extF80_sqrt.c File Reference

#include <stdbool.h>
#include <stdint.h>
#include "platform.h"
#include "internals.h"
#include "specialize.h"
#include "softfloat.h"

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Functions
extFloat80_t	extF80_sqrt (extFloat80_t a)

Function Documentation

extF80_sqrt()

extFloat80_t extF80_sqrt

(

extFloat80_t

a

)

Definition at line 44 of file extF80_sqrt.c.

{
    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, x64, sigZ;
    struct uint128 y, 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 = ((uint32_t) (rem.v64>>2) * (uint_fast64_t) recipSqrt32)>>32;
    x64 = (uint_fast64_t) sig32Z<<32;
    sigZ = x64 + (q<<3);
    y = softfloat_shortShiftLeft128( rem.v64, rem.v0, 29 );
    /*------------------------------------------------------------------------
    | (Repeating this loop is a rare occurrence.)
    *------------------------------------------------------------------------*/
    for (;;) {
        term = softfloat_mul64ByShifted32To128( x64 + sigZ, q );
        rem = softfloat_sub128( y.v64, y.v0, term.v64, term.v0 );
        if ( ! (rem.v64 & UINT64_C( 0x8000000000000000 )) ) break;
        --q;
        sigZ -= 1<<3;
    }
    /*------------------------------------------------------------------------
    *------------------------------------------------------------------------*/
    q = (((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 = (uint32_t) (q<<5) * (uint_fast64_t) (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;
 
}

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