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gcc/libgcc/config/libbid/bid64_to_uint32.c
Jakub Jelinek 99dee82307 Update copyright years.
2021-01-04 10:26:59 +01:00

2271 lines
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/* Copyright (C) 2007-2021 Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
#include "bid_internal.h"
/*****************************************************************************
* BID64_to_uint32_rnint
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_rnint (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_rnint (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2
// => set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 - 1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16
// <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x9fffffffbull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) >= 0x9fffffffb <=>
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1/2 up)
// Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0x9fffffffbull * ten2k64[q - 11];
if (C1 >= tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 1/2
// Note: some of the cases tested for above fall through to this point
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
// return 0
res = 0x00000000;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (C1 <= midpoint64[ind]) {
res = 0x00000000; // return 0
} else if (x_sign) { // n < 0
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // n > 0
res = 0x00000001; // return +1
}
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be
// rounded to nearest to a 32-bit unsigned integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^32-1/2 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits
C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[1] == 0) && fstar.w[0] &&
(fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// the result is a midpoint; round to nearest
if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar--; // Cstar is now even
} // else MP in [ODD, EVEN]
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint32_xrnint
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_xrnint (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_xrnint (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2
// => set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 - 1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16
// <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x9fffffffbull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) >= 0x9fffffffb <=>
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1/2 up)
// Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0x9fffffffbull * ten2k64[q - 11];
if (C1 >= tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 1/2
// Note: some of the cases tested for above fall through to this point
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x00000000;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (C1 <= midpoint64[ind]) {
res = 0x00000000; // return 0
} else if (x_sign) { // n < 0
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // n > 0
res = 0x00000001; // return +1
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be
// rounded to nearest to a 32-bit unsigned integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^32-1/2 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits
C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// if (0 < f* < 10^(-x)) then the result is a midpoint
// if floor(C*) is even then C* = floor(C*) - logical right
// shift; C* has p decimal digits, correct by Prop. 1)
// else if floor(C*) is odd C* = floor(C*)-1 (logical right
// shift; C* has p decimal digits, correct by Pr. 1)
// else
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) { // fstar.w[1] is 0
if (fstar.w[0] > 0x8000000000000000ull) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2
if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] > onehalf128[ind - 1] ||
(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[1] - onehalf128[ind - 1];
if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
}
// if the result was a midpoint it was rounded away from zero, so
// it will need a correction
// check for midpoints
if ((fstar.w[1] == 0) && fstar.w[0] &&
(fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// the result is a midpoint; round to nearest
if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD]
// if floor(C*) is odd C = floor(C*) - 1; the result >= 1
Cstar--; // Cstar is now even
} // else MP in [ODD, EVEN]
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint32_floor
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_floor (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_floor (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
if (x_sign) { // if n < 0 the conversion is invalid
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
// n > 0 and q + exp = 10
// if n >= 2^32 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16
// <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0xa00000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) >= 0xa00000000 <=>
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1/2 up)
// Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0xa00000000ull * ten2k64[q - 11];
if (C1 >= tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
// n is not too large to be converted to int32 if -1 < n < 2^32
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1)
// return 0
res = 0x00000000;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// 1 <= x < 2^32 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint32_xfloor
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_xfloor (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_xfloor (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
if (x_sign) { // if n < 0 the conversion is invalid
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
// if n > 0 and q + exp = 10
// if n >= 2^32 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16
// <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0xa00000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) >= 0xa00000000 <=>
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1/2 up)
// Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0xa00000000ull * ten2k64[q - 11];
if (C1 >= tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
// n is not too large to be converted to int32 if -1 < n < 2^32
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x00000000;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// 1 <= x < 2^32 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// determine inexactness of the rounding of C*
// if (0 < f* < 10^(-x)) then
// the result is exact
// else // if (f* > T*) then
// the result is inexact
if (ind - 1 <= 2) {
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint32_ceil
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_ceil (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_ceil (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1
// => set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // if n > 0 and q + exp = 10
