/* | |

* QEMU float support macros | |

* | |

* The code in this source file is derived from release 2a of the SoftFloat | |

* IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and | |

* some later contributions) are provided under that license, as detailed below. | |

* It has subsequently been modified by contributors to the QEMU Project, | |

* so some portions are provided under: | |

* the SoftFloat-2a license | |

* the BSD license | |

* GPL-v2-or-later | |

* | |

* Any future contributions to this file after December 1st 2014 will be | |

* taken to be licensed under the Softfloat-2a license unless specifically | |

* indicated otherwise. | |

*/ | |

/* | |

=============================================================================== | |

This C source fragment is part of the SoftFloat IEC/IEEE Floating-point | |

Arithmetic Package, Release 2a. | |

Written by John R. Hauser. This work was made possible in part by the | |

International Computer Science Institute, located at Suite 600, 1947 Center | |

Street, Berkeley, California 94704. Funding was partially provided by the | |

National Science Foundation under grant MIP-9311980. The original version | |

of this code was written as part of a project to build a fixed-point vector | |

processor in collaboration with the University of California at Berkeley, | |

overseen by Profs. Nelson Morgan and John Wawrzynek. More information | |

is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/ | |

arithmetic/SoftFloat.html'. | |

THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort | |

has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT | |

TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO | |

PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY | |

AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE. | |

Derivative works are acceptable, even for commercial purposes, so long as | |

(1) they include prominent notice that the work is derivative, and (2) they | |

include prominent notice akin to these four paragraphs for those parts of | |

this code that are retained. | |

=============================================================================== | |

*/ | |

/* BSD licensing: | |

* Copyright (c) 2006, Fabrice Bellard | |

* All rights reserved. | |

* | |

* Redistribution and use in source and binary forms, with or without | |

* modification, are permitted provided that the following conditions are met: | |

* | |

* 1. Redistributions of source code must retain the above copyright notice, | |

* this list of conditions and the following disclaimer. | |

* | |

* 2. Redistributions in binary form must reproduce the above copyright notice, | |

* this list of conditions and the following disclaimer in the documentation | |

* and/or other materials provided with the distribution. | |

* | |

* 3. Neither the name of the copyright holder nor the names of its contributors | |

* may be used to endorse or promote products derived from this software without | |

* specific prior written permission. | |

* | |

* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" | |

* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |

* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |

* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE | |

* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR | |

* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF | |

* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS | |

* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN | |

* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |

* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF | |

* THE POSSIBILITY OF SUCH DAMAGE. | |

*/ | |

/* Portions of this work are licensed under the terms of the GNU GPL, | |

* version 2 or later. See the COPYING file in the top-level directory. | |

*/ | |

/*---------------------------------------------------------------------------- | |

| This macro tests for minimum version of the GNU C compiler. | |

*----------------------------------------------------------------------------*/ | |

#if defined(__GNUC__) && defined(__GNUC_MINOR__) | |

# define SOFTFLOAT_GNUC_PREREQ(maj, min) \ | |

((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min)) | |

#else | |

# define SOFTFLOAT_GNUC_PREREQ(maj, min) 0 | |

#endif | |

/*---------------------------------------------------------------------------- | |

| Shifts `a' right by the number of bits given in `count'. If any nonzero | |

| bits are shifted off, they are ``jammed'' into the least significant bit of | |

| the result by setting the least significant bit to 1. The value of `count' | |

| can be arbitrarily large; in particular, if `count' is greater than 32, the | |

| result will be either 0 or 1, depending on whether `a' is zero or nonzero. | |

| The result is stored in the location pointed to by `zPtr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void shift32RightJamming(uint32_t a, int count, uint32_t *zPtr) | |

