| |
| /*============================================================================ |
| |
| This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic |
| Package, Release 3d, by John R. Hauser. |
| |
| Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 The Regents of the |
| University of California. 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 University 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 REGENTS 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 REGENTS 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. |
| |
| =============================================================================*/ |
| |
| #include <stdbool.h> |
| #include <stdint.h> |
| |
| #include "internals.h" |
| #include "platform.h" |
| #include "softfloat.h" |
| #include "specialize.h" |
| |
| float128_t f128_sqrt( float128_t a ) |
| { |
| union ui128_f128 uA; |
| uint_fast64_t uiA64, uiA0; |
| bool signA; |
| int_fast32_t expA; |
| struct uint128 sigA, uiZ; |
| struct exp32_sig128 normExpSig; |
| int_fast32_t expZ; |
| uint_fast32_t sig32A, recipSqrt32, sig32Z; |
| struct uint128 rem; |
| uint32_t qs[3]; |
| uint_fast32_t q; |
| uint_fast64_t x64, sig64Z; |
| struct uint128 y, term; |
| uint_fast64_t sigZExtra; |
| struct uint128 sigZ; |
| union ui128_f128 uZ; |
| |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| uA.f = a; |
| uiA64 = uA.ui.v64; |
| uiA0 = uA.ui.v0; |
| signA = signF128UI64( uiA64 ); |
| expA = expF128UI64( uiA64 ); |
| sigA.v64 = fracF128UI64( uiA64 ); |
| sigA.v0 = uiA0; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( expA == 0x7FFF ) { |
| if ( sigA.v64 | sigA.v0 ) { |
| uiZ = softfloat_propagateNaNF128UI( uiA64, uiA0, 0, 0 ); |
| goto uiZ; |
| } |
| if ( ! signA ) return a; |
| goto invalid; |
| } |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( signA ) { |
| if ( ! (expA | sigA.v64 | sigA.v0) ) return a; |
| goto invalid; |
| } |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( ! expA ) { |
| if ( ! (sigA.v64 | sigA.v0) ) return a; |
| normExpSig = softfloat_normSubnormalF128Sig( sigA.v64, sigA.v0 ); |
| expA = normExpSig.exp; |
| sigA = normExpSig.sig; |
| } |
| /*------------------------------------------------------------------------ |
| | (`sig32Z' is guaranteed to be a lower bound on the square root of |
| | `sig32A', which makes `sig32Z' also a lower bound on the square root of |
| | `sigA'.) |
| *------------------------------------------------------------------------*/ |
| expZ = ((expA - 0x3FFF)>>1) + 0x3FFE; |
| expA &= 1; |
| sigA.v64 |= UINT64_C( 0x0001000000000000 ); |
| sig32A = sigA.v64>>17; |
| recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A ); |
| sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32; |
| if ( expA ) { |
| sig32Z >>= 1; |
| rem = softfloat_shortShiftLeft128( sigA.v64, sigA.v0, 12 ); |
| } else { |
| rem = softfloat_shortShiftLeft128( sigA.v64, sigA.v0, 13 ); |
| } |
| qs[2] = sig32Z; |
| rem.v64 -= (uint_fast64_t) sig32Z * sig32Z; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| q = ((uint32_t) (rem.v64>>2) * (uint_fast64_t) recipSqrt32)>>32; |
| x64 = (uint_fast64_t) sig32Z<<32; |
| sig64Z = x64 + ((uint_fast64_t) q<<3); |
| y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 ); |
| /*------------------------------------------------------------------------ |
| | (Repeating this loop is a rare occurrence.) |
| *------------------------------------------------------------------------*/ |
| for (;;) { |
| term = softfloat_mul64ByShifted32To128( x64 + sig64Z, q ); |
| rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 ); |
| if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break; |
| --q; |
| sig64Z -= 1<<3; |
| } |
| qs[1] = q; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| q = ((rem.v64>>2) * recipSqrt32)>>32; |
| y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 ); |
| sig64Z <<= 1; |
| /*------------------------------------------------------------------------ |
| | (Repeating this loop is a rare occurrence.) |
| *------------------------------------------------------------------------*/ |
| for (;;) { |
| term = softfloat_shortShiftLeft128( 0, sig64Z, 32 ); |
| term = softfloat_add128( term.v64, term.v0, 0, (uint_fast64_t) q<<6 ); |
| term = softfloat_mul128By32( term.v64, term.v0, q ); |
| rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 ); |
| if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break; |
| --q; |
| } |
| qs[0] = q; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| q = (((rem.v64>>2) * recipSqrt32)>>32) + 2; |
| sigZExtra = (uint64_t) ((uint_fast64_t) q<<59); |
| term = softfloat_shortShiftLeft128( 0, qs[1], 53 ); |
| sigZ = |
| softfloat_add128( |
| (uint_fast64_t) qs[2]<<18, ((uint_fast64_t) qs[0]<<24) + (q>>5), |
| term.v64, term.v0 |
| ); |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( (q & 0xF) <= 2 ) { |
| q &= ~3; |
| sigZExtra = (uint64_t) ((uint_fast64_t) q<<59); |
| y = softfloat_shortShiftLeft128( sigZ.v64, sigZ.v0, 6 ); |
| y.v0 |= sigZExtra>>58; |
| term = softfloat_sub128( y.v64, y.v0, 0, q ); |
| y = softfloat_mul64ByShifted32To128( term.v0, q ); |
| term = softfloat_mul64ByShifted32To128( term.v64, q ); |
| term = softfloat_add128( term.v64, term.v0, 0, y.v64 ); |
| rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 20 ); |
| term = softfloat_sub128( term.v64, term.v0, rem.v64, rem.v0 ); |
| /*-------------------------------------------------------------------- |
| | The concatenation of `term' and `y.v0' is now the negative remainder |
| | (3 words altogether). |
| *--------------------------------------------------------------------*/ |
| if ( term.v64 & UINT64_C( 0x8000000000000000 ) ) { |
| sigZExtra |= 1; |
| } else { |
| if ( term.v64 | term.v0 | y.v0 ) { |
| if ( sigZExtra ) { |
| --sigZExtra; |
| } else { |
| sigZ = softfloat_sub128( sigZ.v64, sigZ.v0, 0, 1 ); |
| sigZExtra = ~0; |
| } |
| } |
| } |
| } |
| return softfloat_roundPackToF128( 0, expZ, sigZ.v64, sigZ.v0, sigZExtra ); |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| invalid: |
| softfloat_raiseFlags( softfloat_flag_invalid ); |
| uiZ.v64 = defaultNaNF128UI64; |
| uiZ.v0 = defaultNaNF128UI0; |
| uiZ: |
| uZ.ui = uiZ; |
| return uZ.f; |
| |
| } |
| |
