| |
| /*============================================================================ |
| |
| This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic |
| Package, Release 3, by John R. Hauser. |
| |
| Copyright 2011, 2012, 2013, 2014, 2015 The Regents of the University of |
| California (Regents). All Rights Reserved. Redistribution and use in source |
| and binary forms, with or without modification, are permitted provided that |
| the following conditions are met: |
| |
| Redistributions of source code must retain the above copyright notice, |
| this list of conditions, and the following two paragraphs of disclaimer. |
| Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions, and the following two paragraphs of disclaimer in the |
| documentation and/or other materials provided with the distribution. Neither |
| the name of the Regents nor the names of its contributors may be used to |
| endorse or promote products derived from this software without specific prior |
| written permission. |
| |
| IN NO EVENT SHALL REGENTS BE LIABLE TO ANY PARTY FOR DIRECT, INDIRECT, |
| SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, INCLUDING LOST PROFITS, ARISING |
| OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN IF REGENTS HAS |
| BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| |
| REGENTS SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING, BUT NOT LIMITED |
| TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| PURPOSE. THE SOFTWARE AND ACCOMPANYING DOCUMENTATION, IF ANY, PROVIDED |
| HEREUNDER IS PROVIDED "AS IS". REGENTS HAS NO OBLIGATION TO PROVIDE |
| MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS. |
| |
| =============================================================================*/ |
| |
| #include <stdbool.h> |
| #include <stdint.h> |
| #include "platform.h" |
| #include "internals.h" |
| #include "specialize.h" |
| #include "softfloat.h" |
| |
| extFloat80_t extF80_sqrt( extFloat80_t a ) |
| { |
| union { struct extFloat80M s; extFloat80_t f; } uA; |
| uint_fast16_t uiA64; |
| uint_fast64_t uiA0; |
| bool signA; |
| int_fast32_t expA; |
| uint_fast64_t sigA; |
| struct uint128 uiZ; |
| uint_fast16_t uiZ64; |
| uint_fast64_t uiZ0; |
| struct exp32_sig64 normExpSig; |
| int_fast32_t expZ; |
| uint_fast32_t sig32A, recipSqrt32, sig32Z; |
| struct uint128 rem; |
| uint_fast64_t q, sigZ, x64; |
| struct uint128 term; |
| uint_fast64_t sigZExtra; |
| union { struct extFloat80M s; extFloat80_t f; } uZ; |
| |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| uA.f = a; |
| uiA64 = uA.s.signExp; |
| uiA0 = uA.s.signif; |
| signA = signExtF80UI64( uiA64 ); |
| expA = expExtF80UI64( uiA64 ); |
| sigA = uiA0; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( expA == 0x7FFF ) { |
| if ( sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) { |
| uiZ = softfloat_propagateNaNExtF80UI( uiA64, uiA0, 0, 0 ); |
| uiZ64 = uiZ.v64; |
| uiZ0 = uiZ.v0; |
| goto uiZ; |
| } |
| if ( ! signA ) return a; |
| goto invalid; |
| } |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( signA ) { |
| if ( ! sigA ) goto zero; |
| goto invalid; |
| } |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( ! expA ) expA = 1; |
| if ( ! (sigA & UINT64_C( 0x8000000000000000 )) ) { |
| if ( ! sigA ) goto zero; |
| normExpSig = softfloat_normSubnormalExtF80Sig( sigA ); |
| 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) + 0x3FFF; |
| expA &= 1; |
| sig32A = sigA>>32; |
| recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A ); |
| sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32; |
| if ( expA ) { |
| sig32Z >>= 1; |
| rem = softfloat_shortShiftLeft128( 0, sigA, 61 ); |
| } else { |
| rem = softfloat_shortShiftLeft128( 0, sigA, 62 ); |
| } |
| rem.v64 -= (uint_fast64_t) sig32Z * sig32Z; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| q = ((uint_fast64_t) (uint32_t) (rem.v64>>2) * recipSqrt32)>>32; |
| sigZ = ((uint_fast64_t) sig32Z<<32) + (q<<3); |
| x64 = ((uint_fast64_t) sig32Z<<32) + sigZ; |
| term = softfloat_mul64ByShifted32To128( x64, q ); |
| rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 ); |
| rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 ); |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| q = (((uint_fast64_t) (uint32_t) (rem.v64>>2) * recipSqrt32)>>32) + 2; |
| x64 = sigZ; |
| sigZ = (sigZ<<1) + (q>>25); |
| sigZExtra = (uint64_t) (q<<39); |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| if ( (q & 0xFFFFFF) <= 2 ) { |
| q &= ~(uint_fast64_t) 0xFFFF; |
| sigZExtra = (uint64_t) (q<<39); |
| term = softfloat_mul64ByShifted32To128( x64 + (q>>27), q ); |
| x64 = (uint_fast64_t) (uint32_t) (q<<5) * (uint32_t) q; |
| term = softfloat_add128( term.v64, term.v0, 0, x64 ); |
| rem = softfloat_shortShiftLeft128( rem.v64, rem.v0, 28 ); |
| rem = softfloat_sub128( rem.v64, rem.v0, term.v64, term.v0 ); |
| if ( rem.v64 & UINT64_C( 0x8000000000000000 ) ) { |
| if ( ! sigZExtra ) --sigZ; |
| --sigZExtra; |
| } else { |
| if ( rem.v64 | rem.v0 ) sigZExtra |= 1; |
| } |
| } |
| return |
| softfloat_roundPackToExtF80( |
| 0, expZ, sigZ, sigZExtra, extF80_roundingPrecision ); |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| invalid: |
| softfloat_raiseFlags( softfloat_flag_invalid ); |
| uiZ64 = defaultNaNExtF80UI64; |
| uiZ0 = defaultNaNExtF80UI0; |
| goto uiZ; |
| /*------------------------------------------------------------------------ |
| *------------------------------------------------------------------------*/ |
| zero: |
| uiZ64 = packToExtF80UI64( signA, 0 ); |
| uiZ0 = 0; |
| uiZ: |
| uZ.s.signExp = uiZ64; |
| uZ.s.signif = uiZ0; |
| return uZ.f; |
| |
| } |
| |