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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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* BID128_to_int32_rnint |
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****************************************************************************/ |
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BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_rnint, x) |
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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.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are 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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UINT128 C1, C; |
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UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
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UINT256 fstar; |
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UINT256 P256; |
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// unpack x |
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x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
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x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
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C1.w[1] = x.w[1] & MASK_COEFF; |
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C1.w[0] = x.w[0]; |
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// check for NaN or Infinity |
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if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
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// x is special |
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if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
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if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
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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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} else { // x is QNaN |
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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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} |
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BID_RETURN (res); |
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} else { // x is not a NaN, so it must be infinity |
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if (!x_sign) { // x is +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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} else { // x is -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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} |
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BID_RETURN (res); |
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} |
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} |
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// check for non-canonical values (after the check for special values) |
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if ((C1.w[1] > 0x0001ed09bead87c0ull) |
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|| (C1.w[1] == 0x0001ed09bead87c0ull |
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&& (C1.w[0] > 0x378d8e63ffffffffull)) |
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|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
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res = 0x00000000; |
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BID_RETURN (res); |
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} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 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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} else { // x is not special and is not zero |
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// q = nr. of decimal digits in x |
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// determine first the nr. of bits in x |
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if (C1.w[1] == 0) { |
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if (C1.w[0] >= 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.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
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tmp1.d = (double) (C1.w[0] >> 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.w[0]); // 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.w[0]; // 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 { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
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tmp1.d = (double) C1.w[1]; // exact conversion |
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x_nr_bits = |
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65 + ((((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.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
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|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
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&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
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q++; |
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} |
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exp = (x_exp >> 49) - 6176; |
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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 a signed 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 |
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// if n < -2^31 - 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) > 2^31+1/2 |
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// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=34 |
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if (q <= 11) { |
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tmp64 = C1.w[0] * 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 > 0x500000005ull) { |
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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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} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
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// 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005 <=> |
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// C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23 |
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// (scale 2^31+1/2 up) |
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tmp64 = 0x500000005ull; |
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if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
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__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
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} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
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__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
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} |
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if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[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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} |
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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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} else { // if n > 0 and q + exp = 10 |
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// if n >= 2^31 - 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) >= 2^31-1/2 |
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// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34 |
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if (q <= 11) { |
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tmp64 = C1.w[0] * 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 >= 0x4fffffffbull) { |
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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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} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
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// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=> |
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// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 |
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// (scale 2^31-1/2 up) |
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tmp64 = 0x4fffffffbull; |
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if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
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__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
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} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
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__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
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} |
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if (C1.w[1] > C.w[1] |
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|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[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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} |
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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: -2^31 - 1/2 < n < 2^31 - 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 |
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// res = +/-1 |
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ind = q - 1; |
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if (ind <= 18) { // 0 <= ind <= 18 |
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if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { |
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res = 0x00000000; // return 0 |
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} else if (x_sign) { // n < 0 |
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res = 0xffffffff; // return -1 |
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} else { // n > 0 |
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res = 0x00000001; // return +1 |
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} |
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} else { // 19 <= ind <= 33 |
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if ((C1.w[1] < midpoint128[ind - 19].w[1]) |
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|| ((C1.w[1] == midpoint128[ind - 19].w[1]) |
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&& (C1.w[0] <= midpoint128[ind - 19].w[0]))) { |
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res = 0x00000000; // return 0 |
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} else if (x_sign) { // n < 0 |
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res = 0xffffffff; // return -1 |
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} else { // n > 0 |
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res = 0x00000001; // return +1 |
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} |
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} |
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} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
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// -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded |
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// to nearest to a 32-bit signed integer |
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if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
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ind = -exp; // 1 <= ind <= 33; 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 127 bits |
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tmp64 = C1.w[0]; |
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if (ind <= 19) { |
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C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
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} else { |
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C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
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C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
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} |
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if (C1.w[0] < tmp64) |
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C1.w[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 <= 33 |
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// kx = 10^(-x) = ten2mk128[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 118 bits |
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__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
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if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
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Cstar.w[1] = P256.w[3]; |
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Cstar.w[0] = P256.w[2]; |
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fstar.w[3] = 0; |
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fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
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fstar.w[1] = P256.w[1]; |
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fstar.w[0] = P256.w[0]; |
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} else { // 22 <= ind - 1 <= 33 |
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Cstar.w[1] = 0; |
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Cstar.w[0] = P256.w[3]; |
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fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
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fstar.w[2] = P256.w[2]; |
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fstar.w[1] = P256.w[1]; |
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fstar.w[0] = P256.w[0]; |
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} |
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// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
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// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
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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-128 = shiftright128[ind] |
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shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
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if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
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Cstar.w[0] = |
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(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
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// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
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} else { // 22 <= ind - 1 <= 33 |
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Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
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} |
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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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|
311 |
if ((fstar.w[3] == 0) && (fstar.w[2] == 0) |
|
|
312 |
&& (fstar.w[1] || fstar.w[0]) |
|
|
313 |
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] |
|
|
314 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
315 |
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
316 |
// the result is a midpoint; round to nearest |
|
|
317 |
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
|
|
318 |
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
|
|
319 |
Cstar.w[0]--; // Cstar.w[0] is now even |
|
|
320 |
} // else MP in [ODD, EVEN] |
|
|
321 |
} |
|
|
322 |
if (x_sign) |
|
|
323 |
res = -Cstar.w[0]; |
|
|
324 |
else |
|
|
325 |
res = Cstar.w[0]; |
|
|
326 |
} else if (exp == 0) { |
|
|
327 |
// 1 <= q <= 10 |
|
|
328 |
// res = +/-C (exact) |
|
|
329 |
if (x_sign) |
|
|
330 |
res = -C1.w[0]; |
|
|
331 |
else |
|
|
332 |
res = C1.w[0]; |
|
|
333 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
334 |
// res = +/-C * 10^exp (exact) |
|
|
335 |
if (x_sign) |
|
|
336 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
337 |
else |
|
|
338 |
res = C1.w[0] * ten2k64[exp]; |
|
|
339 |
} |
|
|
340 |
} |
|
|
341 |
} |
|
|
342 |
|
|
|
343 |
BID_RETURN (res); |
|
|
344 |
} |
|
|
345 |
|
|
|
346 |
/***************************************************************************** |
|
|
347 |
* BID128_to_int32_xrnint |
|
|
348 |
****************************************************************************/ |
|
|
349 |
|
|
|
350 |
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xrnint, |
|
|
351 |
x) |
|
|
352 |
|
|
|
353 |
int res; |
|
|
354 |
UINT64 x_sign; |
|
|
355 |
UINT64 x_exp; |
|
|
356 |
int exp; // unbiased exponent |
|
|
357 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
358 |
UINT64 tmp64, tmp64A; |
|
|
359 |
BID_UI64DOUBLE tmp1; |
|
|
360 |
unsigned int x_nr_bits; |
|
|
361 |
int q, ind, shift; |
|
|
362 |
UINT128 C1, C; |
|
|
363 |
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
|
|
364 |
UINT256 fstar; |
|
|
365 |
UINT256 P256; |
|
|
366 |
|
|
|
367 |
// unpack x |
|
|
368 |
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
369 |
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
|
|
370 |
C1.w[1] = x.w[1] & MASK_COEFF; |
|
|
371 |
C1.w[0] = x.w[0]; |
|
|
372 |
|
|
|
373 |
// check for NaN or Infinity |
|
|
374 |
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
|
|
375 |
// x is special |
|
|
376 |
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
377 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
|
|
378 |
// set invalid flag |
|
|
379 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
380 |
// return Integer Indefinite |
|
|
381 |
res = 0x80000000; |
|
|
382 |
} else { // x is QNaN |
|
|
383 |
// set invalid flag |
|
|
384 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
385 |
// return Integer Indefinite |
|
|
386 |
res = 0x80000000; |
|
|
387 |
} |
|
|
388 |
BID_RETURN (res); |
|
|
389 |
} else { // x is not a NaN, so it must be infinity |
|
|
390 |
if (!x_sign) { // x is +inf |
|
|
391 |
// set invalid flag |
|
|
392 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
393 |
// return Integer Indefinite |
|
|
394 |
res = 0x80000000; |
|
|
395 |
} else { // x is -inf |
|
|
396 |
// set invalid flag |
|
|
397 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
398 |
// return Integer Indefinite |
|
|
399 |
res = 0x80000000; |
|
|
400 |
} |
|
|
401 |
BID_RETURN (res); |
|
|
402 |
} |
|
|
403 |
} |
|
|
404 |
// check for non-canonical values (after the check for special values) |
|
|
405 |
if ((C1.w[1] > 0x0001ed09bead87c0ull) |
|
|
406 |
|| (C1.w[1] == 0x0001ed09bead87c0ull |
|
|
407 |
&& (C1.w[0] > 0x378d8e63ffffffffull)) |
|
|
408 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
|
|
409 |
res = 0x00000000; |
|
|
410 |
BID_RETURN (res); |
|
|
411 |
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
|
|
412 |
// x is 0 |
|
|
413 |
res = 0x00000000; |
|
|
414 |
BID_RETURN (res); |
|
|
415 |
} else { // x is not special and is not zero |
|
|
416 |
|
|
|
417 |
// q = nr. of decimal digits in x |
|
|
418 |
// determine first the nr. of bits in x |
|
|
419 |
if (C1.w[1] == 0) { |
|
|
420 |
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
421 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
422 |
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
423 |
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
|
|
424 |
x_nr_bits = |
|
|
425 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
426 |
} else { // x < 2^32 |
|
|
427 |
tmp1.d = (double) (C1.w[0]); // exact conversion |
|
|
428 |
x_nr_bits = |
|
|
429 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
430 |
} |
|
|
431 |
} else { // if x < 2^53 |
|
|
432 |
tmp1.d = (double) C1.w[0]; // exact conversion |
|
|
433 |
x_nr_bits = |
|
|
434 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
435 |
} |
|
|
436 |
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
|
|
437 |
tmp1.d = (double) C1.w[1]; // exact conversion |
