mirror of
https://github.com/mamedev/mame.git
synced 2024-11-16 07:48:32 +01:00
486 lines
15 KiB
C
486 lines
15 KiB
C
/*============================================================================
|
|
This source file is an extension to the SoftFloat IEC/IEEE Floating-point
|
|
Arithmetic Package, Release 2b, written for Bochs (x86 achitecture simulator)
|
|
floating point emulation.
|
|
float_raise(float_flag_invalid)
|
|
THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
|
|
been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
|
|
RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
|
|
AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
|
|
COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
|
|
EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
|
|
INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
|
|
OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
|
|
|
|
Derivative works are acceptable, even for commercial purposes, so long as
|
|
(1) the source code for the derivative work includes prominent notice that
|
|
the work is derivative, and (2) the source code includes prominent notice with
|
|
these four paragraphs for those parts of this code that are retained.
|
|
=============================================================================*/
|
|
|
|
/*============================================================================
|
|
* Written for Bochs (x86 achitecture simulator) by
|
|
* Stanislav Shwartsman [sshwarts at sourceforge net]
|
|
* Adapted for lib/softfloat in MESS by Hans Ostermeyer (03/2012)
|
|
* ==========================================================================*/
|
|
|
|
#define FLOAT128
|
|
|
|
#define USE_estimateDiv128To64
|
|
#include "mamesf.h"
|
|
#include "softfloat.h"
|
|
//#include "softfloat-specialize"
|
|
#include "fpu_constant.h"
|
|
|
|
static const floatx80 floatx80_log10_2 = packFloatx80(0, 0x3ffd, 0x9a209a84fbcff798U);
|
|
static const floatx80 floatx80_ln_2 = packFloatx80(0, 0x3ffe, 0xb17217f7d1cf79acU);
|
|
static const floatx80 floatx80_one = packFloatx80(0, 0x3fff, 0x8000000000000000U);
|
|
static const floatx80 floatx80_default_nan = packFloatx80(0, 0xffff, 0xffffffffffffffffU);
|
|
|
|
#define packFloat_128(zHi, zLo) {(zHi), (zLo)}
|
|
#define PACK_FLOAT_128(hi,lo) packFloat_128(LIT64(hi),LIT64(lo))
|
|
|
|
#define EXP_BIAS 0x3FFF
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the fraction bits of the extended double-precision floating-point
|
|
| value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE bits64 extractFloatx80Frac( floatx80 a )
|
|
{
|
|
return a.low;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the exponent bits of the extended double-precision floating-point
|
|
| value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE int32 extractFloatx80Exp( floatx80 a )
|
|
{
|
|
return a.high & 0x7FFF;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the sign bit of the extended double-precision floating-point value
|
|
| `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE flag extractFloatx80Sign( floatx80 a )
|
|
{
|
|
return a.high>>15;
|
|
|
|
}
|
|
|
|
#if 0
|
|
/*----------------------------------------------------------------------------
|
|
| Takes extended double-precision floating-point NaN `a' and returns the
|
|
| appropriate NaN result. If `a' is a signaling NaN, the invalid exception
|
|
| is raised.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE floatx80 propagateFloatx80NaNOneArg(floatx80 a)
|
|
{
|
|
if (floatx80_is_signaling_nan(a))
|
|
float_raise(float_flag_invalid);
|
|
|
|
a.low |= 0xC000000000000000U;
|
|
|
|
return a;
|
|
}
|
|
#endif
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Normalizes the subnormal extended double-precision floating-point value
|
|
| represented by the denormalized significand `aSig'. The normalized exponent
|
|
| and significand are stored at the locations pointed to by `zExpPtr' and
|
|
| `zSigPtr', respectively.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE void normalizeFloatx80Subnormal(uint64_t aSig, int32_t *zExpPtr, uint64_t *zSigPtr)
|
|
{
|
|
int shiftCount = countLeadingZeros64(aSig);
|
|
*zSigPtr = aSig<<shiftCount;
|
|
*zExpPtr = 1 - shiftCount;
|
|
}
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is a
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
INLINE int floatx80_is_nan(floatx80 a)
|
|
{
|
|
