--- /dev/null
+/*============================================================================
+
+This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
+Package, Release 3e, by John R. Hauser.
+
+Copyright 2011, 2012, 2013, 2014 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 "softfloat/platform.h"
+#include "softfloat/internals.h"
+#include "softfloat.h"
+#include "softfloat/specialize.h"
+#include "softfloat/primitives.h"
+#include "softfloat/primitiveTypes.h"
+
+#ifndef THREAD_LOCAL
+#define THREAD_LOCAL
+#endif
+
+THREAD_LOCAL uint_fast8_t softfloat_roundingMode = softfloat_round_near_even;
+THREAD_LOCAL uint_fast8_t softfloat_detectTininess = init_detectTininess;
+THREAD_LOCAL uint_fast8_t softfloat_exceptionFlags = 0;
+
+THREAD_LOCAL uint_fast8_t extF80_roundingPrecision = 80;
+
+#ifndef softfloat_countLeadingZeros64
+
+#define softfloat_countLeadingZeros64 softfloat_countLeadingZeros64
+
+uint_fast8_t softfloat_countLeadingZeros64( uint64_t a )
+{
+ uint_fast8_t count;
+ uint32_t a32;
+
+ count = 0;
+ a32 = a>>32;
+ if ( ! a32 ) {
+ count = 32;
+ a32 = a;
+ }
+ /*------------------------------------------------------------------------
+ | From here, result is current count + count leading zeros of `a32'.
+ *------------------------------------------------------------------------*/
+ if ( a32 < 0x10000 ) {
+ count += 16;
+ a32 <<= 16;
+ }
+ if ( a32 < 0x1000000 ) {
+ count += 8;
+ a32 <<= 8;
+ }
+ count += softfloat_countLeadingZeros8[a32>>24];
+ return count;
+
+}
+
+#endif
+
+#ifndef softfloat_shortShiftRightJamM
+
+void
+ softfloat_shortShiftRightJamM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ uint_fast8_t dist,
+ uint32_t *zPtr
+ )
+{
+ uint_fast8_t uNegDist;
+ unsigned int index, lastIndex;
+ uint32_t partWordZ, wordA;
+
+ uNegDist = -dist;
+ index = indexWordLo( size_words );
+ lastIndex = indexWordHi( size_words );
+ wordA = aPtr[index];
+ partWordZ = wordA>>dist;
+ if ( partWordZ<<dist != wordA ) partWordZ |= 1;
+ while ( index != lastIndex ) {
+ wordA = aPtr[index + wordIncr];
+ zPtr[index] = wordA<<(uNegDist & 31) | partWordZ;
+ index += wordIncr;
+ partWordZ = wordA>>dist;
+ }
+ zPtr[index] = partWordZ;
+
+}
+
+#endif
+
+#ifndef softfloat_shiftRightJamM
+
+#define softfloat_shiftRightJamM softfloat_shiftRightJamM
+
+void
+ softfloat_shiftRightJamM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ uint32_t dist,
+ uint32_t *zPtr
+ )
+{
+ uint32_t wordJam, wordDist, *ptr;
+ uint_fast8_t i, innerDist;
+
+ wordJam = 0;
+ wordDist = dist>>5;
+ if ( wordDist ) {
+ if ( size_words < wordDist ) wordDist = size_words;
+ ptr = (uint32_t *) (aPtr + indexMultiwordLo( size_words, wordDist ));
+ i = wordDist;
+ do {
+ wordJam = *ptr++;
+ if ( wordJam ) break;
+ --i;
+ } while ( i );
+ ptr = zPtr;
+ }
+ if ( wordDist < size_words ) {
+ aPtr += indexMultiwordHiBut( size_words, wordDist );
+ innerDist = dist & 31;
+ if ( innerDist ) {
+ softfloat_shortShiftRightJamM(
+ size_words - wordDist,
+ aPtr,
+ innerDist,
+ zPtr + indexMultiwordLoBut( size_words, wordDist )
+ );
+ if ( ! wordDist ) goto wordJam;
+ } else {
+ aPtr += indexWordLo( size_words - wordDist );
+ ptr = zPtr + indexWordLo( size_words );
+ for ( i = size_words - wordDist; i; --i ) {
+ *ptr = *aPtr;
+ aPtr += wordIncr;
+ ptr += wordIncr;
+ }
+ }
+ ptr = zPtr + indexMultiwordHi( size_words, wordDist );
+ }
+ do {
+ *ptr++ = 0;
+ --wordDist;
+ } while ( wordDist );
+ wordJam:
+ if ( wordJam ) zPtr[indexWordLo( size_words )] |= 1;
+
+}
+
+#endif
+
+
+#ifndef softfloat_shiftRightJam64
+
+uint64_t softfloat_shiftRightJam64( uint64_t a, uint_fast32_t dist )
+{
+
+ return
+ (dist < 63) ? a>>dist | ((uint64_t) (a<<(-dist & 63)) != 0) : (a != 0);
+
+}
+
+#endif
+
+/*----------------------------------------------------------------------------
+| Raises the exceptions specified by 'flags'. Floating-point traps can be
+| defined here if desired. It is currently not possible for such a trap
+| to substitute a result value. If traps are not implemented, this routine
+| should be simply 'softfloat_exceptionFlags |= flags;'.
+*----------------------------------------------------------------------------*/
+void softfloat_raiseFlags( uint_fast8_t flags )
+{
+
+ softfloat_exceptionFlags |= flags;
+
+}
+
+float64_t
+ softfloat_roundPackToF64( bool sign, int_fast16_t exp, uint_fast64_t sig )
+{
+ uint_fast8_t roundingMode;
+ bool roundNearEven;
+ uint_fast16_t roundIncrement, roundBits;
+ bool isTiny;
+ uint_fast64_t uiZ;
+ union ui64_f64 uZ;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ roundingMode = softfloat_roundingMode;
+ roundNearEven = (roundingMode == softfloat_round_near_even);
+ roundIncrement = 0x200;
+ if ( ! roundNearEven && (roundingMode != softfloat_round_near_maxMag) ) {
+ roundIncrement =
+ (roundingMode
+ == (sign ? softfloat_round_min : softfloat_round_max))
+ ? 0x3FF
+ : 0;
+ }
+ roundBits = sig & 0x3FF;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( 0x7FD <= (uint16_t) exp ) {
+ if ( exp < 0 ) {
+ /*----------------------------------------------------------------
+ *----------------------------------------------------------------*/
+ isTiny =
+ (softfloat_detectTininess == softfloat_tininess_beforeRounding)
+ || (exp < -1)
+ || (sig + roundIncrement < UINT64_C( 0x8000000000000000 ));
+ sig = softfloat_shiftRightJam64( sig, -exp );
+ exp = 0;
+ roundBits = sig & 0x3FF;
+ if ( isTiny && roundBits ) {
+ softfloat_raiseFlags( softfloat_flag_underflow );
+ }
+ } else if (
+ (0x7FD < exp)
+ || (UINT64_C( 0x8000000000000000 ) <= sig + roundIncrement)
+ ) {
+ /*----------------------------------------------------------------
+ *----------------------------------------------------------------*/
+ softfloat_raiseFlags(
+ softfloat_flag_overflow | softfloat_flag_inexact );
+ uiZ = packToF64UI( sign, 0x7FF, 0 ) - ! roundIncrement;
+ goto uiZ;
+ }
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ sig = (sig + roundIncrement)>>10;
+ if ( roundBits ) {
+ softfloat_exceptionFlags |= softfloat_flag_inexact;
+#ifdef SOFTFLOAT_ROUND_ODD
+ if ( roundingMode == softfloat_round_odd ) {
+ sig |= 1;
+ goto packReturn;
+ }
+#endif
+ }
+ sig &= ~(uint_fast64_t) (! (roundBits ^ 0x200) & roundNearEven);
+ if ( ! sig ) exp = 0;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ packReturn:
+ uiZ = packToF64UI( sign, exp, sig );
+ uiZ:
+ uZ.ui = uiZ;
+ return uZ.f;
+
+}
+
+float64_t
+ softfloat_normRoundPackToF64( bool sign, int_fast16_t exp, uint_fast64_t sig
+)
+{
+ int_fast8_t shiftDist;
+ union ui64_f64 uZ;
+
+ shiftDist = softfloat_countLeadingZeros64( sig ) - 1;
+ exp -= shiftDist;
+ if ( (10 <= shiftDist) && ((unsigned int) exp < 0x7FD) ) {
+ uZ.ui = packToF64UI( sign, sig ? exp : 0, sig<<(shiftDist - 10) );
+ return uZ.f;
+ } else {
+ return softfloat_roundPackToF64( sign, exp, sig<<shiftDist );
+ }
+
+}
+
+#ifndef softfloat_shortShiftRightJam64
+
+uint64_t softfloat_shortShiftRightJam64( uint64_t a, uint_fast8_t dist )
+{
+
+ return a>>dist | ((a & (((uint_fast64_t) 1<<dist) - 1)) != 0);
+
+}
+
+#endif
+
+uint_fast64_t
+ softfloat_roundMToUI64(
+ bool sign, uint32_t *extSigPtr, uint_fast8_t roundingMode, bool exact )
+{
+ uint64_t sig;
+ uint32_t sigExtra;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ sig =
+ (uint64_t) extSigPtr[indexWord( 3, 2 )]<<32
+ | extSigPtr[indexWord( 3, 1 )];
+ sigExtra = extSigPtr[indexWordLo( 3 )];
+ if (
+ (roundingMode == softfloat_round_near_maxMag)
+ || (roundingMode == softfloat_round_near_even)
+ ) {
+ if ( 0x80000000 <= sigExtra ) goto increment;
+ } else {
+ if ( sign ) {
+ if ( !(sig | sigExtra) ) return 0;
+ if ( roundingMode == softfloat_round_min ) goto invalid;
+#ifdef SOFTFLOAT_ROUND_ODD
+ if ( roundingMode == softfloat_round_odd ) goto invalid;
+#endif
+ } else {
+ if ( (roundingMode == softfloat_round_max) && sigExtra ) {
+ increment:
+ ++sig;
+ if ( !sig ) goto invalid;
+ if (
+ (sigExtra == 0x80000000)
+ && (roundingMode == softfloat_round_near_even)
+ ) {
+ sig &= ~(uint_fast64_t) 1;
+ }
+ }
+ }
+ }
+ if ( sign && sig ) goto invalid;
+ if ( sigExtra ) {
+#ifdef SOFTFLOAT_ROUND_ODD
+ if ( roundingMode == softfloat_round_odd ) sig |= 1;
+#endif
+ if ( exact ) softfloat_exceptionFlags |= softfloat_flag_inexact;
+ }
+ return sig;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ invalid:
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ return sign ? ui64_fromNegOverflow : ui64_fromPosOverflow;
+
+}
+
+int_fast64_t
+ softfloat_roundMToI64(
+ bool sign, uint32_t *extSigPtr, uint_fast8_t roundingMode, bool exact )
+{
+ uint64_t sig;
+ uint32_t sigExtra;
+ union { uint64_t ui; int64_t i; } uZ;
+ int64_t z;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ sig =
+ (uint64_t) extSigPtr[indexWord( 3, 2 )]<<32
+ | extSigPtr[indexWord( 3, 1 )];
+ sigExtra = extSigPtr[indexWordLo( 3 )];
+ if (
+ (roundingMode == softfloat_round_near_maxMag)
+ || (roundingMode == softfloat_round_near_even)
+ ) {
+ if ( 0x80000000 <= sigExtra ) goto increment;
+ } else {
+ if (
+ sigExtra
+ && (sign
+ ? (roundingMode == softfloat_round_min)
+#ifdef SOFTFLOAT_ROUND_ODD
+ || (roundingMode == softfloat_round_odd)
+#endif
+ : (roundingMode == softfloat_round_max))
+ ) {
+ increment:
+ ++sig;
+ if ( !sig ) goto invalid;
+ if (
+ (sigExtra == 0x80000000)
+ && (roundingMode == softfloat_round_near_even)
+ ) {
+ sig &= ~(uint_fast64_t) 1;
+ }
+ }
+ }
+ uZ.ui = sign ? -sig : sig;
+ z = uZ.i;
+ if ( z && ((z < 0) ^ sign) ) goto invalid;
+ if ( sigExtra ) {
+#ifdef SOFTFLOAT_ROUND_ODD
+ if ( roundingMode == softfloat_round_odd ) z |= 1;
+#endif
+ if ( exact ) softfloat_exceptionFlags |= softfloat_flag_inexact;
+ }
+ return z;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ invalid:
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ return sign ? i64_fromNegOverflow : i64_fromPosOverflow;
+
+}
+
+/*----------------------------------------------------------------------------
+| Conversion from int/unsigned int to floating point and vice versa.