// if n > 2^32 - 1 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16
// <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 > 0x9fffffff6ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) > 0x9fffffff6 <=>
// C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1 up)
// Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0x9fffffff6ull * ten2k64[q - 11];
if (C1 > tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32 if -1 < n < 2^32
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
// return 0 or 1
if (x_sign)
res = 0x00000000;
else
res = 0x00000001;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// x <= -1 or 1 <= x <= 2^32 - 1 so if positive, x can be
// rounded to nearest to a 32-bit unsigned integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x <= 2^32 - 1 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// determine inexactness of the rounding of C*
// if (0 < f* < 10^(-x)) then
// the result is exact
// else // if (f* > T*) then
// the result is inexact
if (ind - 1 <= 2) { // fstar.w[1] is 0
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
Cstar++;
} // else the result is exact
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
Cstar++;
} // else the result is exact
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint32_xceil
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_xceil (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_xceil (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1
// => set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // if n > 0 and q + exp = 10
// if n > 2^32 - 1 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1
// <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16
// <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 > 0x9fffffff6ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) > 0x9fffffff6 <=>
// C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1 up)
// Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0x9fffffff6ull * ten2k64[q - 11];
if (C1 > tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32 if -1 < n < 2^32
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0 or 1
if (x_sign)
res = 0x00000000;
else
res = 0x00000001;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// x <= -1 or 1 <= x < 2^32 so if positive, x can be
// rounded to nearest to a 32-bit unsigned integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^32 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// determine inexactness of the rounding of C*
// if (0 < f* < 10^(-x)) then
// the result is exact
// else // if (f* > T*) then
// the result is inexact
if (ind - 1 <= 2) { // fstar.w[1] is 0
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
Cstar++;
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
Cstar++;
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint32_int
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_int (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
{
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_int (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM)
{
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1
// => set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16
// <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0xa00000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) >= 0xa00000000 <=>
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1/2 up)
// Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0xa00000000ull * ten2k64[q - 11];
if (C1 >= tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32 if -1 < n < 2^32
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
// return 0
res = 0x00000000;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// x <= -1 or 1 <= x < 2^32 so if positive, x can be
// rounded to nearest to a 32-bit unsigned integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^32 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint32_xint
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_xint (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_xint (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1
// => set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16
// <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0xa00000000ull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) >= 0xa00000000 <=>
// C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1/2 up)
// Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0xa00000000ull * ten2k64[q - 11];
if (C1 >= tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32 if -1 < n < 2^32
// Note: some of the cases tested for above fall through to this point
if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x00000000;
BID_RETURN (res);
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// x <= -1 or 1 <= x < 2^32 so if positive, x can be
// rounded to nearest to a 32-bit unsigned integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^32 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 fits in 64 bits
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = C1 * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// determine inexactness of the rounding of C*
// if (0 < f* < 10^(-x)) then
// the result is exact
// else // if (f* > T*) then
// the result is inexact
if (ind - 1 <= 2) { // fstar.w[1] is 0
if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
}
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint32_rninta
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_rninta (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_rninta (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2
// => set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 - 1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16
// <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x9fffffffbull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) >= 0x9fffffffb <=>
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1/2 up)
// Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0x9fffffffbull * ten2k64[q - 11];
if (C1 >= tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32 if -1/2 < n < 2^32 - 1/2
// Note: some of the cases tested for above fall through to this point
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
// return 0
res = 0x00000000;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (C1 < midpoint64[ind]) {
res = 0x00000000; // return 0
} else if (x_sign) { // n < 0
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // n > 0
res = 0x00000001; // return +1
}
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be
// rounded to nearest to a 32-bit unsigned integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^32-1/2 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits
C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// if the result was a midpoint it was rounded away from zero
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
/*****************************************************************************
* BID64_to_uint32_xrninta