|
|
438 |
x_nr_bits = |
|
|
439 |
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
440 |
} |
|
|
441 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
442 |
if (q == 0) { |
|
|
443 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
444 |
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
|
|
445 |
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
|
|
446 |
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
|
|
447 |
q++; |
|
|
448 |
} |
|
|
449 |
exp = (x_exp >> 49) - 6176; |
|
|
450 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
451 |
// set invalid flag |
|
|
452 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
453 |
// return Integer Indefinite |
|
|
454 |
res = 0x80000000; |
|
|
455 |
BID_RETURN (res); |
|
|
456 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
457 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
458 |
// so x rounded to an integer may or may not fit in a signed 32-bit int |
|
|
459 |
// the cases that do not fit are identified here; the ones that fit |
|
|
460 |
// fall through and will be handled with other cases further, |
|
|
461 |
// under '1 <= q + exp <= 10' |
|
|
462 |
if (x_sign) { // if n < 0 and q + exp = 10 |
|
|
463 |
// if n < -2^31 - 1/2 then n is too large |
|
|
464 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31+1/2 |
|
|
465 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=34 |
|
|
466 |
if (q <= 11) { |
|
|
467 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
468 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
469 |
if (tmp64 > 0x500000005ull) { |
|
|
470 |
// set invalid flag |
|
|
471 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
472 |
// return Integer Indefinite |
|
|
473 |
res = 0x80000000; |
|
|
474 |
BID_RETURN (res); |
|
|
475 |
} |
|
|
476 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
477 |
// to '1 <= q + exp <= 10' |
|
|
478 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
479 |
// 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005 <=> |
|
|
480 |
// C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
481 |
// (scale 2^31+1/2 up) |
|
|
482 |
tmp64 = 0x500000005ull; |
|
|
483 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
484 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
485 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
486 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
487 |
} |
|
|
488 |
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { |
|
|
489 |
// set invalid flag |
|
|
490 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
491 |
// return Integer Indefinite |
|
|
492 |
res = 0x80000000; |
|
|
493 |
BID_RETURN (res); |
|
|
494 |
} |
|
|
495 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
496 |
// to '1 <= q + exp <= 10' |
|
|
497 |
} |
|
|
498 |
} else { // if n > 0 and q + exp = 10 |
|
|
499 |
// if n >= 2^31 - 1/2 then n is too large |
|
|
500 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 |
|
|
501 |
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34 |
|
|
502 |
if (q <= 11) { |
|
|
503 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
504 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
505 |
if (tmp64 >= 0x4fffffffbull) { |
|
|
506 |
// set invalid flag |
|
|
507 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
508 |
// return Integer Indefinite |
|
|
509 |
res = 0x80000000; |
|
|
510 |
BID_RETURN (res); |
|
|
511 |
} |
|
|
512 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
513 |
// to '1 <= q + exp <= 10' |
|
|
514 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
515 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=> |
|
|
516 |
// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
517 |
// (scale 2^31-1/2 up) |
|
|
518 |
tmp64 = 0x4fffffffbull; |
|
|
519 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
520 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
521 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
522 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
523 |
} |
|
|
524 |
if (C1.w[1] > C.w[1] |
|
|
525 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
526 |
// set invalid flag |
|
|
527 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
528 |
// return Integer Indefinite |
|
|
529 |
res = 0x80000000; |
|
|
530 |
BID_RETURN (res); |
|
|
531 |
} |
|
|
532 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
533 |
// to '1 <= q + exp <= 10' |
|
|
534 |
} |
|
|
535 |
} |
|
|
536 |
} |
|
|
537 |
// n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 |
|
|
538 |
// Note: some of the cases tested for above fall through to this point |
|
|
539 |
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
|
|
540 |
// set inexact flag |
|
|
541 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
542 |
// return 0 |
|
|
543 |
res = 0x00000000; |
|
|
544 |
BID_RETURN (res); |
|
|
545 |
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
|
|
546 |
// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) |
|
|
547 |
// res = 0 |
|
|
548 |
// else |
|
|
549 |
// res = +/-1 |
|
|
550 |
ind = q - 1; |
|
|
551 |
if (ind <= 18) { // 0 <= ind <= 18 |
|
|
552 |
if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) { |
|
|
553 |
res = 0x00000000; // return 0 |
|
|
554 |
} else if (x_sign) { // n < 0 |
|
|
555 |
res = 0xffffffff; // return -1 |
|
|
556 |
} else { // n > 0 |
|
|
557 |
res = 0x00000001; // return +1 |
|
|
558 |
} |
|
|
559 |
} else { // 19 <= ind <= 33 |
|
|
560 |
if ((C1.w[1] < midpoint128[ind - 19].w[1]) |
|
|
561 |
|| ((C1.w[1] == midpoint128[ind - 19].w[1]) |
|
|
562 |
&& (C1.w[0] <= midpoint128[ind - 19].w[0]))) { |
|
|
563 |
res = 0x00000000; // return 0 |
|
|
564 |
} else if (x_sign) { // n < 0 |
|
|
565 |
res = 0xffffffff; // return -1 |
|
|
566 |
} else { // n > 0 |
|
|
567 |
res = 0x00000001; // return +1 |
|
|
568 |
} |
|
|
569 |
} |
|
|
570 |
// set inexact flag |
|
|
571 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
572 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
|
|
573 |
// -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded |
|
|
574 |
// to nearest to a 32-bit signed integer |
|
|
575 |
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
576 |
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
|
|
577 |
// chop off ind digits from the lower part of C1 |
|
|
578 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits |
|
|
579 |
tmp64 = C1.w[0]; |
|
|
580 |
if (ind <= 19) { |
|
|
581 |
C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
|
|
582 |
} else { |
|
|
583 |
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
|
|
584 |
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
|
|
585 |
} |
|
|
586 |
if (C1.w[0] < tmp64) |
|
|
587 |
C1.w[1]++; |
|
|
588 |
// calculate C* and f* |
|
|
589 |
// C* is actually floor(C*) in this case |
|
|
590 |
// C* and f* need shifting and masking, as shown by |
|
|
591 |
// shiftright128[] and maskhigh128[] |
|
|
592 |
// 1 <= x <= 33 |
|
|
593 |
// kx = 10^(-x) = ten2mk128[ind - 1] |
|
|
594 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
595 |
// the approximation of 10^(-x) was rounded up to 118 bits |
|
|
596 |
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
|
|
597 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
598 |
Cstar.w[1] = P256.w[3]; |
|
|
599 |
Cstar.w[0] = P256.w[2]; |
|
|
600 |
fstar.w[3] = 0; |
|
|
601 |
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
|
|
602 |
fstar.w[1] = P256.w[1]; |
|
|
603 |
fstar.w[0] = P256.w[0]; |
|
|
604 |
} else { // 22 <= ind - 1 <= 33 |
|
|
605 |
Cstar.w[1] = 0; |
|
|
606 |
Cstar.w[0] = P256.w[3]; |
|
|
607 |
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
|
|
608 |
fstar.w[2] = P256.w[2]; |
|
|
609 |
fstar.w[1] = P256.w[1]; |
|
|
610 |
fstar.w[0] = P256.w[0]; |
|
|
611 |
} |
|
|
612 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
|
|
613 |
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
|
|
614 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
615 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
616 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
617 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
618 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
619 |
// else |
|
|
620 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
621 |
// correct by Property 1) |
|
|
622 |
// n = C* * 10^(e+x) |
|
|
623 |
|
|
|
624 |
// shift right C* by Ex-128 = shiftright128[ind] |
|
|
625 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
|
|
626 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
627 |
Cstar.w[0] = |
|
|
628 |
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
|
|
629 |
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
|
|
630 |
} else { // 22 <= ind - 1 <= 33 |
|
|
631 |
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
|
|
632 |
} |
|
|
633 |
// determine inexactness of the rounding of C* |
|
|
634 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
635 |
// the result is exact |
|
|
636 |
// else // if (f* - 1/2 > T*) then |
|
|
637 |
// the result is inexact |
|
|
638 |
if (ind - 1 <= 2) { |
|
|
639 |
if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact |
|
|
640 |
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
|
|
641 |
if (tmp64 > ten2mk128trunc[ind - 1].w[1] |
|
|
642 |
|| (tmp64 == ten2mk128trunc[ind - 1].w[1] |
|
|
643 |
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { |
|
|
644 |
// set the inexact flag |
|
|
645 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
646 |
} // else the result is exact |
|
|
647 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
648 |
// set the inexact flag |
|
|
649 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
650 |
} |
|
|
651 |
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
|
|
652 |
if (fstar.w[3] > 0x0 || |
|
|
653 |
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
|
|
654 |
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
|
|
655 |
(fstar.w[1] || fstar.w[0]))) { |
|
|
656 |
// f2* > 1/2 and the result may be exact |
|
|
657 |
// Calculate f2* - 1/2 |
|
|
658 |
tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
|
|
659 |
tmp64A = fstar.w[3]; |
|
|
660 |
if (tmp64 > fstar.w[2]) |
|
|
661 |
tmp64A--; |
|
|
662 |
if (tmp64A || tmp64 |
|
|
663 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
664 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
665 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
666 |
// set the inexact flag |
|
|
667 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
668 |
} // else the result is exact |
|
|
669 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
670 |
// set the inexact flag |
|
|
671 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
672 |
} |
|
|
673 |
} else { // if 22 <= ind <= 33 |
|
|
674 |
if (fstar.w[3] > onehalf128[ind - 1] || |
|
|
675 |
(fstar.w[3] == onehalf128[ind - 1] && |
|
|
676 |
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) { |
|
|
677 |
// f2* > 1/2 and the result may be exact |
|
|
678 |
// Calculate f2* - 1/2 |
|
|
679 |
tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
|
|
680 |
if (tmp64 || fstar.w[2] |
|
|
681 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
682 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
683 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
684 |
// set the inexact flag |
|
|
685 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
686 |
} // else the result is exact |
|
|
687 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
688 |
// set the inexact flag |
|
|
689 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
690 |
} |
|
|
691 |
} |
|
|
692 |
// if the result was a midpoint it was rounded away from zero, so |
|
|
693 |
// it will need a correction |
|
|
694 |
// check for midpoints |
|
|
695 |
if ((fstar.w[3] == 0) && (fstar.w[2] == 0) |
|
|
696 |
&& (fstar.w[1] || fstar.w[0]) |
|
|
697 |
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] |
|
|
698 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
699 |
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
700 |
// the result is a midpoint; round to nearest |
|
|
701 |
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
|
|
702 |
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
|
|
703 |
Cstar.w[0]--; // Cstar.w[0] is now even |
|
|
704 |
} // else MP in [ODD, EVEN] |
|
|
705 |
} |
|
|
706 |
if (x_sign) |
|
|
707 |
res = -Cstar.w[0]; |
|
|
708 |
else |
|
|
709 |
res = Cstar.w[0]; |
|
|
710 |
} else if (exp == 0) { |
|
|
711 |
// 1 <= q <= 10 |
|
|
712 |
// res = +/-C (exact) |
|
|
713 |
if (x_sign) |
|
|
714 |
res = -C1.w[0]; |
|
|
715 |
else |
|
|
716 |
res = C1.w[0]; |
|
|
717 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
718 |
// res = +/-C * 10^exp (exact) |
|
|
719 |
if (x_sign) |
|
|
720 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
721 |
else |
|
|
722 |
res = C1.w[0] * ten2k64[exp]; |
|
|
723 |
} |
|
|
724 |
} |
|
|
725 |
} |
|
|
726 |
|
|
|
727 |
BID_RETURN (res); |
|
|
728 |
} |
|
|
729 |
|
|
|
730 |
/***************************************************************************** |
|
|
731 |
* BID128_to_int32_floor |
|
|
732 |
****************************************************************************/ |
|
|
733 |
|
|
|
734 |
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_floor, x) |
|
|
735 |
|
|
|
736 |
int res; |
|
|
737 |
UINT64 x_sign; |
|
|
738 |
UINT64 x_exp; |
|
|
739 |
int exp; // unbiased exponent |
|
|
740 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
741 |
UINT64 tmp64, tmp64A; |
|
|
742 |
BID_UI64DOUBLE tmp1; |
|
|
743 |
unsigned int x_nr_bits; |
|
|
744 |
int q, ind, shift; |
|
|
745 |
UINT128 C1, C; |
|
|
746 |
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
|
|
747 |
UINT256 fstar; |
|
|
748 |
UINT256 P256; |
|
|
749 |
int is_inexact_lt_midpoint = 0; |
|
|
750 |
int is_inexact_gt_midpoint = 0; |
|
|
751 |
int is_midpoint_lt_even = 0; |
|
|
752 |
int is_midpoint_gt_even = 0; |
|
|
753 |
|
|
|
754 |
// unpack x |
|
|
755 |
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
756 |
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
|
|
757 |
C1.w[1] = x.w[1] & MASK_COEFF; |
|
|
758 |
C1.w[0] = x.w[0]; |
|
|
759 |
|
|
|
760 |
// check for NaN or Infinity |
|
|
761 |
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
|
|
762 |
// x is special |
|
|
763 |
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
764 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
|
|
765 |
// set invalid flag |
|
|
766 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
767 |
// return Integer Indefinite |
|
|
768 |
res = 0x80000000; |
|
|
769 |
} else { // x is QNaN |
|
|
770 |
// set invalid flag |
|
|
771 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
772 |
// return Integer Indefinite |
|
|
773 |
res = 0x80000000; |
|
|
774 |
} |
|
|
775 |
BID_RETURN (res); |
|
|
776 |
} else { // x is not a NaN, so it must be infinity |
|
|
777 |
if (!x_sign) { // x is +inf |
|
|
778 |
// set invalid flag |
|
|
779 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
780 |
// return Integer Indefinite |
|
|
781 |
res = 0x80000000; |
|
|
782 |
} else { // x is -inf |
|
|
783 |
// set invalid flag |
|
|
784 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
785 |
// return Integer Indefinite |
|
|
786 |
res = 0x80000000; |
|
|
787 |
} |
|
|
788 |
BID_RETURN (res); |
|
|
789 |
} |
|
|
790 |
} |
|
|
791 |
// check for non-canonical values (after the check for special values) |
|
|
792 |
if ((C1.w[1] > 0x0001ed09bead87c0ull) |
|
|
793 |
|| (C1.w[1] == 0x0001ed09bead87c0ull |
|
|
794 |
&& (C1.w[0] > 0x378d8e63ffffffffull)) |
|
|
795 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
|
|
796 |
res = 0x00000000; |
|
|
797 |
BID_RETURN (res); |
|
|
798 |
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
|
|
799 |
// x is 0 |
|
|
800 |
res = 0x00000000; |
|
|
801 |
BID_RETURN (res); |
|
|
802 |
} else { // x is not special and is not zero |
|
|
803 |
|
|
|
804 |
// q = nr. of decimal digits in x |
|
|
805 |
// determine first the nr. of bits in x |
|
|
806 |
if (C1.w[1] == 0) { |
|
|
807 |
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
808 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
809 |
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
810 |
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
|
|
811 |
x_nr_bits = |
|
|
812 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
813 |
} else { // x < 2^32 |
|
|
814 |
tmp1.d = (double) (C1.w[0]); // exact conversion |
|
|
815 |
x_nr_bits = |
|
|
816 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
817 |
} |
|
|
818 |
} else { // if x < 2^53 |
|
|
819 |
tmp1.d = (double) C1.w[0]; // exact conversion |
|
|
820 |
x_nr_bits = |
|
|
821 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
822 |
} |
|
|
823 |
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
|
|
824 |
tmp1.d = (double) C1.w[1]; // exact conversion |
|
|
825 |
x_nr_bits = |
|
|
826 |
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
827 |
} |
|
|
828 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
829 |
if (q == 0) { |
|
|
830 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
831 |
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
|
|
832 |
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
|
|
833 |
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
|
|
834 |
q++; |
|
|
835 |
} |
|
|
836 |
exp = (x_exp >> 49) - 6176; |
|
|
837 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
838 |
// set invalid flag |
|
|
839 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
840 |
// return Integer Indefinite |
|
|
841 |
res = 0x80000000; |
|
|
842 |
BID_RETURN (res); |
|
|
843 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
844 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
845 |
// so x rounded to an integer may or may not fit in a signed 32-bit int |
|
|
846 |
// the cases that do not fit are identified here; the ones that fit |
|
|
847 |
// fall through and will be handled with other cases further, |
|
|
848 |
// under '1 <= q + exp <= 10' |
|
|
849 |
if (x_sign) { // if n < 0 and q + exp = 10 |
|
|
850 |
// if n < -2^31 then n is too large |
|
|
851 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 |
|
|
852 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=34 |
|
|
853 |
if (q <= 11) { |
|
|
854 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
855 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
856 |
if (tmp64 > 0x500000000ull) { |
|
|
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 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
866 |
// 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000 <=> |
|
|
867 |
// C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
868 |
// (scale 2^31 up) |
|
|
869 |
tmp64 = 0x500000000ull; |
|
|
870 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
871 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
872 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
873 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
874 |
} |
|
|
875 |
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { |
|
|
876 |
// set invalid flag |
|
|
877 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
878 |
// return Integer Indefinite |
|
|
879 |
res = 0x80000000; |
|
|
880 |
BID_RETURN (res); |
|
|
881 |
} |
|
|
882 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
883 |
// to '1 <= q + exp <= 10' |
|
|
884 |
} |
|
|
885 |
} else { // if n > 0 and q + exp = 10 |
|
|
886 |
// if n >= 2^31 then n is too large |
|
|
887 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 |
|
|
888 |
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34 |
|
|
889 |
if (q <= 11) { |
|
|
890 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
891 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
892 |
if (tmp64 >= 0x500000000ull) { |
|
|
893 |
// set invalid flag |
|
|
894 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
895 |
// return Integer Indefinite |
|
|
896 |
res = 0x80000000; |
|
|
897 |
BID_RETURN (res); |
|
|
898 |
} |
|
|
899 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
900 |
// to '1 <= q + exp <= 10' |
|
|
901 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
902 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=> |
|
|
903 |
// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
904 |
// (scale 2^31 up) |
|
|
905 |
tmp64 = 0x500000000ull; |
|