{ | |

uint32_t z; | |

if ( count == 0 ) { | |

z = a; | |

} | |

else if ( count < 32 ) { | |

z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 ); | |

} | |

else { | |

z = ( a != 0 ); | |

} | |

*zPtr = z; | |

} | |

/*---------------------------------------------------------------------------- | |

| Shifts `a' right by the number of bits given in `count'. If any nonzero | |

| bits are shifted off, they are ``jammed'' into the least significant bit of | |

| the result by setting the least significant bit to 1. The value of `count' | |

| can be arbitrarily large; in particular, if `count' is greater than 64, the | |

| result will be either 0 or 1, depending on whether `a' is zero or nonzero. | |

| The result is stored in the location pointed to by `zPtr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void shift64RightJamming(uint64_t a, int count, uint64_t *zPtr) | |

{ | |

uint64_t z; | |

if ( count == 0 ) { | |

z = a; | |

} | |

else if ( count < 64 ) { | |

z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 ); | |

} | |

else { | |

z = ( a != 0 ); | |

} | |

*zPtr = z; | |

} | |

/*---------------------------------------------------------------------------- | |

| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64 | |

| _plus_ the number of bits given in `count'. The shifted result is at most | |

| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The | |

| bits shifted off form a second 64-bit result as follows: The _last_ bit | |

| shifted off is the most-significant bit of the extra result, and the other | |

| 63 bits of the extra result are all zero if and only if _all_but_the_last_ | |

| bits shifted off were all zero. This extra result is stored in the location | |

| pointed to by `z1Ptr'. The value of `count' can be arbitrarily large. | |

| (This routine makes more sense if `a0' and `a1' are considered to form a | |

| fixed-point value with binary point between `a0' and `a1'. This fixed-point | |

| value is shifted right by the number of bits given in `count', and the | |

| integer part of the result is returned at the location pointed to by | |

| `z0Ptr'. The fractional part of the result may be slightly corrupted as | |

| described above, and is returned at the location pointed to by `z1Ptr'.) | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

shift64ExtraRightJamming( | |

uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr) | |

{ | |

uint64_t z0, z1; | |

int8_t negCount = ( - count ) & 63; | |

if ( count == 0 ) { | |

z1 = a1; | |

z0 = a0; | |

} | |

else if ( count < 64 ) { | |

z1 = ( a0<<negCount ) | ( a1 != 0 ); | |

z0 = a0>>count; | |

} | |

else { | |

if ( count == 64 ) { | |

z1 = a0 | ( a1 != 0 ); | |

} | |

else { | |

z1 = ( ( a0 | a1 ) != 0 ); | |

} | |

z0 = 0; | |

} | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the | |

| number of bits given in `count'. Any bits shifted off are lost. The value | |

| of `count' can be arbitrarily large; in particular, if `count' is greater | |

| than 128, the result will be 0. The result is broken into two 64-bit pieces | |

| which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

shift128Right( | |

uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr) | |

{ | |

uint64_t z0, z1; | |

int8_t negCount = ( - count ) & 63; | |

if ( count == 0 ) { | |

z1 = a1; | |

z0 = a0; | |

} | |

else if ( count < 64 ) { | |

z1 = ( a0<<negCount ) | ( a1>>count ); | |

z0 = a0>>count; | |

} | |

else { | |

z1 = (count < 128) ? (a0 >> (count & 63)) : 0; | |

z0 = 0; | |

} | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the | |

| number of bits given in `count'. If any nonzero bits are shifted off, they | |

| are ``jammed'' into the least significant bit of the result by setting the | |

| least significant bit to 1. The value of `count' can be arbitrarily large; | |

| in particular, if `count' is greater than 128, the result will be either | |

| 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or | |

| nonzero. The result is broken into two 64-bit pieces which are stored at | |

| the locations pointed to by `z0Ptr' and `z1Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

