|
|
567 |
UINT128 P128; |
|
|
568 |
|
|
|
569 |
// check for NaN or Infinity |
|
|
570 |
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
|
|
571 |
// set invalid flag |
|
|
572 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
573 |
// return Integer Indefinite |
|
|
574 |
res = 0x80000000; |
|
|
575 |
BID_RETURN (res); |
|
|
576 |
} |
|
|
577 |
// unpack x |
|
|
578 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
579 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
580 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
581 |
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
|
|
582 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
583 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
584 |
x_exp = 0; |
|
|
585 |
C1 = 0; |
|
|
586 |
} |
|
|
587 |
} else { |
|
|
588 |
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
|
|
589 |
C1 = x & MASK_BINARY_SIG1; |
|
|
590 |
} |
|
|
591 |
|
|
|
592 |
// check for zeros (possibly from non-canonical values) |
|
|
593 |
if (C1 == 0x0ull) { |
|
|
594 |
// x is 0 |
|
|
595 |
res = 0x00000000; |
|
|
596 |
BID_RETURN (res); |
|
|
597 |
} |
|
|
598 |
// x is not special and is not zero |
|
|
599 |
|
|
|
600 |
if (x_sign) { // if n < 0 the conversion is invalid |
|
|
601 |
// set invalid flag |
|
|
602 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
603 |
// return Integer Indefinite |
|
|
604 |
res = 0x80000000; |
|
|
605 |
BID_RETURN (res); |
|
|
606 |
} |
|
|
607 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
608 |
// determine first the nr. of bits in x |
|
|
609 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
610 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
611 |
if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
612 |
tmp1.d = (double) (C1 >> 32); // exact conversion |
|
|
613 |
x_nr_bits = |
|
|
614 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
615 |
} else { // x < 2^32 |
|
|
616 |
tmp1.d = (double) C1; // exact conversion |
|
|
617 |
x_nr_bits = |
|
|
618 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
619 |
} |
|
|
620 |
} else { // if x < 2^53 |
|
|
621 |
tmp1.d = (double) C1; // exact conversion |
|
|
622 |
x_nr_bits = |
|
|
623 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
624 |
} |
|
|
625 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
626 |
if (q == 0) { |
|
|
627 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
628 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
629 |
q++; |
|
|
630 |
} |
|
|
631 |
exp = x_exp - 398; // unbiased exponent |
|
|
632 |
|
|
|
633 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
634 |
// set invalid flag |
|
|
635 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
636 |
// return Integer Indefinite |
|
|
637 |
res = 0x80000000; |
|
|
638 |
BID_RETURN (res); |
|
|
639 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
640 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
641 |
// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
|
|
642 |
// the cases that do not fit are identified here; the ones that fit |
|
|
643 |
// fall through and will be handled with other cases further, |
|
|
644 |
// under '1 <= q + exp <= 10' |
|
|
645 |
// n > 0 and q + exp = 10 |
|
|
646 |
// if n >= 2^32 then n is too large |
|
|
647 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 |
|
|
648 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 |
|
|
649 |
// <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 |
|
|
650 |
if (q <= 11) { |
|
|
651 |
// Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits |
|
|
652 |
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
653 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
654 |
if (tmp64 >= 0xa00000000ull) { |
|
|
655 |
// set invalid flag |
|
|
656 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
657 |
// return Integer Indefinite |
|
|
658 |
res = 0x80000000; |
|
|
659 |
BID_RETURN (res); |
|
|
660 |
} |
|
|
661 |
// else cases that can be rounded to a 32-bit unsigned int fall through |
|
|
662 |
// to '1 <= q + exp <= 10' |
|
|
663 |
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
|
|
664 |
// C * 10^(11-q) >= 0xa00000000 <=> |
|
|
665 |
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 |
|
|
666 |
// (scale 2^32-1/2 up) |
|
|
667 |
// Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 |
|
|
668 |
tmp64 = 0xa00000000ull * ten2k64[q - 11]; |
|
|
669 |
if (C1 >= tmp64) { |
|
|
670 |
// set invalid flag |
|
|
671 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
672 |
// return Integer Indefinite |
|
|
673 |
res = 0x80000000; |
|
|
674 |
BID_RETURN (res); |
|
|
675 |
} |
|
|
676 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
677 |
// to '1 <= q + exp <= 10' |
|
|
678 |
} |
|
|
679 |
} |
|
|
680 |
// n is not too large to be converted to int32 if -1 < n < 2^32 |
|
|
681 |
// Note: some of the cases tested for above fall through to this point |
|
|
682 |
if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) |
|
|
683 |
// return 0 |
|
|
684 |
res = 0x00000000; |
|
|
685 |
BID_RETURN (res); |
|
|
686 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
|
|
687 |
// 1 <= x < 2^32 so x can be rounded |
|
|
688 |
// to nearest to a 32-bit unsigned integer |
|
|
689 |
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
690 |
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
|
|
691 |
// chop off ind digits from the lower part of C1 |
|
|
692 |
// C1 fits in 64 bits |
|
|
693 |
// calculate C* and f* |
|
|
694 |
// C* is actually floor(C*) in this case |
|
|
695 |
// C* and f* need shifting and masking, as shown by |
|
|
696 |
// shiftright128[] and maskhigh128[] |
|
|
697 |
// 1 <= x <= 15 |
|
|
698 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
699 |
// C* = C1 * 10^(-x) |
|
|
700 |
// the approximation of 10^(-x) was rounded up to 54 bits |
|
|
701 |
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
|
|
702 |
Cstar = P128.w[1]; |
|
|
703 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
|
|
704 |
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
|
|
705 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
706 |
// correct by Property 1) |
|
|
707 |
// n = C* * 10^(e+x) |
|
|
708 |
|
|
|
709 |
// shift right C* by Ex-64 = shiftright128[ind] |
|
|
710 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
|
|
711 |
Cstar = Cstar >> shift; |
|
|
712 |
|
|
|
713 |
res = Cstar; // the result is positive |
|
|
714 |
} else if (exp == 0) { |
|
|
715 |
// 1 <= q <= 10 |
|
|
716 |
// res = +C (exact) |
|
|
717 |
res = C1; // the result is positive |
|
|
718 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
719 |
// res = +C * 10^exp (exact) |
|
|
720 |
res = C1 * ten2k64[exp]; // the result is positive |
|
|
721 |
} |
|
|
722 |
} |
|
|
723 |
BID_RETURN (res); |
|
|
724 |
} |
|
|
725 |
|
|
|
726 |
/***************************************************************************** |
|
|
727 |
* BID64_to_uint32_xfloor |
|
|
728 |
****************************************************************************/ |
|
|
729 |
|
|
|
730 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
731 |
void |
|
|
732 |
bid64_to_uint32_xfloor (unsigned int *pres, UINT64 * px |
|
|
733 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
734 |
_EXC_INFO_PARAM) { |
|
|
735 |
UINT64 x = *px; |
|
|
736 |
#else |
|
|
737 |
unsigned int |
|
|
738 |
bid64_to_uint32_xfloor (UINT64 x |
|
|
739 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
740 |
_EXC_INFO_PARAM) { |
|
|
741 |
#endif |
|
|
742 |
unsigned int res; |
|
|
743 |
UINT64 x_sign; |
|
|
744 |
UINT64 x_exp; |
|
|
745 |
int exp; // unbiased exponent |
|
|
746 |
// Note: C1 represents x_significand (UINT64) |
|
|
747 |
UINT64 tmp64; |
|
|
748 |
BID_UI64DOUBLE tmp1; |
|
|
749 |
unsigned int x_nr_bits; |
|
|
750 |
int q, ind, shift; |
|
|
751 |
UINT64 C1; |
|
|
752 |
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
|
|
753 |
UINT128 fstar; |
|
|
754 |
UINT128 P128; |
|
|
755 |
|
|
|
756 |
// check for NaN or Infinity |
|
|
757 |
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
|
|
758 |
// set invalid flag |
|
|
759 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
760 |
// return Integer Indefinite |
|
|
761 |
res = 0x80000000; |
|
|
762 |
BID_RETURN (res); |
|
|
763 |
} |
|
|
764 |
// unpack x |
|
|
765 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
766 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
767 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
768 |
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
|
|
769 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
770 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
771 |
x_exp = 0; |
|
|
772 |
C1 = 0; |
|
|
773 |
} |
|
|
774 |
} else { |
|
|
775 |
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
|
|
776 |
C1 = x & MASK_BINARY_SIG1; |
|
|
777 |
} |
|
|
778 |
|
|
|
779 |
// check for zeros (possibly from non-canonical values) |
|
|
780 |
if (C1 == 0x0ull) { |
|
|
781 |
// x is 0 |
|
|
782 |
res = 0x00000000; |
|
|
783 |
BID_RETURN (res); |
|
|
784 |
} |
|
|
785 |
// x is not special and is not zero |
|
|
786 |
|
|
|
787 |
if (x_sign) { // if n < 0 the conversion is invalid |
|
|
788 |
// set invalid flag |
|
|
