f128_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
float128_t	f128_sqrt (float128_t a)

Function Documentation

f128_sqrt()

float128_t f128_sqrt

(

float128_t

a

)

Definition at line 44 of file f128_sqrt.c.

{
    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;
 
}

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