+ ----------------------------------------------------------------------------*/
+
+float64_t i64_to_f64( int64_t a )
+{
+ bool sign;
+ union ui64_f64 uZ;
+ uint_fast64_t absA;
+
+ sign = (a < 0);
+ if ( ! (a & UINT64_C( 0x7FFFFFFFFFFFFFFF )) ) {
+ uZ.ui = sign ? packToF64UI( 1, 0x43E, 0 ) : 0;
+ return uZ.f;
+ }
+ absA = sign ? -(uint_fast64_t) a : (uint_fast64_t) a;
+ return softfloat_normRoundPackToF64( sign, 0x43C, absA );
+}
+
+int_fast64_t f64_to_i64( float64_t a, uint_fast8_t roundingMode, bool exact )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ bool sign;
+ int_fast16_t exp;
+ uint_fast64_t sig;
+ int_fast16_t shiftDist;
+#ifdef SOFTFLOAT_FAST_INT64
+ struct uint64_extra sigExtra;
+#else
+ uint32_t extSig[3];
+#endif
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ uA.f = a;
+ uiA = uA.ui;
+ sign = signF64UI( uiA );
+ exp = expF64UI( uiA );
+ sig = fracF64UI( uiA );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( exp ) sig |= UINT64_C( 0x0010000000000000 );
+ shiftDist = 0x433 - exp;
+#ifdef SOFTFLOAT_FAST_INT64
+ if ( shiftDist <= 0 ) {
+ if ( shiftDist < -11 ) goto invalid;
+ sigExtra.v = sig<<-shiftDist;
+ sigExtra.extra = 0;
+ } else {
+ sigExtra = softfloat_shiftRightJam64Extra( sig, 0, shiftDist );
+ }
+ return
+ softfloat_roundToI64(
+ sign, sigExtra.v, sigExtra.extra, roundingMode, exact );
+#else
+ extSig[indexWord( 3, 0 )] = 0;
+ if ( shiftDist <= 0 ) {
+ if ( shiftDist < -11 ) goto invalid;
+ sig <<= -shiftDist;
+ extSig[indexWord( 3, 2 )] = sig>>32;
+ extSig[indexWord( 3, 1 )] = sig;
+ } else {
+ extSig[indexWord( 3, 2 )] = sig>>32;
+ extSig[indexWord( 3, 1 )] = sig;
+ softfloat_shiftRightJam96M( extSig, shiftDist, extSig );
+ }
+ return softfloat_roundMToI64( sign, extSig, roundingMode, exact );
+#endif
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ invalid:
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ return
+ (exp == 0x7FF) && fracF64UI( uiA ) ? i64_fromNaN
+ : sign ? i64_fromNegOverflow : i64_fromPosOverflow;
+
+}
+
+/*----------------------------------------------------------------------------
+| Converts the common NaN pointed to by 'aPtr' into a 64-bit floating-point
+| NaN, and returns the bit pattern of this value as an unsigned integer.
+*----------------------------------------------------------------------------*/
+uint_fast64_t softfloat_commonNaNToF64UI( const struct commonNaN *aPtr )
+{
+ return
+ (uint_fast64_t) aPtr->sign<<63 | UINT64_C( 0x7FF8000000000000 )
+ | aPtr->v64>>12;
+}
+
+/*----------------------------------------------------------------------------
+| Assuming 'uiA' has the bit pattern of a 64-bit floating-point NaN, converts
+| this NaN to the common NaN form, and stores the resulting common NaN at the
+| location pointed to by 'zPtr'. If the NaN is a signaling NaN, the invalid
+| exception is raised.
+*----------------------------------------------------------------------------*/
+void softfloat_f64UIToCommonNaN( uint_fast64_t uiA, struct commonNaN *zPtr )
+{
+ if ( softfloat_isSigNaNF64UI( uiA ) ) {
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ }
+ zPtr->sign = uiA>>63;
+ zPtr->v64 = uiA<<12;
+ zPtr->v0 = 0;
+}
+
+/*----------------------------------------------------------------------------
+| Interpreting 'uiA' and 'uiB' as the bit patterns of two 64-bit floating-
+| point values, at least one of which is a NaN, returns the bit pattern of
+| the combined NaN result. If either 'uiA' or 'uiB' has the pattern of a
+| signaling NaN, the invalid exception is raised.
+*----------------------------------------------------------------------------*/
+uint_fast64_t
+ softfloat_propagateNaNF64UI( uint_fast64_t uiA, uint_fast64_t uiB )
+{
+ bool isSigNaNA;
+
+ isSigNaNA = softfloat_isSigNaNF64UI( uiA );
+ if ( isSigNaNA || softfloat_isSigNaNF64UI( uiB ) ) {
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ return (isSigNaNA ? uiA : uiB) | UINT64_C( 0x0008000000000000 );
+ }
+ return isNaNF64UI( uiA ) ? uiA : uiB;
+}
+
+/*------------------------------------------------------------------------
+|Converting a fp to a str
+*------------------------------------------------------------------------*/
+
+char* itoa(uint64_t val)
+{
+ int base = 10;
+ static char buf[32] = {0};
+
+ int i = 30;
+ while (i != 0)
+ {
+
+ buf[i] = "0123456789abcdef"[val % base];
+ val /= base;
+ i--;
+ if (!(val && i)) break;
+ }
+
+ return &buf[i+1];
+}
+
+void f64_to_str( char *result, int outlen, float64_t a, int precision )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ bool sign;
+ uint_fast32_t exp;
+ uint_fast64_t sig;
+
+ char *iPart;
+ char *fTemp;
+ uint64_t fPart;
+ uint64_t base;
+ uint64_t temp;
+
+ int lastNum;
+ int numAfterLast;
+ int i;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ uA.f = a;
+ uiA = uA.ui;
+ sign = signF64UI( uiA );
+ exp = expF64UI( uiA );
+ sig = fracF64UI( uiA );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+
+ if ( exp ) sig |= UINT64_C( 0x0010000000000000 );
+ exp = exp - 1023;
+ memset(result, '\0', outlen);
+ if (sign) strcat(result, "-");
+ iPart = itoa(sig >> (52 - exp));
+ strcat(result, iPart);
+ strcat(result, ".");
+ fPart = sig & (((uint64_t)1 << (52 - exp)) - 1);
+ base = (uint64_t)1 << (52 - exp);
+ temp = 0;
+ i = 0;
+ while (i++ < precision-1)
+ {
+ fPart *= 10;
+ fTemp = itoa(fPart/base);
+ strcat(result, fTemp);
+ fPart %= base;
+ }
+
+ fPart *= 10;
+ lastNum = fPart/base;
+ fPart %= base;
+
+ numAfterLast = 0;
+
+ if (fPart != 0)
+ {
+ fPart*= 10;
+ numAfterLast = fPart/base;
+ }
+
+ if (numAfterLast >= 5) lastNum++;
+ fTemp = itoa(lastNum);
+ strcat(result, fTemp);
+}
+
+/*------------------------------------------------------------------------
+| Converting string to 64 bit floating point
+| code logic from:
+| https://codereview.stackexchange.com/questions/158519/c-program-to-convert-string-to-floating-point
+*------------------------------------------------------------------------*/
+float64_t str_to_f64(const char *s)
+{
+ float64_t zero;
+ float64_t one;
+ float64_t ten;
+
+ float64_t result;
+ float64_t power;
+ float64_t power2;/*The number following the E*/
+ float64_t value;
+ float64_t char_val;
+
+ float64_t sign;
+ int sign_val;
+
+ float64_t powersign;
+ int powersign_val; /*The sign following the E*/
+
+ float64_t nan;
+
+ int i;
+
+ nan.v = defaultNaNF64UI;
+ zero = i64_to_f64(0);
+ one = i64_to_f64(1);
+ ten = i64_to_f64(10);
+
+ i = 0;
+ sign_val = (s[i] == '-')? -1 : 1; /*The sign of the number*/
+ sign = i64_to_f64(sign_val);
+
+ if(s[i] == '-' || s[i] == '+')
+ {
+ ++i;
+ }
+
+ value = zero;
+ for(; isdigit(s[i]); ++i)
+ {
+ char_val = i64_to_f64(s[i] - '0');
+ value = f64_add(f64_mul(value, ten), char_val) ;
+ }
+
+ if(s[i] == '.')