|
906 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
907 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
908 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
909 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
910 |
} |
|
|
911 |
if (C1.w[1] > C.w[1] |
|
|
912 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
913 |
// set invalid flag |
|
|
914 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
915 |
// return Integer Indefinite |
|
|
916 |
res = 0x80000000; |
|
|
917 |
BID_RETURN (res); |
|
|
918 |
} |
|
|
919 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
920 |
// to '1 <= q + exp <= 10' |
|
|
921 |
} |
|
|
922 |
} |
|
|
923 |
} |
|
|
924 |
// n is not too large to be converted to int32: -2^31 <= n < 2^31 |
|
|
925 |
// Note: some of the cases tested for above fall through to this point |
|
|
926 |
if ((q + exp) <= 0) { |
|
|
927 |
// n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) |
|
|
928 |
// return 0 |
|
|
929 |
if (x_sign) |
|
|
930 |
res = 0xffffffff; |
|
|
931 |
else |
|
|
932 |
res = 0x00000000; |
|
|
933 |
BID_RETURN (res); |
|
|
934 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
|
|
935 |
// -2^31 <= x <= -1 or 1 <= x < 2^31 so x can be rounded |
|
|
936 |
// toward negative infinity to a 32-bit signed integer |
|
|
937 |
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
938 |
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
|
|
939 |
// chop off ind digits from the lower part of C1 |
|
|
940 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits |
|
|
941 |
tmp64 = C1.w[0]; |
|
|
942 |
if (ind <= 19) { |
|
|
943 |
C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
|
|
944 |
} else { |
|
|
945 |
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
|
|
946 |
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
|
|
947 |
} |
|
|
948 |
if (C1.w[0] < tmp64) |
|
|
949 |
C1.w[1]++; |
|
|
950 |
// calculate C* and f* |
|
|
951 |
// C* is actually floor(C*) in this case |
|
|
952 |
// C* and f* need shifting and masking, as shown by |
|
|
953 |
// shiftright128[] and maskhigh128[] |
|
|
954 |
// 1 <= x <= 33 |
|
|
955 |
// kx = 10^(-x) = ten2mk128[ind - 1] |
|
|
956 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
957 |
// the approximation of 10^(-x) was rounded up to 118 bits |
|
|
958 |
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
|
|
959 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
960 |
Cstar.w[1] = P256.w[3]; |
|
|
961 |
Cstar.w[0] = P256.w[2]; |
|
|
962 |
fstar.w[3] = 0; |
|
|
963 |
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
|
|
964 |
fstar.w[1] = P256.w[1]; |
|
|
965 |
fstar.w[0] = P256.w[0]; |
|
|
966 |
} else { // 22 <= ind - 1 <= 33 |
|
|
967 |
Cstar.w[1] = 0; |
|
|
968 |
Cstar.w[0] = P256.w[3]; |
|
|
969 |
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
|
|
970 |
fstar.w[2] = P256.w[2]; |
|
|
971 |
fstar.w[1] = P256.w[1]; |
|
|
972 |
fstar.w[0] = P256.w[0]; |
|
|
973 |
} |
|
|
974 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
|
|
975 |
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
|
|
976 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
977 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
978 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
979 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
980 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
981 |
// else |
|
|
982 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
983 |
// correct by Property 1) |
|
|
984 |
// n = C* * 10^(e+x) |
|
|
985 |
|
|
|
986 |
// shift right C* by Ex-128 = shiftright128[ind] |
|
|
987 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
|
|
988 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
989 |
Cstar.w[0] = |
|
|
990 |
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
|
|
991 |
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
|
|
992 |
} else { // 22 <= ind - 1 <= 33 |
|
|
993 |
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
|
|
994 |
} |
|
|
995 |
// determine inexactness of the rounding of C* |
|
|
996 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
997 |
// the result is exact |
|
|
998 |
// else // if (f* - 1/2 > T*) then |
|
|
999 |
// the result is inexact |
|
|
1000 |
if (ind - 1 <= 2) { |
|
|
1001 |
if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact |
|
|
1002 |
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
|
|
1003 |
if (tmp64 > ten2mk128trunc[ind - 1].w[1] |
|
|
1004 |
|| (tmp64 == ten2mk128trunc[ind - 1].w[1] |
|
|
1005 |
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { |
|
|
1006 |
is_inexact_lt_midpoint = 1; |
|
|
1007 |
} // else the result is exact |
|
|
1008 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
1009 |
is_inexact_gt_midpoint = 1; |
|
|
1010 |
} |
|
|
1011 |
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
|
|
1012 |
if (fstar.w[3] > 0x0 || |
|
|
1013 |
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
|
|
1014 |
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
|
|
1015 |
(fstar.w[1] || fstar.w[0]))) { |
|
|
1016 |
// f2* > 1/2 and the result may be exact |
|
|
1017 |
// Calculate f2* - 1/2 |
|
|
1018 |
tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
|
|
1019 |
tmp64A = fstar.w[3]; |
|
|
1020 |
if (tmp64 > fstar.w[2]) |
|
|
1021 |
tmp64A--; |
|
|
1022 |
if (tmp64A || tmp64 |
|
|
1023 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
1024 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
1025 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
1026 |
is_inexact_lt_midpoint = 1; |
|
|
1027 |
} // else the result is exact |
|
|
1028 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
1029 |
is_inexact_gt_midpoint = 1; |
|
|
1030 |
} |
|
|
1031 |
} else { // if 22 <= ind <= 33 |
|
|
1032 |
if (fstar.w[3] > onehalf128[ind - 1] || |
|
|
1033 |
(fstar.w[3] == onehalf128[ind - 1] && |
|
|
1034 |
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) { |
|
|
1035 |
// f2* > 1/2 and the result may be exact |
|
|
1036 |
// Calculate f2* - 1/2 |
|
|
1037 |
tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
|
|
1038 |
if (tmp64 || fstar.w[2] |
|
|
1039 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
1040 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
1041 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
1042 |
is_inexact_lt_midpoint = 1; |
|
|
1043 |
} // else the result is exact |
|
|
1044 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
1045 |
is_inexact_gt_midpoint = 1; |
|
|
1046 |
} |
|
|
1047 |
} |
|
|
1048 |
|
|
|
1049 |
// if the result was a midpoint it was rounded away from zero, so |
|
|
1050 |
// it will need a correction |
|
|
1051 |
// check for midpoints |
|
|
1052 |
if ((fstar.w[3] == 0) && (fstar.w[2] == 0) |
|
|
1053 |
&& (fstar.w[1] || fstar.w[0]) |
|
|
1054 |
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] |
|
|
1055 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
1056 |
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
1057 |
// the result is a midpoint; round to nearest |
|
|
1058 |
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
|
|
1059 |
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
|
|
1060 |
Cstar.w[0]--; // Cstar.w[0] is now even |
|
|
1061 |
is_midpoint_gt_even = 1; |
|
|
1062 |
is_inexact_lt_midpoint = 0; |
|
|
1063 |
is_inexact_gt_midpoint = 0; |
|
|
1064 |
} else { // else MP in [ODD, EVEN] |
|
|
1065 |
is_midpoint_lt_even = 1; |
|
|
1066 |
is_inexact_lt_midpoint = 0; |
|
|
1067 |
is_inexact_gt_midpoint = 0; |
|
|
1068 |
} |
|
|
1069 |
} |
|
|
1070 |
// general correction for RM |
|
|
1071 |
if (x_sign && (is_midpoint_gt_even || is_inexact_lt_midpoint)) { |
|
|
1072 |
Cstar.w[0] = Cstar.w[0] + 1; |
|
|
1073 |
} else if (!x_sign |
|
|
1074 |
&& (is_midpoint_lt_even || is_inexact_gt_midpoint)) { |
|
|
1075 |
Cstar.w[0] = Cstar.w[0] - 1; |
|
|
1076 |
} else { |
|
|
1077 |
; // the result is already correct |
|
|
1078 |
} |
|
|
1079 |
if (x_sign) |
|
|
1080 |
res = -Cstar.w[0]; |
|
|
1081 |
else |
|
|
1082 |
res = Cstar.w[0]; |
|
|
1083 |
} else if (exp == 0) { |
|
|
1084 |
// 1 <= q <= 10 |
|
|
1085 |
// res = +/-C (exact) |
|
|
1086 |
if (x_sign) |
|
|
1087 |
res = -C1.w[0]; |
|
|
1088 |
else |
|
|
1089 |
res = C1.w[0]; |
|
|
1090 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
1091 |
// res = +/-C * 10^exp (exact) |
|
|
1092 |
if (x_sign) |
|
|
1093 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
1094 |
else |
|
|
1095 |
res = C1.w[0] * ten2k64[exp]; |
|
|
1096 |
} |
|
|
1097 |
} |
|
|
1098 |
} |
|
|
1099 |
|
|
|
1100 |
BID_RETURN (res); |
|
|
1101 |
} |
|
|
1102 |
|
|
|
1103 |
|
|
|
1104 |
/***************************************************************************** |
|
|
1105 |
* BID128_to_int32_xfloor |
|
|
1106 |
****************************************************************************/ |
|
|
1107 |
|
|
|
1108 |
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xfloor, |
|
|
1109 |
x) |
|
|
1110 |
|
|
|
1111 |
int res; |
|
|
1112 |
UINT64 x_sign; |
|
|
1113 |
UINT64 x_exp; |
|
|
1114 |
int exp; // unbiased exponent |
|
|
1115 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
1116 |
UINT64 tmp64, tmp64A; |
|
|
1117 |
BID_UI64DOUBLE tmp1; |
|
|
1118 |
unsigned int x_nr_bits; |
|
|
1119 |
int q, ind, shift; |
|
|
1120 |
UINT128 C1, C; |
|
|
1121 |
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
|
|
1122 |
UINT256 fstar; |
|
|
1123 |
UINT256 P256; |
|
|
1124 |
int is_inexact_lt_midpoint = 0; |
|
|
1125 |
int is_inexact_gt_midpoint = 0; |
|
|
1126 |
int is_midpoint_lt_even = 0; |
|
|
1127 |
int is_midpoint_gt_even = 0; |
|
|
1128 |
|
|
|
1129 |
// unpack x |
|
|
1130 |
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
1131 |
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
|
|
1132 |
C1.w[1] = x.w[1] & MASK_COEFF; |
|
|
1133 |
C1.w[0] = x.w[0]; |
|
|
1134 |
|
|
|
1135 |
// check for NaN or Infinity |
|
|
1136 |
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
|
|
1137 |
// x is special |
|
|
1138 |
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
1139 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
|
|
1140 |
// set invalid flag |
|
|
1141 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1142 |
// return Integer Indefinite |
|
|
1143 |
res = 0x80000000; |
|
|
1144 |
} else { // x is QNaN |
|
|
1145 |
// set invalid flag |
|
|
1146 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1147 |
// return Integer Indefinite |
|
|
1148 |
res = 0x80000000; |
|
|
1149 |
} |
|
|
1150 |
BID_RETURN (res); |
|
|
1151 |
} else { // x is not a NaN, so it must be infinity |
|
|
1152 |
if (!x_sign) { // x is +inf |
|
|
1153 |
// set invalid flag |
|
|
1154 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1155 |
// return Integer Indefinite |
|
|
1156 |
res = 0x80000000; |
|
|
1157 |
} else { // x is -inf |
|
|
1158 |
// set invalid flag |
|
|
1159 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1160 |
// return Integer Indefinite |
|
|
1161 |
res = 0x80000000; |
|
|
1162 |
} |
|
|
1163 |
BID_RETURN (res); |
|
|
1164 |
} |
|
|
1165 |
} |
|
|
1166 |
// check for non-canonical values (after the check for special values) |
|
|
1167 |
if ((C1.w[1] > 0x0001ed09bead87c0ull) |
|
|
1168 |
|| (C1.w[1] == 0x0001ed09bead87c0ull |
|
|
1169 |
&& (C1.w[0] > 0x378d8e63ffffffffull)) |
|
|
1170 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
|
|
1171 |
res = 0x00000000; |
|
|
1172 |
BID_RETURN (res); |
|
|
1173 |
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
|
|
1174 |
// x is 0 |
|
|
1175 |
res = 0x00000000; |
|
|
1176 |
BID_RETURN (res); |
|
|
1177 |
} else { // x is not special and is not zero |
|
|
1178 |
|
|
|
1179 |
// q = nr. of decimal digits in x |
|
|
1180 |
// determine first the nr. of bits in x |
|
|
1181 |
if (C1.w[1] == 0) { |
|
|
1182 |
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1183 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
1184 |
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
1185 |
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
|
|
1186 |
x_nr_bits = |
|
|
1187 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1188 |
} else { // x < 2^32 |
|
|
1189 |
tmp1.d = (double) (C1.w[0]); // exact conversion |
|
|
1190 |
x_nr_bits = |
|
|
1191 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1192 |
} |
|
|
1193 |
} else { // if x < 2^53 |
|
|
1194 |
tmp1.d = (double) C1.w[0]; // exact conversion |
|
|
1195 |
x_nr_bits = |
|
|
1196 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1197 |
} |
|
|
1198 |
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
|
|
1199 |
tmp1.d = (double) C1.w[1]; // exact conversion |
|
|
1200 |
x_nr_bits = |
|
|
1201 |
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1202 |
} |
|
|
1203 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1204 |
if (q == 0) { |
|
|
1205 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1206 |
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
|
|
1207 |
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
|
|
1208 |
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
|
|
1209 |
q++; |
|
|
1210 |
} |
|
|
1211 |
exp = (x_exp >> 49) - 6176; |
|
|
1212 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
1213 |
// set invalid flag |
|
|
1214 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1215 |
// return Integer Indefinite |
|
|
1216 |
res = 0x80000000; |
|
|
1217 |
BID_RETURN (res); |
|
|
1218 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
1219 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
1220 |
// so x rounded to an integer may or may not fit in a signed 32-bit int |
|
|
1221 |
// the cases that do not fit are identified here; the ones that fit |
|
|
1222 |
// fall through and will be handled with other cases further, |
|
|
1223 |
// under '1 <= q + exp <= 10' |
|
|
1224 |
if (x_sign) { // if n < 0 and q + exp = 10 |
|
|
1225 |
// if n < -2^31 then n is too large |
|
|
1226 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 |
|
|
1227 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=34 |
|
|
1228 |
if (q <= 11) { |
|
|
1229 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1230 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1231 |
if (tmp64 > 0x500000000ull) { |
|
|
1232 |
// set invalid flag |
|
|
1233 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1234 |
// return Integer Indefinite |
|
|
1235 |
res = 0x80000000; |
|
|
1236 |
BID_RETURN (res); |
|
|
1237 |
} |
|
|
1238 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1239 |
// to '1 <= q + exp <= 10' |
|
|
1240 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
1241 |
// 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000 <=> |
|
|
1242 |
// C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
1243 |
// (scale 2^31 up) |
|
|
1244 |
tmp64 = 0x500000000ull; |
|
|
1245 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
1246 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
1247 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
1248 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
1249 |
} |
|
|
1250 |
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { |
|
|
1251 |
// set invalid flag |
|
|
1252 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1253 |
// return Integer Indefinite |
|
|
1254 |
res = 0x80000000; |
|
|
1255 |
BID_RETURN (res); |
|
|
1256 |
} |
|
|
1257 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1258 |
// to '1 <= q + exp <= 10' |
|
|
1259 |
} |
|
|
1260 |
} else { // if n > 0 and q + exp = 10 |
|
|
1261 |
// if n >= 2^31 then n is too large |
|
|
1262 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 |
|
|
1263 |
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34 |
|
|
1264 |
if (q <= 11) { |
|
|
1265 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1266 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1267 |
if (tmp64 >= 0x500000000ull) { |
|
|
1268 |
// set invalid flag |
|
|
1269 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1270 |
// return Integer Indefinite |
|
|
1271 |
res = 0x80000000; |
|
|
1272 |
BID_RETURN (res); |
|
|
1273 |
} |
|
|
1274 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1275 |
// to '1 <= q + exp <= 10' |
|
|
1276 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
1277 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=> |
|
|
1278 |
// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
1279 |
// (scale 2^31 up) |
|
|
1280 |
tmp64 = 0x500000000ull; |
|
|
1281 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
1282 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
1283 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
1284 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
1285 |
} |
|
|
1286 |
if (C1.w[1] > C.w[1] |
|
|
1287 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
1288 |
// set invalid flag |
|
|
1289 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1290 |
// return Integer Indefinite |
|
|
1291 |
res = 0x80000000; |
|
|
1292 |
BID_RETURN (res); |
|
|
1293 |
} |
|
|
1294 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1295 |
// to '1 <= q + exp <= 10' |
|
|
1296 |
} |
|
|
1297 |
} |
|
|
1298 |
} |
|
|
1299 |
// n is not too large to be converted to int32: -2^31 <= n < 2^31 |
|
|
1300 |
// Note: some of the cases tested for above fall through to this point |
|
|
1301 |
if ((q + exp) <= 0) { |
|
|
1302 |
// n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) |
|
|
1303 |
// set inexact flag |
|
|
1304 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1305 |
// return 0 |
|
|
1306 |
if (x_sign) |
|
|
1307 |
res = 0xffffffff; |
|
|
1308 |
else |
|
|
1309 |
res = 0x00000000; |
|
|
1310 |
BID_RETURN (res); |
|
|
1311 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
|
|
1312 |
// -2^31 <= x <= -1 or 1 <= x < 2^31 so x can be rounded |
|
|
1313 |
// toward negative infinity to a 32-bit signed integer |
|
|
1314 |
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
1315 |
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
|
|
1316 |
// chop off ind digits from the lower part of C1 |
|
|
1317 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits |
|
|
1318 |
tmp64 = C1.w[0]; |
|
|
1319 |
if (ind <= 19) { |
|
|
1320 |
C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
|
|
1321 |
} else { |
|
|
1322 |
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
|
|
1323 |
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
|
|
1324 |
} |
|
|
1325 |
if (C1.w[0] < tmp64) |
|
|
1326 |
C1.w[1]++; |
|
|
1327 |
// calculate C* and f* |
|
|
1328 |
// C* is actually floor(C*) in this case |
|
|
1329 |
// C* and f* need shifting and masking, as shown by |
|
|
1330 |
// shiftright128[] and maskhigh128[] |
|
|
1331 |
// 1 <= x <= 33 |
|
|
1332 |
// kx = 10^(-x) = ten2mk128[ind - 1] |
|
|
1333 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
1334 |
// the approximation of 10^(-x) was rounded up to 118 bits |
|
|
1335 |
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
|
|
1336 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
1337 |
Cstar.w[1] = P256.w[3]; |
|
|
1338 |
Cstar.w[0] = P256.w[2]; |
|
|
1339 |
fstar.w[3] = 0; |
|
|
1340 |
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
|
|
1341 |
fstar.w[1] = P256.w[1]; |
|
|
1342 |
fstar.w[0] = P256.w[0]; |
|
|
1343 |
} else { // 22 <= ind - 1 <= 33 |
|
|
1344 |
Cstar.w[1] = 0; |
|
|
1345 |
Cstar.w[0] = P256.w[3]; |
|
|
1346 |
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
|
|
1347 |
fstar.w[2] = P256.w[2]; |
|
|
1348 |
fstar.w[1] = P256.w[1]; |
|
|
1349 |
fstar.w[0] = P256.w[0]; |
|
|
1350 |
} |
|
|
1351 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
|
|
1352 |
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
|
|
1353 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
1354 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
1355 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
1356 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
1357 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
1358 |
// else |
|
|
1359 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
1360 |
// correct by Property 1) |
|
|
1361 |
// n = C* * 10^(e+x) |
|
|
1362 |
|
|
|
1363 |
// shift right C* by Ex-128 = shiftright128[ind] |
|
|
1364 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
|
|
1365 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
1366 |
Cstar.w[0] = |
|
|
1367 |
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