789 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
790 |
// return Integer Indefinite |
|
|
791 |
res = 0x80000000; |
|
|
792 |
BID_RETURN (res); |
|
|
793 |
} |
|
|
794 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
795 |
// determine first the nr. of bits in x |
|
|
796 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
797 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
798 |
if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
799 |
tmp1.d = (double) (C1 >> 32); // exact conversion |
|
|
800 |
x_nr_bits = |
|
|
801 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
802 |
} else { // x < 2^32 |
|
|
803 |
tmp1.d = (double) C1; // exact conversion |
|
|
804 |
x_nr_bits = |
|
|
805 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
806 |
} |
|
|
807 |
} else { // if x < 2^53 |
|
|
808 |
tmp1.d = (double) C1; // exact conversion |
|
|
809 |
x_nr_bits = |
|
|
810 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
811 |
} |
|
|
812 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
813 |
if (q == 0) { |
|
|
814 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
815 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
816 |
q++; |
|
|
817 |
} |
|
|
818 |
exp = x_exp - 398; // unbiased exponent |
|
|
819 |
|
|
|
820 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
821 |
// set invalid flag |
|
|
822 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
823 |
// return Integer Indefinite |
|
|
824 |
res = 0x80000000; |
|
|
825 |
BID_RETURN (res); |
|
|
826 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
827 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
828 |
// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
|
|
829 |
// the cases that do not fit are identified here; the ones that fit |
|
|
830 |
// fall through and will be handled with other cases further, |
|
|
831 |
// under '1 <= q + exp <= 10' |
|
|
832 |
// if n > 0 and q + exp = 10 |
|
|
833 |
// if n >= 2^32 then n is too large |
|
|
834 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 |
|
|
835 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 |
|
|
836 |
// <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 |
|
|
837 |
if (q <= 11) { |
|
|
838 |
// Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits |
|
|
839 |
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
840 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
841 |
if (tmp64 >= 0xa00000000ull) { |
|
|
842 |
// set invalid flag |
|
|
843 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
844 |
// return Integer Indefinite |
|
|
845 |
res = 0x80000000; |
|
|
846 |
BID_RETURN (res); |
|
|
847 |
} |
|
|
848 |
// else cases that can be rounded to a 32-bit unsigned int fall through |
|
|
849 |
// to '1 <= q + exp <= 10' |
|
|
850 |
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
|
|
851 |
// C * 10^(11-q) >= 0xa00000000 <=> |
|
|
852 |
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 |
|
|
853 |
// (scale 2^32-1/2 up) |
|
|
854 |
// Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 |
|
|
855 |
tmp64 = 0xa00000000ull * ten2k64[q - 11]; |
|
|
856 |
if (C1 >= tmp64) { |
|
|
857 |
// set invalid flag |
|
|
858 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
859 |
// return Integer Indefinite |
|
|
860 |
res = 0x80000000; |
|
|
861 |
BID_RETURN (res); |
|
|
862 |
} |
|
|
863 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
864 |
// to '1 <= q + exp <= 10' |
|
|
865 |
} |
|
|
866 |
} |
|
|
867 |
// n is not too large to be converted to int32 if -1 < n < 2^32 |
|
|
868 |
// Note: some of the cases tested for above fall through to this point |
|
|
869 |
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) |
|
|
870 |
// set inexact flag |
|
|
871 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
872 |
// return 0 |
|
|
873 |
res = 0x00000000; |
|
|
874 |
BID_RETURN (res); |
|
|
875 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
|
|
876 |
// 1 <= x < 2^32 so x can be rounded |
|
|
877 |
// to nearest to a 32-bit unsigned integer |
|
|
878 |
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
879 |
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
|
|
880 |
// chop off ind digits from the lower part of C1 |
|
|
881 |
// C1 fits in 64 bits |
|
|
882 |
// calculate C* and f* |
|
|
883 |
// C* is actually floor(C*) in this case |
|
|
884 |
// C* and f* need shifting and masking, as shown by |
|
|
885 |
// shiftright128[] and maskhigh128[] |
|
|
886 |
// 1 <= x <= 15 |
|
|
887 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
888 |
// C* = C1 * 10^(-x) |
|
|
889 |
// the approximation of 10^(-x) was rounded up to 54 bits |
|
|
890 |
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
|
|
891 |
Cstar = P128.w[1]; |
|
|
892 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
893 |
fstar.w[0] = P128.w[0]; |
|
|
894 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
|
|
895 |
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
|
|
896 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
897 |
// correct by Property 1) |
|
|
898 |
// n = C* * 10^(e+x) |
|
|
899 |
|
|
|
900 |
// shift right C* by Ex-64 = shiftright128[ind] |
|
|
901 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
|
|
902 |
Cstar = Cstar >> shift; |
|
|
903 |
// determine inexactness of the rounding of C* |
|
|
904 |
// if (0 < f* < 10^(-x)) then |
|
|
905 |
// the result is exact |
|
|
906 |
// else // if (f* > T*) then |
|
|
907 |
// the result is inexact |
|
|
908 |
if (ind - 1 <= 2) { |
|
|
909 |
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
910 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
911 |
// ten2mk128[ind -1].w[1] |
|
|
912 |
// set the inexact flag |
|
|
913 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
914 |
} // else the result is exact |
|
|
915 |
} else { // if 3 <= ind - 1 <= 14 |
|
|
916 |
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
917 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
918 |
// ten2mk128[ind -1].w[1] |
|
|
919 |
// set the inexact flag |
|
|
920 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
921 |
} // else the result is exact |
|
|
922 |
} |
|
|
923 |
|
|
|
924 |
res = Cstar; // the result is positive |
|
|
925 |
} else if (exp == 0) { |
|
|
926 |
// 1 <= q <= 10 |
|
|
927 |
// res = +C (exact) |
|
|
928 |
res = C1; // the result is positive |
|
|
929 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
930 |
// res = +C * 10^exp (exact) |
|
|
931 |
res = C1 * ten2k64[exp]; // the result is positive |
|
|
932 |
} |
|
|
933 |
} |
|
|
934 |
BID_RETURN (res); |
|
|
935 |
} |
|
|
936 |
|
|
|
937 |
/***************************************************************************** |
|
|
938 |
* BID64_to_uint32_ceil |
|
|
939 |
****************************************************************************/ |
|
|
940 |
|
|
|
941 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
942 |
void |
|
|
943 |
bid64_to_uint32_ceil (unsigned int *pres, UINT64 * px |
|
|
944 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
945 |
_EXC_INFO_PARAM) { |
|
|
946 |
UINT64 x = *px; |
|
|
947 |
#else |
|
|
948 |
unsigned int |
|
|
949 |
bid64_to_uint32_ceil (UINT64 x |
|
|
950 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
951 |
_EXC_INFO_PARAM) { |
|
|
952 |
#endif |
|
|
953 |
unsigned int res; |
|
|
954 |
UINT64 x_sign; |
|
|
955 |
UINT64 x_exp; |
|
|
956 |
int exp; // unbiased exponent |
|
|
957 |
// Note: C1 represents x_significand (UINT64) |
|
|
958 |
UINT64 tmp64; |
|
|
959 |
BID_UI64DOUBLE tmp1; |
|
|
960 |
unsigned int x_nr_bits; |
|
|
961 |
int q, ind, shift; |
|
|
962 |
UINT64 C1; |
|
|
963 |
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
|
|
964 |
UINT128 fstar; |
|
|
965 |
UINT128 P128; |
|
|
966 |
|
|
|
967 |
// check for NaN or Infinity |
|
|
968 |
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
|
|
969 |
// set invalid flag |
|
|
970 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
971 |
// return Integer Indefinite |
|
|
972 |
res = 0x80000000; |
|
|
973 |
BID_RETURN (res); |
|
|
974 |
} |
|
|
975 |
// unpack x |
|
|
976 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
977 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
978 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
979 |
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
|
|
980 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
981 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
982 |
x_exp = 0; |
|
|
983 |
C1 = 0; |
|
|
984 |
} |
|
|
985 |
} else { |
|
|
986 |
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
|
|
987 |
C1 = x & MASK_BINARY_SIG1; |
|
|
988 |
} |
|
|
989 |
|
|
|
990 |
// check for zeros (possibly from non-canonical values) |
|
|
991 |
if (C1 == 0x0ull) { |
|
|
992 |
// x is 0 |
|
|
993 |
res = 0x00000000; |
|
|
994 |
BID_RETURN (res); |
|
|
995 |
} |
|
|
996 |
// x is not special and is not zero |
|
|
997 |
|
|
|
998 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
999 |
// determine first the nr. of bits in x |
|
|
1000 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1001 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
1002 |
if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
1003 |
tmp1.d = (double) (C1 >> 32); // exact conversion |
|
|
1004 |