+ {
+ ++i;
+ }
+
+ power = one;
+ for(; isdigit(s[i]); ++i)
+ {
+ char_val = i64_to_f64(s[i] - '0');
+ value = f64_add(f64_mul(value, ten), char_val);
+ power = f64_mul(power, ten);
+ }
+
+ if(s[i] == 'e' || s[i] == 'E')
+ {
+ ++i;
+
+ powersign_val = (s[i] == '-')? -1 : 1;
+ powersign = i64_to_f64(powersign_val);
+
+ if(s[i] == '-' || s[i] == '+')
+ ++i;
+
+ power2 = zero;
+ for(; isdigit(s[i]); ++i)
+ {
+ char_val = i64_to_f64(s[i] - '0');
+ power2 = f64_add(f64_mul(power2, ten), char_val);
+ }
+
+ if(powersign_val == -1)
+ {
+ while(f64_eq(power2, zero) == 0)
+ {
+ power = f64_mul(power, ten);
+ power2 = f64_sub(power2, one);
+ }
+ }
+ else{
+ while(f64_eq(power2, zero) == 0)
+ {
+ power = f64_div(power, ten);
+ power2 = f64_sub(power2, one);
+ }
+ }
+ }
+
+ if(s[i] == '\0')
+ return f64_mul(sign, f64_div(value, power));
+ else
+ return nan;
+}
+
+/*------------------------------------------------------------------------
+| float64_t arithmetic helper functions
+*------------------------------------------------------------------------*/
+#ifndef softfloat_subM
+
+void
+ softfloat_subM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ const uint32_t *bPtr,
+ uint32_t *zPtr
+ )
+{
+ unsigned int index, lastIndex;
+ uint_fast8_t borrow;
+ uint32_t wordA, wordB;
+
+ index = indexWordLo( size_words );
+ lastIndex = indexWordHi( size_words );
+ borrow = 0;
+ for (;;) {
+ wordA = aPtr[index];
+ wordB = bPtr[index];
+ zPtr[index] = wordA - wordB - borrow;
+ if ( index == lastIndex ) break;
+ borrow = borrow ? (wordA <= wordB) : (wordA < wordB);
+ index += wordIncr;
+ }
+}
+
+#endif
+
+#ifndef softfloat_shortShiftRightM
+
+void
+ softfloat_shortShiftRightM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ uint_fast8_t dist,
+ uint32_t *zPtr
+ )
+{
+ uint_fast8_t uNegDist;
+ unsigned int index, lastIndex;
+ uint32_t partWordZ, wordA;
+
+ uNegDist = -dist;
+ index = indexWordLo( size_words );
+ lastIndex = indexWordHi( size_words );
+ partWordZ = aPtr[index]>>dist;
+ while ( index != lastIndex ) {
+ wordA = aPtr[index + wordIncr];
+ zPtr[index] = wordA<<(uNegDist & 31) | partWordZ;
+ index += wordIncr;
+ partWordZ = wordA>>dist;
+ }
+ zPtr[index] = partWordZ;
+}
+
+#endif
+
+#ifndef softfloat_shortShiftLeftM
+
+void
+ softfloat_shortShiftLeftM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ uint_fast8_t dist,
+ uint32_t *zPtr
+ )
+{
+ uint_fast8_t uNegDist;
+ unsigned int index, lastIndex;
+ uint32_t partWordZ, wordA;
+
+ uNegDist = -dist;
+ index = indexWordHi( size_words );
+ lastIndex = indexWordLo( size_words );
+ partWordZ = aPtr[index]<<dist;
+ while ( index != lastIndex ) {
+ wordA = aPtr[index - wordIncr];
+ zPtr[index] = partWordZ | wordA>>(uNegDist & 31);
+ index -= wordIncr;
+ partWordZ = wordA<<dist;
+ }
+ zPtr[index] = partWordZ;
+}
+
+#endif
+
+#ifndef softfloat_shiftLeftM
+
+#define softfloat_shiftLeftM softfloat_shiftLeftM
+
+void
+ softfloat_shiftLeftM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ uint32_t dist,
+ uint32_t *zPtr
+ )
+{
+ uint32_t wordDist;
+ uint_fast8_t innerDist;
+ uint32_t *destPtr;
+ uint_fast8_t i;
+
+ wordDist = dist>>5;
+ if ( wordDist < size_words ) {
+ aPtr += indexMultiwordLoBut( size_words, wordDist );
+ innerDist = dist & 31;
+ if ( innerDist ) {
+ softfloat_shortShiftLeftM(
+ size_words - wordDist,
+ aPtr,
+ innerDist,
+ zPtr + indexMultiwordHiBut( size_words, wordDist )
+ );
+ if ( ! wordDist ) return;
+ } else {
+ aPtr += indexWordHi( size_words - wordDist );
+ destPtr = zPtr + indexWordHi( size_words );
+ for ( i = size_words - wordDist; i; --i ) {
+ *destPtr = *aPtr;
+ aPtr -= wordIncr;
+ destPtr -= wordIncr;
+ }
+ }
+ zPtr += indexMultiwordLo( size_words, wordDist );
+ } else {
+ wordDist = size_words;
+ }
+ do {
+ *zPtr++ = 0;
+ --wordDist;
+ } while ( wordDist );
+}
+
+#endif
+
+#ifndef softfloat_negXM
+
+void softfloat_negXM( uint_fast8_t size_words, uint32_t *zPtr )
+{
+ unsigned int index, lastIndex;
+ uint_fast8_t carry;
+ uint32_t word;
+
+ index = indexWordLo( size_words );
+ lastIndex = indexWordHi( size_words );
+ carry = 1;
+ for (;;) {
+ word = ~zPtr[index] + carry;
+ zPtr[index] = word;
+ if ( index == lastIndex ) break;
+ index += wordIncr;
+ if ( word ) carry = 0;
+ }
+}
+
+#endif
+
+const uint16_t softfloat_approxRecipSqrt_1k0s[16] = {
+ 0xB4C9, 0xFFAB, 0xAA7D, 0xF11C, 0xA1C5, 0xE4C7, 0x9A43, 0xDA29,
+ 0x93B5, 0xD0E5, 0x8DED, 0xC8B7, 0x88C6, 0xC16D, 0x8424, 0xBAE1
+};
+const uint16_t softfloat_approxRecipSqrt_1k1s[16] = {
+ 0xA5A5, 0xEA42, 0x8C21, 0xC62D, 0x788F, 0xAA7F, 0x6928, 0x94B6,
+ 0x5CC7, 0x8335, 0x52A6, 0x74E2, 0x4A3E, 0x68FE, 0x432B, 0x5EFD
+};
+
+const uint16_t softfloat_approxRecip_1k0s[16] = {
+ 0xFFC4, 0xF0BE, 0xE363, 0xD76F, 0xCCAD, 0xC2F0, 0xBA16, 0xB201,
+ 0xAA97, 0xA3C6, 0x9D7A, 0x97A6, 0x923C, 0x8D32, 0x887E, 0x8417
+};
+const uint16_t softfloat_approxRecip_1k1s[16] = {
+ 0xF0F1, 0xD62C, 0xBFA1, 0xAC77, 0x9C0A, 0x8DDB, 0x8185, 0x76BA,
+ 0x6D3B, 0x64D4, 0x5D5C, 0x56B1, 0x50B6, 0x4B55, 0x4679, 0x4211
+};
+
+
+
+#ifdef SOFTFLOAT_FAST_INT64
+
+float64_t
+ softfloat_mulAddF64(
+ uint_fast64_t uiA, uint_fast64_t uiB, uint_fast64_t uiC, uint_fast8_t op )
+{
+ bool signA;
+ int_fast16_t expA;
+ uint_fast64_t sigA;
+ bool signB;
+ int_fast16_t expB;
+ uint_fast64_t sigB;
+ bool signC;
+ int_fast16_t expC;
+ uint_fast64_t sigC;
+ bool signZ;
+ uint_fast64_t magBits, uiZ;
+ struct exp16_sig64 normExpSig;
+ int_fast16_t expZ;
+ struct uint128 sig128Z;
+ uint_fast64_t sigZ;
+ int_fast16_t expDiff;
+ struct uint128 sig128C;
+ int_fast8_t shiftDist;
+ union ui64_f64 uZ;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ signA = signF64UI( uiA );
+ expA = expF64UI( uiA );
+ sigA = fracF64UI( uiA );
+ signB = signF64UI( uiB );
+ expB = expF64UI( uiB );
+ sigB = fracF64UI( uiB );
+ signC = signF64UI( uiC ) ^ (op == softfloat_mulAdd_subC);
+ expC = expF64UI( uiC );
+ sigC = fracF64UI( uiC );
+ signZ = signA ^ signB ^ (op == softfloat_mulAdd_subProd);
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( expA == 0x7FF ) {
+ if ( sigA || ((expB == 0x7FF) && sigB) ) goto propagateNaN_ABC;
+ magBits = expB | sigB;
+ goto infProdArg;
+ }
+ if ( expB == 0x7FF ) {
+ if ( sigB ) goto propagateNaN_ABC;
+ magBits = expA | sigA;
+ goto infProdArg;
+ }
+ if ( expC == 0x7FF ) {
+ if ( sigC ) {
+ uiZ = 0;
+ goto propagateNaN_ZC;
+ }
+ uiZ = uiC;
+ goto uiZ;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( ! expA ) {
+ if ( ! sigA ) goto zeroProd;
+ normExpSig = softfloat_normSubnormalF64Sig( sigA );
+ expA = normExpSig.exp;
+ sigA = normExpSig.sig;
+ }
+ if ( ! expB ) {
+ if ( ! sigB ) goto zeroProd;
+ normExpSig = softfloat_normSubnormalF64Sig( sigB );
+ expB = normExpSig.exp;
+ sigB = normExpSig.sig;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expZ = expA + expB - 0x3FE;
+ sigA = (sigA | UINT64_C( 0x0010000000000000 ))<<10;
+ sigB = (sigB | UINT64_C( 0x0010000000000000 ))<<10;
+ sig128Z = softfloat_mul64To128( sigA, sigB );
+ if ( sig128Z.v64 < UINT64_C( 0x2000000000000000 ) ) {
+ --expZ;
+ sig128Z =
+ softfloat_add128(
+ sig128Z.v64, sig128Z.v0, sig128Z.v64, sig128Z.v0 );
+ }
+ if ( ! expC ) {
+ if ( ! sigC ) {
+ --expZ;
+ sigZ = sig128Z.v64<<1 | (sig128Z.v0 != 0);
+ goto roundPack;
+ }
+ normExpSig = softfloat_normSubnormalF64Sig( sigC );
+ expC = normExpSig.exp;
+ sigC = normExpSig.sig;
+ }
+ sigC = (sigC | UINT64_C( 0x0010000000000000 ))<<9;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expDiff = expZ - expC;
+ if ( expDiff < 0 ) {
+ expZ = expC;
+ if ( (signZ == signC) || (expDiff < -1) ) {
+ sig128Z.v64 = softfloat_shiftRightJam64( sig128Z.v64, -expDiff );
+ } else {
+ sig128Z =
+ softfloat_shortShiftRightJam128( sig128Z.v64, sig128Z.v0, 1 );
+ }
+ } else if ( expDiff ) {
+ sig128C = softfloat_shiftRightJam128( sigC, 0, expDiff );
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( signZ == signC ) {
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ if ( expDiff <= 0 ) {
+ sigZ = (sigC + sig128Z.v64) | (sig128Z.v0 != 0);
+ } else {
+ sig128Z =
+ softfloat_add128(
+ sig128Z.v64, sig128Z.v0, sig128C.v64, sig128C.v0 );
+ sigZ = sig128Z.v64 | (sig128Z.v0 != 0);
+ }
+ if ( sigZ < UINT64_C( 0x4000000000000000 ) ) {
+ --expZ;
+ sigZ <<= 1;
+ }
+ } else {
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ if ( expDiff < 0 ) {
+ signZ = signC;