|
|
1368 |
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
|
|
1369 |
} else { // 22 <= ind - 1 <= 33 |
|
|
1370 |
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
|
|
1371 |
} |
|
|
1372 |
// determine inexactness of the rounding of C* |
|
|
1373 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
1374 |
// the result is exact |
|
|
1375 |
// else // if (f* - 1/2 > T*) then |
|
|
1376 |
// the result is inexact |
|
|
1377 |
if (ind - 1 <= 2) { |
|
|
1378 |
if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact |
|
|
1379 |
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
|
|
1380 |
if (tmp64 > ten2mk128trunc[ind - 1].w[1] |
|
|
1381 |
|| (tmp64 == ten2mk128trunc[ind - 1].w[1] |
|
|
1382 |
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { |
|
|
1383 |
// set the inexact flag |
|
|
1384 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1385 |
is_inexact_lt_midpoint = 1; |
|
|
1386 |
} // else the result is exact |
|
|
1387 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
1388 |
// set the inexact flag |
|
|
1389 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1390 |
is_inexact_gt_midpoint = 1; |
|
|
1391 |
} |
|
|
1392 |
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
|
|
1393 |
if (fstar.w[3] > 0x0 || |
|
|
1394 |
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
|
|
1395 |
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
|
|
1396 |
(fstar.w[1] || fstar.w[0]))) { |
|
|
1397 |
// f2* > 1/2 and the result may be exact |
|
|
1398 |
// Calculate f2* - 1/2 |
|
|
1399 |
tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
|
|
1400 |
tmp64A = fstar.w[3]; |
|
|
1401 |
if (tmp64 > fstar.w[2]) |
|
|
1402 |
tmp64A--; |
|
|
1403 |
if (tmp64A || tmp64 |
|
|
1404 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
1405 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
1406 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
1407 |
// set the inexact flag |
|
|
1408 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1409 |
is_inexact_lt_midpoint = 1; |
|
|
1410 |
} // else the result is exact |
|
|
1411 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
1412 |
// set the inexact flag |
|
|
1413 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1414 |
is_inexact_gt_midpoint = 1; |
|
|
1415 |
} |
|
|
1416 |
} else { // if 22 <= ind <= 33 |
|
|
1417 |
if (fstar.w[3] > onehalf128[ind - 1] || |
|
|
1418 |
(fstar.w[3] == onehalf128[ind - 1] && |
|
|
1419 |
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) { |
|
|
1420 |
// f2* > 1/2 and the result may be exact |
|
|
1421 |
// Calculate f2* - 1/2 |
|
|
1422 |
tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
|
|
1423 |
if (tmp64 || fstar.w[2] |
|
|
1424 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
1425 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
1426 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
1427 |
// set the inexact flag |
|
|
1428 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1429 |
is_inexact_lt_midpoint = 1; |
|
|
1430 |
} // else the result is exact |
|
|
1431 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
1432 |
// set the inexact flag |
|
|
1433 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
1434 |
is_inexact_gt_midpoint = 1; |
|
|
1435 |
} |
|
|
1436 |
} |
|
|
1437 |
|
|
|
1438 |
// if the result was a midpoint it was rounded away from zero, so |
|
|
1439 |
// it will need a correction |
|
|
1440 |
// check for midpoints |
|
|
1441 |
if ((fstar.w[3] == 0) && (fstar.w[2] == 0) |
|
|
1442 |
&& (fstar.w[1] || fstar.w[0]) |
|
|
1443 |
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] |
|
|
1444 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
1445 |
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
1446 |
// the result is a midpoint; round to nearest |
|
|
1447 |
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
|
|
1448 |
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
|
|
1449 |
Cstar.w[0]--; // Cstar.w[0] is now even |
|
|
1450 |
is_midpoint_gt_even = 1; |
|
|
1451 |
is_inexact_lt_midpoint = 0; |
|
|
1452 |
is_inexact_gt_midpoint = 0; |
|
|
1453 |
} else { // else MP in [ODD, EVEN] |
|
|
1454 |
is_midpoint_lt_even = 1; |
|
|
1455 |
is_inexact_lt_midpoint = 0; |
|
|
1456 |
is_inexact_gt_midpoint = 0; |
|
|
1457 |
} |
|
|
1458 |
} |
|
|
1459 |
// general correction for RM |
|
|
1460 |
if (x_sign && (is_midpoint_gt_even || is_inexact_lt_midpoint)) { |
|
|
1461 |
Cstar.w[0] = Cstar.w[0] + 1; |
|
|
1462 |
} else if (!x_sign |
|
|
1463 |
&& (is_midpoint_lt_even || is_inexact_gt_midpoint)) { |
|
|
1464 |
Cstar.w[0] = Cstar.w[0] - 1; |
|
|
1465 |
} else { |
|
|
1466 |
; // the result is already correct |
|
|
1467 |
} |
|
|
1468 |
if (x_sign) |
|
|
1469 |
res = -Cstar.w[0]; |
|
|
1470 |
else |
|
|
1471 |
res = Cstar.w[0]; |
|
|
1472 |
} else if (exp == 0) { |
|
|
1473 |
// 1 <= q <= 10 |
|
|
1474 |
// res = +/-C (exact) |
|
|
1475 |
if (x_sign) |
|
|
1476 |
res = -C1.w[0]; |
|
|
1477 |
else |
|
|
1478 |
res = C1.w[0]; |
|
|
1479 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
1480 |
// res = +/-C * 10^exp (exact) |
|
|
1481 |
if (x_sign) |
|
|
1482 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
1483 |
else |
|
|
1484 |
res = C1.w[0] * ten2k64[exp]; |
|
|
1485 |
} |
|
|
1486 |
} |
|
|
1487 |
} |
|
|
1488 |
|
|
|
1489 |
BID_RETURN (res); |
|
|
1490 |
} |
|
|
1491 |
|
|
|
1492 |
/***************************************************************************** |
|
|
1493 |
* BID128_to_int32_ceil |
|
|
1494 |
****************************************************************************/ |
|
|
1495 |
|
|
|
1496 |
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_ceil, x) |
|
|
1497 |
|
|
|
1498 |
int res; |
|
|
1499 |
UINT64 x_sign; |
|
|
1500 |
UINT64 x_exp; |
|
|
1501 |
int exp; // unbiased exponent |
|
|
1502 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
1503 |
UINT64 tmp64, tmp64A; |
|
|
1504 |
BID_UI64DOUBLE tmp1; |
|
|
1505 |
unsigned int x_nr_bits; |
|
|
1506 |
int q, ind, shift; |
|
|
1507 |
UINT128 C1, C; |
|
|
1508 |
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
|
|
1509 |
UINT256 fstar; |
|
|
1510 |
UINT256 P256; |
|
|
1511 |
int is_inexact_lt_midpoint = 0; |
|
|
1512 |
int is_inexact_gt_midpoint = 0; |
|
|
1513 |
int is_midpoint_lt_even = 0; |
|
|
1514 |
int is_midpoint_gt_even = 0; |
|
|
1515 |
|
|
|
1516 |
// unpack x |
|
|
1517 |
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
1518 |
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
|
|
1519 |
C1.w[1] = x.w[1] & MASK_COEFF; |
|
|
1520 |
C1.w[0] = x.w[0]; |
|
|
1521 |
|
|
|
1522 |
// check for NaN or Infinity |
|
|
1523 |
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
|
|
1524 |
// x is special |
|
|
1525 |
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
1526 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
|
|
1527 |
// set invalid flag |
|
|
1528 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1529 |
// return Integer Indefinite |
|
|
1530 |
res = 0x80000000; |
|
|
1531 |
} else { // x is QNaN |
|
|
1532 |
// set invalid flag |
|
|
1533 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1534 |
// return Integer Indefinite |
|
|
1535 |
res = 0x80000000; |
|
|
1536 |
} |
|
|
1537 |
BID_RETURN (res); |
|
|
1538 |
} else { // x is not a NaN, so it must be infinity |
|
|
1539 |
if (!x_sign) { // x is +inf |
|
|
1540 |
// set invalid flag |
|
|
1541 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1542 |
// return Integer Indefinite |
|
|
1543 |
res = 0x80000000; |
|
|
1544 |
} else { // x is -inf |
|
|
1545 |
// set invalid flag |
|
|
1546 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1547 |
// return Integer Indefinite |
|
|
1548 |
res = 0x80000000; |
|
|
1549 |
} |
|
|
1550 |
BID_RETURN (res); |
|
|
1551 |
} |
|
|
1552 |
} |
|
|
1553 |
// check for non-canonical values (after the check for special values) |
|
|
1554 |
if ((C1.w[1] > 0x0001ed09bead87c0ull) |
|
|
1555 |
|| (C1.w[1] == 0x0001ed09bead87c0ull |
|
|
1556 |
&& (C1.w[0] > 0x378d8e63ffffffffull)) |
|
|
1557 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
|
|
1558 |
res = 0x00000000; |
|
|
1559 |
BID_RETURN (res); |
|
|
1560 |
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
|
|
1561 |
// x is 0 |
|
|
1562 |
res = 0x00000000; |
|
|
1563 |
BID_RETURN (res); |
|
|
1564 |
} else { // x is not special and is not zero |
|
|
1565 |
|
|
|
1566 |
// q = nr. of decimal digits in x |
|
|
1567 |
// determine first the nr. of bits in x |
|
|
1568 |
if (C1.w[1] == 0) { |
|
|
1569 |
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1570 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
1571 |
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
1572 |
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
|
|
1573 |
x_nr_bits = |
|
|
1574 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1575 |
} else { // x < 2^32 |
|
|
1576 |
tmp1.d = (double) (C1.w[0]); // exact conversion |
|
|
1577 |
x_nr_bits = |
|
|
1578 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1579 |
} |
|
|
1580 |
} else { // if x < 2^53 |
|
|
1581 |
tmp1.d = (double) C1.w[0]; // exact conversion |
|
|
1582 |
x_nr_bits = |
|
|
1583 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1584 |
} |
|
|
1585 |
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
|
|
1586 |
tmp1.d = (double) C1.w[1]; // exact conversion |
|
|
1587 |
x_nr_bits = |
|
|
1588 |
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1589 |
} |
|
|
1590 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1591 |
if (q == 0) { |
|
|
1592 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1593 |
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
|
|
1594 |
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
|
|
1595 |
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
|
|
1596 |
q++; |
|
|
1597 |
} |
|
|
1598 |
exp = (x_exp >> 49) - 6176; |
|
|
1599 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
1600 |
// set invalid flag |
|
|
1601 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1602 |
// return Integer Indefinite |
|
|
1603 |
res = 0x80000000; |
|
|
1604 |
BID_RETURN (res); |
|
|
1605 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
1606 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
1607 |
// so x rounded to an integer may or may not fit in a signed 32-bit int |
|
|
1608 |
// the cases that do not fit are identified here; the ones that fit |
|
|
1609 |
// fall through and will be handled with other cases further, |
|
|
1610 |
// under '1 <= q + exp <= 10' |
|
|
1611 |
if (x_sign) { // if n < 0 and q + exp = 10 |
|
|
1612 |
// if n <= -2^31-1 then n is too large |
|
|
1613 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 |
|
|
1614 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 |
|
|
1615 |
if (q <= 11) { |
|
|
1616 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1617 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1618 |
if (tmp64 >= 0x50000000aull) { |
|
|
1619 |
// set invalid flag |
|
|
1620 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1621 |
// return Integer Indefinite |
|
|
1622 |
res = 0x80000000; |
|
|
1623 |
BID_RETURN (res); |
|
|
1624 |
} |
|
|
1625 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1626 |
// to '1 <= q + exp <= 10' |
|
|
1627 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
1628 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=> |
|
|
1629 |
// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
1630 |
// (scale 2^31+1 up) |
|
|
1631 |
tmp64 = 0x50000000aull; |
|
|
1632 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
1633 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
1634 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
1635 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
1636 |
} |
|
|
1637 |
if (C1.w[1] > C.w[1] |
|
|
1638 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
1639 |
// set invalid flag |
|
|
1640 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1641 |
// return Integer Indefinite |
|
|
1642 |
res = 0x80000000; |
|
|
1643 |
BID_RETURN (res); |
|
|
1644 |
} |
|
|
1645 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1646 |
// to '1 <= q + exp <= 10' |
|
|
1647 |
} |
|
|
1648 |
} else { // if n > 0 and q + exp = 10 |
|
|
1649 |
// if n > 2^31 - 1 then n is too large |
|
|
1650 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1 |
|
|
1651 |
// too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=34 |
|
|
1652 |
if (q <= 11) { |
|
|
1653 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1654 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1655 |
if (tmp64 > 0x4fffffff6ull) { |
|
|
1656 |
// set invalid flag |
|
|
1657 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1658 |
// return Integer Indefinite |
|
|
1659 |
res = 0x80000000; |
|
|
1660 |
BID_RETURN (res); |
|
|
1661 |
} |
|
|
1662 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1663 |
// to '1 <= q + exp <= 10' |
|
|
1664 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
1665 |
// 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6 <=> |
|
|
1666 |
// C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
1667 |
// (scale 2^31 up) |
|
|
1668 |
tmp64 = 0x4fffffff6ull; |
|
|
1669 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
1670 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
1671 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
1672 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
1673 |
} |
|
|
1674 |
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { |
|
|
1675 |
// set invalid flag |
|
|
1676 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1677 |
// return Integer Indefinite |
|
|
1678 |
res = 0x80000000; |
|
|
1679 |
BID_RETURN (res); |
|
|
1680 |
} |
|
|
1681 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1682 |
// to '1 <= q + exp <= 10' |
|
|
1683 |
} |
|
|
1684 |
} |
|
|
1685 |
} |
|
|
1686 |
// n is not too large to be converted to int32: -2^31-1 < n <= 2^31-1 |
|
|
1687 |
// Note: some of the cases tested for above fall through to this point |
|
|
1688 |
if ((q + exp) <= 0) { |
|
|
1689 |
// n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) |
|
|
1690 |
// return 0 |
|
|
1691 |
if (x_sign) |
|
|
1692 |
res = 0x00000000; |
|
|
1693 |
else |
|
|
1694 |
res = 0x00000001; |
|
|
1695 |
BID_RETURN (res); |
|
|
1696 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
|
|
1697 |
// -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded |
|
|
1698 |
// toward positive infinity to a 32-bit signed integer |
|
|
1699 |
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
1700 |
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
|
|
1701 |
// chop off ind digits from the lower part of C1 |
|
|
1702 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits |
|
|
1703 |
tmp64 = C1.w[0]; |
|
|
1704 |
if (ind <= 19) { |
|
|
1705 |
C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
|
|
1706 |
} else { |
|
|
1707 |
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
|
|
1708 |
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
|
|
1709 |
} |
|
|
1710 |
if (C1.w[0] < tmp64) |
|
|
1711 |
C1.w[1]++; |
|
|
1712 |
// calculate C* and f* |
|
|
1713 |
// C* is actually floor(C*) in this case |
|
|
1714 |
// C* and f* need shifting and masking, as shown by |
|
|
1715 |
// shiftright128[] and maskhigh128[] |
|
|
1716 |
// 1 <= x <= 33 |
|
|
1717 |
// kx = 10^(-x) = ten2mk128[ind - 1] |
|
|
1718 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
1719 |
// the approximation of 10^(-x) was rounded up to 118 bits |
|
|
1720 |
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
|
|
1721 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
1722 |
Cstar.w[1] = P256.w[3]; |
|
|
1723 |
Cstar.w[0] = P256.w[2]; |
|
|
1724 |
fstar.w[3] = 0; |
|
|
1725 |
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
|
|
1726 |
fstar.w[1] = P256.w[1]; |
|
|
1727 |
fstar.w[0] = P256.w[0]; |
|
|
1728 |
} else { // 22 <= ind - 1 <= 33 |
|
|
1729 |
Cstar.w[1] = 0; |
|
|
1730 |
Cstar.w[0] = P256.w[3]; |
|
|
1731 |
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
|
|
1732 |
fstar.w[2] = P256.w[2]; |
|
|
1733 |
fstar.w[1] = P256.w[1]; |
|
|
1734 |
fstar.w[0] = P256.w[0]; |
|
|
1735 |
} |
|
|
1736 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
|
|
1737 |
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
|
|
1738 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
1739 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
1740 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
1741 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
1742 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
1743 |
// else |
|
|
1744 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
1745 |
// correct by Property 1) |
|
|
1746 |
// n = C* * 10^(e+x) |
|
|
1747 |
|
|
|
1748 |
// shift right C* by Ex-128 = shiftright128[ind] |
|
|
1749 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
|
|
1750 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
1751 |
Cstar.w[0] = |
|
|
1752 |
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
|
|
1753 |
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
|
|
1754 |
} else { // 22 <= ind - 1 <= 33 |
|
|
1755 |
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
|
|
1756 |
} |
|
|
1757 |
// determine inexactness of the rounding of C* |
|
|
1758 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
1759 |
// the result is exact |
|
|
1760 |
// else // if (f* - 1/2 > T*) then |
|
|
1761 |
// the result is inexact |
|
|
1762 |
if (ind - 1 <= 2) { |
|
|
1763 |
if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact |
|
|
1764 |
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
|
|
1765 |
if (tmp64 > ten2mk128trunc[ind - 1].w[1] |
|
|
1766 |
|| (tmp64 == ten2mk128trunc[ind - 1].w[1] |
|
|
1767 |
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { |
|
|
1768 |
is_inexact_lt_midpoint = 1; |
|
|
1769 |
} // else the result is exact |
|
|
1770 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
1771 |
is_inexact_gt_midpoint = 1; |
|
|
1772 |
} |
|
|
1773 |
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
|
|
1774 |
if (fstar.w[3] > 0x0 || |
|
|
1775 |
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
|
|
1776 |
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
|
|
1777 |
(fstar.w[1] || fstar.w[0]))) { |
|
|
1778 |
// f2* > 1/2 and the result may be exact |
|
|
1779 |
// Calculate f2* - 1/2 |
|
|
1780 |
tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
|
|
1781 |
tmp64A = fstar.w[3]; |
|
|
1782 |
if (tmp64 > fstar.w[2]) |
|
|
1783 |
tmp64A--; |
|
|
1784 |
if (tmp64A || tmp64 |
|
|
1785 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
1786 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
1787 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
1788 |
is_inexact_lt_midpoint = 1; |
|
|
1789 |
} // else the result is exact |
|
|
1790 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
1791 |
is_inexact_gt_midpoint = 1; |
|
|
1792 |
} |
|
|
1793 |
} else { // if 22 <= ind <= 33 |
|
|
1794 |
if (fstar.w[3] > onehalf128[ind - 1] || |
|
|
1795 |
(fstar.w[3] == onehalf128[ind - 1] && |
|
|
1796 |
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) { |
|
|
1797 |
// f2* > 1/2 and the result may be exact |
|
|
1798 |
// Calculate f2* - 1/2 |
|
|
1799 |
tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
|
|
1800 |
if (tmp64 || fstar.w[2] |
|
|
1801 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
1802 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
1803 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
1804 |
is_inexact_lt_midpoint = 1; |
|
|
1805 |
} // else the result is exact |
|
|
1806 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
1807 |
is_inexact_gt_midpoint = 1; |
|
|
1808 |
} |
|
|
1809 |
} |
|
|
1810 |
|
|
|
1811 |
// if the result was a midpoint it was rounded away from zero, so |
|
|
1812 |
// it will need a correction |
|
|
1813 |
// check for midpoints |
|
|
1814 |
if ((fstar.w[3] == 0) && (fstar.w[2] == 0) |
|
|
1815 |
&& (fstar.w[1] || fstar.w[0]) |
|
|
1816 |
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] |
|
|
1817 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
1818 |
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
1819 |
// the result is a midpoint; round to nearest |
|
|
1820 |
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