shift128RightJamming( | |

uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr) | |

{ | |

uint64_t z0, z1; | |

int8_t negCount = ( - count ) & 63; | |

if ( count == 0 ) { | |

z1 = a1; | |

z0 = a0; | |

} | |

else if ( count < 64 ) { | |

z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 ); | |

z0 = a0>>count; | |

} | |

else { | |

if ( count == 64 ) { | |

z1 = a0 | ( a1 != 0 ); | |

} | |

else if ( count < 128 ) { | |

z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 ); | |

} | |

else { | |

z1 = ( ( a0 | a1 ) != 0 ); | |

} | |

z0 = 0; | |

} | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right | |

| by 64 _plus_ the number of bits given in `count'. The shifted result is | |

| at most 128 nonzero bits; these are broken into two 64-bit pieces which are | |

| stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted | |

| off form a third 64-bit result as follows: The _last_ bit shifted off is | |

| the most-significant bit of the extra result, and the other 63 bits of the | |

| extra result are all zero if and only if _all_but_the_last_ bits shifted off | |

| were all zero. This extra result is stored in the location pointed to by | |

| `z2Ptr'. The value of `count' can be arbitrarily large. | |

| (This routine makes more sense if `a0', `a1', and `a2' are considered | |

| to form a fixed-point value with binary point between `a1' and `a2'. This | |

| fixed-point value is shifted right by the number of bits given in `count', | |

| and the integer part of the result is returned at the locations pointed to | |

| by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly | |

| corrupted as described above, and is returned at the location pointed to by | |

| `z2Ptr'.) | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

shift128ExtraRightJamming( | |

uint64_t a0, | |

uint64_t a1, | |

uint64_t a2, | |

int count, | |

uint64_t *z0Ptr, | |

uint64_t *z1Ptr, | |

uint64_t *z2Ptr | |

) | |

{ | |

uint64_t z0, z1, z2; | |

int8_t negCount = ( - count ) & 63; | |

if ( count == 0 ) { | |

z2 = a2; | |

z1 = a1; | |

z0 = a0; | |

} | |

else { | |

if ( count < 64 ) { | |

z2 = a1<<negCount; | |

z1 = ( a0<<negCount ) | ( a1>>count ); | |

z0 = a0>>count; | |

} | |

else { | |

if ( count == 64 ) { | |

z2 = a1; | |

z1 = a0; | |

} | |

else { | |

a2 |= a1; | |

if ( count < 128 ) { | |

z2 = a0<<negCount; | |

z1 = a0>>( count & 63 ); | |

} | |

else { | |

z2 = ( count == 128 ) ? a0 : ( a0 != 0 ); | |

z1 = 0; | |

} | |

} | |

z0 = 0; | |

} | |

z2 |= ( a2 != 0 ); | |

} | |

*z2Ptr = z2; | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the | |

| number of bits given in `count'. Any bits shifted off are lost. The value | |

| of `count' must be less than 64. The result is broken into two 64-bit | |

| pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

shortShift128Left( | |

uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr) | |

{ | |

*z1Ptr = a1<<count; | |

*z0Ptr = | |

( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) ); | |

} | |

/*---------------------------------------------------------------------------- | |

| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left | |

| by the number of bits given in `count'. Any bits shifted off are lost. | |

| The value of `count' must be less than 64. The result is broken into three | |

| 64-bit pieces which are stored at the locations pointed to by `z0Ptr', | |

| `z1Ptr', and `z2Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

shortShift192Left( | |

uint64_t a0, | |

uint64_t a1, | |

uint64_t a2, | |

int count, | |

uint64_t *z0Ptr, | |

uint64_t *z1Ptr, | |

uint64_t *z2Ptr | |

) | |

{ | |

uint64_t z0, z1, z2; | |

int8_t negCount; | |

z2 = a2<<count; | |

z1 = a1<<count; | |

z0 = a0<<count; | |

if ( 0 < count ) { | |

negCount = ( ( - count ) & 63 ); | |

z1 |= a2>>negCount; | |

z0 |= a1>>negCount; | |

} | |

*z2Ptr = z2; | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit | |

| value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so | |

| any carry out is lost. The result is broken into two 64-bit pieces which | |

| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

add128( | |

uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr ) | |

{ | |

uint64_t z1; | |

z1 = a1 + b1; | |

*z1Ptr = z1; | |

*z0Ptr = a0 + b0 + ( z1 < a1 ); | |

} | |

/*---------------------------------------------------------------------------- | |

| Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the | |

| 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is | |

| modulo 2^192, so any carry out is lost. The result is broken into three | |

| 64-bit pieces which are stored at the locations pointed to by `z0Ptr', | |

| `z1Ptr', and `z2Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

add192( | |

uint64_t a0, | |

uint64_t a1, | |

uint64_t a2, | |

uint64_t b0, | |

uint64_t b1, | |

uint64_t b2, | |

uint64_t *z0Ptr, | |

uint64_t *z1Ptr, | |

uint64_t *z2Ptr | |

) | |

{ | |

uint64_t z0, z1, z2; | |

int8_t carry0, carry1; | |

z2 = a2 + b2; | |

carry1 = ( z2 < a2 ); | |

z1 = a1 + b1; | |

carry0 = ( z1 < a1 ); | |

z0 = a0 + b0; | |

z1 += carry1; | |

z0 += ( z1 < carry1 ); | |

z0 += carry0; | |

*z2Ptr = z2; | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the | |

| 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo | |

| 2^128, so any borrow out (carry out) is lost. The result is broken into two | |

| 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and | |

| `z1Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

sub128( | |

uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr ) | |

{ | |

*z1Ptr = a1 - b1; | |

*z0Ptr = a0 - b0 - ( a1 < b1 ); | |

} | |

/*---------------------------------------------------------------------------- | |

| Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2' | |

| from the 192-bit value formed by concatenating `a0', `a1', and `a2'. | |

| Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The | |

| result is broken into three 64-bit pieces which are stored at the locations | |

| pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

sub192( | |

uint64_t a0, | |

uint64_t a1, | |

uint64_t a2, | |

uint64_t b0, | |

uint64_t b1, | |

uint64_t b2, | |

uint64_t *z0Ptr, | |

uint64_t *z1Ptr, | |

uint64_t *z2Ptr | |

) | |

{ | |

uint64_t z0, z1, z2; | |

int8_t borrow0, borrow1; | |

z2 = a2 - b2; | |

borrow1 = ( a2 < b2 ); | |

z1 = a1 - b1; | |

borrow0 = ( a1 < b1 ); | |

z0 = a0 - b0; | |

z0 -= ( z1 < borrow1 ); | |

z1 -= borrow1; | |

z0 -= borrow0; | |

*z2Ptr = z2; | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Multiplies `a' by `b' to obtain a 128-bit product. The product is broken | |

| into two 64-bit pieces which are stored at the locations pointed to by | |

| `z0Ptr' and `z1Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void mul64To128( uint64_t a, uint64_t b, uint64_t *z0Ptr, uint64_t *z1Ptr ) | |

{ | |

uint32_t aHigh, aLow, bHigh, bLow; | |

uint64_t z0, zMiddleA, zMiddleB, z1; | |

aLow = a; | |

aHigh = a>>32; | |

bLow = b; | |

bHigh = b>>32; | |

z1 = ( (uint64_t) aLow ) * bLow; | |

zMiddleA = ( (uint64_t) aLow ) * bHigh; | |

zMiddleB = ( (uint64_t) aHigh ) * bLow; | |

z0 = ( (uint64_t) aHigh ) * bHigh; | |

zMiddleA += zMiddleB; | |

z0 += ( ( (uint64_t) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 ); | |

zMiddleA <<= 32; | |

z1 += zMiddleA; | |

z0 += ( z1 < zMiddleA ); | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Multiplies the 128-bit value formed by concatenating `a0' and `a1' by | |