+ sig128Z = softfloat_sub128( sigC, 0, sig128Z.v64, sig128Z.v0 );
+ } else if ( ! expDiff ) {
+ sig128Z.v64 = sig128Z.v64 - sigC;
+ if ( ! (sig128Z.v64 | sig128Z.v0) ) goto completeCancellation;
+ if ( sig128Z.v64 & UINT64_C( 0x8000000000000000 ) ) {
+ signZ = ! signZ;
+ sig128Z = softfloat_sub128( 0, 0, sig128Z.v64, sig128Z.v0 );
+ }
+ } else {
+ sig128Z =
+ softfloat_sub128(
+ sig128Z.v64, sig128Z.v0, sig128C.v64, sig128C.v0 );
+ }
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ if ( ! sig128Z.v64 ) {
+ expZ -= 64;
+ sig128Z.v64 = sig128Z.v0;
+ sig128Z.v0 = 0;
+ }
+ shiftDist = softfloat_countLeadingZeros64( sig128Z.v64 ) - 1;
+ expZ -= shiftDist;
+ if ( shiftDist < 0 ) {
+ sigZ = softfloat_shortShiftRightJam64( sig128Z.v64, -shiftDist );
+ } else {
+ sig128Z =
+ softfloat_shortShiftLeft128(
+ sig128Z.v64, sig128Z.v0, shiftDist );
+ sigZ = sig128Z.v64;
+ }
+ sigZ |= (sig128Z.v0 != 0);
+ }
+ roundPack:
+ return softfloat_roundPackToF64( signZ, expZ, sigZ );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ propagateNaN_ABC:
+ uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
+ goto propagateNaN_ZC;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ infProdArg:
+ if ( magBits ) {
+ uiZ = packToF64UI( signZ, 0x7FF, 0 );
+ if ( expC != 0x7FF ) goto uiZ;
+ if ( sigC ) goto propagateNaN_ZC;
+ if ( signZ == signC ) goto uiZ;
+ }
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ uiZ = defaultNaNF64UI;
+ propagateNaN_ZC:
+ uiZ = softfloat_propagateNaNF64UI( uiZ, uiC );
+ goto uiZ;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ zeroProd:
+ uiZ = uiC;
+ if ( ! (expC | sigC) && (signZ != signC) ) {
+ completeCancellation:
+ uiZ =
+ packToF64UI(
+ (softfloat_roundingMode == softfloat_round_min), 0, 0 );
+ }
+ uiZ:
+ uZ.ui = uiZ;
+ return uZ.f;
+}
+
+#else
+
+float64_t
+ softfloat_mulAddF64(
+ uint_fast64_t uiA, uint_fast64_t uiB, uint_fast64_t uiC, uint_fast8_t op )
+{
+ bool signA;
+ int_fast16_t expA;
+ uint64_t sigA;
+ bool signB;
+ int_fast16_t expB;
+ uint64_t sigB;
+ bool signC;
+ int_fast16_t expC;
+ uint64_t sigC;
+ bool signZ;
+ uint64_t magBits, uiZ;
+ struct exp16_sig64 normExpSig;
+ int_fast16_t expZ;
+ uint32_t sig128Z[4];
+ uint64_t sigZ;
+ int_fast16_t shiftDist, expDiff;
+ uint32_t sig128C[4];
+ union ui64_f64 uZ;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ signA = signF64UI( uiA );
+ expA = expF64UI( uiA );
+ sigA = fracF64UI( uiA );
+ signB = signF64UI( uiB );
+ expB = expF64UI( uiB );
+ sigB = fracF64UI( uiB );
+ signC = signF64UI( uiC ) ^ (op == softfloat_mulAdd_subC);
+ expC = expF64UI( uiC );
+ sigC = fracF64UI( uiC );
+ signZ = signA ^ signB ^ (op == softfloat_mulAdd_subProd);
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( expA == 0x7FF ) {
+ if ( sigA || ((expB == 0x7FF) && sigB) ) goto propagateNaN_ABC;
+ magBits = expB | sigB;
+ goto infProdArg;
+ }
+ if ( expB == 0x7FF ) {
+ if ( sigB ) goto propagateNaN_ABC;
+ magBits = expA | sigA;
+ goto infProdArg;
+ }
+ if ( expC == 0x7FF ) {
+ if ( sigC ) {
+ uiZ = 0;
+ goto propagateNaN_ZC;
+ }
+ uiZ = uiC;
+ goto uiZ;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( ! expA ) {
+ if ( ! sigA ) goto zeroProd;
+ normExpSig = softfloat_normSubnormalF64Sig( sigA );
+ expA = normExpSig.exp;
+ sigA = normExpSig.sig;
+ }
+ if ( ! expB ) {
+ if ( ! sigB ) goto zeroProd;
+ normExpSig = softfloat_normSubnormalF64Sig( sigB );
+ expB = normExpSig.exp;
+ sigB = normExpSig.sig;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expZ = expA + expB - 0x3FE;
+ sigA = (sigA | UINT64_C( 0x0010000000000000 ))<<10;
+ sigB = (sigB | UINT64_C( 0x0010000000000000 ))<<11;
+ softfloat_mul64To128M( sigA, sigB, sig128Z );
+ sigZ =
+ (uint64_t) sig128Z[indexWord( 4, 3 )]<<32 | sig128Z[indexWord( 4, 2 )];
+ shiftDist = 0;
+ if ( ! (sigZ & UINT64_C( 0x4000000000000000 )) ) {
+ --expZ;
+ shiftDist = -1;
+ }
+ if ( ! expC ) {
+ if ( ! sigC ) {
+ if ( shiftDist ) sigZ <<= 1;
+ goto sigZ;
+ }
+ normExpSig = softfloat_normSubnormalF64Sig( sigC );
+ expC = normExpSig.exp;
+ sigC = normExpSig.sig;
+ }
+ sigC = (sigC | UINT64_C( 0x0010000000000000 ))<<10;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expDiff = expZ - expC;
+ if ( expDiff < 0 ) {
+ expZ = expC;
+ if ( (signZ == signC) || (expDiff < -1) ) {
+ shiftDist -= expDiff;
+ if ( shiftDist) {
+ sigZ = softfloat_shiftRightJam64( sigZ, shiftDist );
+ }
+ } else {
+ if ( ! shiftDist ) {
+ softfloat_shortShiftRight128M( sig128Z, 1, sig128Z );
+ }
+ }
+ } else {
+ if ( shiftDist ) softfloat_add128M( sig128Z, sig128Z, sig128Z );
+ if ( ! expDiff ) {
+ sigZ =
+ (uint64_t) sig128Z[indexWord( 4, 3 )]<<32
+ | sig128Z[indexWord( 4, 2 )];
+ } else {
+ sig128C[indexWord( 4, 3 )] = sigC>>32;
+ sig128C[indexWord( 4, 2 )] = sigC;
+ sig128C[indexWord( 4, 1 )] = 0;
+ sig128C[indexWord( 4, 0 )] = 0;
+ softfloat_shiftRightJam128M( sig128C, expDiff, sig128C );
+ }
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( signZ == signC ) {
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ if ( expDiff <= 0 ) {
+ sigZ += sigC;
+ } else {
+ softfloat_add128M( sig128Z, sig128C, sig128Z );
+ sigZ =
+ (uint64_t) sig128Z[indexWord( 4, 3 )]<<32
+ | sig128Z[indexWord( 4, 2 )];
+ }
+ if ( sigZ & UINT64_C( 0x8000000000000000 ) ) {
+ ++expZ;
+ sigZ = softfloat_shortShiftRightJam64( sigZ, 1 );
+ }
+ } else {
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ if ( expDiff < 0 ) {
+ signZ = signC;
+ if ( expDiff < -1 ) {
+ sigZ = sigC - sigZ;
+ if (
+ sig128Z[indexWord( 4, 1 )] || sig128Z[indexWord( 4, 0 )]
+ ) {
+ sigZ = (sigZ - 1) | 1;
+ }
+ if ( ! (sigZ & UINT64_C( 0x4000000000000000 )) ) {
+ --expZ;
+ sigZ <<= 1;
+ }
+ goto roundPack;
+ } else {
+ sig128C[indexWord( 4, 3 )] = sigC>>32;
+ sig128C[indexWord( 4, 2 )] = sigC;
+ sig128C[indexWord( 4, 1 )] = 0;
+ sig128C[indexWord( 4, 0 )] = 0;
+ softfloat_sub128M( sig128C, sig128Z, sig128Z );
+ }
+ } else if ( ! expDiff ) {
+ sigZ -= sigC;
+ if (
+ ! sigZ && ! sig128Z[indexWord( 4, 1 )]
+ && ! sig128Z[indexWord( 4, 0 )]
+ ) {
+ goto completeCancellation;
+ }
+ sig128Z[indexWord( 4, 3 )] = sigZ>>32;
+ sig128Z[indexWord( 4, 2 )] = sigZ;
+ if ( sigZ & UINT64_C( 0x8000000000000000 ) ) {
+ signZ = ! signZ;
+ softfloat_negX128M( sig128Z );
+ }
+ } else {
+ softfloat_sub128M( sig128Z, sig128C, sig128Z );
+ if ( 1 < expDiff ) {
+ sigZ =
+ (uint64_t) sig128Z[indexWord( 4, 3 )]<<32
+ | sig128Z[indexWord( 4, 2 )];
+ if ( ! (sigZ & UINT64_C( 0x4000000000000000 )) ) {
+ --expZ;
+ sigZ <<= 1;
+ }
+ goto sigZ;
+ }
+ }
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ shiftDist = 0;
+ sigZ =
+ (uint64_t) sig128Z[indexWord( 4, 3 )]<<32
+ | sig128Z[indexWord( 4, 2 )];
+ if ( ! sigZ ) {
+ shiftDist = 64;
+ sigZ =
+ (uint64_t) sig128Z[indexWord( 4, 1 )]<<32
+ | sig128Z[indexWord( 4, 0 )];
+ }
+ shiftDist += softfloat_countLeadingZeros64( sigZ ) - 1;
+ if ( shiftDist ) {
+ expZ -= shiftDist;
+ softfloat_shiftLeft128M( sig128Z, shiftDist, sig128Z );
+ sigZ =
+ (uint64_t) sig128Z[indexWord( 4, 3 )]<<32
+ | sig128Z[indexWord( 4, 2 )];
+ }
+ }
+ sigZ:
+ if ( sig128Z[indexWord( 4, 1 )] || sig128Z[indexWord( 4, 0 )] ) sigZ |= 1;
+ roundPack:
+ return softfloat_roundPackToF64( signZ, expZ - 1, sigZ );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ propagateNaN_ABC:
+ uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
+ goto propagateNaN_ZC;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ infProdArg:
+ if ( magBits ) {
+ uiZ = packToF64UI( signZ, 0x7FF, 0 );
+ if ( expC != 0x7FF ) goto uiZ;
+ if ( sigC ) goto propagateNaN_ZC;
+ if ( signZ == signC ) goto uiZ;
+ }
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ uiZ = defaultNaNF64UI;
+ propagateNaN_ZC:
+ uiZ = softfloat_propagateNaNF64UI( uiZ, uiC );
+ goto uiZ;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ zeroProd:
+ uiZ = uiC;
+ if ( ! (expC | sigC) && (signZ != signC) ) {
+ completeCancellation:
+ uiZ =
+ packToF64UI(
+ (softfloat_roundingMode == softfloat_round_min), 0, 0 );
+ }
+ uiZ:
+ uZ.ui = uiZ;
+ return uZ.f;
+}
+
+#endif
+
+#ifndef softfloat_addM
+
+void
+ softfloat_addM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ const uint32_t *bPtr,
+ uint32_t *zPtr
+ )
+{
+ unsigned int index, lastIndex;
+ uint_fast8_t carry;
+ uint32_t wordA, wordZ;
+
+ index = indexWordLo( size_words );
+ lastIndex = indexWordHi( size_words );