x_nr_bits = |
|
|
1005 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1006 |
} else { // x < 2^32 |
|
|
1007 |
tmp1.d = (double) C1; // exact conversion |
|
|
1008 |
x_nr_bits = |
|
|
1009 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1010 |
} |
|
|
1011 |
} else { // if x < 2^53 |
|
|
1012 |
tmp1.d = (double) C1; // exact conversion |
|
|
1013 |
x_nr_bits = |
|
|
1014 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1015 |
} |
|
|
1016 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1017 |
if (q == 0) { |
|
|
1018 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1019 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
1020 |
q++; |
|
|
1021 |
} |
|
|
1022 |
exp = x_exp - 398; // unbiased exponent |
|
|
1023 |
|
|
|
1024 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
1025 |
// set invalid flag |
|
|
1026 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1027 |
// return Integer Indefinite |
|
|
1028 |
res = 0x80000000; |
|
|
1029 |
BID_RETURN (res); |
|
|
1030 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
1031 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
1032 |
// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
|
|
1033 |
// the cases that do not fit are identified here; the ones that fit |
|
|
1034 |
// fall through and will be handled with other cases further, |
|
|
1035 |
// under '1 <= q + exp <= 10' |
|
|
1036 |
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 |
|
|
1037 |
// => set invalid flag |
|
|
1038 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1039 |
// return Integer Indefinite |
|
|
1040 |
res = 0x80000000; |
|
|
1041 |
BID_RETURN (res); |
|
|
1042 |
} else { // if n > 0 and q + exp = 10 |
|
|
1043 |
// if n > 2^32 - 1 then n is too large |
|
|
1044 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 |
|
|
1045 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16 |
|
|
1046 |
// <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16 |
|
|
1047 |
if (q <= 11) { |
|
|
1048 |
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits |
|
|
1049 |
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1050 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1051 |
if (tmp64 > 0x9fffffff6ull) { |
|
|
1052 |
// set invalid flag |
|
|
1053 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1054 |
// return Integer Indefinite |
|
|
1055 |
res = 0x80000000; |
|
|
1056 |
BID_RETURN (res); |
|
|
1057 |
} |
|
|
1058 |
// else cases that can be rounded to a 32-bit unsigned int fall through |
|
|
1059 |
// to '1 <= q + exp <= 10' |
|
|
1060 |
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
|
|
1061 |
// C * 10^(11-q) > 0x9fffffff6 <=> |
|
|
1062 |
// C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 |
|
|
1063 |
// (scale 2^32-1 up) |
|
|
1064 |
// Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 |
|
|
1065 |
tmp64 = 0x9fffffff6ull * ten2k64[q - 11]; |
|
|
1066 |
if (C1 > tmp64) { |
|
|
1067 |
// set invalid flag |
|
|
1068 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1069 |
// return Integer Indefinite |
|
|
1070 |
res = 0x80000000; |
|
|
1071 |
BID_RETURN (res); |
|
|
1072 |
} |
|
|
1073 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1074 |
// to '1 <= q + exp <= 10' |
|
|
1075 |
} |
|
|
1076 |
} |
|
|
1077 |
} |
|
|
1078 |
// n is not too large to be converted to int32 if -1 < n < 2^32 |
|
|
1079 |
// Note: some of the cases tested for above fall through to this point |
|
|
1080 |
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) |
|
|
1081 |
// return 0 or 1 |
|
|
1082 |
if (x_sign) |
|
|
1083 |
res = 0x00000000; |
|
|
1084 |
else |
|
|
1085 |
res = 0x00000001; |
|
|
1086 |
BID_RETURN (res); |
|
|
1087 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
|
|
1088 |
// x <= -1 or 1 <= x <= 2^32 - 1 so if positive, x can be |
|
|
1089 |
// rounded to nearest to a 32-bit unsigned integer |
|
|
1090 |
if (x_sign) { // x <= -1 |
|
|
1091 |
// set invalid flag |
|
|
1092 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1093 |
// return Integer Indefinite |
|
|
1094 |
res = 0x80000000; |
|
|
1095 |
BID_RETURN (res); |
|
|
1096 |
} |
|
|
1097 |
// 1 <= x <= 2^32 - 1 so x can be rounded |
|
|
1098 |
// to nearest to a 32-bit unsigned integer |
|
|
1099 |
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
1100 |
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
|
|
1101 |
// chop off ind digits from the lower part of C1 |
|
|
1102 |
// C1 fits in 64 bits |
|
|
1103 |
// calculate C* and f* |
|
|
1104 |
// C* is actually floor(C*) in this case |
|
|
1105 |
// C* and f* need shifting and masking, as shown by |
|
|
1106 |
// shiftright128[] and maskhigh128[] |
|
|
1107 |
// 1 <= x <= 15 |
|
|
1108 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
1109 |
// C* = C1 * 10^(-x) |
|
|
1110 |
// the approximation of 10^(-x) was rounded up to 54 bits |
|
|
1111 |
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
|
|
1112 |
Cstar = P128.w[1]; |
|
|
1113 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
1114 |
fstar.w[0] = P128.w[0]; |
|
|
1115 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
|
|
1116 |
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
|
|
1117 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
1118 |
// correct by Property 1) |
|
|
1119 |
// n = C* * 10^(e+x) |
|
|
1120 |
|
|
|
1121 |
// shift right C* by Ex-64 = shiftright128[ind] |
|
|
1122 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
|
|
1123 |
Cstar = Cstar >> shift; |
|
|
1124 |
// determine inexactness of the rounding of C* |
|
|
1125 |
// if (0 < f* < 10^(-x)) then |
|
|
1126 |
// the result is exact |
|
|
1127 |
// else // if (f* > T*) then |
|
|
1128 |
// the result is inexact |
|
|
1129 |
if (ind - 1 <= 2) { // fstar.w[1] is 0 |
|
|
1130 |
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
1131 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
1132 |
// ten2mk128[ind -1].w[1] |
|
|
1133 |
Cstar++; |
|
|
1134 |
} // else the result is exact |
|
|
1135 |
} else { // if 3 <= ind - 1 <= 14 |
|
|
1136 |
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
1137 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
1138 |
// ten2mk128[ind -1].w[1] |
|
|
1139 |
Cstar++; |
|
|
1140 |
} // else the result is exact |
|
|
1141 |
} |
|
|
1142 |
|
|
|
1143 |
res = Cstar; // the result is positive |
|
|
1144 |
} else if (exp == 0) { |
|
|
1145 |
// 1 <= q <= 10 |
|
|
1146 |
// res = +C (exact) |
|
|
1147 |
res = C1; // the result is positive |
|
|
1148 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
1149 |
// res = +C * 10^exp (exact) |
|
|
1150 |
res = C1 * ten2k64[exp]; // the result is positive |
|
|
1151 |
} |
|
|
1152 |
} |
|
|
1153 |
BID_RETURN (res); |
|
|
1154 |
} |
|
|
1155 |
|
|
|
1156 |
/***************************************************************************** |
|
|
1157 |
* BID64_to_uint32_xceil |
|
|
1158 |
****************************************************************************/ |
|
|
1159 |
|
|
|
1160 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
1161 |
void |
|
|
1162 |
bid64_to_uint32_xceil (unsigned int *pres, UINT64 * px |
|
|
1163 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
1164 |
_EXC_INFO_PARAM) { |
|
|
1165 |
UINT64 x = *px; |
|
|
1166 |
#else |
|
|
1167 |
unsigned int |
|
|
1168 |
bid64_to_uint32_xceil (UINT64 x |
|
|
1169 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
1170 |
_EXC_INFO_PARAM) { |
|
|
1171 |
#endif |
|
|
1172 |
unsigned int res; |
|
|
1173 |
UINT64 x_sign; |
|
|
1174 |
UINT64 x_exp; |
|
|
1175 |
int exp; // unbiased exponent |
|
|
1176 |
// Note: C1 represents x_significand (UINT64) |
|
|
1177 |
UINT64 tmp64; |
|
|
1178 |
BID_UI64DOUBLE tmp1; |
|
|
1179 |
unsigned int x_nr_bits; |
|
|
1180 |
int q, ind, shift; |
|
|
1181 |
UINT64 C1; |
|
|
1182 |
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
|
|
1183 |
UINT128 fstar; |
|
|
1184 |
UINT128 P128; |
|
|
1185 |
|
|
|
1186 |
// check for NaN or Infinity |
|
|
1187 |
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
|
|
1188 |
// set invalid flag |
|
|
1189 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1190 |
// return Integer Indefinite |
|
|
1191 |
res = 0x80000000; |
|
|
1192 |
BID_RETURN (res); |
|
|
1193 |
} |
|
|
1194 |
// unpack x |
|
|
1195 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
1196 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
1197 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
1198 |
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
|
|
1199 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
1200 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
1201 |
x_exp = 0; |
|
|
1202 |
C1 = 0; |
|
|
1203 |
} |
|
|
1204 |
} else { |
|
|
1205 |
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
|
|
1206 |
C1 = x & MASK_BINARY_SIG1; |
|
|
1207 |
} |
|
|
1208 |
|
|
|
1209 |
// check for zeros (possibly from non-canonical values) |
|
|
1210 |
if (C1 == 0x0ull) { |
|
|
1211 |
// x is 0 |
|
|
1212 |
res = 0x00000000; |
|
|
1213 |
BID_RETURN (res); |
|
|
1214 |
} |
|
|
1215 |
// x is not special and is not zero |
|
|
1216 |
|
|
|
1217 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
1218 |
// determine first the nr. of bits in x |
|
|