|
|
1821 |
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
|
|
1822 |
Cstar.w[0]--; // Cstar.w[0] is now even |
|
|
1823 |
is_midpoint_gt_even = 1; |
|
|
1824 |
is_inexact_lt_midpoint = 0; |
|
|
1825 |
is_inexact_gt_midpoint = 0; |
|
|
1826 |
} else { // else MP in [ODD, EVEN] |
|
|
1827 |
is_midpoint_lt_even = 1; |
|
|
1828 |
is_inexact_lt_midpoint = 0; |
|
|
1829 |
is_inexact_gt_midpoint = 0; |
|
|
1830 |
} |
|
|
1831 |
} |
|
|
1832 |
// general correction for RM |
|
|
1833 |
if (x_sign && (is_midpoint_lt_even || is_inexact_gt_midpoint)) { |
|
|
1834 |
Cstar.w[0] = Cstar.w[0] - 1; |
|
|
1835 |
} else if (!x_sign |
|
|
1836 |
&& (is_midpoint_gt_even || is_inexact_lt_midpoint)) { |
|
|
1837 |
Cstar.w[0] = Cstar.w[0] + 1; |
|
|
1838 |
} else { |
|
|
1839 |
; // the result is already correct |
|
|
1840 |
} |
|
|
1841 |
if (x_sign) |
|
|
1842 |
res = -Cstar.w[0]; |
|
|
1843 |
else |
|
|
1844 |
res = Cstar.w[0]; |
|
|
1845 |
} else if (exp == 0) { |
|
|
1846 |
// 1 <= q <= 10 |
|
|
1847 |
// res = +/-C (exact) |
|
|
1848 |
if (x_sign) |
|
|
1849 |
res = -C1.w[0]; |
|
|
1850 |
else |
|
|
1851 |
res = C1.w[0]; |
|
|
1852 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
1853 |
// res = +/-C * 10^exp (exact) |
|
|
1854 |
if (x_sign) |
|
|
1855 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
1856 |
else |
|
|
1857 |
res = C1.w[0] * ten2k64[exp]; |
|
|
1858 |
} |
|
|
1859 |
} |
|
|
1860 |
} |
|
|
1861 |
|
|
|
1862 |
BID_RETURN (res); |
|
|
1863 |
} |
|
|
1864 |
|
|
|
1865 |
/***************************************************************************** |
|
|
1866 |
* BID128_to_int32_xceil |
|
|
1867 |
****************************************************************************/ |
|
|
1868 |
|
|
|
1869 |
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xceil, x) |
|
|
1870 |
|
|
|
1871 |
int res; |
|
|
1872 |
UINT64 x_sign; |
|
|
1873 |
UINT64 x_exp; |
|
|
1874 |
int exp; // unbiased exponent |
|
|
1875 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
1876 |
UINT64 tmp64, tmp64A; |
|
|
1877 |
BID_UI64DOUBLE tmp1; |
|
|
1878 |
unsigned int x_nr_bits; |
|
|
1879 |
int q, ind, shift; |
|
|
1880 |
UINT128 C1, C; |
|
|
1881 |
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
|
|
1882 |
UINT256 fstar; |
|
|
1883 |
UINT256 P256; |
|
|
1884 |
int is_inexact_lt_midpoint = 0; |
|
|
1885 |
int is_inexact_gt_midpoint = 0; |
|
|
1886 |
int is_midpoint_lt_even = 0; |
|
|
1887 |
int is_midpoint_gt_even = 0; |
|
|
1888 |
|
|
|
1889 |
// unpack x |
|
|
1890 |
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
1891 |
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
|
|
1892 |
C1.w[1] = x.w[1] & MASK_COEFF; |
|
|
1893 |
C1.w[0] = x.w[0]; |
|
|
1894 |
|
|
|
1895 |
// check for NaN or Infinity |
|
|
1896 |
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
|
|
1897 |
// x is special |
|
|
1898 |
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
1899 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
|
|
1900 |
// set invalid flag |
|
|
1901 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1902 |
// return Integer Indefinite |
|
|
1903 |
res = 0x80000000; |
|
|
1904 |
} else { // x is QNaN |
|
|
1905 |
// set invalid flag |
|
|
1906 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1907 |
// return Integer Indefinite |
|
|
1908 |
res = 0x80000000; |
|
|
1909 |
} |
|
|
1910 |
BID_RETURN (res); |
|
|
1911 |
} else { // x is not a NaN, so it must be infinity |
|
|
1912 |
if (!x_sign) { // x is +inf |
|
|
1913 |
// set invalid flag |
|
|
1914 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1915 |
// return Integer Indefinite |
|
|
1916 |
res = 0x80000000; |
|
|
1917 |
} else { // x is -inf |
|
|
1918 |
// set invalid flag |
|
|
1919 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1920 |
// return Integer Indefinite |
|
|
1921 |
res = 0x80000000; |
|
|
1922 |
} |
|
|
1923 |
BID_RETURN (res); |
|
|
1924 |
} |
|
|
1925 |
} |
|
|
1926 |
// check for non-canonical values (after the check for special values) |
|
|
1927 |
if ((C1.w[1] > 0x0001ed09bead87c0ull) |
|
|
1928 |
|| (C1.w[1] == 0x0001ed09bead87c0ull |
|
|
1929 |
&& (C1.w[0] > 0x378d8e63ffffffffull)) |
|
|
1930 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
|
|
1931 |
res = 0x00000000; |
|
|
1932 |
BID_RETURN (res); |
|
|
1933 |
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
|
|
1934 |
// x is 0 |
|
|
1935 |
res = 0x00000000; |
|
|
1936 |
BID_RETURN (res); |
|
|
1937 |
} else { // x is not special and is not zero |
|
|
1938 |
|
|
|
1939 |
// q = nr. of decimal digits in x |
|
|
1940 |
// determine first the nr. of bits in x |
|
|
1941 |
if (C1.w[1] == 0) { |
|
|
1942 |
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
1943 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
1944 |
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
1945 |
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
|
|
1946 |
x_nr_bits = |
|
|
1947 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1948 |
} else { // x < 2^32 |
|
|
1949 |
tmp1.d = (double) (C1.w[0]); // exact conversion |
|
|
1950 |
x_nr_bits = |
|
|
1951 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1952 |
} |
|
|
1953 |
} else { // if x < 2^53 |
|
|
1954 |
tmp1.d = (double) C1.w[0]; // exact conversion |
|
|
1955 |
x_nr_bits = |
|
|
1956 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1957 |
} |
|
|
1958 |
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
|
|
1959 |
tmp1.d = (double) C1.w[1]; // exact conversion |
|
|
1960 |
x_nr_bits = |
|
|
1961 |
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
1962 |
} |
|
|
1963 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
1964 |
if (q == 0) { |
|
|
1965 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
1966 |
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
|
|
1967 |
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
|
|
1968 |
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
|
|
1969 |
q++; |
|
|
1970 |
} |
|
|
1971 |
exp = (x_exp >> 49) - 6176; |
|
|
1972 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
1973 |
// set invalid flag |
|
|
1974 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1975 |
// return Integer Indefinite |
|
|
1976 |
res = 0x80000000; |
|
|
1977 |
BID_RETURN (res); |
|
|
1978 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
1979 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
1980 |
// so x rounded to an integer may or may not fit in a signed 32-bit int |
|
|
1981 |
// the cases that do not fit are identified here; the ones that fit |
|
|
1982 |
// fall through and will be handled with other cases further, |
|
|
1983 |
// under '1 <= q + exp <= 10' |
|
|
1984 |
if (x_sign) { // if n < 0 and q + exp = 10 |
|
|
1985 |
// if n <= -2^31-1 then n is too large |
|
|
1986 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 |
|
|
1987 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 |
|
|
1988 |
if (q <= 11) { |
|
|
1989 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
1990 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
1991 |
if (tmp64 >= 0x50000000aull) { |
|
|
1992 |
// set invalid flag |
|
|
1993 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
1994 |
// return Integer Indefinite |
|
|
1995 |
res = 0x80000000; |
|
|
1996 |
BID_RETURN (res); |
|
|
1997 |
} |
|
|
1998 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
1999 |
// to '1 <= q + exp <= 10' |
|
|
2000 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
2001 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=> |
|
|
2002 |
// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
2003 |
// (scale 2^31+1 up) |
|
|
2004 |
tmp64 = 0x50000000aull; |
|
|
2005 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
2006 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
2007 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
2008 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
2009 |
} |
|
|
2010 |
if (C1.w[1] > C.w[1] |
|
|
2011 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
2012 |
// set invalid flag |
|
|
2013 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2014 |
// return Integer Indefinite |
|
|
2015 |
res = 0x80000000; |
|
|
2016 |
BID_RETURN (res); |
|
|
2017 |
} |
|
|
2018 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2019 |
// to '1 <= q + exp <= 10' |
|
|
2020 |
} |
|
|
2021 |
} else { // if n > 0 and q + exp = 10 |
|
|
2022 |
// if n > 2^31 - 1 then n is too large |
|
|
2023 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1 |
|
|
2024 |
// too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=34 |
|
|
2025 |
if (q <= 11) { |
|
|
2026 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
2027 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
2028 |
if (tmp64 > 0x4fffffff6ull) { |
|
|
2029 |
// set invalid flag |
|
|
2030 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2031 |
// return Integer Indefinite |
|
|
2032 |
res = 0x80000000; |
|
|
2033 |
BID_RETURN (res); |
|
|
2034 |
} |
|
|
2035 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2036 |
// to '1 <= q + exp <= 10' |
|
|
2037 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
2038 |
// 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6 <=> |
|
|
2039 |
// C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
2040 |
// (scale 2^31 up) |
|
|
2041 |
tmp64 = 0x4fffffff6ull; |
|
|
2042 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
2043 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
2044 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
2045 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
2046 |
} |
|
|
2047 |
if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) { |
|
|
2048 |
// set invalid flag |
|
|
2049 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2050 |
// return Integer Indefinite |
|
|
2051 |
res = 0x80000000; |
|
|
2052 |
BID_RETURN (res); |
|
|
2053 |
} |
|
|
2054 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2055 |
// to '1 <= q + exp <= 10' |
|
|
2056 |
} |
|
|
2057 |
} |
|
|
2058 |
} |
|
|
2059 |
// n is not too large to be converted to int32: -2^31-1 < n <= 2^31-1 |
|
|
2060 |
// Note: some of the cases tested for above fall through to this point |
|
|
2061 |
if ((q + exp) <= 0) { |
|
|
2062 |
// n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) |
|
|
2063 |
// set inexact flag |
|
|
2064 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2065 |
// return 0 |
|
|
2066 |
if (x_sign) |
|
|
2067 |
res = 0x00000000; |
|
|
2068 |
else |
|
|
2069 |
res = 0x00000001; |
|
|
2070 |
BID_RETURN (res); |
|
|
2071 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
|
|
2072 |
// -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded |
|
|
2073 |
// toward positive infinity to a 32-bit signed integer |
|
|
2074 |
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
2075 |
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
|
|
2076 |
// chop off ind digits from the lower part of C1 |
|
|
2077 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits |
|
|
2078 |
tmp64 = C1.w[0]; |
|
|
2079 |
if (ind <= 19) { |
|
|
2080 |
C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
|
|
2081 |
} else { |
|
|
2082 |
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
|
|
2083 |
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
|
|
2084 |
} |
|
|
2085 |
if (C1.w[0] < tmp64) |
|
|
2086 |
C1.w[1]++; |
|
|
2087 |
// calculate C* and f* |
|
|
2088 |
// C* is actually floor(C*) in this case |
|
|
2089 |
// C* and f* need shifting and masking, as shown by |
|
|
2090 |
// shiftright128[] and maskhigh128[] |
|
|
2091 |
// 1 <= x <= 33 |
|
|
2092 |
// kx = 10^(-x) = ten2mk128[ind - 1] |
|
|
2093 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
2094 |
// the approximation of 10^(-x) was rounded up to 118 bits |
|
|
2095 |
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
|
|
2096 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
2097 |
Cstar.w[1] = P256.w[3]; |
|
|
2098 |
Cstar.w[0] = P256.w[2]; |
|
|
2099 |
fstar.w[3] = 0; |
|
|
2100 |
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
|
|
2101 |
fstar.w[1] = P256.w[1]; |
|
|
2102 |
fstar.w[0] = P256.w[0]; |
|
|
2103 |
} else { // 22 <= ind - 1 <= 33 |
|
|
2104 |
Cstar.w[1] = 0; |
|
|
2105 |
Cstar.w[0] = P256.w[3]; |
|
|
2106 |
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
|
|
2107 |
fstar.w[2] = P256.w[2]; |
|
|
2108 |
fstar.w[1] = P256.w[1]; |
|
|
2109 |
fstar.w[0] = P256.w[0]; |
|
|
2110 |
} |
|
|
2111 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
|
|
2112 |
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
|
|
2113 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
2114 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
2115 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
2116 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
2117 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
2118 |
// else |
|
|
2119 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
2120 |
// correct by Property 1) |
|
|
2121 |
// n = C* * 10^(e+x) |
|
|
2122 |
|
|
|
2123 |
// shift right C* by Ex-128 = shiftright128[ind] |
|
|
2124 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
|
|
2125 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
2126 |
Cstar.w[0] = |
|
|
2127 |
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
|
|
2128 |
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
|
|
2129 |
} else { // 22 <= ind - 1 <= 33 |
|
|
2130 |
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
|
|
2131 |
} |
|
|
2132 |
// determine inexactness of the rounding of C* |
|
|
2133 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
2134 |
// the result is exact |
|
|
2135 |
// else // if (f* - 1/2 > T*) then |
|
|
2136 |
// the result is inexact |
|
|
2137 |
if (ind - 1 <= 2) { |
|
|
2138 |
if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact |
|
|
2139 |
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
|
|
2140 |
if (tmp64 > ten2mk128trunc[ind - 1].w[1] |
|
|
2141 |
|| (tmp64 == ten2mk128trunc[ind - 1].w[1] |
|
|
2142 |
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { |
|
|
2143 |
// set the inexact flag |
|
|
2144 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2145 |
is_inexact_lt_midpoint = 1; |
|
|
2146 |
} // else the result is exact |
|
|
2147 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2148 |
// set the inexact flag |
|
|
2149 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2150 |
is_inexact_gt_midpoint = 1; |
|
|
2151 |
} |
|
|
2152 |
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
|
|
2153 |
if (fstar.w[3] > 0x0 || |
|
|
2154 |
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
|
|
2155 |
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
|
|
2156 |
(fstar.w[1] || fstar.w[0]))) { |
|
|
2157 |
// f2* > 1/2 and the result may be exact |
|
|
2158 |
// Calculate f2* - 1/2 |
|
|
2159 |
tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
|
|
2160 |
tmp64A = fstar.w[3]; |
|
|
2161 |
if (tmp64 > fstar.w[2]) |
|
|
2162 |
tmp64A--; |
|
|
2163 |
if (tmp64A || tmp64 |
|
|
2164 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
2165 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
2166 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
2167 |
// set the inexact flag |
|
|
2168 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2169 |
is_inexact_lt_midpoint = 1; |
|
|
2170 |
} // else the result is exact |
|
|
2171 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2172 |
// set the inexact flag |
|
|
2173 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2174 |
is_inexact_gt_midpoint = 1; |
|
|
2175 |
} |
|
|
2176 |
} else { // if 22 <= ind <= 33 |
|
|
2177 |
if (fstar.w[3] > onehalf128[ind - 1] || |
|
|
2178 |
(fstar.w[3] == onehalf128[ind - 1] && |
|
|
2179 |
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) { |
|
|
2180 |
// f2* > 1/2 and the result may be exact |
|
|
2181 |
// Calculate f2* - 1/2 |
|
|
2182 |
tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
|
|
2183 |
if (tmp64 || fstar.w[2] |
|
|
2184 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
2185 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
2186 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
2187 |
// set the inexact flag |
|
|
2188 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2189 |
is_inexact_lt_midpoint = 1; |
|
|
2190 |
} // else the result is exact |
|
|
2191 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2192 |
// set the inexact flag |
|
|
2193 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2194 |
is_inexact_gt_midpoint = 1; |
|
|
2195 |
} |
|
|
2196 |
} |
|
|
2197 |
|
|
|
2198 |
// if the result was a midpoint it was rounded away from zero, so |
|
|
2199 |
// it will need a correction |
|
|
2200 |
// check for midpoints |
|
|
2201 |
if ((fstar.w[3] == 0) && (fstar.w[2] == 0) |
|
|
2202 |
&& (fstar.w[1] || fstar.w[0]) |
|
|
2203 |
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] |
|
|
2204 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
2205 |
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
2206 |
// the result is a midpoint; round to nearest |
|
|
2207 |
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
|
|
2208 |
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
|
|
2209 |
Cstar.w[0]--; // Cstar.w[0] is now even |
|
|
2210 |
is_midpoint_gt_even = 1; |
|
|
2211 |
is_inexact_lt_midpoint = 0; |
|
|
2212 |
is_inexact_gt_midpoint = 0; |
|
|
2213 |
} else { // else MP in [ODD, EVEN] |
|
|
2214 |
is_midpoint_lt_even = 1; |
|
|
2215 |
is_inexact_lt_midpoint = 0; |
|
|
2216 |
is_inexact_gt_midpoint = 0; |
|
|
2217 |
} |
|
|
2218 |
} |
|
|
2219 |
// general correction for RM |
|
|
2220 |
if (x_sign && (is_midpoint_lt_even || is_inexact_gt_midpoint)) { |
|
|
2221 |
Cstar.w[0] = Cstar.w[0] - 1; |
|
|
2222 |
} else if (!x_sign |
|
|
2223 |
&& (is_midpoint_gt_even || is_inexact_lt_midpoint)) { |
|
|
2224 |
Cstar.w[0] = Cstar.w[0] + 1; |
|
|
2225 |
} else { |
|
|
2226 |
; // the result is already correct |
|
|
2227 |
} |
|
|
2228 |
if (x_sign) |
|
|
2229 |
res = -Cstar.w[0]; |
|
|
2230 |
else |
|
|
2231 |
res = Cstar.w[0]; |
|
|
2232 |
} else if (exp == 0) { |
|
|
2233 |
// 1 <= q <= 10 |
|
|
2234 |
// res = +/-C (exact) |
|
|
2235 |
if (x_sign) |
|
|
2236 |
res = -C1.w[0]; |
|
|
2237 |
else |
|
|
2238 |
res = C1.w[0]; |
|
|
2239 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
2240 |
// res = +/-C * 10^exp (exact) |
|
|
2241 |
if (x_sign) |
|
|
2242 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
2243 |
else |
|
|
2244 |
res = C1.w[0] * ten2k64[exp]; |
|
|
2245 |
} |
|
|
2246 |
} |
|
|
2247 |
} |
|
|
2248 |
|
|
|
2249 |
BID_RETURN (res); |
|
|
2250 |
} |
|
|
2251 |
|
|
|
2252 |
/***************************************************************************** |
|
|
2253 |
* BID128_to_int32_int |
|
|
2254 |
****************************************************************************/ |
|
|
2255 |
|
|
|
2256 |
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_int, x) |
|
|
2257 |
|
|
|
2258 |
int res; |
|
|
2259 |
UINT64 x_sign; |
|
|
2260 |
UINT64 x_exp; |
|
|
2261 |
int exp; // unbiased exponent |
|
|
2262 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
2263 |
UINT64 tmp64, tmp64A; |
|
|
2264 |
BID_UI64DOUBLE tmp1; |
|
|
2265 |
unsigned int x_nr_bits; |
|
|
2266 |
int q, ind, shift; |
|
|
2267 |
UINT128 C1, C; |
|
|
2268 |
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
|
|
2269 |
UINT256 fstar; |
|
|
2270 |
UINT256 P256; |
|
|
2271 |
int is_inexact_gt_midpoint = 0; |
|
|
2272 |
int is_midpoint_lt_even = 0; |
|
|
2273 |
|
|
|
2274 |
// unpack x |
|
|
2275 |
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
2276 |
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
|
|
2277 |
C1.w[1] = x.w[1] & MASK_COEFF; |
|
|
2278 |
C1.w[0] = x.w[0]; |
|
|
2279 |
|
|
|
2280 |
// check for NaN or Infinity |
|
|
2281 |
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
|
|
2282 |
// x is special |
|
|
2283 |
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
2284 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
|
|
2285 |
// set invalid flag |
|
|
2286 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2287 |
// return Integer Indefinite |
|
|
2288 |
res = 0x80000000; |
|
|
2289 |
} else { // x is QNaN |
|
|
2290 |
// set invalid flag |
|
|
2291 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2292 |