+ carry = 0;
+ for (;;) {
+ wordA = aPtr[index];
+ wordZ = wordA + bPtr[index] + carry;
+ zPtr[index] = wordZ;
+ if ( index == lastIndex ) break;
+ if ( wordZ != wordA ) carry = (wordZ < wordA);
+ index += wordIncr;
+ }
+}
+
+#endif
+
+float64_t
+ softfloat_addMagsF64( uint_fast64_t uiA, uint_fast64_t uiB, bool signZ )
+{
+ int_fast16_t expA;
+ uint_fast64_t sigA;
+ int_fast16_t expB;
+ uint_fast64_t sigB;
+ int_fast16_t expDiff;
+ uint_fast64_t uiZ;
+ int_fast16_t expZ;
+ uint_fast64_t sigZ;
+ union ui64_f64 uZ;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expA = expF64UI( uiA );
+ sigA = fracF64UI( uiA );
+ expB = expF64UI( uiB );
+ sigB = fracF64UI( uiB );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expDiff = expA - expB;
+ if ( ! expDiff ) {
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ if ( ! expA ) {
+ uiZ = uiA + sigB;
+ goto uiZ;
+ }
+ if ( expA == 0x7FF ) {
+ if ( sigA | sigB ) goto propagateNaN;
+ uiZ = uiA;
+ goto uiZ;
+ }
+ expZ = expA;
+ sigZ = UINT64_C( 0x0020000000000000 ) + sigA + sigB;
+ sigZ <<= 9;
+ } else {
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ sigA <<= 9;
+ sigB <<= 9;
+ if ( expDiff < 0 ) {
+ if ( expB == 0x7FF ) {
+ if ( sigB ) goto propagateNaN;
+ uiZ = packToF64UI( signZ, 0x7FF, 0 );
+ goto uiZ;
+ }
+ expZ = expB;
+ if ( expA ) {
+ sigA += UINT64_C( 0x2000000000000000 );
+ } else {
+ sigA <<= 1;
+ }
+ sigA = softfloat_shiftRightJam64( sigA, -expDiff );
+ } else {
+ if ( expA == 0x7FF ) {
+ if ( sigA ) goto propagateNaN;
+ uiZ = uiA;
+ goto uiZ;
+ }
+ expZ = expA;
+ if ( expB ) {
+ sigB += UINT64_C( 0x2000000000000000 );
+ } else {
+ sigB <<= 1;
+ }
+ sigB = softfloat_shiftRightJam64( sigB, expDiff );
+ }
+ sigZ = UINT64_C( 0x2000000000000000 ) + sigA + sigB;
+ if ( sigZ < UINT64_C( 0x4000000000000000 ) ) {
+ --expZ;
+ sigZ <<= 1;
+ }
+ }
+ return softfloat_roundPackToF64( signZ, expZ, sigZ );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ propagateNaN:
+ uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
+ uiZ:
+ uZ.ui = uiZ;
+ return uZ.f;
+}
+
+float64_t
+ softfloat_subMagsF64( uint_fast64_t uiA, uint_fast64_t uiB, bool signZ )
+{
+ int_fast16_t expA;
+ uint_fast64_t sigA;
+ int_fast16_t expB;
+ uint_fast64_t sigB;
+ int_fast16_t expDiff;
+ uint_fast64_t uiZ;
+ int_fast64_t sigDiff;
+ int_fast8_t shiftDist;
+ int_fast16_t expZ;
+ uint_fast64_t sigZ;
+ union ui64_f64 uZ;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expA = expF64UI( uiA );
+ sigA = fracF64UI( uiA );
+ expB = expF64UI( uiB );
+ sigB = fracF64UI( uiB );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expDiff = expA - expB;
+ if ( ! expDiff ) {
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ if ( expA == 0x7FF ) {
+ if ( sigA | sigB ) goto propagateNaN;
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ uiZ = defaultNaNF64UI;
+ goto uiZ;
+ }
+ sigDiff = sigA - sigB;
+ if ( ! sigDiff ) {
+ uiZ =
+ packToF64UI(
+ (softfloat_roundingMode == softfloat_round_min), 0, 0 );
+ goto uiZ;
+ }
+ if ( expA ) --expA;
+ if ( sigDiff < 0 ) {
+ signZ = ! signZ;
+ sigDiff = -sigDiff;
+ }
+ shiftDist = softfloat_countLeadingZeros64( sigDiff ) - 11;
+ expZ = expA - shiftDist;
+ if ( expZ < 0 ) {
+ shiftDist = expA;
+ expZ = 0;
+ }
+ uiZ = packToF64UI( signZ, expZ, sigDiff<<shiftDist );
+ goto uiZ;
+ } else {
+ /*--------------------------------------------------------------------
+ *--------------------------------------------------------------------*/
+ sigA <<= 10;
+ sigB <<= 10;
+ if ( expDiff < 0 ) {
+ /*----------------------------------------------------------------
+ *----------------------------------------------------------------*/
+ signZ = ! signZ;
+ if ( expB == 0x7FF ) {
+ if ( sigB ) goto propagateNaN;
+ uiZ = packToF64UI( signZ, 0x7FF, 0 );
+ goto uiZ;
+ }
+ sigA += expA ? UINT64_C( 0x4000000000000000 ) : sigA;
+ sigA = softfloat_shiftRightJam64( sigA, -expDiff );
+ sigB |= UINT64_C( 0x4000000000000000 );
+ expZ = expB;
+ sigZ = sigB - sigA;
+ } else {
+ /*----------------------------------------------------------------
+ *----------------------------------------------------------------*/
+ if ( expA == 0x7FF ) {
+ if ( sigA ) goto propagateNaN;
+ uiZ = uiA;
+ goto uiZ;
+ }
+ sigB += expB ? UINT64_C( 0x4000000000000000 ) : sigB;
+ sigB = softfloat_shiftRightJam64( sigB, expDiff );
+ sigA |= UINT64_C( 0x4000000000000000 );
+ expZ = expA;
+ sigZ = sigA - sigB;
+ }
+ return softfloat_normRoundPackToF64( signZ, expZ - 1, sigZ );
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ propagateNaN:
+ uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
+ uiZ:
+ uZ.ui = uiZ;
+ return uZ.f;
+}
+
+#ifndef softfloat_approxRecip32_1
+
+uint32_t softfloat_approxRecip32_1( uint32_t a )
+{
+ int index;
+ uint16_t eps, r0;
+ uint32_t sigma0;
+ uint_fast32_t r;
+ uint32_t sqrSigma0;
+
+ index = a>>27 & 0xF;
+ eps = (uint16_t) (a>>11);
+ r0 = softfloat_approxRecip_1k0s[index]
+ - ((softfloat_approxRecip_1k1s[index] * (uint_fast32_t) eps)>>20);
+ sigma0 = ~(uint_fast32_t) ((r0 * (uint_fast64_t) a)>>7);
+ r = ((uint_fast32_t) r0<<16) + ((r0 * (uint_fast64_t) sigma0)>>24);
+ sqrSigma0 = ((uint_fast64_t) sigma0 * sigma0)>>32;
+ r += ((uint32_t) r * (uint_fast64_t) sqrSigma0)>>48;
+ return r;
+}
+
+#endif
+
+#ifndef softfloat_approxRecipSqrt32_1
+
+uint32_t softfloat_approxRecipSqrt32_1( unsigned int oddExpA, uint32_t a )
+{
+ int index;
+ uint16_t eps, r0;
+ uint_fast32_t ESqrR0;
+ uint32_t sigma0;
+ uint_fast32_t r;
+ uint32_t sqrSigma0;
+
+ index = (a>>27 & 0xE) + oddExpA;
+ eps = (uint16_t) (a>>12);
+ r0 = softfloat_approxRecipSqrt_1k0s[index]
+ - ((softfloat_approxRecipSqrt_1k1s[index] * (uint_fast32_t) eps)
+ >>20);
+ ESqrR0 = (uint_fast32_t) r0 * r0;
+ if ( ! oddExpA ) ESqrR0 <<= 1;
+ sigma0 = ~(uint_fast32_t) (((uint32_t) ESqrR0 * (uint_fast64_t) a)>>23);
+ r = ((uint_fast32_t) r0<<16) + ((r0 * (uint_fast64_t) sigma0)>>25);
+ sqrSigma0 = ((uint_fast64_t) sigma0 * sigma0)>>32;
+ r += ((uint32_t) ((r>>1) + (r>>3) - ((uint_fast32_t) r0<<14))
+ * (uint_fast64_t) sqrSigma0)
+ >>48;
+ if ( ! (r & 0x80000000) ) r = 0x80000000;
+ return r;
+}
+
+#endif
+
+#ifndef softfloat_mul64To128M
+
+void softfloat_mul64To128M( uint64_t a, uint64_t b, uint32_t *zPtr )
+{
+ uint32_t a32, a0, b32, b0;
+ uint64_t z0, mid1, z64, mid;
+
+ a32 = a>>32;
+ a0 = a;
+ b32 = b>>32;
+ b0 = b;
+ z0 = (uint64_t) a0 * b0;
+ mid1 = (uint64_t) a32 * b0;
+ mid = mid1 + (uint64_t) a0 * b32;
+ z64 = (uint64_t) a32 * b32;
+ z64 += (uint64_t) (mid < mid1)<<32 | mid>>32;
+ mid <<= 32;
+ z0 += mid;
+ zPtr[indexWord( 4, 1 )] = z0>>32;
+ zPtr[indexWord( 4, 0 )] = z0;
+ z64 += (z0 < mid);
+ zPtr[indexWord( 4, 3 )] = z64>>32;
+ zPtr[indexWord( 4, 2 )] = z64;
+}
+
+#endif
+
+struct exp16_sig64 softfloat_normSubnormalF64Sig( uint_fast64_t sig )
+{
+ int_fast8_t shiftDist;
+ struct exp16_sig64 z;
+
+ shiftDist = softfloat_countLeadingZeros64( sig ) - 11;
+ z.exp = 1 - shiftDist;
+ z.sig = sig<<shiftDist;
+ return z;
+}
+
+/*------------------------------------------------------------------------
+| float64_t arithmetic
+*------------------------------------------------------------------------*/
+
+float64_t f64_add( float64_t a, float64_t b )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ bool signA;
+ union ui64_f64 uB;
+ uint_fast64_t uiB;
+ bool signB;
+#if ! defined INLINE_LEVEL || (INLINE_LEVEL < 2)
+ float64_t (*magsFuncPtr)( uint_fast64_t, uint_fast64_t, bool );
+#endif
+
+ uA.f = a;
+ uiA = uA.ui;
+ signA = signF64UI( uiA );
+ uB.f = b;
+ uiB = uB.ui;
+ signB = signF64UI( uiB );
+#if defined INLINE_LEVEL && (2 <= INLINE_LEVEL)
+ if ( signA == signB ) {
+ return softfloat_addMagsF64( uiA, uiB, signA );
+ } else {
+ return softfloat_subMagsF64( uiA, uiB, signA );
+ }
+#else
+ magsFuncPtr =
+ (signA == signB) ? softfloat_addMagsF64 : softfloat_subMagsF64;
+ return (*magsFuncPtr)( uiA, uiB, signA );
+#endif
+
+}
+
+float64_t f64_sub( float64_t a, float64_t b )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ bool signA;
+ union ui64_f64 uB;
+ uint_fast64_t uiB;
+ bool signB;
+#if ! defined INLINE_LEVEL || (INLINE_LEVEL < 2)
+ float64_t (*magsFuncPtr)( uint_fast64_t, uint_fast64_t, bool );
+#endif
+
+ uA.f = a;
+ uiA = uA.ui;
+ signA = signF64UI( uiA );
+ uB.f = b;
+ uiB = uB.ui;
+ signB = signF64UI( uiB );