1219 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1220 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
1221 |
if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
1222 |
tmp1.d = (double) (C1 >> 32); // exact conversion |
|
|
1223 |
x_nr_bits = |
|
|
1224 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1225 |
} else { // x < 2^32 |
|
|
1226 |
tmp1.d = (double) C1; // exact conversion |
|
|
1227 |
x_nr_bits = |
|
|
1228 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1229 |
} |
|
|
1230 |
} else { // if x < 2^53 |
|
|
1231 |
tmp1.d = (double) C1; // exact conversion |
|
|
1232 |
x_nr_bits = |
|
|
1233 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1234 |
} |
|
|
1235 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1236 |
if (q == 0) { |
|
|
1237 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1238 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
1239 |
q++; |
|
|
1240 |
} |
|
|
1241 |
exp = x_exp - 398; // unbiased exponent |
|
|
1242 |
|
|
|
1243 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
1244 |
// set invalid flag |
|
|
1245 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1246 |
// return Integer Indefinite |
|
|
1247 |
res = 0x80000000; |
|
|
1248 |
BID_RETURN (res); |
|
|
1249 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
1250 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
1251 |
// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
|
|
1252 |
// the cases that do not fit are identified here; the ones that fit |
|
|
1253 |
// fall through and will be handled with other cases further, |
|
|
1254 |
// under '1 <= q + exp <= 10' |
|
|
1255 |
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 |
|
|
1256 |
// => set invalid flag |
|
|
1257 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1258 |
// return Integer Indefinite |
|
|
1259 |
res = 0x80000000; |
|
|
1260 |
BID_RETURN (res); |
|
|
1261 |
} else { // if n > 0 and q + exp = 10 |
|
|
1262 |
// if n > 2^32 - 1 then n is too large |
|
|
1263 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 |
|
|
1264 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16 |
|
|
1265 |
// <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16 |
|
|
1266 |
if (q <= 11) { |
|
|
1267 |
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits |
|
|
1268 |
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1269 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1270 |
if (tmp64 > 0x9fffffff6ull) { |
|
|
1271 |
// set invalid flag |
|
|
1272 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1273 |
// return Integer Indefinite |
|
|
1274 |
res = 0x80000000; |
|
|
1275 |
BID_RETURN (res); |
|
|
1276 |
} |
|
|
1277 |
// else cases that can be rounded to a 32-bit unsigned int fall through |
|
|
1278 |
// to '1 <= q + exp <= 10' |
|
|
1279 |
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
|
|
1280 |
// C * 10^(11-q) > 0x9fffffff6 <=> |
|
|
1281 |
// C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 |
|
|
1282 |
// (scale 2^32-1 up) |
|
|
1283 |
// Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 |
|
|
1284 |
tmp64 = 0x9fffffff6ull * ten2k64[q - 11]; |
|
|
1285 |
if (C1 > tmp64) { |
|
|
1286 |
// set invalid flag |
|
|
1287 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1288 |
// return Integer Indefinite |
|
|
1289 |
res = 0x80000000; |
|
|
1290 |
BID_RETURN (res); |
|
|
1291 |
} |
|
|
1292 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1293 |
// to '1 <= q + exp <= 10' |
|
|
1294 |
} |
|
|
1295 |
} |
|
|
1296 |
} |
|
|
1297 |
// n is not too large to be converted to int32 if -1 < n < 2^32 |
|
|
1298 |
// Note: some of the cases tested for above fall through to this point |
|
|
1299 |
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) |
|
|
1300 |
// set inexact flag |
|
|
1301 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1302 |
// return 0 or 1 |
|
|
1303 |
if (x_sign) |
|
|
1304 |
res = 0x00000000; |
|
|
1305 |
else |
|
|
1306 |
res = 0x00000001; |
|
|
1307 |
BID_RETURN (res); |
|
|
1308 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
|
|
1309 |
// x <= -1 or 1 <= x < 2^32 so if positive, x can be |
|
|
1310 |
// rounded to nearest to a 32-bit unsigned integer |
|
|
1311 |
if (x_sign) { // x <= -1 |
|
|
1312 |
// set invalid flag |
|
|
1313 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1314 |
// return Integer Indefinite |
|
|
1315 |
res = 0x80000000; |
|
|
1316 |
BID_RETURN (res); |
|
|
1317 |
} |
|
|
1318 |
// 1 <= x < 2^32 so x can be rounded |
|
|
1319 |
// to nearest to a 32-bit unsigned integer |
|
|
1320 |
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
1321 |
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
|
|
1322 |
// chop off ind digits from the lower part of C1 |
|
|
1323 |
// C1 fits in 64 bits |
|
|
1324 |
// calculate C* and f* |
|
|
1325 |
// C* is actually floor(C*) in this case |
|
|
1326 |
// C* and f* need shifting and masking, as shown by |
|
|
1327 |
// shiftright128[] and maskhigh128[] |
|
|
1328 |
// 1 <= x <= 15 |
|
|
1329 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
1330 |
// C* = C1 * 10^(-x) |
|
|
1331 |
// the approximation of 10^(-x) was rounded up to 54 bits |
|
|
1332 |
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
|
|
1333 |
Cstar = P128.w[1]; |
|
|
1334 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
1335 |
fstar.w[0] = P128.w[0]; |
|
|
1336 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
|
|
1337 |
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
|
|
1338 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
1339 |
// correct by Property 1) |
|
|
1340 |
// n = C* * 10^(e+x) |
|
|
1341 |
|
|
|
1342 |
// shift right C* by Ex-64 = shiftright128[ind] |
|
|
1343 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
|
|
1344 |
Cstar = Cstar >> shift; |
|
|
1345 |
// determine inexactness of the rounding of C* |
|
|
1346 |
// if (0 < f* < 10^(-x)) then |
|
|
1347 |
// the result is exact |
|
|
1348 |
// else // if (f* > T*) then |
|
|
1349 |
// the result is inexact |
|
|
1350 |
if (ind - 1 <= 2) { // fstar.w[1] is 0 |
|
|
1351 |
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
1352 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
1353 |
// ten2mk128[ind -1].w[1] |
|
|
1354 |
Cstar++; |
|
|
1355 |
// set the inexact flag |
|
|
1356 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1357 |
} // else the result is exact |
|
|
1358 |
} else { // if 3 <= ind - 1 <= 14 |
|
|
1359 |
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
1360 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
1361 |
// ten2mk128[ind -1].w[1] |
|
|
1362 |
Cstar++; |
|
|
1363 |
// set the inexact flag |
|
|
1364 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1365 |
} // else the result is exact |
|
|
1366 |
} |
|
|
1367 |
|
|
|
1368 |
res = Cstar; // the result is positive |
|
|
1369 |
} else if (exp == 0) { |
|
|
1370 |
// 1 <= q <= 10 |
|
|
1371 |
// res = +C (exact) |
|
|
1372 |
res = C1; // the result is positive |
|
|
1373 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
1374 |
// res = +C * 10^exp (exact) |
|
|
1375 |
res = C1 * ten2k64[exp]; // the result is positive |
|
|
1376 |
} |
|
|
1377 |
} |
|
|
1378 |
BID_RETURN (res); |
|
|
1379 |
} |
|
|
1380 |
|
|
|
1381 |
/***************************************************************************** |
|
|
1382 |
* BID64_to_uint32_int |
|
|
1383 |
****************************************************************************/ |
|
|
1384 |
|
|
|
1385 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
1386 |
void |
|
|
1387 |
bid64_to_uint32_int (unsigned int *pres, UINT64 * px |
|
|
1388 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) |
|
|
1389 |
{ |
|
|
1390 |
UINT64 x = *px; |
|
|
1391 |
#else |
|
|
1392 |
unsigned int |
|
|
1393 |
bid64_to_uint32_int (UINT64 x |
|
|
1394 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) |
|
|
1395 |
{ |
|
|
1396 |
#endif |
|
|
1397 |
unsigned int res; |
|
|
1398 |
UINT64 x_sign; |
|
|
1399 |
UINT64 x_exp; |
|
|
1400 |
int exp; // unbiased exponent |
|
|
1401 |
// Note: C1 represents x_significand (UINT64) |
|
|
1402 |
UINT64 tmp64; |
|
|
1403 |
BID_UI64DOUBLE tmp1; |
|
|
1404 |
unsigned int x_nr_bits; |
|
|
1405 |
int q, ind, shift; |
|
|
1406 |
UINT64 C1; |
|
|
1407 |
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
|
|
1408 |
UINT128 P128; |
|
|
1409 |
|
|
|
1410 |
// check for NaN or Infinity |
|
|
1411 |
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
|
|
1412 |
// set invalid flag |
|
|
1413 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1414 |
// return Integer Indefinite |
|
|
1415 |
res = 0x80000000; |
|
|
1416 |
BID_RETURN (res); |
|
|
1417 |
} |
|
|
1418 |
// unpack x |
|
|
1419 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
1420 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
1421 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
1422 |
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
|
|
1423 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
1424 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
1425 |
x_exp = 0; |
|
|
1426 |
C1 = 0; |
|
|
1427 |
} |
|
|
1428 |
} else { |
|
|
1429 |
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
|
|
1430 |
C1 = x & MASK_BINARY_SIG1; |
