diff options
Diffstat (limited to 'include/fpu/softfloat-macros.h')
-rw-r--r-- | include/fpu/softfloat-macros.h | 700 |
1 files changed, 700 insertions, 0 deletions
diff --git a/include/fpu/softfloat-macros.h b/include/fpu/softfloat-macros.h new file mode 100644 index 000000000..f35cdbfa6 --- /dev/null +++ b/include/fpu/softfloat-macros.h @@ -0,0 +1,700 @@ +/* + * 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 + * + * 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. + */ + +#ifndef FPU_SOFTFLOAT_MACROS_H +#define FPU_SOFTFLOAT_MACROS_H + +#include "fpu/softfloat-types.h" +#include "qemu/host-utils.h" + +/** + * shl_double: double-word merging left shift + * @l: left or most-significant word + * @r: right or least-significant word + * @c: shift count + * + * Shift @l left by @c bits, shifting in bits from @r. + */ +static inline uint64_t shl_double(uint64_t l, uint64_t r, int c) +{ +#if defined(__x86_64__) + asm("shld %b2, %1, %0" : "+r"(l) : "r"(r), "ci"(c)); + return l; +#else + return c ? (l << c) | (r >> (64 - c)) : l; +#endif +} + +/** + * shr_double: double-word merging right shift + * @l: left or most-significant word + * @r: right or least-significant word + * @c: shift count + * + * Shift @r right by @c bits, shifting in bits from @l. + */ +static inline uint64_t shr_double(uint64_t l, uint64_t r, int c) +{ +#if defined(__x86_64__) + asm("shrd %b2, %1, %0" : "+r"(r) : "r"(l), "ci"(c)); + return r; +#else + return c ? (r >> c) | (l << (64 - c)) : r; +#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 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' may be greater 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 shift128Left(uint64_t a0, uint64_t a1, int count, + uint64_t *z0Ptr, uint64_t *z1Ptr) +{ + if (count < 64) { + *z1Ptr = a1 << count; + *z0Ptr = count == 0 ? a0 : (a0 << count) | (a1 >> (-count & 63)); + } else { + *z1Ptr = 0; + *z0Ptr = a1 << (count - 64); + } +} + +/*---------------------------------------------------------------------------- +| 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) +{ + bool c = 0; + *z1Ptr = uadd64_carry(a1, b1, &c); + *z0Ptr = uadd64_carry(a0, b0, &c); +} + +/*---------------------------------------------------------------------------- +| 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) +{ + bool c = 0; + *z2Ptr = uadd64_carry(a2, b2, &c); + *z1Ptr = uadd64_carry(a1, b1, &c); + *z0Ptr = uadd64_carry(a0, b0, &c); +} + +/*---------------------------------------------------------------------------- +| 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) +{ + bool c = 0; + *z1Ptr = usub64_borrow(a1, b1, &c); + *z0Ptr = usub64_borrow(a0, b0, &c); +} + +/*---------------------------------------------------------------------------- +| 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) +{ + bool c = 0; + *z2Ptr = usub64_borrow(a2, b2, &c); + *z1Ptr = usub64_borrow(a1, b1, &c); + *z0Ptr = usub64_borrow(a0, b0, &c); +} + +/*---------------------------------------------------------------------------- +| 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) +{ + mulu64(z1Ptr, z0Ptr, a, b); +} + +/*---------------------------------------------------------------------------- +| 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, m1; + + mul64To128(a1, b, &m1, z2Ptr); + mul64To128(a0, b, &z0, &z1); + add128(z0, z1, 0, m1, z0Ptr, z1Ptr); +} + +/*---------------------------------------------------------------------------- +| 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; + uint64_t m0, m1, m2, n1, n2; + + mul64To128(a1, b0, &m1, &m2); + mul64To128(a0, b1, &n1, &n2); + mul64To128(a1, b1, &z2, z3Ptr); + mul64To128(a0, b0, &z0, &z1); + + add192( 0, m1, m2, 0, n1, n2, &m0, &m1, &m2); + add192(m0, m1, m2, z0, z1, z2, z0Ptr, z1Ptr, z2Ptr); +} + +/*---------------------------------------------------------------------------- +| 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 inline 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 UINT64_C(0xFFFFFFFFFFFFFFFF); + b0 = b>>32; + z = ( b0<<32 <= a0 ) ? UINT64_C(0xFFFFFFFF00000000) : ( a0 / b0 )<<32; + mul64To128( b, z, &term0, &term1 ); + sub128( a0, a1, term0, term1, &rem0, &rem1 ); + while ( ( (int64_t) rem0 ) < 0 ) { + z -= UINT64_C(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 inline 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 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 bool 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 bool 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 bool 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 bool ne128(uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1) +{ + return a0 != b0 || a1 != b1; +} + +/* + * Similarly, comparisons of 192-bit values. + */ + +static inline bool eq192(uint64_t a0, uint64_t a1, uint64_t a2, + uint64_t b0, uint64_t b1, uint64_t b2) +{ + return ((a0 ^ b0) | (a1 ^ b1) | (a2 ^ b2)) == 0; +} + +static inline bool le192(uint64_t a0, uint64_t a1, uint64_t a2, + uint64_t b0, uint64_t b1, uint64_t b2) +{ + if (a0 != b0) { + return a0 < b0; + } + if (a1 != b1) { + return a1 < b1; + } + return a2 <= b2; +} + +static inline bool lt192(uint64_t a0, uint64_t a1, uint64_t a2, + uint64_t b0, uint64_t b1, uint64_t b2) +{ + if (a0 != b0) { + return a0 < b0; + } + if (a1 != b1) { + return a1 < b1; + } + return a2 < b2; +} + +#endif |