+#if defined INLINE_LEVEL && (2 <= INLINE_LEVEL)
+ if ( signA == signB ) {
+ return softfloat_subMagsF64( uiA, uiB, signA );
+ } else {
+ return softfloat_addMagsF64( uiA, uiB, signA );
+ }
+#else
+ magsFuncPtr =
+ (signA == signB) ? softfloat_subMagsF64 : softfloat_addMagsF64;
+ return (*magsFuncPtr)( uiA, uiB, signA );
+#endif
+}
+
+
+float64_t f64_mul( float64_t a, float64_t b )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ bool signA;
+ int_fast16_t expA;
+ uint_fast64_t sigA;
+ union ui64_f64 uB;
+ uint_fast64_t uiB;
+ bool signB;
+ int_fast16_t expB;
+ uint_fast64_t sigB;
+ bool signZ;
+ uint_fast64_t magBits;
+ struct exp16_sig64 normExpSig;
+ int_fast16_t expZ;
+#ifdef SOFTFLOAT_FAST_INT64
+ struct uint128 sig128Z;
+#else
+ uint32_t sig128Z[4];
+#endif
+ uint_fast64_t sigZ, uiZ;
+ union ui64_f64 uZ;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ uA.f = a;
+ uiA = uA.ui;
+ signA = signF64UI( uiA );
+ expA = expF64UI( uiA );
+ sigA = fracF64UI( uiA );
+ uB.f = b;
+ uiB = uB.ui;
+ signB = signF64UI( uiB );
+ expB = expF64UI( uiB );
+ sigB = fracF64UI( uiB );
+ signZ = signA ^ signB;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( expA == 0x7FF ) {
+ if ( sigA || ((expB == 0x7FF) && sigB) ) goto propagateNaN;
+ magBits = expB | sigB;
+ goto infArg;
+ }
+ if ( expB == 0x7FF ) {
+ if ( sigB ) goto propagateNaN;
+ magBits = expA | sigA;
+ goto infArg;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( ! expA ) {
+ if ( ! sigA ) goto zero;
+ normExpSig = softfloat_normSubnormalF64Sig( sigA );
+ expA = normExpSig.exp;
+ sigA = normExpSig.sig;
+ }
+ if ( ! expB ) {
+ if ( ! sigB ) goto zero;
+ normExpSig = softfloat_normSubnormalF64Sig( sigB );
+ expB = normExpSig.exp;
+ sigB = normExpSig.sig;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expZ = expA + expB - 0x3FF;
+ sigA = (sigA | UINT64_C( 0x0010000000000000 ))<<10;
+ sigB = (sigB | UINT64_C( 0x0010000000000000 ))<<11;
+#ifdef SOFTFLOAT_FAST_INT64
+ sig128Z = softfloat_mul64To128( sigA, sigB );
+ sigZ = sig128Z.v64 | (sig128Z.v0 != 0);
+#else
+ softfloat_mul64To128M( sigA, sigB, sig128Z );
+ sigZ =
+ (uint64_t) sig128Z[indexWord( 4, 3 )]<<32 | sig128Z[indexWord( 4, 2 )];
+ if ( sig128Z[indexWord( 4, 1 )] || sig128Z[indexWord( 4, 0 )] ) sigZ |= 1;
+#endif
+ if ( sigZ < UINT64_C( 0x4000000000000000 ) ) {
+ --expZ;
+ sigZ <<= 1;
+ }
+ return softfloat_roundPackToF64( signZ, expZ, sigZ );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ propagateNaN:
+ uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
+ goto uiZ;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ infArg:
+ if ( ! magBits ) {
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ uiZ = defaultNaNF64UI;
+ } else {
+ uiZ = packToF64UI( signZ, 0x7FF, 0 );
+ }
+ goto uiZ;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ zero:
+ uiZ = packToF64UI( signZ, 0, 0 );
+ uiZ:
+ uZ.ui = uiZ;
+ return uZ.f;
+}
+
+float64_t f64_mulAdd( float64_t a, float64_t b, float64_t c )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ union ui64_f64 uB;
+ uint_fast64_t uiB;
+ union ui64_f64 uC;
+ uint_fast64_t uiC;
+
+ uA.f = a;
+ uiA = uA.ui;
+ uB.f = b;
+ uiB = uB.ui;
+ uC.f = c;
+ uiC = uC.ui;
+ return softfloat_mulAddF64( uiA, uiB, uiC, 0 );
+}
+
+float64_t f64_div( float64_t a, float64_t b )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ bool signA;
+ int_fast16_t expA;
+ uint_fast64_t sigA;
+ union ui64_f64 uB;
+ uint_fast64_t uiB;
+ bool signB;
+ int_fast16_t expB;
+ uint_fast64_t sigB;
+ bool signZ;
+ struct exp16_sig64 normExpSig;
+ int_fast16_t expZ;
+ uint32_t recip32, sig32Z, doubleTerm;
+ uint_fast64_t rem;
+ uint32_t q;
+ uint_fast64_t sigZ;
+ uint_fast64_t uiZ;
+ union ui64_f64 uZ;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ uA.f = a;
+ uiA = uA.ui;
+ signA = signF64UI( uiA );
+ expA = expF64UI( uiA );
+ sigA = fracF64UI( uiA );
+ uB.f = b;
+ uiB = uB.ui;
+ signB = signF64UI( uiB );
+ expB = expF64UI( uiB );
+ sigB = fracF64UI( uiB );
+ signZ = signA ^ signB;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( expA == 0x7FF ) {
+ if ( sigA ) goto propagateNaN;
+ if ( expB == 0x7FF ) {
+ if ( sigB ) goto propagateNaN;
+ goto invalid;
+ }
+ goto infinity;
+ }
+ if ( expB == 0x7FF ) {
+ if ( sigB ) goto propagateNaN;
+ goto zero;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( ! expB ) {
+ if ( ! sigB ) {
+ if ( ! (expA | sigA) ) goto invalid;
+ softfloat_raiseFlags( softfloat_flag_infinite );
+ goto infinity;
+ }
+ normExpSig = softfloat_normSubnormalF64Sig( sigB );
+ expB = normExpSig.exp;
+ sigB = normExpSig.sig;
+ }
+ if ( ! expA ) {
+ if ( ! sigA ) goto zero;
+ normExpSig = softfloat_normSubnormalF64Sig( sigA );
+ expA = normExpSig.exp;
+ sigA = normExpSig.sig;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ expZ = expA - expB + 0x3FE;
+ sigA |= UINT64_C( 0x0010000000000000 );
+ sigB |= UINT64_C( 0x0010000000000000 );
+ if ( sigA < sigB ) {
+ --expZ;
+ sigA <<= 11;
+ } else {
+ sigA <<= 10;
+ }
+ sigB <<= 11;
+ recip32 = softfloat_approxRecip32_1( sigB>>32 ) - 2;
+ sig32Z = ((uint32_t) (sigA>>32) * (uint_fast64_t) recip32)>>32;
+ doubleTerm = sig32Z<<1;
+ rem =
+ ((sigA - (uint_fast64_t) doubleTerm * (uint32_t) (sigB>>32))<<28)
+ - (uint_fast64_t) doubleTerm * ((uint32_t) sigB>>4);
+ q = (((uint32_t) (rem>>32) * (uint_fast64_t) recip32)>>32) + 4;
+ sigZ = ((uint_fast64_t) sig32Z<<32) + ((uint_fast64_t) q<<4);
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( (sigZ & 0x1FF) < 4<<4 ) {
+ q &= ~7;
+ sigZ &= ~(uint_fast64_t) 0x7F;
+ doubleTerm = q<<1;
+ rem =
+ ((rem - (uint_fast64_t) doubleTerm * (uint32_t) (sigB>>32))<<28)
+ - (uint_fast64_t) doubleTerm * ((uint32_t) sigB>>4);
+ if ( rem & UINT64_C( 0x8000000000000000 ) ) {
+ sigZ -= 1<<7;
+ } else {
+ if ( rem ) sigZ |= 1;
+ }
+ }
+ return softfloat_roundPackToF64( signZ, expZ, sigZ );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ propagateNaN:
+ uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
+ goto uiZ;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ invalid:
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ uiZ = defaultNaNF64UI;
+ goto uiZ;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ infinity:
+ uiZ = packToF64UI( signZ, 0x7FF, 0 );
+ goto uiZ;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ zero:
+ uiZ = packToF64UI( signZ, 0, 0 );
+ uiZ:
+ uZ.ui = uiZ;
+ return uZ.f;
+}
+
+
+float64_t f64_rem( float64_t a, float64_t b )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ bool signA;
+ int_fast16_t expA;
+ uint_fast64_t sigA;
+ union ui64_f64 uB;
+ uint_fast64_t uiB;
+ int_fast16_t expB;
+ uint_fast64_t sigB;
+ struct exp16_sig64 normExpSig;
+ uint64_t rem;
+ int_fast16_t expDiff;
+ uint32_t q, recip32;
+ uint_fast64_t q64;
+ uint64_t altRem, meanRem;
+ bool signRem;
+ uint_fast64_t uiZ;
+ union ui64_f64 uZ;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ uA.f = a;
+ uiA = uA.ui;
+ signA = signF64UI( uiA );
+ expA = expF64UI( uiA );
+ sigA = fracF64UI( uiA );
+ uB.f = b;
+ uiB = uB.ui;
+ expB = expF64UI( uiB );
+ sigB = fracF64UI( uiB );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( expA == 0x7FF ) {
+ if ( sigA || ((expB == 0x7FF) && sigB) ) goto propagateNaN;
+ goto invalid;
+ }
+ if ( expB == 0x7FF ) {
+ if ( sigB ) goto propagateNaN;
+ return a;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( expA < expB - 1 ) return a;
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( ! expB ) {
+ if ( ! sigB ) goto invalid;
+ normExpSig = softfloat_normSubnormalF64Sig( sigB );
+ expB = normExpSig.exp;
+ sigB = normExpSig.sig;
+ }
+ if ( ! expA ) {
+ if ( ! sigA ) return a;
+ normExpSig = softfloat_normSubnormalF64Sig( sigA );
+ expA = normExpSig.exp;
+ sigA = normExpSig.sig;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ rem = sigA | UINT64_C( 0x0010000000000000 );
+ sigB |= UINT64_C( 0x0010000000000000 );
+ expDiff = expA - expB;
+ if ( expDiff < 1 ) {
+ if ( expDiff < -1 ) return a;
+ sigB <<= 9;
+ if ( expDiff ) {
+ rem <<= 8;
+ q = 0;
+ } else {
+ rem <<= 9;
+ q = (sigB <= rem);
+ if ( q ) rem -= sigB;
+ }
+ } else {
+ recip32 = softfloat_approxRecip32_1( sigB>>21 );
+ /*--------------------------------------------------------------------
+ | Changing the shift of `rem' here requires also changing the initial
+ | subtraction from `expDiff'.