|
|
1431 |
} |
|
|
1432 |
|
|
|
1433 |
// check for zeros (possibly from non-canonical values) |
|
|
1434 |
if (C1 == 0x0ull) { |
|
|
1435 |
// x is 0 |
|
|
1436 |
res = 0x00000000; |
|
|
1437 |
BID_RETURN (res); |
|
|
1438 |
} |
|
|
1439 |
// x is not special and is not zero |
|
|
1440 |
|
|
|
1441 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
1442 |
// determine first the nr. of bits in x |
|
|
1443 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1444 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
1445 |
if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
1446 |
tmp1.d = (double) (C1 >> 32); // exact conversion |
|
|
1447 |
x_nr_bits = |
|
|
1448 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1449 |
} else { // x < 2^32 |
|
|
1450 |
tmp1.d = (double) C1; // exact conversion |
|
|
1451 |
x_nr_bits = |
|
|
1452 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1453 |
} |
|
|
1454 |
} else { // if x < 2^53 |
|
|
1455 |
tmp1.d = (double) C1; // exact conversion |
|
|
1456 |
x_nr_bits = |
|
|
1457 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1458 |
} |
|
|
1459 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1460 |
if (q == 0) { |
|
|
1461 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1462 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
1463 |
q++; |
|
|
1464 |
} |
|
|
1465 |
exp = x_exp - 398; // unbiased exponent |
|
|
1466 |
|
|
|
1467 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
1468 |
// set invalid flag |
|
|
1469 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1470 |
// return Integer Indefinite |
|
|
1471 |
res = 0x80000000; |
|
|
1472 |
BID_RETURN (res); |
|
|
1473 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
1474 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
1475 |
// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
|
|
1476 |
// the cases that do not fit are identified here; the ones that fit |
|
|
1477 |
// fall through and will be handled with other cases further, |
|
|
1478 |
// under '1 <= q + exp <= 10' |
|
|
1479 |
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 |
|
|
1480 |
// => set invalid flag |
|
|
1481 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1482 |
// return Integer Indefinite |
|
|
1483 |
res = 0x80000000; |
|
|
1484 |
BID_RETURN (res); |
|
|
1485 |
} else { // if n > 0 and q + exp = 10 |
|
|
1486 |
// if n >= 2^32 then n is too large |
|
|
1487 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 |
|
|
1488 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 |
|
|
1489 |
// <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 |
|
|
1490 |
if (q <= 11) { |
|
|
1491 |
// Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits |
|
|
1492 |
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1493 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1494 |
if (tmp64 >= 0xa00000000ull) { |
|
|
1495 |
// set invalid flag |
|
|
1496 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1497 |
// return Integer Indefinite |
|
|
1498 |
res = 0x80000000; |
|
|
1499 |
BID_RETURN (res); |
|
|
1500 |
} |
|
|
1501 |
// else cases that can be rounded to a 32-bit unsigned int fall through |
|
|
1502 |
// to '1 <= q + exp <= 10' |
|
|
1503 |
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
|
|
1504 |
// C * 10^(11-q) >= 0xa00000000 <=> |
|
|
1505 |
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 |
|
|
1506 |
// (scale 2^32-1/2 up) |
|
|
1507 |
// Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 |
|
|
1508 |
tmp64 = 0xa00000000ull * ten2k64[q - 11]; |
|
|
1509 |
if (C1 >= tmp64) { |
|
|
1510 |
// set invalid flag |
|
|
1511 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1512 |
// return Integer Indefinite |
|
|
1513 |
res = 0x80000000; |
|
|
1514 |
BID_RETURN (res); |
|
|
1515 |
} |
|
|
1516 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1517 |
// to '1 <= q + exp <= 10' |
|
|
1518 |
} |
|
|
1519 |
} |
|
|
1520 |
} |
|
|
1521 |
// n is not too large to be converted to int32 if -1 < n < 2^32 |
|
|
1522 |
// Note: some of the cases tested for above fall through to this point |
|
|
1523 |
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) |
|
|
1524 |
// return 0 |
|
|
1525 |
res = 0x00000000; |
|
|
1526 |
BID_RETURN (res); |
|
|
1527 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
|
|
1528 |
// x <= -1 or 1 <= x < 2^32 so if positive, x can be |
|
|
1529 |
// rounded to nearest to a 32-bit unsigned integer |
|
|
1530 |
if (x_sign) { // x <= -1 |
|
|
1531 |
// set invalid flag |
|
|
1532 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1533 |
// return Integer Indefinite |
|
|
1534 |
res = 0x80000000; |
|
|
1535 |
BID_RETURN (res); |
|
|
1536 |
} |
|
|
1537 |
// 1 <= x < 2^32 so x can be rounded |
|
|
1538 |
// to nearest to a 32-bit unsigned integer |
|
|
1539 |
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
1540 |
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
|
|
1541 |
// chop off ind digits from the lower part of C1 |
|
|
1542 |
// C1 fits in 64 bits |
|
|
1543 |
// calculate C* and f* |
|
|
1544 |
// C* is actually floor(C*) in this case |
|
|
1545 |
// C* and f* need shifting and masking, as shown by |
|
|
1546 |
// shiftright128[] and maskhigh128[] |
|
|
1547 |
// 1 <= x <= 15 |
|
|
1548 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
1549 |
// C* = C1 * 10^(-x) |
|
|
1550 |
// the approximation of 10^(-x) was rounded up to 54 bits |
|
|
1551 |
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
|
|
1552 |
Cstar = P128.w[1]; |
|
|
1553 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
|
|
1554 |
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
|
|
1555 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
1556 |
// correct by Property 1) |
|
|
1557 |
// n = C* * 10^(e+x) |
|
|
1558 |
|
|
|
1559 |
// shift right C* by Ex-64 = shiftright128[ind] |
|
|
1560 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
|
|
1561 |
Cstar = Cstar >> shift; |
|
|
1562 |
|
|
|
1563 |
res = Cstar; // the result is positive |
|
|
1564 |
} else if (exp == 0) { |
|
|
1565 |
// 1 <= q <= 10 |
|
|
1566 |
// res = +C (exact) |
|
|
1567 |
res = C1; // the result is positive |
|
|
1568 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
1569 |
// res = +C * 10^exp (exact) |
|
|
1570 |
res = C1 * ten2k64[exp]; // the result is positive |
|
|
1571 |
} |
|
|
1572 |
} |
|
|
1573 |
BID_RETURN (res); |
|
|
1574 |
} |
|
|
1575 |
|
|
|
1576 |
/***************************************************************************** |
|
|
1577 |
* BID64_to_uint32_xint |
|
|
1578 |
****************************************************************************/ |
|
|
1579 |
|
|
|
1580 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
1581 |
void |
|
|
1582 |
bid64_to_uint32_xint (unsigned int *pres, UINT64 * px |
|
|
1583 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
1584 |
_EXC_INFO_PARAM) { |
|
|
1585 |
UINT64 x = *px; |
|
|
1586 |
#else |
|
|
1587 |
unsigned int |
|
|
1588 |
bid64_to_uint32_xint (UINT64 x |
|
|
1589 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
1590 |
_EXC_INFO_PARAM) { |
|
|
1591 |
#endif |
|
|
1592 |
unsigned int res; |
|
|
1593 |
UINT64 x_sign; |
|
|
1594 |
UINT64 x_exp; |
|
|
1595 |
int exp; // unbiased exponent |
|
|
1596 |
// Note: C1 represents x_significand (UINT64) |
|
|
1597 |
UINT64 tmp64; |
|
|
1598 |
BID_UI64DOUBLE tmp1; |
|
|
1599 |
unsigned int x_nr_bits; |
|
|
1600 |
int q, ind, shift; |
|
|
1601 |
UINT64 C1; |
|
|
1602 |
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
|
|
1603 |
UINT128 fstar; |
|
|
1604 |
UINT128 P128; |
|
|
1605 |
|
|
|
1606 |
// check for NaN or Infinity |
|
|
1607 |
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
|
|
1608 |
// set invalid flag |
|
|
1609 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1610 |
// return Integer Indefinite |
|
|
1611 |
res = 0x80000000; |
|
|
1612 |
BID_RETURN (res); |
|
|
1613 |
} |
|
|
1614 |
// unpack x |
|
|
1615 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
1616 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
1617 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
1618 |
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
|
|
1619 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
1620 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
1621 |
x_exp = 0; |
|
|
1622 |
C1 = 0; |
|
|
1623 |
} |
|
|
1624 |
} else { |
|
|
1625 |
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
|
|
1626 |
C1 = x & MASK_BINARY_SIG1; |
|
|
1627 |
} |
|
|
1628 |
|
|
|
1629 |
// check for zeros (possibly from non-canonical values) |
|
|
1630 |
if (C1 == 0x0ull) { |
|
|
1631 |
// x is 0 |
|
|
1632 |
res = 0x00000000; |
|
|
1633 |
BID_RETURN (res); |
|
|
1634 |
} |
|
|
1635 |
// x is not special and is not zero |
|
|
1636 |
|
|
|
1637 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
1638 |
// determine first the nr. of bits in x |
|
|
1639 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1640 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
1641 |
if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
1642 |
tmp1.d = (double) (C1 >> 32); // exact conversion |
|
|
1643 |
x_nr_bits = |
|
|
1644 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1645 |