| `b' to obtain a 192-bit product. The product is broken into three 64-bit | |

| pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and | |

| `z2Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

mul128By64To192( | |

uint64_t a0, | |

uint64_t a1, | |

uint64_t b, | |

uint64_t *z0Ptr, | |

uint64_t *z1Ptr, | |

uint64_t *z2Ptr | |

) | |

{ | |

uint64_t z0, z1, z2, more1; | |

mul64To128( a1, b, &z1, &z2 ); | |

mul64To128( a0, b, &z0, &more1 ); | |

add128( z0, more1, 0, z1, &z0, &z1 ); | |

*z2Ptr = z2; | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the | |

| 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit | |

| product. The product is broken into four 64-bit pieces which are stored at | |

| the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'. | |

*----------------------------------------------------------------------------*/ | |

static inline void | |

mul128To256( | |

uint64_t a0, | |

uint64_t a1, | |

uint64_t b0, | |

uint64_t b1, | |

uint64_t *z0Ptr, | |

uint64_t *z1Ptr, | |

uint64_t *z2Ptr, | |

uint64_t *z3Ptr | |

) | |

{ | |

uint64_t z0, z1, z2, z3; | |

uint64_t more1, more2; | |

mul64To128( a1, b1, &z2, &z3 ); | |

mul64To128( a1, b0, &z1, &more2 ); | |

add128( z1, more2, 0, z2, &z1, &z2 ); | |

mul64To128( a0, b0, &z0, &more1 ); | |

add128( z0, more1, 0, z1, &z0, &z1 ); | |

mul64To128( a0, b1, &more1, &more2 ); | |

add128( more1, more2, 0, z2, &more1, &z2 ); | |

add128( z0, z1, 0, more1, &z0, &z1 ); | |

*z3Ptr = z3; | |

*z2Ptr = z2; | |

*z1Ptr = z1; | |

*z0Ptr = z0; | |

} | |

/*---------------------------------------------------------------------------- | |

| Returns an approximation to the 64-bit integer quotient obtained by dividing | |

| `b' into the 128-bit value formed by concatenating `a0' and `a1'. The | |

| divisor `b' must be at least 2^63. If q is the exact quotient truncated | |

| toward zero, the approximation returned lies between q and q + 2 inclusive. | |

| If the exact quotient q is larger than 64 bits, the maximum positive 64-bit | |

| unsigned integer is returned. | |

*----------------------------------------------------------------------------*/ | |

static uint64_t estimateDiv128To64( uint64_t a0, uint64_t a1, uint64_t b ) | |

{ | |

uint64_t b0, b1; | |

uint64_t rem0, rem1, term0, term1; | |

uint64_t z; | |

if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF ); | |

b0 = b>>32; | |

z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32; | |

mul64To128( b, z, &term0, &term1 ); | |

sub128( a0, a1, term0, term1, &rem0, &rem1 ); | |

while ( ( (int64_t) rem0 ) < 0 ) { | |

z -= LIT64( 0x100000000 ); | |

b1 = b<<32; | |

add128( rem0, rem1, b0, b1, &rem0, &rem1 ); | |

} | |

rem0 = ( rem0<<32 ) | ( rem1>>32 ); | |

z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0; | |

return z; | |

} | |

/*---------------------------------------------------------------------------- | |

| Returns an approximation to the square root of the 32-bit significand given | |

| by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of | |

| `aExp' (the least significant bit) is 1, the integer returned approximates | |

| 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp' | |

| is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either | |

| case, the approximation returned lies strictly within +/-2 of the exact | |

| value. | |

*----------------------------------------------------------------------------*/ | |