+ *--------------------------------------------------------------------*/
+ rem <<= 9;
+ expDiff -= 30;
+ /*--------------------------------------------------------------------
+ | The scale of `sigB' affects how many bits are obtained during each
+ | cycle of the loop. Currently this is 29 bits per loop iteration,
+ | the maximum possible.
+ *--------------------------------------------------------------------*/
+ sigB <<= 9;
+ for (;;) {
+ q64 = (uint32_t) (rem>>32) * (uint_fast64_t) recip32;
+ if ( expDiff < 0 ) break;
+ q = (q64 + 0x80000000)>>32;
+#ifdef SOFTFLOAT_FAST_INT64
+ rem <<= 29;
+#else
+ rem = (uint_fast64_t) (uint32_t) (rem>>3)<<32;
+#endif
+ rem -= q * (uint64_t) sigB;
+ if ( rem & UINT64_C( 0x8000000000000000 ) ) rem += sigB;
+ expDiff -= 29;
+ }
+ /*--------------------------------------------------------------------
+ | (`expDiff' cannot be less than -29 here.)
+ *--------------------------------------------------------------------*/
+ q = (uint32_t) (q64>>32)>>(~expDiff & 31);
+ rem = (rem<<(expDiff + 30)) - q * (uint64_t) sigB;
+ if ( rem & UINT64_C( 0x8000000000000000 ) ) {
+ altRem = rem + sigB;
+ goto selectRem;
+ }
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ do {
+ altRem = rem;
+ ++q;
+ rem -= sigB;
+ } while ( ! (rem & UINT64_C( 0x8000000000000000 )) );
+ selectRem:
+ meanRem = rem + altRem;
+ if (
+ (meanRem & UINT64_C( 0x8000000000000000 )) || (! meanRem && (q & 1))
+ ) {
+ rem = altRem;
+ }
+ signRem = signA;
+ if ( rem & UINT64_C( 0x8000000000000000 ) ) {
+ signRem = ! signRem;
+ rem = -rem;
+ }
+ return softfloat_normRoundPackToF64( signRem, expB, rem );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ propagateNaN:
+ uiZ = softfloat_propagateNaNF64UI( uiA, uiB );
+ goto uiZ;
+ invalid:
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ uiZ = defaultNaNF64UI;
+ uiZ:
+ uZ.ui = uiZ;
+ return uZ.f;
+}
+
+
+
+float64_t f64_sqrt( float64_t a )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ bool signA;
+ int_fast16_t expA;
+ uint_fast64_t sigA, uiZ;
+ struct exp16_sig64 normExpSig;
+ int_fast16_t expZ;
+ uint32_t sig32A, recipSqrt32, sig32Z;
+ uint_fast64_t rem;
+ uint32_t q;
+ uint_fast64_t sigZ, shiftedSigZ;
+ union ui64_f64 uZ;
+
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ uA.f = a;
+ uiA = uA.ui;
+ signA = signF64UI( uiA );
+ expA = expF64UI( uiA );
+ sigA = fracF64UI( uiA );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( expA == 0x7FF ) {
+ if ( sigA ) {
+ uiZ = softfloat_propagateNaNF64UI( uiA, 0 );
+ goto uiZ;
+ }
+ if ( ! signA ) return a;
+ goto invalid;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( signA ) {
+ if ( ! (expA | sigA) ) return a;
+ goto invalid;
+ }
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( ! expA ) {
+ if ( ! sigA ) return a;
+ normExpSig = softfloat_normSubnormalF64Sig( 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 - 0x3FF)>>1) + 0x3FE;
+ expA &= 1;
+ sigA |= UINT64_C( 0x0010000000000000 );
+ sig32A = sigA>>21;
+ recipSqrt32 = softfloat_approxRecipSqrt32_1( expA, sig32A );
+ sig32Z = ((uint_fast64_t) sig32A * recipSqrt32)>>32;
+ if ( expA ) {
+ sigA <<= 8;
+ sig32Z >>= 1;
+ } else {
+ sigA <<= 9;
+ }
+ rem = sigA - (uint_fast64_t) sig32Z * sig32Z;
+ q = ((uint32_t) (rem>>2) * (uint_fast64_t) recipSqrt32)>>32;
+ sigZ = ((uint_fast64_t) sig32Z<<32 | 1<<5) + ((uint_fast64_t) q<<3);
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ if ( (sigZ & 0x1FF) < 0x22 ) {
+ sigZ &= ~(uint_fast64_t) 0x3F;
+ shiftedSigZ = sigZ>>6;
+ rem = (sigA<<52) - shiftedSigZ * shiftedSigZ;
+ if ( rem & UINT64_C( 0x8000000000000000 ) ) {
+ --sigZ;
+ } else {
+ if ( rem ) sigZ |= 1;
+ }
+ }
+ return softfloat_roundPackToF64( 0, expZ, sigZ );
+ /*------------------------------------------------------------------------
+ *------------------------------------------------------------------------*/
+ invalid:
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ uiZ = defaultNaNF64UI;
+ uiZ:
+ uZ.ui = uiZ;
+ return uZ.f;
+}
+
+/*------------------------------------------------------------------------
+| float64_t comparison funcions
+*------------------------------------------------------------------------*/
+
+bool f64_eq( float64_t a, float64_t b )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ union ui64_f64 uB;
+ uint_fast64_t uiB;
+
+ uA.f = a;
+ uiA = uA.ui;
+ uB.f = b;
+ uiB = uB.ui;
+ if ( isNaNF64UI( uiA ) || isNaNF64UI( uiB ) ) {
+ if (
+ softfloat_isSigNaNF64UI( uiA ) || softfloat_isSigNaNF64UI( uiB )
+ ) {
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ }
+ return false;
+ }
+ return (uiA == uiB) || ! ((uiA | uiB) & UINT64_C( 0x7FFFFFFFFFFFFFFF ));
+}
+
+/*less than or equal to*/
+bool f64_le( float64_t a, float64_t b )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ union ui64_f64 uB;
+ uint_fast64_t uiB;
+ bool signA, signB;
+
+ uA.f = a;
+ uiA = uA.ui;
+ uB.f = b;
+ uiB = uB.ui;
+ if ( isNaNF64UI( uiA ) || isNaNF64UI( uiB ) ) {
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ return false;
+ }
+ signA = signF64UI( uiA );
+ signB = signF64UI( uiB );
+ return
+ (signA != signB)
+ ? signA || ! ((uiA | uiB) & UINT64_C( 0x7FFFFFFFFFFFFFFF ))
+ : (uiA == uiB) || (signA ^ (uiA < uiB));
+}
+
+/*less than*/
+bool f64_lt( float64_t a, float64_t b )
+{
+ union ui64_f64 uA;
+ uint_fast64_t uiA;
+ union ui64_f64 uB;
+ uint_fast64_t uiB;
+ bool signA, signB;
+
+ uA.f = a;
+ uiA = uA.ui;
+ uB.f = b;
+ uiB = uB.ui;
+ if ( isNaNF64UI( uiA ) || isNaNF64UI( uiB ) ) {
+ softfloat_raiseFlags( softfloat_flag_invalid );
+ return false;
+ }
+ signA = signF64UI( uiA );
+ signB = signF64UI( uiB );
+ return
+ (signA != signB)
+ ? signA && ((uiA | uiB) & UINT64_C( 0x7FFFFFFFFFFFFFFF ))
+ : (uiA != uiB) && (signA ^ (uiA < uiB));
+}
--- /dev/null
+
+/*============================================================================
+
+This C header file is part of the SoftFloat IEEE Floating-Point Arithmetic
+
+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.
+
+=============================================================================*/
+
+#ifndef primitives_h
+#define primitives_h 1
+#define primitives_h 1
+
+// #include <stdbool.h>
+// #include <stdint.h>
+#include "softfloat/primitiveTypes.h"
+
+#ifndef softfloat_shortShiftRightJam64
+/*----------------------------------------------------------------------------
+| Shifts 'a' right by the number of bits given in 'dist', which must be in
+| the range 1 to 63. If any nonzero bits are shifted off, they are "jammed"
+| into the least-significant bit of the shifted value by setting the least-
+| significant bit to 1. This shifted-and-jammed value is returned.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && (2 <= INLINE_LEVEL)
+INLINE
+uint64_t softfloat_shortShiftRightJam64( uint64_t a, uint_fast8_t dist )
+ { return a>>dist | ((a & (((uint_fast64_t) 1<<dist) - 1)) != 0); }
+#else
+uint64_t softfloat_shortShiftRightJam64( uint64_t a, uint_fast8_t dist );
+#endif
+#endif
+
+#ifndef softfloat_shiftRightJam64
+/*----------------------------------------------------------------------------
+| Shifts 'a' right by the number of bits given in 'dist', which must not
+| be zero. If any nonzero bits are shifted off, they are "jammed" into the
+| least-significant bit of the shifted value by setting the least-significant
+| bit to 1. This shifted-and-jammed value is returned.
+| The value of 'dist' can be arbitrarily large. In particular, if 'dist' is
+| greater than 64, the result will be either 0 or 1, depending on whether 'a'
+| is zero or nonzero.
+*----------------------------------------------------------------------------*/
+#if defined INLINE_LEVEL && (3 <= INLINE_LEVEL)
+INLINE uint64_t softfloat_shiftRightJam64( uint64_t a, uint_fast32_t dist )
+{
+ return
+ (dist < 63) ? a>>dist | ((uint64_t) (a<<(-dist & 63)) != 0) : (a != 0);
+}
+#else
+uint64_t softfloat_shiftRightJam64( uint64_t a, uint_fast32_t dist );
+#endif
+#endif
+
+#ifndef softfloat_shortShiftRightM
+/*----------------------------------------------------------------------------
+| Shifts the N-bit unsigned integer pointed to by 'aPtr' right by the number
+| of bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
+| must be in the range 1 to 31. Any nonzero bits shifted off are lost. The
+| shifted N-bit result is stored at the location pointed to by 'zPtr'. Each
+| of 'aPtr' and 'zPtr' points to a 'size_words'-long array of 32-bit elements
+| that concatenate in the platform's normal endian order to form an N-bit
+| integer.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_shortShiftRightM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ uint_fast8_t dist,
+ uint32_t *zPtr
+ );
+#endif
+
+#ifndef softfloat_shortShiftRight128M
+/*----------------------------------------------------------------------------
+| This function or macro is the same as 'softfloat_shortShiftRightM' with
+| 'size_words' = 4 (N = 128).