} else { // x < 2^32 |
|
|
1646 |
tmp1.d = (double) C1; // exact conversion |
|
|
1647 |
x_nr_bits = |
|
|
1648 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1649 |
} |
|
|
1650 |
} else { // if x < 2^53 |
|
|
1651 |
tmp1.d = (double) C1; // exact conversion |
|
|
1652 |
x_nr_bits = |
|
|
1653 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1654 |
} |
|
|
1655 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1656 |
if (q == 0) { |
|
|
1657 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1658 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
1659 |
q++; |
|
|
1660 |
} |
|
|
1661 |
exp = x_exp - 398; // unbiased exponent |
|
|
1662 |
|
|
|
1663 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
1664 |
// set invalid flag |
|
|
1665 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1666 |
// return Integer Indefinite |
|
|
1667 |
res = 0x80000000; |
|
|
1668 |
BID_RETURN (res); |
|
|
1669 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
1670 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
1671 |
// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
|
|
1672 |
// the cases that do not fit are identified here; the ones that fit |
|
|
1673 |
// fall through and will be handled with other cases further, |
|
|
1674 |
// under '1 <= q + exp <= 10' |
|
|
1675 |
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 |
|
|
1676 |
// => set invalid flag |
|
|
1677 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1678 |
// return Integer Indefinite |
|
|
1679 |
res = 0x80000000; |
|
|
1680 |
BID_RETURN (res); |
|
|
1681 |
} else { // if n > 0 and q + exp = 10 |
|
|
1682 |
// if n >= 2^32 then n is too large |
|
|
1683 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 |
|
|
1684 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 |
|
|
1685 |
// <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 |
|
|
1686 |
if (q <= 11) { |
|
|
1687 |
// Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits |
|
|
1688 |
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1689 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1690 |
if (tmp64 >= 0xa00000000ull) { |
|
|
1691 |
// set invalid flag |
|
|
1692 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1693 |
// return Integer Indefinite |
|
|
1694 |
res = 0x80000000; |
|
|
1695 |
BID_RETURN (res); |
|
|
1696 |
} |
|
|
1697 |
// else cases that can be rounded to a 32-bit unsigned int fall through |
|
|
1698 |
// to '1 <= q + exp <= 10' |
|
|
1699 |
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
|
|
1700 |
// C * 10^(11-q) >= 0xa00000000 <=> |
|
|
1701 |
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 |
|
|
1702 |
// (scale 2^32-1/2 up) |
|
|
1703 |
// Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 |
|
|
1704 |
tmp64 = 0xa00000000ull * ten2k64[q - 11]; |
|
|
1705 |
if (C1 >= tmp64) { |
|
|
1706 |
// set invalid flag |
|
|
1707 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1708 |
// return Integer Indefinite |
|
|
1709 |
res = 0x80000000; |
|
|
1710 |
BID_RETURN (res); |
|
|
1711 |
} |
|
|
1712 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1713 |
// to '1 <= q + exp <= 10' |
|
|
1714 |
} |
|
|
1715 |
} |
|
|
1716 |
} |
|
|
1717 |
// n is not too large to be converted to int32 if -1 < n < 2^32 |
|
|
1718 |
// Note: some of the cases tested for above fall through to this point |
|
|
1719 |
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) |
|
|
1720 |
// set inexact flag |
|
|
1721 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1722 |
// return 0 |
|
|
1723 |
res = 0x00000000; |
|
|
1724 |
BID_RETURN (res); |
|
|
1725 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
|
|
1726 |
// x <= -1 or 1 <= x < 2^32 so if positive, x can be |
|
|
1727 |
// rounded to nearest to a 32-bit unsigned integer |
|
|
1728 |
if (x_sign) { // x <= -1 |
|
|
1729 |
// set invalid flag |
|
|
1730 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1731 |
// return Integer Indefinite |
|
|
1732 |
res = 0x80000000; |
|
|
1733 |
BID_RETURN (res); |
|
|
1734 |
} |
|
|
1735 |
// 1 <= x < 2^32 so x can be rounded |
|
|
1736 |
// to nearest to a 32-bit unsigned integer |
|
|
1737 |
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
1738 |
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
|
|
1739 |
// chop off ind digits from the lower part of C1 |
|
|
1740 |
// C1 fits in 64 bits |
|
|
1741 |
// calculate C* and f* |
|
|
1742 |
// C* is actually floor(C*) in this case |
|
|
1743 |
// C* and f* need shifting and masking, as shown by |
|
|
1744 |
// shiftright128[] and maskhigh128[] |
|
|
1745 |
// 1 <= x <= 15 |
|
|
1746 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
1747 |
// C* = C1 * 10^(-x) |
|
|
1748 |
// the approximation of 10^(-x) was rounded up to 54 bits |
|
|
1749 |
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
|
|
1750 |
Cstar = P128.w[1]; |
|
|
1751 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
1752 |
fstar.w[0] = P128.w[0]; |
|
|
1753 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
|
|
1754 |
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
|
|
1755 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
1756 |
// correct by Property 1) |
|
|
1757 |
// n = C* * 10^(e+x) |
|
|
1758 |
|
|
|
1759 |
// shift right C* by Ex-64 = shiftright128[ind] |
|
|
1760 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
|
|
1761 |
Cstar = Cstar >> shift; |
|
|
1762 |
// determine inexactness of the rounding of C* |
|
|
1763 |
// if (0 < f* < 10^(-x)) then |
|
|
1764 |
// the result is exact |
|
|
1765 |
// else // if (f* > T*) then |
|
|
1766 |
// the result is inexact |
|
|
1767 |
if (ind - 1 <= 2) { // fstar.w[1] is 0 |
|
|
1768 |
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
1769 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
1770 |
// ten2mk128[ind -1].w[1] |
|
|
1771 |
// set the inexact flag |
|
|
1772 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1773 |
} // else the result is exact |
|
|
1774 |
} else { // if 3 <= ind - 1 <= 14 |
|
|
1775 |
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
1776 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
1777 |
// ten2mk128[ind -1].w[1] |
|
|
1778 |
// set the inexact flag |
|
|
1779 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1780 |
} // else the result is exact |
|
|
1781 |
} |
|
|
1782 |
|
|
|
1783 |
res = Cstar; // the result is positive |
|
|
1784 |
} else if (exp == 0) { |
|
|
1785 |
// 1 <= q <= 10 |
|
|
1786 |
// res = +C (exact) |
|
|
1787 |
res = C1; // the result is positive |
|
|
1788 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
1789 |
// res = +C * 10^exp (exact) |
|
|
1790 |
res = C1 * ten2k64[exp]; // the result is positive |
|
|
1791 |
} |
|
|
1792 |
} |
|
|
1793 |
BID_RETURN (res); |
|
|
1794 |
} |
|
|
1795 |
|
|
|
1796 |
/***************************************************************************** |
|
|
1797 |
* BID64_to_uint32_rninta |
|
|
1798 |
****************************************************************************/ |
|
|
1799 |
|
|
|
1800 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
1801 |
void |
|
|
1802 |
bid64_to_uint32_rninta (unsigned int *pres, UINT64 * px |
|
|
1803 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
1804 |
_EXC_INFO_PARAM) { |
|
|
1805 |
UINT64 x = *px; |
|
|
1806 |
#else |
|
|
1807 |
unsigned int |
|
|
1808 |
bid64_to_uint32_rninta (UINT64 x |
|
|
1809 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
1810 |
_EXC_INFO_PARAM) { |
|
|
1811 |
#endif |
|
|
1812 |
unsigned int res; |
|
|
1813 |
UINT64 x_sign; |
|
|
1814 |
UINT64 x_exp; |
|
|
1815 |
int exp; // unbiased exponent |
|
|
1816 |
// Note: C1 represents x_significand (UINT64) |
|
|
1817 |
UINT64 tmp64; |
|
|
1818 |
BID_UI64DOUBLE tmp1; |
|
|
1819 |
unsigned int x_nr_bits; |
|
|
1820 |
int q, ind, shift; |
|
|
1821 |
UINT64 C1; |
|
|
1822 |
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
|
|
1823 |
UINT128 P128; |
|
|
1824 |
|
|
|
1825 |
// check for NaN or Infinity |
|
|
1826 |
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
|
|
1827 |
// set invalid flag |
|
|
1828 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1829 |
// return Integer Indefinite |
|
|
1830 |
res = 0x80000000; |
|
|
1831 |
BID_RETURN (res); |
|
|
1832 |
} |
|
|
1833 |
// unpack x |
|
|
1834 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
1835 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
1836 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
1837 |
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
|
|
1838 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
1839 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
1840 |
x_exp = 0; |
|
|
1841 |
C1 = 0; |
|
|
1842 |
} |
|
|
1843 |
} else { |
|
|
1844 |
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
|
|
1845 |
C1 = x & MASK_BINARY_SIG1; |
|
|
1846 |
} |
|
|
1847 |
|
|
|
1848 |
// check for zeros (possibly from non-canonical values) |
|
|
1849 |
if (C1 == 0x0ull) { |
|
|
1850 |
// x is 0 |
|
|
1851 |
res = 0x00000000; |
|
|
1852 |
BID_RETURN (res); |
|
|
1853 |
} |
|
|
1854 |
// x is not special and is not zero |
|
|
1855 |
|
|
|
1856 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
1857 |
// determine first the nr. of bits in x |
|
|