static uint32_t estimateSqrt32(int aExp, uint32_t a) | |

{ | |

static const uint16_t sqrtOddAdjustments[] = { | |

0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0, | |

0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67 | |

}; | |

static const uint16_t sqrtEvenAdjustments[] = { | |

0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E, | |

0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002 | |

}; | |

int8_t index; | |

uint32_t z; | |

index = ( a>>27 ) & 15; | |

if ( aExp & 1 ) { | |

z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ (int)index ]; | |

z = ( ( a / z )<<14 ) + ( z<<15 ); | |

a >>= 1; | |

} | |

else { | |

z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ (int)index ]; | |

z = a / z + z; | |

z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 ); | |

if ( z <= a ) return (uint32_t) ( ( (int32_t) a )>>1 ); | |

} | |

return ( (uint32_t) ( ( ( (uint64_t) a )<<31 ) / z ) ) + ( z>>1 ); | |

} | |

/*---------------------------------------------------------------------------- | |

| Returns the number of leading 0 bits before the most-significant 1 bit of | |

| `a'. If `a' is zero, 32 is returned. | |

*----------------------------------------------------------------------------*/ | |

static int8_t countLeadingZeros32( uint32_t a ) | |

{ | |

#if SOFTFLOAT_GNUC_PREREQ(3, 4) | |

if (a) { | |

return __builtin_clz(a); | |

} else { | |

return 32; | |

} | |

#else | |

static const int8_t countLeadingZerosHigh[] = { | |

8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, | |

3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, | |

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, | |

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, | |

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, | |

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, | |

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, | |

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, | |

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, | |

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, | |

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, | |

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, | |

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, | |

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, | |

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, | |

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | |

}; | |

int8_t shiftCount; | |

shiftCount = 0; | |

if ( a < 0x10000 ) { | |

shiftCount += 16; | |

a <<= 16; | |

} | |

if ( a < 0x1000000 ) { | |

shiftCount += 8; | |

a <<= 8; | |

} | |

shiftCount += countLeadingZerosHigh[ a>>24 ]; | |

return shiftCount; | |

#endif | |

} | |

/*---------------------------------------------------------------------------- | |

| Returns the number of leading 0 bits before the most-significant 1 bit of | |

| `a'. If `a' is zero, 64 is returned. | |

*----------------------------------------------------------------------------*/ | |

static int8_t countLeadingZeros64( uint64_t a ) | |

{ | |

#if SOFTFLOAT_GNUC_PREREQ(3, 4) | |

if (a) { | |

return __builtin_clzll(a); | |

} else { | |

return 64; | |

} | |

#else | |

int8_t shiftCount; | |

shiftCount = 0; | |

if ( a < ( (uint64_t) 1 )<<32 ) { | |

shiftCount += 32; | |

} | |

else { | |

a >>= 32; | |

} | |

shiftCount += countLeadingZeros32( a ); | |

return shiftCount; | |

#endif | |

} | |

/*---------------------------------------------------------------------------- | |

| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' | |

| is equal to the 128-bit value formed by concatenating `b0' and `b1'. | |

| Otherwise, returns 0. | |

*----------------------------------------------------------------------------*/ | |

static inline flag eq128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) | |

{ | |

return ( a0 == b0 ) && ( a1 == b1 ); | |

} | |

/*---------------------------------------------------------------------------- | |

| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less | |

| than or equal to the 128-bit value formed by concatenating `b0' and `b1'. | |

| Otherwise, returns 0. | |

*----------------------------------------------------------------------------*/ | |

static inline flag le128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) | |

{ | |

return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) ); | |

} | |

/*---------------------------------------------------------------------------- | |

| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less | |

| than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise, | |

| returns 0. | |

*----------------------------------------------------------------------------*/ | |

static inline flag lt128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) | |

{ | |

return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) ); | |

} | |

/*---------------------------------------------------------------------------- | |

| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is | |

| not equal to the 128-bit value formed by concatenating `b0' and `b1'. | |

| Otherwise, returns 0. | |

*----------------------------------------------------------------------------*/ | |

static inline flag ne128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) | |

{ | |

return ( a0 != b0 ) || ( a1 != b1 ); | |

} |