****************************************************************************/
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_to_uint32_xrninta (unsigned int *pres, UINT64 * px
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
UINT64 x = *px;
#else
unsigned int
bid64_to_uint32_xrninta (UINT64 x
_EXC_FLAGS_PARAM _EXC_MASKS_PARAM
_EXC_INFO_PARAM) {
#endif
unsigned int res;
UINT64 x_sign;
UINT64 x_exp;
int exp; // unbiased exponent
// Note: C1 represents x_significand (UINT64)
UINT64 tmp64;
BID_UI64DOUBLE tmp1;
unsigned int x_nr_bits;
int q, ind, shift;
UINT64 C1;
UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits
UINT128 fstar;
UINT128 P128;
// check for NaN or Infinity
if ((x & MASK_NAN) == MASK_NAN || (x & MASK_INF) == MASK_INF) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// unpack x
x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
// if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased
C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
if (C1 > 9999999999999999ull) { // non-canonical
x_exp = 0;
C1 = 0;
}
} else {
x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased
C1 = x & MASK_BINARY_SIG1;
}
// check for zeros (possibly from non-canonical values)
if (C1 == 0x0ull) {
// x is 0
res = 0x00000000;
BID_RETURN (res);
}
// x is not special and is not zero
// q = nr. of decimal digits in x (1 <= q <= 54)
// determine first the nr. of bits in x
if (C1 >= 0x0020000000000000ull) { // x >= 2^53
// split the 64-bit value in two 32-bit halves to avoid rounding errors
if (C1 >= 0x0000000100000000ull) { // x >= 2^32
tmp1.d = (double) (C1 >> 32); // exact conversion
x_nr_bits =
33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
} else { // x < 2^32
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
} else { // if x < 2^53
tmp1.d = (double) C1; // exact conversion
x_nr_bits =
1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
}
q = nr_digits[x_nr_bits - 1].digits;
if (q == 0) {
q = nr_digits[x_nr_bits - 1].digits1;
if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)
q++;
}
exp = x_exp - 398; // unbiased exponent
if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1)
// in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
// so x rounded to an integer may or may not fit in an unsigned 32-bit int
// the cases that do not fit are identified here; the ones that fit
// fall through and will be handled with other cases further,
// under '1 <= q + exp <= 10'
if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2
// => set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // if n > 0 and q + exp = 10
// if n >= 2^32 - 1/2 then n is too large
// too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2
// <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16
// <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16
if (q <= 11) {
// Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits
tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int
// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
if (tmp64 >= 0x9fffffffbull) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit unsigned int fall through
// to '1 <= q + exp <= 10'
} else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2
// C * 10^(11-q) >= 0x9fffffffb <=>
// C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5
// (scale 2^32-1/2 up)
// Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16
tmp64 = 0x9fffffffbull * ten2k64[q - 11];
if (C1 >= tmp64) {
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// else cases that can be rounded to a 32-bit int fall through
// to '1 <= q + exp <= 10'
}
}
}
// n is not too large to be converted to int32 if -1/2 < n < 2^32 - 1/2
// Note: some of the cases tested for above fall through to this point
if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
// return 0
res = 0x00000000;
BID_RETURN (res);
} else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
// if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
// res = 0
// else if x > 0
// res = +1
// else // if x < 0
// invalid exc
ind = q - 1;
if (C1 < midpoint64[ind]) {
res = 0x00000000; // return 0
} else if (x_sign) { // n < 0
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
} else { // n > 0
res = 0x00000001; // return +1
}
// set inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9)
// -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be
// rounded to nearest to a 32-bit unsigned integer
if (x_sign) { // x <= -1
// set invalid flag
*pfpsf |= INVALID_EXCEPTION;
// return Integer Indefinite
res = 0x80000000;
BID_RETURN (res);
}
// 1 <= x < 2^32-1/2 so x can be rounded
// to nearest to a 32-bit unsigned integer
if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10
ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x'
// chop off ind digits from the lower part of C1
// C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits
C1 = C1 + midpoint64[ind - 1];
// calculate C* and f*
// C* is actually floor(C*) in this case
// C* and f* need shifting and masking, as shown by
// shiftright128[] and maskhigh128[]
// 1 <= x <= 15
// kx = 10^(-x) = ten2mk64[ind - 1]
// C* = (C1 + 1/2 * 10^x) * 10^(-x)
// the approximation of 10^(-x) was rounded up to 54 bits
__mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);
Cstar = P128.w[1];
fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];
fstar.w[0] = P128.w[0];
// the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.
// if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999
// C* = floor(C*) (logical right shift; C has p decimal digits,
// correct by Property 1)
// n = C* * 10^(e+x)
// shift right C* by Ex-64 = shiftright128[ind]
shift = shiftright128[ind - 1]; // 0 <= shift <= 39
Cstar = Cstar >> shift;
// determine inexactness of the rounding of C*
// if (0 < f* - 1/2 < 10^(-x)) then
// the result is exact
// else // if (f* - 1/2 > T*) then
// the result is inexact
if (ind - 1 <= 2) { // fstar.w[1] is 0
if (fstar.w[0] > 0x8000000000000000ull) {
// f* > 1/2 and the result may be exact
tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2
if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
} else { // if 3 <= ind - 1 <= 14
if (fstar.w[1] > onehalf128[ind - 1] ||
(fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {
// f2* > 1/2 and the result may be exact
// Calculate f2* - 1/2
tmp64 = fstar.w[1] - onehalf128[ind - 1];
if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {
// ten2mk128trunc[ind -1].w[1] is identical to
// ten2mk128[ind -1].w[1]
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
} // else the result is exact
} else { // the result is inexact; f2* <= 1/2
// set the inexact flag
*pfpsf |= INEXACT_EXCEPTION;
}
}
// if the result was a midpoint it was rounded away from zero
res = Cstar; // the result is positive
} else if (exp == 0) {
// 1 <= q <= 10
// res = +C (exact)
res = C1; // the result is positive
} else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
// res = +C * 10^exp (exact)
res = C1 * ten2k64[exp]; // the result is positive
}
}
BID_RETURN (res);
}
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