// return Integer Indefinite |
|
|
2293 |
res = 0x80000000; |
|
|
2294 |
} |
|
|
2295 |
BID_RETURN (res); |
|
|
2296 |
} else { // x is not a NaN, so it must be infinity |
|
|
2297 |
if (!x_sign) { // x is +inf |
|
|
2298 |
// set invalid flag |
|
|
2299 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2300 |
// return Integer Indefinite |
|
|
2301 |
res = 0x80000000; |
|
|
2302 |
} else { // x is -inf |
|
|
2303 |
// set invalid flag |
|
|
2304 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2305 |
// return Integer Indefinite |
|
|
2306 |
res = 0x80000000; |
|
|
2307 |
} |
|
|
2308 |
BID_RETURN (res); |
|
|
2309 |
} |
|
|
2310 |
} |
|
|
2311 |
// check for non-canonical values (after the check for special values) |
|
|
2312 |
if ((C1.w[1] > 0x0001ed09bead87c0ull) |
|
|
2313 |
|| (C1.w[1] == 0x0001ed09bead87c0ull |
|
|
2314 |
&& (C1.w[0] > 0x378d8e63ffffffffull)) |
|
|
2315 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
|
|
2316 |
res = 0x00000000; |
|
|
2317 |
BID_RETURN (res); |
|
|
2318 |
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
|
|
2319 |
// x is 0 |
|
|
2320 |
res = 0x00000000; |
|
|
2321 |
BID_RETURN (res); |
|
|
2322 |
} else { // x is not special and is not zero |
|
|
2323 |
|
|
|
2324 |
// q = nr. of decimal digits in x |
|
|
2325 |
// determine first the nr. of bits in x |
|
|
2326 |
if (C1.w[1] == 0) { |
|
|
2327 |
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
2328 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
2329 |
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
2330 |
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
|
|
2331 |
x_nr_bits = |
|
|
2332 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2333 |
} else { // x < 2^32 |
|
|
2334 |
tmp1.d = (double) (C1.w[0]); // exact conversion |
|
|
2335 |
x_nr_bits = |
|
|
2336 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2337 |
} |
|
|
2338 |
} else { // if x < 2^53 |
|
|
2339 |
tmp1.d = (double) C1.w[0]; // exact conversion |
|
|
2340 |
x_nr_bits = |
|
|
2341 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2342 |
} |
|
|
2343 |
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
|
|
2344 |
tmp1.d = (double) C1.w[1]; // exact conversion |
|
|
2345 |
x_nr_bits = |
|
|
2346 |
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2347 |
} |
|
|
2348 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
2349 |
if (q == 0) { |
|
|
2350 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
2351 |
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
|
|
2352 |
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
|
|
2353 |
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
|
|
2354 |
q++; |
|
|
2355 |
} |
|
|
2356 |
exp = (x_exp >> 49) - 6176; |
|
|
2357 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
2358 |
// set invalid flag |
|
|
2359 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2360 |
// return Integer Indefinite |
|
|
2361 |
res = 0x80000000; |
|
|
2362 |
BID_RETURN (res); |
|
|
2363 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
2364 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
2365 |
// so x rounded to an integer may or may not fit in a signed 32-bit int |
|
|
2366 |
// the cases that do not fit are identified here; the ones that fit |
|
|
2367 |
// fall through and will be handled with other cases further, |
|
|
2368 |
// under '1 <= q + exp <= 10' |
|
|
2369 |
if (x_sign) { // if n < 0 and q + exp = 10 |
|
|
2370 |
// if n <= -2^31 - 1 then n is too large |
|
|
2371 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 |
|
|
2372 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 |
|
|
2373 |
if (q <= 11) { |
|
|
2374 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
2375 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
2376 |
if (tmp64 >= 0x50000000aull) { |
|
|
2377 |
// set invalid flag |
|
|
2378 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2379 |
// return Integer Indefinite |
|
|
2380 |
res = 0x80000000; |
|
|
2381 |
BID_RETURN (res); |
|
|
2382 |
} |
|
|
2383 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2384 |
// to '1 <= q + exp <= 10' |
|
|
2385 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
2386 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=> |
|
|
2387 |
// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
2388 |
// (scale 2^31+1 up) |
|
|
2389 |
tmp64 = 0x50000000aull; |
|
|
2390 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
2391 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
2392 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
2393 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
2394 |
} |
|
|
2395 |
if (C1.w[1] > C.w[1] |
|
|
2396 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
2397 |
// set invalid flag |
|
|
2398 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2399 |
// return Integer Indefinite |
|
|
2400 |
res = 0x80000000; |
|
|
2401 |
BID_RETURN (res); |
|
|
2402 |
} |
|
|
2403 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2404 |
// to '1 <= q + exp <= 10' |
|
|
2405 |
} |
|
|
2406 |
} else { // if n > 0 and q + exp = 10 |
|
|
2407 |
// if n >= 2^31 then n is too large |
|
|
2408 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 |
|
|
2409 |
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34 |
|
|
2410 |
if (q <= 11) { |
|
|
2411 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
2412 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
2413 |
if (tmp64 >= 0x500000000ull) { |
|
|
2414 |
// set invalid flag |
|
|
2415 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2416 |
// return Integer Indefinite |
|
|
2417 |
res = 0x80000000; |
|
|
2418 |
BID_RETURN (res); |
|
|
2419 |
} |
|
|
2420 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2421 |
// to '1 <= q + exp <= 10' |
|
|
2422 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
2423 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=> |
|
|
2424 |
// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
2425 |
// (scale 2^31-1/2 up) |
|
|
2426 |
tmp64 = 0x500000000ull; |
|
|
2427 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
2428 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
2429 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
2430 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
2431 |
} |
|
|
2432 |
if (C1.w[1] > C.w[1] |
|
|
2433 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
2434 |
// set invalid flag |
|
|
2435 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2436 |
// return Integer Indefinite |
|
|
2437 |
res = 0x80000000; |
|
|
2438 |
BID_RETURN (res); |
|
|
2439 |
} |
|
|
2440 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2441 |
// to '1 <= q + exp <= 10' |
|
|
2442 |
} |
|
|
2443 |
} |
|
|
2444 |
} |
|
|
2445 |
// n is not too large to be converted to int32: -2^31 - 1 < n < 2^31 |
|
|
2446 |
// Note: some of the cases tested for above fall through to this point |
|
|
2447 |
if ((q + exp) <= 0) { |
|
|
2448 |
// n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) |
|
|
2449 |
// return 0 |
|
|
2450 |
res = 0x00000000; |
|
|
2451 |
BID_RETURN (res); |
|
|
2452 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
|
|
2453 |
// -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded |
|
|
2454 |
// toward zero to a 32-bit signed integer |
|
|
2455 |
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
2456 |
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
|
|
2457 |
// chop off ind digits from the lower part of C1 |
|
|
2458 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits |
|
|
2459 |
tmp64 = C1.w[0]; |
|
|
2460 |
if (ind <= 19) { |
|
|
2461 |
C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
|
|
2462 |
} else { |
|
|
2463 |
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
|
|
2464 |
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
|
|
2465 |
} |
|
|
2466 |
if (C1.w[0] < tmp64) |
|
|
2467 |
C1.w[1]++; |
|
|
2468 |
// calculate C* and f* |
|
|
2469 |
// C* is actually floor(C*) in this case |
|
|
2470 |
// C* and f* need shifting and masking, as shown by |
|
|
2471 |
// shiftright128[] and maskhigh128[] |
|
|
2472 |
// 1 <= x <= 33 |
|
|
2473 |
// kx = 10^(-x) = ten2mk128[ind - 1] |
|
|
2474 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
2475 |
// the approximation of 10^(-x) was rounded up to 118 bits |
|
|
2476 |
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
|
|
2477 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
2478 |
Cstar.w[1] = P256.w[3]; |
|
|
2479 |
Cstar.w[0] = P256.w[2]; |
|
|
2480 |
fstar.w[3] = 0; |
|
|
2481 |
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
|
|
2482 |
fstar.w[1] = P256.w[1]; |
|
|
2483 |
fstar.w[0] = P256.w[0]; |
|
|
2484 |
} else { // 22 <= ind - 1 <= 33 |
|
|
2485 |
Cstar.w[1] = 0; |
|
|
2486 |
Cstar.w[0] = P256.w[3]; |
|
|
2487 |
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
|
|
2488 |
fstar.w[2] = P256.w[2]; |
|
|
2489 |
fstar.w[1] = P256.w[1]; |
|
|
2490 |
fstar.w[0] = P256.w[0]; |
|
|
2491 |
} |
|
|
2492 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
|
|
2493 |
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
|
|
2494 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
2495 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
2496 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
2497 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
2498 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
2499 |
// else |
|
|
2500 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
2501 |
// correct by Property 1) |
|
|
2502 |
// n = C* * 10^(e+x) |
|
|
2503 |
|
|
|
2504 |
// shift right C* by Ex-128 = shiftright128[ind] |
|
|
2505 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
|
|
2506 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
2507 |
Cstar.w[0] = |
|
|
2508 |
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
|
|
2509 |
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
|
|
2510 |
} else { // 22 <= ind - 1 <= 33 |
|
|
2511 |
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
|
|
2512 |
} |
|
|
2513 |
// determine inexactness of the rounding of C* |
|
|
2514 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
2515 |
// the result is exact |
|
|
2516 |
// else // if (f* - 1/2 > T*) then |
|
|
2517 |
// the result is inexact |
|
|
2518 |
if (ind - 1 <= 2) { |
|
|
2519 |
if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact |
|
|
2520 |
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
|
|
2521 |
if ((tmp64 > ten2mk128trunc[ind - 1].w[1] |
|
|
2522 |
|| (tmp64 == ten2mk128trunc[ind - 1].w[1] |
|
|
2523 |
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
2524 |
} // else the result is exact |
|
|
2525 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2526 |
is_inexact_gt_midpoint = 1; |
|
|
2527 |
} |
|
|
2528 |
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
|
|
2529 |
if (fstar.w[3] > 0x0 || |
|
|
2530 |
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
|
|
2531 |
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
|
|
2532 |
(fstar.w[1] || fstar.w[0]))) { |
|
|
2533 |
// f2* > 1/2 and the result may be exact |
|
|
2534 |
// Calculate f2* - 1/2 |
|
|
2535 |
tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
|
|
2536 |
tmp64A = fstar.w[3]; |
|
|
2537 |
if (tmp64 > fstar.w[2]) |
|
|
2538 |
tmp64A--; |
|
|
2539 |
if (tmp64A || tmp64 |
|
|
2540 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
2541 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
2542 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
2543 |
} // else the result is exact |
|
|
2544 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2545 |
is_inexact_gt_midpoint = 1; |
|
|
2546 |
} |
|
|
2547 |
} else { // if 22 <= ind <= 33 |
|
|
2548 |
if (fstar.w[3] > onehalf128[ind - 1] || |
|
|
2549 |
(fstar.w[3] == onehalf128[ind - 1] && |
|
|
2550 |
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) { |
|
|
2551 |
// f2* > 1/2 and the result may be exact |
|
|
2552 |
// Calculate f2* - 1/2 |
|
|
2553 |
tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
|
|
2554 |
if (tmp64 || fstar.w[2] |
|
|
2555 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
2556 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
2557 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
2558 |
} // else the result is exact |
|
|
2559 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2560 |
is_inexact_gt_midpoint = 1; |
|
|
2561 |
} |
|
|
2562 |
} |
|
|
2563 |
|
|
|
2564 |
// if the result was a midpoint it was rounded away from zero, so |
|
|
2565 |
// it will need a correction |
|
|
2566 |
// check for midpoints |
|
|
2567 |
if ((fstar.w[3] == 0) && (fstar.w[2] == 0) && |
|
|
2568 |
(fstar.w[1] || fstar.w[0]) && |
|
|
2569 |
(fstar.w[1] < ten2mk128trunc[ind - 1].w[1] || |
|
|
2570 |
(fstar.w[1] == ten2mk128trunc[ind - 1].w[1] && |
|
|
2571 |
fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
2572 |
// the result is a midpoint; round to nearest |
|
|
2573 |
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
|
|
2574 |
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
|
|
2575 |
Cstar.w[0]--; // Cstar.w[0] is now even |
|
|
2576 |
is_inexact_gt_midpoint = 0; |
|
|
2577 |
} else { // else MP in [ODD, EVEN] |
|
|
2578 |
is_midpoint_lt_even = 1; |
|
|
2579 |
is_inexact_gt_midpoint = 0; |
|
|
2580 |
} |
|
|
2581 |
} |
|
|
2582 |
// general correction for RZ |
|
|
2583 |
if (is_midpoint_lt_even || is_inexact_gt_midpoint) { |
|
|
2584 |
Cstar.w[0] = Cstar.w[0] - 1; |
|
|
2585 |
} else { |
|
|
2586 |
; // exact, the result is already correct |
|
|
2587 |
} |
|
|
2588 |
if (x_sign) |
|
|
2589 |
res = -Cstar.w[0]; |
|
|
2590 |
else |
|
|
2591 |
res = Cstar.w[0]; |
|
|
2592 |
} else if (exp == 0) { |
|
|
2593 |
// 1 <= q <= 10 |
|
|
2594 |
// res = +/-C (exact) |
|
|
2595 |
if (x_sign) |
|
|
2596 |
res = -C1.w[0]; |
|
|
2597 |
else |
|
|
2598 |
res = C1.w[0]; |
|
|
2599 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
2600 |
// res = +/-C * 10^exp (exact) |
|
|
2601 |
if (x_sign) |
|
|
2602 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
2603 |
else |
|
|
2604 |
res = C1.w[0] * ten2k64[exp]; |
|
|
2605 |
} |
|
|
2606 |
} |
|
|
2607 |
} |
|
|
2608 |
|
|
|
2609 |
BID_RETURN (res); |
|
|
2610 |
} |
|
|
2611 |
|
|
|
2612 |
/***************************************************************************** |
|
|
2613 |
* BID128_to_int32_xint |
|
|
2614 |
****************************************************************************/ |
|
|
2615 |
|
|
|
2616 |
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xint, x) |
|
|
2617 |
|
|
|
2618 |
int res; |
|
|
2619 |
UINT64 x_sign; |
|
|
2620 |
UINT64 x_exp; |
|
|
2621 |
int exp; // unbiased exponent |
|
|
2622 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
2623 |
UINT64 tmp64, tmp64A; |
|
|
2624 |
BID_UI64DOUBLE tmp1; |
|
|
2625 |
unsigned int x_nr_bits; |
|
|
2626 |
int q, ind, shift; |
|
|
2627 |
UINT128 C1, C; |
|
|
2628 |
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
|
|
2629 |
UINT256 fstar; |
|
|
2630 |
UINT256 P256; |
|
|
2631 |
int is_inexact_gt_midpoint = 0; |
|
|
2632 |
int is_midpoint_lt_even = 0; |
|
|
2633 |
|
|
|
2634 |
// unpack x |
|
|
2635 |
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
2636 |
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
|
|
2637 |
C1.w[1] = x.w[1] & MASK_COEFF; |
|
|
2638 |
C1.w[0] = x.w[0]; |
|
|
2639 |
|
|
|
2640 |
// check for NaN or Infinity |
|
|
2641 |
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
|
|
2642 |
// x is special |
|
|
2643 |
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
2644 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
|
|
2645 |
// set invalid flag |
|
|
2646 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2647 |
// return Integer Indefinite |
|
|
2648 |
res = 0x80000000; |
|
|
2649 |
} else { // x is QNaN |
|
|
2650 |
// set invalid flag |
|
|
2651 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2652 |
// return Integer Indefinite |
|
|
2653 |
res = 0x80000000; |
|
|
2654 |
} |
|
|
2655 |
BID_RETURN (res); |
|
|
2656 |
} else { // x is not a NaN, so it must be infinity |
|
|
2657 |
if (!x_sign) { // x is +inf |
|
|
2658 |
// set invalid flag |
|
|
2659 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2660 |
// return Integer Indefinite |
|
|
2661 |
res = 0x80000000; |
|
|
2662 |
} else { // x is -inf |
|
|
2663 |
// set invalid flag |
|
|
2664 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2665 |
// return Integer Indefinite |
|
|
2666 |
res = 0x80000000; |
|
|
2667 |
} |
|
|
2668 |
BID_RETURN (res); |
|
|
2669 |
} |
|
|
2670 |
} |
|
|
2671 |
// check for non-canonical values (after the check for special values) |
|
|
2672 |
if ((C1.w[1] > 0x0001ed09bead87c0ull) |
|
|
2673 |
|| (C1.w[1] == 0x0001ed09bead87c0ull |
|
|
2674 |
&& (C1.w[0] > 0x378d8e63ffffffffull)) |
|
|
2675 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
|
|
2676 |
res = 0x00000000; |
|
|
2677 |
BID_RETURN (res); |
|
|
2678 |
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
|
|
2679 |
// x is 0 |
|
|
2680 |
res = 0x00000000; |
|
|
2681 |
BID_RETURN (res); |
|
|
2682 |
} else { // x is not special and is not zero |
|
|
2683 |
|
|
|
2684 |
// q = nr. of decimal digits in x |
|
|
2685 |
// determine first the nr. of bits in x |
|
|
2686 |
if (C1.w[1] == 0) { |
|
|
2687 |
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
2688 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
2689 |
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
2690 |
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
|
|
2691 |
x_nr_bits = |
|
|
2692 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2693 |
} else { // x < 2^32 |
|
|
2694 |
tmp1.d = (double) (C1.w[0]); // exact conversion |
|
|
2695 |
x_nr_bits = |
|
|
2696 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2697 |
} |
|
|
2698 |
} else { // if x < 2^53 |
|
|
2699 |
tmp1.d = (double) C1.w[0]; // exact conversion |
|
|
2700 |
x_nr_bits = |
|
|
2701 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2702 |
} |
|
|
2703 |
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
|
|
2704 |
tmp1.d = (double) C1.w[1]; // exact conversion |
|
|
2705 |
x_nr_bits = |
|
|
2706 |
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
2707 |
} |
|
|
2708 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
2709 |
if (q == 0) { |
|
|
2710 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
2711 |
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
|
|
2712 |
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
|
|
2713 |
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
|
|
2714 |
q++; |
|
|
2715 |
} |
|
|
2716 |
exp = (x_exp >> 49) - 6176; |
|
|
2717 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
2718 |
// set invalid flag |
|
|
2719 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2720 |
// return Integer Indefinite |
|
|
2721 |
res = 0x80000000; |
|
|
2722 |
BID_RETURN (res); |
|
|
2723 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
2724 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
2725 |
// so x rounded to an integer may or may not fit in a signed 32-bit int |
|
|
2726 |
// the cases that do not fit are identified here; the ones that fit |
|
|
2727 |
// fall through and will be handled with other cases further, |
|
|
2728 |
// under '1 <= q + exp <= 10' |
|
|
2729 |
if (x_sign) { // if n < 0 and q + exp = 10 |
|
|
2730 |
// if n <= -2^31 - 1 then n is too large |
|
|
2731 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1 |
|
|
2732 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34 |
|
|
2733 |
if (q <= 11) { |
|
|
2734 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
2735 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
2736 |
if (tmp64 >= 0x50000000aull) { |
|
|
2737 |
// set invalid flag |
|
|
2738 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2739 |
// return Integer Indefinite |
|
|
2740 |
res = 0x80000000; |
|
|
2741 |
BID_RETURN (res); |
|
|
2742 |
} |
|
|
2743 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2744 |
// to '1 <= q + exp <= 10' |
|
|
2745 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
2746 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=> |
|
|
2747 |
// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
2748 |
// (scale 2^31+1 up) |
|
|
2749 |
tmp64 = 0x50000000aull; |
|
|
2750 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