+*----------------------------------------------------------------------------*/
+#define softfloat_shortShiftRight128M( aPtr, dist, zPtr ) softfloat_shortShiftRightM( 4, aPtr, dist, zPtr )
+#endif
+
+#ifndef softfloat_shortShiftRightJamM
+/*----------------------------------------------------------------------------
+| Shifts the N-bit unsigned integer pointed to by 'aPtr' right by the number
+| of bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
+| must be in the range 1 to 31. If any nonzero bits are shifted off, they are
+| "jammed" into the least-significant bit of the shifted value by setting the
+| least-significant bit to 1. This shifted-and-jammed N-bit result is stored
+| at the location pointed to by 'zPtr'. Each of 'aPtr' and 'zPtr' points
+| to a 'size_words'-long array of 32-bit elements that concatenate in the
+| platform's normal endian order to form an N-bit integer.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_shortShiftRightJamM(
+ uint_fast8_t, const uint32_t *, uint_fast8_t, uint32_t * );
+#endif
+
+#ifndef softfloat_shiftRightJamM
+/*----------------------------------------------------------------------------
+| Shifts the N-bit unsigned integer pointed to by 'aPtr' right by the number
+| of bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
+| must not be zero. If any nonzero bits are shifted off, they are "jammed"
+| into the least-significant bit of the shifted value by setting the least-
+| significant bit to 1. This shifted-and-jammed N-bit result is stored
+| at the location pointed to by 'zPtr'. Each of 'aPtr' and 'zPtr' points
+| to a 'size_words'-long array of 32-bit elements that concatenate in the
+| platform's normal endian order to form an N-bit integer.
+| The value of 'dist' can be arbitrarily large. In particular, if 'dist'
+| is greater than N, the stored result will be either 0 or 1, depending on
+| whether the original N bits are all zeros.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_shiftRightJamM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ uint32_t dist,
+ uint32_t *zPtr
+ );
+#endif
+
+#ifndef softfloat_shiftRightJam96M
+/*----------------------------------------------------------------------------
+| This function or macro is the same as 'softfloat_shiftRightJamM' with
+| 'size_words' = 3 (N = 96).
+*----------------------------------------------------------------------------*/
+#define softfloat_shiftRightJam96M( aPtr, dist, zPtr ) softfloat_shiftRightJamM( 3, aPtr, dist, zPtr )
+#endif
+
+#ifndef softfloat_shiftRightJam128M
+/*----------------------------------------------------------------------------
+| This function or macro is the same as 'softfloat_shiftRightJamM' with
+| 'size_words' = 4 (N = 128).
+*----------------------------------------------------------------------------*/
+#define softfloat_shiftRightJam128M( aPtr, dist, zPtr ) softfloat_shiftRightJamM( 4, aPtr, dist, zPtr )
+#endif
+
+#ifndef softfloat_shortShiftLeftM
+/*----------------------------------------------------------------------------
+| Shifts the N-bit unsigned integer pointed to by 'aPtr' left by the number
+| of bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
+| must be in the range 1 to 31. Any nonzero bits shifted off are lost. The
+| shifted N-bit result is stored at the location pointed to by 'zPtr'. Each
+| of 'aPtr' and 'zPtr' points to a 'size_words'-long array of 32-bit elements
+| that concatenate in the platform's normal endian order to form an N-bit
+| integer.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_shortShiftLeftM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ uint_fast8_t dist,
+ uint32_t *zPtr
+ );
+#endif
+
+#ifndef softfloat_shiftLeftM
+/*----------------------------------------------------------------------------
+| Shifts the N-bit unsigned integer pointed to by 'aPtr' left by the number
+| of bits given in 'dist', where N = 'size_words' * 32. The value of 'dist'
+| must not be zero. Any nonzero bits shifted off are lost. The shifted
+| N-bit result is stored at the location pointed to by 'zPtr'. Each of 'aPtr'
+| and 'zPtr' points to a 'size_words'-long array of 32-bit elements that
+| concatenate in the platform's normal endian order to form an N-bit integer.
+| The value of 'dist' can be arbitrarily large. In particular, if 'dist' is
+| greater than N, the stored result will be 0.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_shiftLeftM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ uint32_t dist,
+ uint32_t *zPtr
+ );
+#endif
+
+#ifndef softfloat_shiftLeft128M
+/*----------------------------------------------------------------------------
+| This function or macro is the same as 'softfloat_shiftLeftM' with
+| 'size_words' = 4 (N = 128).
+*----------------------------------------------------------------------------*/
+#define softfloat_shiftLeft128M( aPtr, dist, zPtr ) softfloat_shiftLeftM( 4, aPtr, dist, zPtr )
+#endif
+
+#ifndef softfloat_countLeadingZeros64
+/*----------------------------------------------------------------------------
+| Returns the number of leading 0 bits before the most-significant 1 bit of
+| 'a'. If 'a' is zero, 64 is returned.
+*----------------------------------------------------------------------------*/
+uint_fast8_t softfloat_countLeadingZeros64( uint64_t a );
+#endif
+
+extern const uint16_t softfloat_approxRecip_1k0s[16];
+extern const uint16_t softfloat_approxRecip_1k1s[16];
+
+#ifndef softfloat_approxRecip32_1
+/*----------------------------------------------------------------------------
+| Returns an approximation to the reciprocal of the number represented by 'a',
+| where 'a' is interpreted as an unsigned fixed-point number with one integer
+| bit and 31 fraction bits. The 'a' input must be "normalized", meaning that
+| its most-significant bit (bit 31) must be 1. Thus, if A is the value of
+| the fixed-point interpretation of 'a', then 1 <= A < 2. The returned value
+| is interpreted as a pure unsigned fraction, having no integer bits and 32
+| fraction bits. The approximation returned is never greater than the true
+| reciprocal 1/A, and it differs from the true reciprocal by at most 2.006 ulp
+| (units in the last place).
+*----------------------------------------------------------------------------*/
+#ifdef SOFTFLOAT_FAST_DIV64TO32
+#define softfloat_approxRecip32_1( a ) ((uint32_t) (UINT64_C( 0x7FFFFFFFFFFFFFFF ) / (uint32_t) (a)))
+#else
+uint32_t softfloat_approxRecip32_1( uint32_t a );
+#endif
+#endif
+
+extern const uint16_t softfloat_approxRecipSqrt_1k0s[16];
+extern const uint16_t softfloat_approxRecipSqrt_1k1s[16];
+
+#ifndef softfloat_approxRecipSqrt32_1
+/*----------------------------------------------------------------------------
+| Returns an approximation to the reciprocal of the square root of the number
+| represented by 'a', where 'a' is interpreted as an unsigned fixed-point
+| number either with one integer bit and 31 fraction bits or with two integer
+| bits and 30 fraction bits. The format of 'a' is determined by 'oddExpA',
+| which must be either 0 or 1. If 'oddExpA' is 1, 'a' is interpreted as
+| having one integer bit, and if 'oddExpA' is 0, 'a' is interpreted as having
+| two integer bits. The 'a' input must be "normalized", meaning that its
+| most-significant bit (bit 31) must be 1. Thus, if A is the value of the
+| fixed-point interpretation of 'a', it follows that 1 <= A < 2 when 'oddExpA'
+| is 1, and 2 <= A < 4 when 'oddExpA' is 0.
+| The returned value is interpreted as a pure unsigned fraction, having
+| no integer bits and 32 fraction bits. The approximation returned is never
+| greater than the true reciprocal 1/sqrt(A), and it differs from the true
+| reciprocal by at most 2.06 ulp (units in the last place). The approximation
+| returned is also always within the range 0.5 to 1; thus, the most-
+| significant bit of the result is always set.
+*----------------------------------------------------------------------------*/
+uint32_t softfloat_approxRecipSqrt32_1( unsigned int oddExpA, uint32_t a );
+#endif
+
+#ifndef softfloat_mul64To128M
+/*----------------------------------------------------------------------------
+| Multiplies 'a' and 'b' and stores the 128-bit product at the location
+| pointed to by 'zPtr'. Argument 'zPtr' points to an array of four 32-bit
+| elements that concatenate in the platform's normal endian order to form a
+| 128-bit integer.
+*----------------------------------------------------------------------------*/
+void softfloat_mul64To128M( uint64_t a, uint64_t b, uint32_t *zPtr );
+#endif
+
+#ifndef softfloat_negXM
+/*----------------------------------------------------------------------------
+| Replaces the N-bit unsigned integer pointed to by 'zPtr' by the
+| 2s-complement of itself, where N = 'size_words' * 32. Argument 'zPtr'
+| points to a 'size_words'-long array of 32-bit elements that concatenate in
+| the platform's normal endian order to form an N-bit integer.
+*----------------------------------------------------------------------------*/
+void softfloat_negXM( uint_fast8_t size_words, uint32_t *zPtr );
+#endif
+
+#ifndef softfloat_negX128M
+/*----------------------------------------------------------------------------
+| This function or macro is the same as 'softfloat_negXM' with 'size_words'
+| = 4 (N = 128).
+*----------------------------------------------------------------------------*/
+#define softfloat_negX128M( zPtr ) softfloat_negXM( 4, zPtr )
+#endif
+
+#ifndef softfloat_addM
+/*----------------------------------------------------------------------------
+| Adds the two N-bit integers pointed to by 'aPtr' and 'bPtr', where N =
+| 'size_words' * 32. The addition is modulo 2^N, so any carry out is lost.
+| The N-bit sum is stored at the location pointed to by 'zPtr'. Each of
+| 'aPtr', 'bPtr', and 'zPtr' points to a 'size_words'-long array of 32-bit
+| elements that concatenate in the platform's normal endian order to form an
+| N-bit integer.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_addM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ const uint32_t *bPtr,
+ uint32_t *zPtr
+ );
+#endif
+
+#ifndef softfloat_add128M
+/*----------------------------------------------------------------------------
+| This function or macro is the same as 'softfloat_addM' with 'size_words'
+| = 4 (N = 128).
+*----------------------------------------------------------------------------*/
+#define softfloat_add128M( aPtr, bPtr, zPtr ) softfloat_addM( 4, aPtr, bPtr, zPtr )
+#endif
+
+#ifndef softfloat_subM
+/*----------------------------------------------------------------------------
+| Subtracts the two N-bit integers pointed to by 'aPtr' and 'bPtr', where N =
+| 'size_words' * 32. The subtraction is modulo 2^N, so any borrow out (carry
+| out) is lost. The N-bit difference is stored at the location pointed to by
+| 'zPtr'. Each of 'aPtr', 'bPtr', and 'zPtr' points to a 'size_words'-long
+| array of 32-bit elements that concatenate in the platform's normal endian
+| order to form an N-bit integer.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_subM(
+ uint_fast8_t size_words,
+ const uint32_t *aPtr,
+ const uint32_t *bPtr,
+ uint32_t *zPtr
+ );
+#endif
+
+#ifndef softfloat_sub128M
+/*----------------------------------------------------------------------------
+| This function or macro is the same as 'softfloat_subM' with 'size_words'
+| = 4 (N = 128).
+*----------------------------------------------------------------------------*/
+#define softfloat_sub128M( aPtr, bPtr, zPtr ) softfloat_subM( 4, aPtr, bPtr, zPtr )
+#endif
+
+#endif
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