1858 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1859 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
1860 |
if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
1861 |
tmp1.d = (double) (C1 >> 32); // exact conversion |
|
|
1862 |
x_nr_bits = |
|
|
1863 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1864 |
} else { // x < 2^32 |
|
|
1865 |
tmp1.d = (double) C1; // exact conversion |
|
|
1866 |
x_nr_bits = |
|
|
1867 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1868 |
} |
|
|
1869 |
} else { // if x < 2^53 |
|
|
1870 |
tmp1.d = (double) C1; // exact conversion |
|
|
1871 |
x_nr_bits = |
|
|
1872 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1873 |
} |
|
|
1874 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1875 |
if (q == 0) { |
|
|
1876 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1877 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
1878 |
q++; |
|
|
1879 |
} |
|
|
1880 |
exp = x_exp - 398; // unbiased exponent |
|
|
1881 |
|
|
|
1882 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
1883 |
// set invalid flag |
|
|
1884 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1885 |
// return Integer Indefinite |
|
|
1886 |
res = 0x80000000; |
|
|
1887 |
BID_RETURN (res); |
|
|
1888 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
1889 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
1890 |
// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
|
|
1891 |
// the cases that do not fit are identified here; the ones that fit |
|
|
1892 |
// fall through and will be handled with other cases further, |
|
|
1893 |
// under '1 <= q + exp <= 10' |
|
|
1894 |
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 |
|
|
1895 |
// => set invalid flag |
|
|
1896 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1897 |
// return Integer Indefinite |
|
|
1898 |
res = 0x80000000; |
|
|
1899 |
BID_RETURN (res); |
|
|
1900 |
} else { // if n > 0 and q + exp = 10 |
|
|
1901 |
// if n >= 2^32 - 1/2 then n is too large |
|
|
1902 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 |
|
|
1903 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 |
|
|
1904 |
// <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 |
|
|
1905 |
if (q <= 11) { |
|
|
1906 |
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits |
|
|
1907 |
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1908 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1909 |
if (tmp64 >= 0x9fffffffbull) { |
|
|
1910 |
// set invalid flag |
|
|
1911 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1912 |
// return Integer Indefinite |
|
|
1913 |
res = 0x80000000; |
|
|
1914 |
BID_RETURN (res); |
|
|
1915 |
} |
|
|
1916 |
// else cases that can be rounded to a 32-bit unsigned int fall through |
|
|
1917 |
// to '1 <= q + exp <= 10' |
|
|
1918 |
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
|
|
1919 |
// C * 10^(11-q) >= 0x9fffffffb <=> |
|
|
1920 |
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 |
|
|
1921 |
// (scale 2^32-1/2 up) |
|
|
1922 |
// Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 |
|
|
1923 |
tmp64 = 0x9fffffffbull * ten2k64[q - 11]; |
|
|
1924 |
if (C1 >= tmp64) { |
|
|
1925 |
// set invalid flag |
|
|
1926 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1927 |
// return Integer Indefinite |
|
|
1928 |
res = 0x80000000; |
|
|
1929 |
BID_RETURN (res); |
|
|
1930 |
} |
|
|
1931 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1932 |
// to '1 <= q + exp <= 10' |
|
|
1933 |
} |
|
|
1934 |
} |
|
|
1935 |
} |
|
|
1936 |
// n is not too large to be converted to int32 if -1/2 < n < 2^32 - 1/2 |
|
|
1937 |
// Note: some of the cases tested for above fall through to this point |
|
|
1938 |
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
|
|
1939 |
// return 0 |
|
|
1940 |
res = 0x00000000; |
|
|
1941 |
BID_RETURN (res); |
|
|
1942 |
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
|
|
1943 |
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) |
|
|
1944 |
// res = 0 |
|
|
1945 |
// else if x > 0 |
|
|
1946 |
// res = +1 |
|
|
1947 |
// else // if x < 0 |
|
|
1948 |
// invalid exc |
|
|
1949 |
ind = q - 1; |
|
|
1950 |
if (C1 < midpoint64[ind]) { |
|
|
1951 |
res = 0x00000000; // return 0 |
|
|
1952 |
} else if (x_sign) { // n < 0 |
|
|
1953 |
// set invalid flag |
|
|
1954 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1955 |
// return Integer Indefinite |
|
|
1956 |
res = 0x80000000; |
|
|
1957 |
BID_RETURN (res); |
|
|
1958 |
} else { // n > 0 |
|
|
1959 |
res = 0x00000001; // return +1 |
|
|
1960 |
} |
|
|
1961 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
|
|
1962 |
// -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be |
|
|
1963 |
// rounded to nearest to a 32-bit unsigned integer |
|
|
1964 |
if (x_sign) { // x <= -1 |
|
|
1965 |
// set invalid flag |
|
|
1966 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1967 |
// return Integer Indefinite |
|
|
1968 |
res = 0x80000000; |
|
|
1969 |
BID_RETURN (res); |
|
|
1970 |
} |
|
|
1971 |
// 1 <= x < 2^32-1/2 so x can be rounded |
|
|
1972 |
// to nearest to a 32-bit unsigned integer |
|
|
1973 |
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
1974 |
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
|
|
1975 |
// chop off ind digits from the lower part of C1 |
|
|
1976 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits |
|
|
1977 |
C1 = C1 + midpoint64[ind - 1]; |
|
|
1978 |
// calculate C* and f* |
|
|
1979 |
// C* is actually floor(C*) in this case |
|
|
1980 |
// C* and f* need shifting and masking, as shown by |
|
|
1981 |
// shiftright128[] and maskhigh128[] |
|
|
1982 |
// 1 <= x <= 15 |
|
|
1983 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
1984 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
1985 |
// the approximation of 10^(-x) was rounded up to 54 bits |
|
|
1986 |
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
|
|
1987 |
Cstar = P128.w[1]; |
|
|
1988 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
|
|
1989 |
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
|
|
1990 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
1991 |
// correct by Property 1) |
|
|
1992 |
// n = C* * 10^(e+x) |
|
|
1993 |
|
|
|
1994 |
// shift right C* by Ex-64 = shiftright128[ind] |
|
|
1995 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
|
|
1996 |
Cstar = Cstar >> shift; |
|
|
1997 |
|
|
|
1998 |
// if the result was a midpoint it was rounded away from zero |
|
|
1999 |
res = Cstar; // the result is positive |
|
|
2000 |
} else if (exp == 0) { |
|
|
2001 |
// 1 <= q <= 10 |
|
|
2002 |
// res = +C (exact) |
|
|
2003 |
res = C1; // the result is positive |
|
|
2004 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
2005 |
// res = +C * 10^exp (exact) |
|
|
2006 |
res = C1 * ten2k64[exp]; // the result is positive |
|
|
2007 |
} |
|
|
2008 |
} |
|
|
2009 |
BID_RETURN (res); |
|
|
2010 |
} |
|
|
2011 |
|
|
|
2012 |
/***************************************************************************** |
|
|
2013 |
* BID64_to_uint32_xrninta |
|
|
2014 |
****************************************************************************/ |
|
|
2015 |
|
|
|
2016 |
#if DECIMAL_CALL_BY_REFERENCE |
|
|
2017 |
void |
|
|
2018 |
bid64_to_uint32_xrninta (unsigned int *pres, UINT64 * px |
|
|
2019 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
2020 |
_EXC_INFO_PARAM) { |
|
|
2021 |
UINT64 x = *px; |
|
|
2022 |
#else |
|
|
2023 |
unsigned int |
|
|
2024 |
bid64_to_uint32_xrninta (UINT64 x |
|
|
2025 |
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM |
|
|
2026 |
_EXC_INFO_PARAM) { |
|
|
2027 |
#endif |
|
|
2028 |
unsigned int res; |
|
|
2029 |
UINT64 x_sign; |
|
|
2030 |
UINT64 x_exp; |
|
|
2031 |
int exp; // unbiased exponent |
|
|
2032 |
// Note: C1 represents x_significand (UINT64) |
|
|
2033 |
UINT64 tmp64; |
|
|
2034 |
BID_UI64DOUBLE tmp1; |
|
|
2035 |
unsigned int x_nr_bits; |
|
|
2036 |
int q, ind, shift; |
|
|
2037 |
UINT64 C1; |
|
|
2038 |
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits |
|
|
2039 |
UINT128 fstar; |
|
|
2040 |
UINT128 P128; |
|
|
2041 |
|
|
|
2042 |
// check for NaN or Infinity |
|
|
2043 |
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) { |
|
|
2044 |
// set invalid flag |
|
|
2045 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2046 |
// return Integer Indefinite |
|
|
2047 |
res = 0x80000000; |
|
|
2048 |
BID_RETURN (res); |
|
|
2049 |
} |
|
|
2050 |
// unpack x |
|
|
2051 |
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
2052 |
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => |
|
|
2053 |
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { |
|
|
2054 |
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased |
|
|
2055 |
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; |
|
|
2056 |
if (C1 > 9999999999999999ull) { // non-canonical |
|
|
2057 |
x_exp = 0; |
|
|
2058 |
C1 = 0; |
|
|
2059 |
} |
|
|
2060 |
} else { |
|
|
2061 |
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased |
|
|
2062 |
C1 = x & MASK_BINARY_SIG1; |
|
|
2063 |
} |
|
|
2064 |
|
|
|
2065 |
// check for zeros (possibly from non-canonical values) |
|
|
2066 |
if (C1 == 0x0ull) { |
|
|
2067 |
// x is 0 |
|
|
2068 |
res = 0x00000000; |
|
|
2069 |