2751 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
2752 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
2753 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
2754 |
} |
|
|
2755 |
if (C1.w[1] > C.w[1] |
|
|
2756 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
2757 |
// set invalid flag |
|
|
2758 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2759 |
// return Integer Indefinite |
|
|
2760 |
res = 0x80000000; |
|
|
2761 |
BID_RETURN (res); |
|
|
2762 |
} |
|
|
2763 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2764 |
// to '1 <= q + exp <= 10' |
|
|
2765 |
} |
|
|
2766 |
} else { // if n > 0 and q + exp = 10 |
|
|
2767 |
// if n >= 2^31 then n is too large |
|
|
2768 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31 |
|
|
2769 |
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34 |
|
|
2770 |
if (q <= 11) { |
|
|
2771 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
2772 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
2773 |
if (tmp64 >= 0x500000000ull) { |
|
|
2774 |
// set invalid flag |
|
|
2775 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2776 |
// return Integer Indefinite |
|
|
2777 |
res = 0x80000000; |
|
|
2778 |
BID_RETURN (res); |
|
|
2779 |
} |
|
|
2780 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2781 |
// to '1 <= q + exp <= 10' |
|
|
2782 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
2783 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=> |
|
|
2784 |
// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
2785 |
// (scale 2^31-1/2 up) |
|
|
2786 |
tmp64 = 0x500000000ull; |
|
|
2787 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
2788 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
2789 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
2790 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
2791 |
} |
|
|
2792 |
if (C1.w[1] > C.w[1] |
|
|
2793 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
2794 |
// set invalid flag |
|
|
2795 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
2796 |
// return Integer Indefinite |
|
|
2797 |
res = 0x80000000; |
|
|
2798 |
BID_RETURN (res); |
|
|
2799 |
} |
|
|
2800 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
2801 |
// to '1 <= q + exp <= 10' |
|
|
2802 |
} |
|
|
2803 |
} |
|
|
2804 |
} |
|
|
2805 |
// n is not too large to be converted to int32: -2^31 - 1 < n < 2^31 |
|
|
2806 |
// Note: some of the cases tested for above fall through to this point |
|
|
2807 |
if ((q + exp) <= 0) { |
|
|
2808 |
// n = +/-0.0...c(0)c(1)...c(q-1) or n = +/-0.c(0)c(1)...c(q-1) |
|
|
2809 |
// set inexact flag |
|
|
2810 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2811 |
// return 0 |
|
|
2812 |
res = 0x00000000; |
|
|
2813 |
BID_RETURN (res); |
|
|
2814 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
|
|
2815 |
// -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded |
|
|
2816 |
// toward zero to a 32-bit signed integer |
|
|
2817 |
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
2818 |
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
|
|
2819 |
// chop off ind digits from the lower part of C1 |
|
|
2820 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits |
|
|
2821 |
tmp64 = C1.w[0]; |
|
|
2822 |
if (ind <= 19) { |
|
|
2823 |
C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
|
|
2824 |
} else { |
|
|
2825 |
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
|
|
2826 |
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
|
|
2827 |
} |
|
|
2828 |
if (C1.w[0] < tmp64) |
|
|
2829 |
C1.w[1]++; |
|
|
2830 |
// calculate C* and f* |
|
|
2831 |
// C* is actually floor(C*) in this case |
|
|
2832 |
// C* and f* need shifting and masking, as shown by |
|
|
2833 |
// shiftright128[] and maskhigh128[] |
|
|
2834 |
// 1 <= x <= 33 |
|
|
2835 |
// kx = 10^(-x) = ten2mk128[ind - 1] |
|
|
2836 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
2837 |
// the approximation of 10^(-x) was rounded up to 118 bits |
|
|
2838 |
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
|
|
2839 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
2840 |
Cstar.w[1] = P256.w[3]; |
|
|
2841 |
Cstar.w[0] = P256.w[2]; |
|
|
2842 |
fstar.w[3] = 0; |
|
|
2843 |
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
|
|
2844 |
fstar.w[1] = P256.w[1]; |
|
|
2845 |
fstar.w[0] = P256.w[0]; |
|
|
2846 |
} else { // 22 <= ind - 1 <= 33 |
|
|
2847 |
Cstar.w[1] = 0; |
|
|
2848 |
Cstar.w[0] = P256.w[3]; |
|
|
2849 |
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
|
|
2850 |
fstar.w[2] = P256.w[2]; |
|
|
2851 |
fstar.w[1] = P256.w[1]; |
|
|
2852 |
fstar.w[0] = P256.w[0]; |
|
|
2853 |
} |
|
|
2854 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
|
|
2855 |
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
|
|
2856 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
2857 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
2858 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
2859 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
2860 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
2861 |
// else |
|
|
2862 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
2863 |
// correct by Property 1) |
|
|
2864 |
// n = C* * 10^(e+x) |
|
|
2865 |
|
|
|
2866 |
// shift right C* by Ex-128 = shiftright128[ind] |
|
|
2867 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
|
|
2868 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
2869 |
Cstar.w[0] = |
|
|
2870 |
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
|
|
2871 |
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
|
|
2872 |
} else { // 22 <= ind - 1 <= 33 |
|
|
2873 |
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
|
|
2874 |
} |
|
|
2875 |
// determine inexactness of the rounding of C* |
|
|
2876 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
2877 |
// the result is exact |
|
|
2878 |
// else // if (f* - 1/2 > T*) then |
|
|
2879 |
// the result is inexact |
|
|
2880 |
if (ind - 1 <= 2) { |
|
|
2881 |
if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact |
|
|
2882 |
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
|
|
2883 |
if (tmp64 > ten2mk128trunc[ind - 1].w[1] |
|
|
2884 |
|| (tmp64 == ten2mk128trunc[ind - 1].w[1] |
|
|
2885 |
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) { |
|
|
2886 |
// set the inexact flag |
|
|
2887 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2888 |
} // else the result is exact |
|
|
2889 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2890 |
// set the inexact flag |
|
|
2891 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2892 |
is_inexact_gt_midpoint = 1; |
|
|
2893 |
} |
|
|
2894 |
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
|
|
2895 |
if (fstar.w[3] > 0x0 || |
|
|
2896 |
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
|
|
2897 |
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
|
|
2898 |
(fstar.w[1] || fstar.w[0]))) { |
|
|
2899 |
// f2* > 1/2 and the result may be exact |
|
|
2900 |
// Calculate f2* - 1/2 |
|
|
2901 |
tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
|
|
2902 |
tmp64A = fstar.w[3]; |
|
|
2903 |
if (tmp64 > fstar.w[2]) |
|
|
2904 |
tmp64A--; |
|
|
2905 |
if (tmp64A || tmp64 |
|
|
2906 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
2907 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
2908 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
2909 |
// set the inexact flag |
|
|
2910 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2911 |
} // else the result is exact |
|
|
2912 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2913 |
// set the inexact flag |
|
|
2914 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2915 |
is_inexact_gt_midpoint = 1; |
|
|
2916 |
} |
|
|
2917 |
} else { // if 22 <= ind <= 33 |
|
|
2918 |
if (fstar.w[3] > onehalf128[ind - 1] || |
|
|
2919 |
(fstar.w[3] == onehalf128[ind - 1] && (fstar.w[2] || |
|
|
2920 |
fstar.w[1] |
|
|
2921 |
|| fstar.w[0]))) { |
|
|
2922 |
// f2* > 1/2 and the result may be exact |
|
|
2923 |
// Calculate f2* - 1/2 |
|
|
2924 |
tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
|
|
2925 |
if (tmp64 || fstar.w[2] |
|
|
2926 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
2927 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
2928 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
2929 |
// set the inexact flag |
|
|
2930 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2931 |
} // else the result is exact |
|
|
2932 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
2933 |
// set the inexact flag |
|
|
2934 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
2935 |
is_inexact_gt_midpoint = 1; |
|
|
2936 |
} |
|
|
2937 |
} |
|
|
2938 |
|
|
|
2939 |
// if the result was a midpoint it was rounded away from zero, so |
|
|
2940 |
// it will need a correction |
|
|
2941 |
// check for midpoints |
|
|
2942 |
if ((fstar.w[3] == 0) && (fstar.w[2] == 0) |
|
|
2943 |
&& (fstar.w[1] || fstar.w[0]) |
|
|
2944 |
&& (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] |
|
|
2945 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
2946 |
&& fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
2947 |
// the result is a midpoint; round to nearest |
|
|
2948 |
if (Cstar.w[0] & 0x01) { // Cstar.w[0] is odd; MP in [EVEN, ODD] |
|
|
2949 |
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1 |
|
|
2950 |
Cstar.w[0]--; // Cstar.w[0] is now even |
|
|
2951 |
is_inexact_gt_midpoint = 0; |
|
|
2952 |
} else { // else MP in [ODD, EVEN] |
|
|
2953 |
is_midpoint_lt_even = 1; |
|
|
2954 |
is_inexact_gt_midpoint = 0; |
|
|
2955 |
} |
|
|
2956 |
} |
|
|
2957 |
// general correction for RZ |
|
|
2958 |
if (is_midpoint_lt_even || is_inexact_gt_midpoint) { |
|
|
2959 |
Cstar.w[0] = Cstar.w[0] - 1; |
|
|
2960 |
} else { |
|
|
2961 |
; // exact, the result is already correct |
|
|
2962 |
} |
|
|
2963 |
if (x_sign) |
|
|
2964 |
res = -Cstar.w[0]; |
|
|
2965 |
else |
|
|
2966 |
res = Cstar.w[0]; |
|
|
2967 |
} else if (exp == 0) { |
|
|
2968 |
// 1 <= q <= 10 |
|
|
2969 |
// res = +/-C (exact) |
|
|
2970 |
if (x_sign) |
|
|
2971 |
res = -C1.w[0]; |
|
|
2972 |
else |
|
|
2973 |
res = C1.w[0]; |
|
|
2974 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
2975 |
// res = +/-C * 10^exp (exact) |
|
|
2976 |
if (x_sign) |
|
|
2977 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
2978 |
else |
|
|
2979 |
res = C1.w[0] * ten2k64[exp]; |
|
|
2980 |
} |
|
|
2981 |
} |
|
|
2982 |
} |
|
|
2983 |
|
|
|
2984 |
BID_RETURN (res); |
|
|
2985 |
} |
|
|
2986 |
|
|
|
2987 |
/***************************************************************************** |
|
|
2988 |
* BID128_to_int32_rninta |
|
|
2989 |
****************************************************************************/ |
|
|
2990 |
|
|
|
2991 |
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_rninta, |
|
|
2992 |
x) |
|
|
2993 |
|
|
|
2994 |
int res; |
|
|
2995 |
UINT64 x_sign; |
|
|
2996 |
UINT64 x_exp; |
|
|
2997 |
int exp; // unbiased exponent |
|
|
2998 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
2999 |
UINT64 tmp64; |
|
|
3000 |
BID_UI64DOUBLE tmp1; |
|
|
3001 |
unsigned int x_nr_bits; |
|
|
3002 |
int q, ind, shift; |
|
|
3003 |
UINT128 C1, C; |
|
|
3004 |
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
|
|
3005 |
UINT256 P256; |
|
|
3006 |
|
|
|
3007 |
// unpack x |
|
|
3008 |
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
3009 |
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
|
|
3010 |
C1.w[1] = x.w[1] & MASK_COEFF; |
|
|
3011 |
C1.w[0] = x.w[0]; |
|
|
3012 |
|
|
|
3013 |
// check for NaN or Infinity |
|
|
3014 |
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
|
|
3015 |
// x is special |
|
|
3016 |
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
3017 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
|
|
3018 |
// set invalid flag |
|
|
3019 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3020 |
// return Integer Indefinite |
|
|
3021 |
res = 0x80000000; |
|
|
3022 |
} else { // x is QNaN |
|
|
3023 |
// set invalid flag |
|
|
3024 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3025 |
// return Integer Indefinite |
|
|
3026 |
res = 0x80000000; |
|
|
3027 |
} |
|
|
3028 |
BID_RETURN (res); |
|
|
3029 |
} else { // x is not a NaN, so it must be infinity |
|
|
3030 |
if (!x_sign) { // x is +inf |
|
|
3031 |
// set invalid flag |
|
|
3032 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3033 |
// return Integer Indefinite |
|
|
3034 |
res = 0x80000000; |
|
|
3035 |
} else { // x is -inf |
|
|
3036 |
// set invalid flag |
|
|
3037 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3038 |
// return Integer Indefinite |
|
|
3039 |
res = 0x80000000; |
|
|
3040 |
} |
|
|
3041 |
BID_RETURN (res); |
|
|
3042 |
} |
|
|
3043 |
} |
|
|
3044 |
// check for non-canonical values (after the check for special values) |
|
|
3045 |
if ((C1.w[1] > 0x0001ed09bead87c0ull) |
|
|
3046 |
|| (C1.w[1] == 0x0001ed09bead87c0ull |
|
|
3047 |
&& (C1.w[0] > 0x378d8e63ffffffffull)) |
|
|
3048 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
|
|
3049 |
res = 0x00000000; |
|
|
3050 |
BID_RETURN (res); |
|
|
3051 |
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
|
|
3052 |
// x is 0 |
|
|
3053 |
res = 0x00000000; |
|
|
3054 |
BID_RETURN (res); |
|
|
3055 |
} else { // x is not special and is not zero |
|
|
3056 |
|
|
|
3057 |
// q = nr. of decimal digits in x |
|
|
3058 |
// determine first the nr. of bits in x |
|
|
3059 |
if (C1.w[1] == 0) { |
|
|
3060 |
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
3061 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
3062 |
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
3063 |
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
|
|
3064 |
x_nr_bits = |
|
|
3065 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
3066 |
} else { // x < 2^32 |
|
|
3067 |
tmp1.d = (double) (C1.w[0]); // exact conversion |
|
|
3068 |
x_nr_bits = |
|
|
3069 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
3070 |
} |
|
|
3071 |
} else { // if x < 2^53 |
|
|
3072 |
tmp1.d = (double) C1.w[0]; // exact conversion |
|
|
3073 |
x_nr_bits = |
|
|
3074 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
3075 |
} |
|
|
3076 |
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
|
|
3077 |
tmp1.d = (double) C1.w[1]; // exact conversion |
|
|
3078 |
x_nr_bits = |
|
|
3079 |
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
3080 |
} |
|
|
3081 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
3082 |
if (q == 0) { |
|
|
3083 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
3084 |
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
|
|
3085 |
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
|
|
3086 |
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
|
|
3087 |
q++; |
|
|
3088 |
} |
|
|
3089 |
exp = (x_exp >> 49) - 6176; |
|
|
3090 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
3091 |
// set invalid flag |
|
|
3092 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3093 |
// return Integer Indefinite |
|
|
3094 |
res = 0x80000000; |
|
|
3095 |
BID_RETURN (res); |
|
|
3096 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
3097 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
3098 |
// so x rounded to an integer may or may not fit in a signed 32-bit int |
|
|
3099 |
// the cases that do not fit are identified here; the ones that fit |
|
|
3100 |
// fall through and will be handled with other cases further, |
|
|
3101 |
// under '1 <= q + exp <= 10' |
|
|
3102 |
if (x_sign) { // if n < 0 and q + exp = 10 |
|
|
3103 |
// if n <= -2^31 - 1/2 then n is too large |
|
|
3104 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2 |
|
|
3105 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=34 |
|
|
3106 |
if (q <= 11) { |
|
|
3107 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
3108 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
3109 |
if (tmp64 >= 0x500000005ull) { |
|
|
3110 |
// set invalid flag |
|
|
3111 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3112 |
// return Integer Indefinite |
|
|
3113 |
res = 0x80000000; |
|
|
3114 |
BID_RETURN (res); |
|
|
3115 |
} |
|
|
3116 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
3117 |
// to '1 <= q + exp <= 10' |
|
|
3118 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
3119 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005 <=> |
|
|
3120 |
// C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
3121 |
// (scale 2^31+1/2 up) |
|
|
3122 |
tmp64 = 0x500000005ull; |
|
|
3123 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
3124 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
3125 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
3126 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
3127 |
} |
|
|
3128 |
if (C1.w[1] > C.w[1] |
|
|
3129 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
3130 |
// set invalid flag |
|
|
3131 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3132 |
// return Integer Indefinite |
|
|
3133 |
res = 0x80000000; |
|
|
3134 |
BID_RETURN (res); |
|
|
3135 |
} |
|
|
3136 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
3137 |
// to '1 <= q + exp <= 10' |
|
|
3138 |
} |
|
|
3139 |
} else { // if n > 0 and q + exp = 10 |
|
|
3140 |
// if n >= 2^31 - 1/2 then n is too large |
|
|
3141 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 |
|
|
3142 |
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34 |
|
|
3143 |
if (q <= 11) { |
|
|
3144 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
3145 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
3146 |
if (tmp64 >= 0x4fffffffbull) { |
|
|
3147 |
// set invalid flag |
|
|
3148 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3149 |
// return Integer Indefinite |
|
|
3150 |
res = 0x80000000; |
|
|
3151 |
BID_RETURN (res); |
|
|
3152 |
} |
|
|
3153 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
3154 |
// to '1 <= q + exp <= 10' |
|
|
3155 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
3156 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=> |
|
|
3157 |
// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
3158 |
// (scale 2^31-1/2 up) |
|
|
3159 |
tmp64 = 0x4fffffffbull; |
|
|
3160 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
3161 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
3162 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
3163 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
3164 |
} |
|
|
3165 |
if (C1.w[1] > C.w[1] |
|
|
3166 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
3167 |
// set invalid flag |
|
|
3168 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3169 |
// return Integer Indefinite |
|
|
3170 |
res = 0x80000000; |
|
|
3171 |
BID_RETURN (res); |
|
|
3172 |
} |
|
|
3173 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
3174 |
// to '1 <= q + exp <= 10' |
|
|
3175 |
} |
|
|
3176 |
} |
|
|
3177 |
} |
|
|
3178 |
// n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 |
|
|
3179 |
// Note: some of the cases tested for above fall through to this point |
|
|
3180 |
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
|
|
3181 |
// return 0 |
|
|
3182 |
res = 0x00000000; |
|
|
3183 |
BID_RETURN (res); |
|
|
3184 |
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
|
|
3185 |
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) |
|
|
3186 |
// res = 0 |
|
|
3187 |
// else |
|
|
3188 |
// res = +/-1 |
|
|
3189 |
ind = q - 1; |
|
|
3190 |
if (ind <= 18) { // 0 <= ind <= 18 |
|
|
3191 |
if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { |
|
|
3192 |
res = 0x00000000; // return 0 |
|
|
3193 |
} else if (x_sign) { // n < 0 |
|
|
3194 |
res = 0xffffffff; // return -1 |
|
|
3195 |
} else { // n > 0 |
|
|
3196 |
res = 0x00000001; // return +1 |
|
|
3197 |
} |
|
|
3198 |
} else { // 19 <= ind <= 33 |
|
|
3199 |
if ((C1.w[1] < midpoint128[ind - 19].w[1]) |
|
|
3200 |
|| ((C1.w[1] == midpoint128[ind - 19].w[1]) |
|
|
3201 |
&& (C1.w[0] < midpoint128[ind - 19].w[0]))) { |
|
|
3202 |
res = 0x00000000; // return 0 |
|
|
3203 |
} else if (x_sign) { // n < 0 |
|
|
3204 |
res = 0xffffffff; // return -1 |
|
|
3205 |
} else { // n > 0 |
|
|
3206 |
res = 0x00000001; // return +1 |
|
|
3207 |
} |
|
|
3208 |
} |
|
|
3209 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
|
|
3210 |
// -2^31-1/2 < x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded |
|
|
3211 |
// to nearest-away to a 32-bit signed integer |
|
|
3212 |
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
3213 |
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
|
|
3214 |
// chop off ind digits from the lower part of C1 |
|
|
3215 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits |
|
|
3216 |
tmp64 = C1.w[0]; |
|
|
3217 |
if (ind <= 19) { |
|
|
3218 |
C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
|
|
3219 |
} else { |
|
|
3220 |
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
|
|
3221 |
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
|
|
3222 |
} |
|
|
3223 |
if (C1.w[0] < tmp64) |
|
|
3224 |
C1.w[1]++; |
|
|
3225 |
// calculate C* and f* |
|
|
3226 |
// C* is actually floor(C*) in this case |
|
|
3227 |
// C* and f* need shifting and masking, as shown by |
|
|
3228 |
// shiftright128[] and maskhigh128[] |
|
|
3229 |
// 1 <= x <= 33 |
|
|
3230 |
// kx = 10^(-x) = ten2mk128[ind - 1] |
|
|
3231 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
3232 |
// the approximation of 10^(-x) was rounded up to 118 bits |
|
|
3233 |
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
|
|
3234 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
3235 |
Cstar.w[1] = P256.w[3]; |
|
|
3236 |
Cstar.w[0] = P256.w[2]; |
|
|
3237 |
} else { // 22 <= ind - 1 <= 33 |
|
|
3238 |
Cstar.w[1] = 0; |
|
|
3239 |
Cstar.w[0] = P256.w[3]; |
|
|
3240 |
} |
|
|
3241 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
|
|
3242 |
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
|
|
3243 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
3244 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
3245 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
3246 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
3247 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
3248 |
// else |
|
|
3249 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
3250 |
// correct by Property 1) |
|
|
3251 |
// n = C* * 10^(e+x) |
|
|
3252 |
|
|
|
3253 |
// shift right C* by Ex-128 = shiftright128[ind] |
|
|
3254 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
|
|
3255 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
3256 |
Cstar.w[0] = |
|
|
3257 |
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
|
|
3258 |
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
|
|
3259 |
} else { // 22 <= ind - 1 <= 33 |
|
|
3260 |
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
|
|
3261 |
} |
|
|
3262 |
// if the result was a midpoint, it was already rounded away from zero |
|
|
3263 |
if (x_sign) |
|
|
3264 |
res = -Cstar.w[0]; |
|
|
3265 |
else |
|
|
3266 |
res = Cstar.w[0]; |
|
|
3267 |
// no need to check for midpoints - already rounded away from zero! |
|
|
3268 |
} else if (exp == 0) { |
|
|
3269 |
// 1 <= q <= 10 |
|
|
3270 |
// res = +/-C (exact) |
|
|
3271 |
if (x_sign) |
|
|
3272 |
res = -C1.w[0]; |
|
|
3273 |
else |
|
|
3274 |
res = C1.w[0]; |
|
|
3275 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
3276 |
// res = +/-C * 10^exp (exact) |
|
|
3277 |
if (x_sign) |
|
|
3278 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
3279 |
else |
|
|
3280 |
res = C1.w[0] * ten2k64[exp]; |
|
|
3281 |
} |
|
|
3282 |
} |
|
|
3283 |
} |
|
|
3284 |
|
|
|
3285 |
BID_RETURN (res); |
|
|
3286 |
} |
|
|
3287 |
|
|
|
3288 |
/***************************************************************************** |
|
|
3289 |
* BID128_to_int32_xrninta |
|
|
3290 |
****************************************************************************/ |
|
|
3291 |
|
|
|
3292 |
BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xrninta, |
|
|
3293 |
x) |
|
|
3294 |
|
|
|
3295 |
int res; |
|
|
3296 |
UINT64 x_sign; |
|
|
3297 |
UINT64 x_exp; |
|
|
3298 |
int exp; // unbiased exponent |
|
|
3299 |
// Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64) |
|
|
3300 |
UINT64 tmp64, tmp64A; |
|
|
3301 |
BID_UI64DOUBLE tmp1; |
|
|
3302 |
unsigned int x_nr_bits; |
|
|
3303 |
int q, ind, shift; |
|
|
3304 |
UINT128 C1, C; |
|
|
3305 |
UINT128 Cstar; // C* represents up to 34 decimal digits ~ 113 bits |
|
|
3306 |
UINT256 fstar; |
|
|
3307 |
UINT256 P256; |
|
|
3308 |
|
|
|
3309 |
// unpack x |
|
|
3310 |
x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative |
|
|
3311 |
x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bit positions |
|
|
3312 |
C1.w[1] = x.w[1] & MASK_COEFF; |
|
|
3313 |
C1.w[0] = x.w[0]; |
|
|
3314 |
|
|
|
3315 |
// check for NaN or Infinity |
|
|
3316 |
if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) { |
|
|
3317 |
// x is special |
|
|
3318 |
if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN |
|
|
3319 |
if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN |
|
|
3320 |
// set invalid flag |
|
|
3321 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3322 |
// return Integer Indefinite |
|
|
3323 |
res = 0x80000000; |
|
|
3324 |
} else { // x is QNaN |
|
|
3325 |
// set invalid flag |
|
|
3326 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3327 |
// return Integer Indefinite |
|
|
3328 |
res = 0x80000000; |
|
|
3329 |
} |
|
|
3330 |
BID_RETURN (res); |
|
|
3331 |
} else { // x is not a NaN, so it must be infinity |
|
|
3332 |
if (!x_sign) { // x is +inf |
|
|
3333 |
// set invalid flag |
|
|
3334 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3335 |
// return Integer Indefinite |
|
|
3336 |
res = 0x80000000; |
|
|
3337 |
} else { // x is -inf |
|
|
3338 |
// set invalid flag |
|
|
3339 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3340 |
// return Integer Indefinite |
|
|
3341 |
res = 0x80000000; |
|
|
3342 |
} |
|
|
3343 |
BID_RETURN (res); |
|
|
3344 |
} |
|
|
3345 |
} |
|
|
3346 |
// check for non-canonical values (after the check for special values) |
|
|
3347 |
if ((C1.w[1] > 0x0001ed09bead87c0ull) |
|
|
3348 |
|| (C1.w[1] == 0x0001ed09bead87c0ull |
|
|
3349 |
&& (C1.w[0] > 0x378d8e63ffffffffull)) |
|
|
3350 |
|| ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) { |
|
|
3351 |
res = 0x00000000; |
|
|
3352 |
BID_RETURN (res); |
|
|
3353 |
} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) { |
|
|
3354 |
// x is 0 |
|
|
3355 |
res = 0x00000000; |
|
|
3356 |
BID_RETURN (res); |
|
|
3357 |
} else { // x is not special and is not zero |
|
|
3358 |
|
|
|
3359 |
// q = nr. of decimal digits in x |
|
|
3360 |
// determine first the nr. of bits in x |
|
|
3361 |
if (C1.w[1] == 0) { |
|
|
3362 |
if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53 |
|
|
3363 |
// split the 64-bit value in two 32-bit halves to avoid rounding errors |
|
|
3364 |
if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32 |
|
|
3365 |
tmp1.d = (double) (C1.w[0] >> 32); // exact conversion |
|
|
3366 |
x_nr_bits = |
|
|
3367 |
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
3368 |
} else { // x < 2^32 |
|
|
3369 |
tmp1.d = (double) (C1.w[0]); // exact conversion |
|
|
3370 |
x_nr_bits = |
|
|
3371 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
3372 |
} |
|
|
3373 |
} else { // if x < 2^53 |
|
|
3374 |
tmp1.d = (double) C1.w[0]; // exact conversion |
|
|
3375 |
x_nr_bits = |
|
|
3376 |
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
3377 |
} |
|
|
3378 |
} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1]) |
|
|
3379 |
tmp1.d = (double) C1.w[1]; // exact conversion |
|
|
3380 |
x_nr_bits = |
|
|
3381 |
65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); |
|
|
3382 |
} |
|
|
3383 |
q = nr_digits[x_nr_bits - 1].digits; |
|
|
3384 |
if (q == 0) { |
|
|
3385 |
q = nr_digits[x_nr_bits - 1].digits1; |
|
|
3386 |
if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi |
|
|
3387 |
|| (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi |
|
|
3388 |
&& C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo)) |
|
|
3389 |
q++; |
|
|
3390 |
} |
|
|
3391 |
exp = (x_exp >> 49) - 6176; |
|
|
3392 |
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) |
|
|
3393 |
// set invalid flag |
|
|
3394 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3395 |
// return Integer Indefinite |
|
|
3396 |
res = 0x80000000; |
|
|
3397 |
BID_RETURN (res); |
|
|
3398 |
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) |
|
|
3399 |
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... |
|
|
3400 |
// so x rounded to an integer may or may not fit in a signed 32-bit int |
|
|
3401 |
// the cases that do not fit are identified here; the ones that fit |
|
|
3402 |
// fall through and will be handled with other cases further, |
|
|
3403 |
// under '1 <= q + exp <= 10' |
|
|
3404 |
if (x_sign) { // if n < 0 and q + exp = 10 |
|
|
3405 |
// if n <= -2^31 - 1/2 then n is too large |
|
|
3406 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2 |
|
|
3407 |
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=34 |
|
|
3408 |
if (q <= 11) { |
|
|
3409 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
3410 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
3411 |
if (tmp64 >= 0x500000005ull) { |
|
|
3412 |
// set invalid flag |
|
|
3413 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3414 |
// return Integer Indefinite |
|
|
3415 |
res = 0x80000000; |
|
|
3416 |
BID_RETURN (res); |
|
|
3417 |
} |
|
|
3418 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
3419 |
// to '1 <= q + exp <= 10' |
|
|
3420 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
3421 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005 <=> |
|
|
3422 |
// C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
3423 |
// (scale 2^31+1/2 up) |
|
|
3424 |
tmp64 = 0x500000005ull; |
|
|
3425 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
3426 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
3427 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
3428 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
3429 |
} |
|
|
3430 |
if (C1.w[1] > C.w[1] |
|
|
3431 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
3432 |
// set invalid flag |
|
|
3433 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3434 |
// return Integer Indefinite |
|
|
3435 |
res = 0x80000000; |
|
|
3436 |
BID_RETURN (res); |
|
|
3437 |
} |
|
|
3438 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
3439 |
// to '1 <= q + exp <= 10' |
|
|
3440 |
} |
|
|
3441 |
} else { // if n > 0 and q + exp = 10 |
|
|
3442 |
// if n >= 2^31 - 1/2 then n is too large |
|
|
3443 |
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2 |
|
|
3444 |
// too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34 |
|
|
3445 |
if (q <= 11) { |
|
|
3446 |
tmp64 = C1.w[0] * ten2k64[11 - q]; // C scaled up to 11-digit int |
|
|
3447 |
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) |
|
|
3448 |
if (tmp64 >= 0x4fffffffbull) { |
|
|
3449 |
// set invalid flag |
|
|
3450 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3451 |
// return Integer Indefinite |
|
|
3452 |
res = 0x80000000; |
|
|
3453 |
BID_RETURN (res); |
|
|
3454 |
} |
|
|
3455 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
3456 |
// to '1 <= q + exp <= 10' |
|
|
3457 |
} else { // if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2 |
|
|
3458 |
// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=> |
|
|
3459 |
// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23 |
|
|
3460 |
// (scale 2^31-1/2 up) |
|
|
3461 |
tmp64 = 0x4fffffffbull; |
|
|
3462 |
if (q - 11 <= 19) { // 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits |
|
|
3463 |
__mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]); |
|
|
3464 |
} else { // 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits |
|
|
3465 |
__mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]); |
|
|
3466 |
} |
|
|
3467 |
if (C1.w[1] > C.w[1] |
|
|
3468 |
|| (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) { |
|
|
3469 |
// set invalid flag |
|
|
3470 |
*pfpsf |= INVALID_EXCEPTION; |
|
|
3471 |
// return Integer Indefinite |
|
|
3472 |
res = 0x80000000; |
|
|
3473 |
BID_RETURN (res); |
|
|
3474 |
} |
|
|
3475 |
// else cases that can be rounded to a 32-bit int fall through |
|
|
3476 |
// to '1 <= q + exp <= 10' |
|
|
3477 |
} |
|
|
3478 |
} |
|
|
3479 |
} |
|
|
3480 |
// n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 1/2 |
|
|
3481 |
// Note: some of the cases tested for above fall through to this point |
|
|
3482 |
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) |
|
|
3483 |
// set inexact flag |
|
|
3484 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
3485 |
// return 0 |
|
|
3486 |
res = 0x00000000; |
|
|
3487 |
BID_RETURN (res); |
|
|
3488 |
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) |
|
|
3489 |
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) |
|
|
3490 |
// res = 0 |
|
|
3491 |
// else |
|
|
3492 |
// res = +/-1 |
|
|
3493 |
ind = q - 1; |
|
|
3494 |
if (ind <= 18) { // 0 <= ind <= 18 |
|
|
3495 |
if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) { |
|
|
3496 |
res = 0x00000000; // return 0 |
|
|
3497 |
} else if (x_sign) { // n < 0 |
|
|
3498 |
res = 0xffffffff; // return -1 |
|
|
3499 |
} else { // n > 0 |
|
|
3500 |
res = 0x00000001; // return +1 |
|
|
3501 |
} |
|
|
3502 |
} else { // 19 <= ind <= 33 |
|
|
3503 |
if ((C1.w[1] < midpoint128[ind - 19].w[1]) |
|
|
3504 |
|| ((C1.w[1] == midpoint128[ind - 19].w[1]) |
|
|
3505 |
&& (C1.w[0] < midpoint128[ind - 19].w[0]))) { |
|
|
3506 |
res = 0x00000000; // return 0 |
|
|
3507 |
} else if (x_sign) { // n < 0 |
|
|
3508 |
res = 0xffffffff; // return -1 |
|
|
3509 |
} else { // n > 0 |
|
|
3510 |
res = 0x00000001; // return +1 |
|
|
3511 |
} |
|
|
3512 |
} |
|
|
3513 |
// set inexact flag |
|
|
3514 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
3515 |
} else { // if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9) |
|
|
3516 |
// -2^31-1/2 < x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded |
|
|
3517 |
// to nearest-away to a 32-bit signed integer |
|
|
3518 |
if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10 |
|
|
3519 |
ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x' |
|
|
3520 |
// chop off ind digits from the lower part of C1 |
|
|
3521 |
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 127 bits |
|
|
3522 |
tmp64 = C1.w[0]; |
|
|
3523 |
if (ind <= 19) { |
|
|
3524 |
C1.w[0] = C1.w[0] + midpoint64[ind - 1]; |
|
|
3525 |
} else { |
|
|
3526 |
C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0]; |
|
|
3527 |
C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1]; |
|
|
3528 |
} |
|
|
3529 |
if (C1.w[0] < tmp64) |
|
|
3530 |
C1.w[1]++; |
|
|
3531 |
// calculate C* and f* |
|
|
3532 |
// C* is actually floor(C*) in this case |
|
|
3533 |
// C* and f* need shifting and masking, as shown by |
|
|
3534 |
// shiftright128[] and maskhigh128[] |
|
|
3535 |
// 1 <= x <= 33 |
|
|
3536 |
// kx = 10^(-x) = ten2mk128[ind - 1] |
|
|
3537 |
// C* = (C1 + 1/2 * 10^x) * 10^(-x) |
|
|
3538 |
// the approximation of 10^(-x) was rounded up to 118 bits |
|
|
3539 |
__mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]); |
|
|
3540 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
3541 |
Cstar.w[1] = P256.w[3]; |
|
|
3542 |
Cstar.w[0] = P256.w[2]; |
|
|
3543 |
fstar.w[3] = 0; |
|
|
3544 |
fstar.w[2] = P256.w[2] & maskhigh128[ind - 1]; |
|
|
3545 |
fstar.w[1] = P256.w[1]; |
|
|
3546 |
fstar.w[0] = P256.w[0]; |
|
|
3547 |
} else { // 22 <= ind - 1 <= 33 |
|
|
3548 |
Cstar.w[1] = 0; |
|
|
3549 |
Cstar.w[0] = P256.w[3]; |
|
|
3550 |
fstar.w[3] = P256.w[3] & maskhigh128[ind - 1]; |
|
|
3551 |
fstar.w[2] = P256.w[2]; |
|
|
3552 |
fstar.w[1] = P256.w[1]; |
|
|
3553 |
fstar.w[0] = P256.w[0]; |
|
|
3554 |
} |
|
|
3555 |
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g. |
|
|
3556 |
// if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999 |
|
|
3557 |
// if (0 < f* < 10^(-x)) then the result is a midpoint |
|
|
3558 |
// if floor(C*) is even then C* = floor(C*) - logical right |
|
|
3559 |
// shift; C* has p decimal digits, correct by Prop. 1) |
|
|
3560 |
// else if floor(C*) is odd C* = floor(C*)-1 (logical right |
|
|
3561 |
// shift; C* has p decimal digits, correct by Pr. 1) |
|
|
3562 |
// else |
|
|
3563 |
// C* = floor(C*) (logical right shift; C has p decimal digits, |
|
|
3564 |
// correct by Property 1) |
|
|
3565 |
// n = C* * 10^(e+x) |
|
|
3566 |
|
|
|
3567 |
// shift right C* by Ex-128 = shiftright128[ind] |
|
|
3568 |
shift = shiftright128[ind - 1]; // 0 <= shift <= 102 |
|
|
3569 |
if (ind - 1 <= 21) { // 0 <= ind - 1 <= 21 |
|
|
3570 |
Cstar.w[0] = |
|
|
3571 |
(Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift)); |
|
|
3572 |
// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift); |
|
|
3573 |
} else { // 22 <= ind - 1 <= 33 |
|
|
3574 |
Cstar.w[0] = (Cstar.w[0] >> (shift - 64)); // 2 <= shift - 64 <= 38 |
|
|
3575 |
} |
|
|
3576 |
// if the result was a midpoint, it was already rounded away from zero |
|
|
3577 |
if (x_sign) |
|
|
3578 |
res = -Cstar.w[0]; |
|
|
3579 |
else |
|
|
3580 |
res = Cstar.w[0]; |
|
|
3581 |
// determine inexactness of the rounding of C* |
|
|
3582 |
// if (0 < f* - 1/2 < 10^(-x)) then |
|
|
3583 |
// the result is exact |
|
|
3584 |
// else // if (f* - 1/2 > T*) then |
|
|
3585 |
// the result is inexact |
|
|
3586 |
if (ind - 1 <= 2) { |
|
|
3587 |
if (fstar.w[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) { // f* > 1/2 and the result may be exact |
|
|
3588 |
tmp64 = fstar.w[1] - 0x8000000000000000ull; // f* - 1/2 |
|
|
3589 |
if ((tmp64 > ten2mk128trunc[ind - 1].w[1] |
|
|
3590 |
|| (tmp64 == ten2mk128trunc[ind - 1].w[1] |
|
|
3591 |
&& fstar.w[0] >= ten2mk128trunc[ind - 1].w[0]))) { |
|
|
3592 |
// set the inexact flag |
|
|
3593 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
3594 |
} // else the result is exact |
|
|
3595 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
3596 |
// set the inexact flag |
|
|
3597 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
3598 |
} |
|
|
3599 |
} else if (ind - 1 <= 21) { // if 3 <= ind <= 21 |
|
|
3600 |
if (fstar.w[3] > 0x0 || |
|
|
3601 |
(fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) || |
|
|
3602 |
(fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] && |
|
|
3603 |
(fstar.w[1] || fstar.w[0]))) { |
|
|
3604 |
// f2* > 1/2 and the result may be exact |
|
|
3605 |
// Calculate f2* - 1/2 |
|
|
3606 |
tmp64 = fstar.w[2] - onehalf128[ind - 1]; |
|
|
3607 |
tmp64A = fstar.w[3]; |
|
|
3608 |
if (tmp64 > fstar.w[2]) |
|
|
3609 |
tmp64A--; |
|
|
3610 |
if (tmp64A || tmp64 |
|
|
3611 |
|| fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
3612 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
3613 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
3614 |
// set the inexact flag |
|
|
3615 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
3616 |
} // else the result is exact |
|
|
3617 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
3618 |
// set the inexact flag |
|
|
3619 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
3620 |
} |
|
|
3621 |
} else { // if 22 <= ind <= 33 |
|
|
3622 |
if (fstar.w[3] > onehalf128[ind - 1] || |
|
|
3623 |
(fstar.w[3] == onehalf128[ind - 1] && |
|
|
3624 |
(fstar.w[2] || fstar.w[1] || fstar.w[0]))) { |
|
|
3625 |
// f2* > 1/2 and the result may be exact |
|
|
3626 |
// Calculate f2* - 1/2 |
|
|
3627 |
tmp64 = fstar.w[3] - onehalf128[ind - 1]; |
|
|
3628 |
if (tmp64 || fstar.w[2] || |
|
|
3629 |
fstar.w[1] > ten2mk128trunc[ind - 1].w[1] |
|
|
3630 |
|| (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] |
|
|
3631 |
&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) { |
|
|
3632 |
// set the inexact flag |
|
|
3633 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
3634 |
} // else the result is exact |
|
|
3635 |
} else { // the result is inexact; f2* <= 1/2 |
|
|
3636 |
// set the inexact flag |
|
|
3637 |
*pfpsf |= INEXACT_EXCEPTION; |
|
|
3638 |
} |
|
|
3639 |
} |
|
|
3640 |
// no need to check for midpoints - already rounded away from zero! |
|
|
3641 |
} else if (exp == 0) { |
|
|
3642 |
// 1 <= q <= 10 |
|
|
3643 |
// res = +/-C (exact) |
|
|
3644 |
if (x_sign) |
|
|
3645 |
res = -C1.w[0]; |
|
|
3646 |
else |
|
|
3647 |
res = C1.w[0]; |
|
|
3648 |
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 |
|
|
3649 |
// res = +/-C * 10^exp (exact) |
|
|
3650 |
if (x_sign) |
|
|
3651 |
res = -C1.w[0] * ten2k64[exp]; |
|
|
3652 |
else |
|
|
3653 |
res = C1.w[0] * ten2k64[exp]; |
|
|
3654 |
} |
|
|
3655 |
} |
|
|
3656 |
} |
|
|
3657 |
|
|
|
3658 |
BID_RETURN (res); |
|
|
3659 |
} |