BID_RETURN (res); |
|
|
2070 |
} |
|
|
2071 |
// x is not special and is not zero |
|
|
2072 |
|
|
|
2073 |
// q = nr. of decimal digits in x (1 <= q <= 54) |
|
|
2074 |
// determine first the nr. of bits in x |
|
|
2075 |
if (C1 >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
2076 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
2077 |
if (C1 >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
2078 |
tmp1.d = (double) (C1 >> 32); // exact conversion |
|
|
2079 |
x_nr_bits = |
|
|
2080 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2081 |
} else { // x < 2^32 |
|
|
2082 |
tmp1.d = (double) C1; // exact conversion |
|
|
2083 |
x_nr_bits = |
|
|
2084 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2085 |
} |
|
|
2086 |
} else { // if x < 2^53 |
|
|
2087 |
tmp1.d = (double) C1; // exact conversion |
|
|
2088 |
x_nr_bits = |
|
|
2089 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2090 |
} |
|
|
2091 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
2092 |
if (q == 0) { |
|
|
2093 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
2094 |
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) |
|
|
2095 |
q++; |
|
|
2096 |
} |
|
|
2097 |
exp = x_exp - 398; // unbiased exponent |
|
|
2098 |
|
|
|
2099 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
2100 |
// set invalid flag |
|
|
2101 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2102 |
// return Integer Indefinite |
|
|
2103 |
res = 0x80000000; |
|
|
2104 |
BID_RETURN (res); |
|
|
2105 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
2106 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
2107 |
// so x rounded to an integer may or may not fit in an unsigned 32-bit int |
|
|
2108 |
// the cases that do not fit are identified here; the ones that fit |
|
|
2109 |
// fall through and will be handled with other cases further, |
|
|
2110 |
// under '1 <= q + exp <= 10' |
|
|
2111 |
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 |
|
|
2112 |
// => set invalid flag |
|
|
2113 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2114 |
// return Integer Indefinite |
|
|
2115 |
res = 0x80000000; |
|
|
2116 |
BID_RETURN (res); |
|
|
2117 |
} else { // if n > 0 and q + exp = 10 |
|
|
2118 |
// if n >= 2^32 - 1/2 then n is too large |
|
|
2119 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 |
|
|
2120 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 |
|
|
2121 |
// <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 |
|
|
2122 |
if (q <= 11) { |
|
|
2123 |
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits |
|
|
2124 |
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
2125 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
2126 |
if (tmp64 >= 0x9fffffffbull) { |
|
|
2127 |
// set invalid flag |
|
|
2128 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2129 |
// return Integer Indefinite |
|
|
2130 |
res = 0x80000000; |
|
|
2131 |
BID_RETURN (res); |
|
|
2132 |
} |
|
|
2133 |
// else cases that can be rounded to a 32-bit unsigned int fall through |
|
|
2134 |
// to '1 <= q + exp <= 10' |
|
|
2135 |
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 |
|
|
2136 |
// C * 10^(11-q) >= 0x9fffffffb <=> |
|
|
2137 |
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 |
|
|
2138 |
// (scale 2^32-1/2 up) |
|
|
2139 |
// Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 |
|
|
2140 |
tmp64 = 0x9fffffffbull * ten2k64[q - 11]; |
|
|
2141 |
if (C1 >= tmp64) { |
|
|
2142 |
// set invalid flag |
|
|
2143 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2144 |
// return Integer Indefinite |
|
|
2145 |
res = 0x80000000; |
|
|
2146 |
BID_RETURN (res); |
|
|
2147 |
} |
|
|
2148 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2149 |
// to '1 <= q + exp <= 10' |
|
|
2150 |
} |
|
|
2151 |
} |
|
|
2152 |
} |
|
|
2153 |
// n is not too large to be converted to int32 if -1/2 < n < 2^32 - 1/2 |
|
|
2154 |
// Note: some of the cases tested for above fall through to this point |
|
|
2155 |
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
|
|
2156 |
// set inexact flag |
|
|
2157 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2158 |
// return 0 |
|
|
2159 |
res = 0x00000000; |
|
|
2160 |
BID_RETURN (res); |
|
|
2161 |
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
|
|
2162 |
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) |
|
|
2163 |
// res = 0 |
|
|
2164 |
// else if x > 0 |
|
|
2165 |
// res = +1 |
|
|
2166 |
// else // if x < 0 |
|
|
2167 |
// invalid exc |
|
|
2168 |
ind = q - 1; |
|
|
2169 |
if (C1 < midpoint64[ind]) { |
|
|
2170 |
res = 0x00000000; // return 0 |
|
|
2171 |
} else if (x_sign) { // n < 0 |
|
|
2172 |
// set invalid flag |
|
|
2173 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2174 |
// return Integer Indefinite |
|
|
2175 |
res = 0x80000000; |
|
|
2176 |
BID_RETURN (res); |
|
|
2177 |
} else { // n > 0 |
|
|
2178 |
res = 0x00000001; // return +1 |
|
|
2179 |
} |
|
|
2180 |
// set inexact flag |
|
|
2181 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2182 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) |
|
|
2183 |
// -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be |
|
|
2184 |
// rounded to nearest to a 32-bit unsigned integer |
|
|
2185 |
if (x_sign) { // x <= -1 |
|
|
2186 |
// set invalid flag |
|
|
2187 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2188 |
// return Integer Indefinite |
|
|
2189 |
res = 0x80000000; |
|
|
2190 |
BID_RETURN (res); |
|
|
2191 |
} |
|
|
2192 |
// 1 <= x < 2^32-1/2 so x can be rounded |
|
|
2193 |
// to nearest to a 32-bit unsigned integer |
|
|
2194 |
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
2195 |
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' |
|
|
2196 |
// chop off ind digits from the lower part of C1 |
|
|
2197 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits |
|
|
2198 |
C1 = C1 + midpoint64[ind - 1]; |
|
|
2199 |
// calculate C* and f* |
|
|
2200 |
// C* is actually floor(C*) in this case |
|
|
2201 |
// C* and f* need shifting and masking, as shown by |
|
|
2202 |
// shiftright128[] and maskhigh128[] |
|
|
2203 |
// 1 <= x <= 15 |
|
|
2204 |
// kx = 10^(-x) = ten2mk64[ind - 1] |
|
|
2205 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
2206 |
// the approximation of 10^(-x) was rounded up to 54 bits |
|
|
2207 |
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); |
|
|
2208 |
Cstar = P128.w[1]; |
|
|
2209 |
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; |
|
|
2210 |
fstar.w[0] = P128.w[0]; |
|
|
2211 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. |
|
|
2212 |
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 |
|
|
2213 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
2214 |
// correct by Property 1) |
|
|
2215 |
// n = C* * 10^(e+x) |
|
|
2216 |
|
|
|
2217 |
// shift right C* by Ex-64 = shiftright128[ind] |
|
|
2218 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 39 |
|
|
2219 |
Cstar = Cstar >> shift; |
|
|
2220 |
|
|
|
2221 |
// determine inexactness of the rounding of C* |
|
|
2222 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
2223 |
// the result is exact |
|
|
2224 |
// else // if (f* - 1/2 > T*) then |
|
|
2225 |
// the result is inexact |
|
|
2226 |
if (ind - 1 <= 2) { // fstar.w[1] is 0 |
|
|
2227 |
if (fstar.w[0] > 0x8000000000000000ull) { |
|
|
2228 |
// f* > 1/2 and the result may be exact |
|
|
2229 |
tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 |
|
|
2230 |
if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { |
|
|
2231 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
2232 |
// ten2mk128[ind -1].w[1] |
|
|
2233 |
// set the inexact flag |
|
|
2234 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2235 |
} // else the result is exact |
|
|
2236 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2237 |
// set the inexact flag |
|
|
2238 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2239 |
} |
|
|
2240 |
} else { // if 3 <= ind - 1 <= 14 |
|
|
2241 |
if (fstar.w[1] > onehalf128[ind - 1] || |
|
|
2242 |
(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { |
|
|
2243 |
// f2* > 1/2 and the result may be exact |
|
|
2244 |
// Calculate f2* - 1/2 |
|
|
2245 |
tmp64 = fstar.w[1] - onehalf128[ind - 1]; |
|
|
2246 |
if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { |
|
|
2247 |
// ten2mk128trunc[ind -1].w[1] is identical to |
|
|
2248 |
// ten2mk128[ind -1].w[1] |
|
|
2249 |
// set the inexact flag |
|
|
2250 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2251 |
} // else the result is exact |
|
|
2252 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2253 |
// set the inexact flag |
|
|
2254 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2255 |
} |
|
|
2256 |
} |
|
|
2257 |
|
|
|
2258 |
// if the result was a midpoint it was rounded away from zero |
|
|
2259 |
res = Cstar; // the result is positive |
|
|
2260 |
} else if (exp == 0) { |
|
|
2261 |
// 1 <= q <= 10 |
|
|
2262 |
// res = +C (exact) |
|
|
2263 |
res = C1; // the result is positive |
|
|
2264 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
2265 |
// res = +C * 10^exp (exact) |
|
|
2266 |
res = C1 * ten2k64[exp]; // the result is positive |
|
|
2267 |
} |
|
|
2268 |
} |
|
|
2269 |
BID_RETURN (res); |
|
|
2270 |
} |