return ((a.high & 0x7FFF) == 0x7FFF) && (int64_t) (a.low<<1);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes two extended double-precision floating-point values `a' and `b', one
|
|
| of which is a NaN, and returns the appropriate NaN result. If either `a' or
|
|
| `b' is a signaling NaN, the invalid exception is raised.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b)
|
|
{
|
|
int aIsNaN = floatx80_is_nan(a);
|
|
int aIsSignalingNaN = floatx80_is_signaling_nan(a);
|
|
int bIsNaN = floatx80_is_nan(b);
|
|
int bIsSignalingNaN = floatx80_is_signaling_nan(b);
|
|
a.low |= 0xC000000000000000U;
|
|
b.low |= 0xC000000000000000U;
|
|
if (aIsSignalingNaN | bIsSignalingNaN) float_raise(float_flag_invalid);
|
|
if (aIsSignalingNaN) {
|
|
if (bIsSignalingNaN) goto returnLargerSignificand;
|
|
return bIsNaN ? b : a;
|
|
}
|
|
else if (aIsNaN) {
|
|
if (bIsSignalingNaN | ! bIsNaN) return a;
|
|
returnLargerSignificand:
|
|
if (a.low < b.low) return b;
|
|
if (b.low < a.low) return a;
|
|
return (a.high < b.high) ? a : b;
|
|
}
|
|
else {
|
|
return b;
|
|
}
|
|
}
|
|
|
|
static const float128 float128_one =
|
|
packFloat_128(0x3fff000000000000U, 0x0000000000000000U);
|
|
static const float128 float128_two =
|
|
packFloat_128(0x4000000000000000U, 0x0000000000000000U);
|
|
|
|
static const float128 float128_ln2inv2 =
|
|
packFloat_128(0x400071547652b82fU, 0xe1777d0ffda0d23aU);
|
|
|
|
#define SQRT2_HALF_SIG 0xb504f333f9de6484U
|
|
|
|
extern float128 OddPoly(float128 x, float128 *arr, unsigned n);
|
|
|
|
#define L2_ARR_SIZE 9
|
|
|
|
static float128 ln_arr[L2_ARR_SIZE] =
|
|
{
|
|
PACK_FLOAT_128(0x3fff000000000000, 0x0000000000000000), /* 1 */
|
|
PACK_FLOAT_128(0x3ffd555555555555, 0x5555555555555555), /* 3 */
|
|
PACK_FLOAT_128(0x3ffc999999999999, 0x999999999999999a), /* 5 */
|
|
PACK_FLOAT_128(0x3ffc249249249249, 0x2492492492492492), /* 7 */
|
|
PACK_FLOAT_128(0x3ffbc71c71c71c71, 0xc71c71c71c71c71c), /* 9 */
|
|
PACK_FLOAT_128(0x3ffb745d1745d174, 0x5d1745d1745d1746), /* 11 */
|
|
PACK_FLOAT_128(0x3ffb3b13b13b13b1, 0x3b13b13b13b13b14), /* 13 */
|
|
PACK_FLOAT_128(0x3ffb111111111111, 0x1111111111111111), /* 15 */
|
|
PACK_FLOAT_128(0x3ffae1e1e1e1e1e1, 0xe1e1e1e1e1e1e1e2) /* 17 */
|
|
};
|
|
|
|
static float128 poly_ln(float128 x1)
|
|
{
|
|
/*
|
|
//
|
|
// 3 5 7 9 11 13 15
|
|
// 1+u u u u u u u u
|
|
// 1/2 ln --- ~ u + --- + --- + --- + --- + ---- + ---- + ---- =
|
|
// 1-u 3 5 7 9 11 13 15
|
|
//
|
|
// 2 4 6 8 10 12 14
|
|
// u u u u u u u
|
|
// = u * [ 1 + --- + --- + --- + --- + ---- + ---- + ---- ] =
|
|
// 3 5 7 9 11 13 15
|
|
//
|
|
// 3 3
|
|
// -- 4k -- 4k+2
|
|
// p(u) = > C * u q(u) = > C * u
|
|
// -- 2k -- 2k+1
|
|
// k=0 k=0
|
|
//
|
|
// 1+u 2
|
|
// 1/2 ln --- ~ u * [ p(u) + u * q(u) ]
|
|
// 1-u
|
|
//
|
|
*/
|
|
return OddPoly(x1, ln_arr, L2_ARR_SIZE);
|
|
}
|
|
|
|
/* required sqrt(2)/2 < x < sqrt(2) */
|
|
static float128 poly_l2(float128 x)
|
|
{
|
|
/* using float128 for approximation */
|
|
float128 x_p1 = float128_add(x, float128_one);
|
|
float128 x_m1 = float128_sub(x, float128_one);
|
|
x = float128_div(x_m1, x_p1);
|
|
x = poly_ln(x);
|
|
x = float128_mul(x, float128_ln2inv2);
|
|
return x;
|
|
}
|
|
|
|
static float128 poly_l2p1(float128 x)
|
|
{
|
|
/* using float128 for approximation */
|
|
float128 x_p2 = float128_add(x, float128_two);
|
|
x = float128_div(x, x_p2);
|
|
x = poly_ln(x);
|
|
x = float128_mul(x, float128_ln2inv2);
|
|
return x;
|
|
}
|
|
|
|
// =================================================
|
|
// FYL2X Compute y * log (x)
|
|
// 2
|
|
// =================================================
|
|
|
|
//
|
|
// Uses the following identities:
|
|
//
|
|
// 1. ----------------------------------------------------------
|
|
// ln(x)
|
|
// log (x) = -------, ln (x*y) = ln(x) + ln(y)
|
|
// 2 ln(2)
|
|
//
|
|
// 2. ----------------------------------------------------------
|
|
// 1+u x-1
|
|
// ln (x) = ln -----, when u = -----
|
|
// 1-u x+1
|
|
//
|
|
// 3. ----------------------------------------------------------
|
|
// 3 5 7 2n+1
|
|
// 1+u u u u u
|
|
// ln ----- = 2 [ u + --- + --- + --- + ... + ------ + ... ]
|
|
// 1-u 3 5 7 2n+1
|
|
//
|
|
|
|
floatx80 fyl2x(floatx80 a, floatx80 b)
|
|
{
|
|
uint64_t aSig = extractFloatx80Frac(a);
|
|
int32_t aExp = extractFloatx80Exp(a);
|
|
int aSign = extractFloatx80Sign(a);
|
|
uint64_t bSig = extractFloatx80Frac(b);
|
|
int32_t bExp = extractFloatx80Exp(b);
|
|
int bSign = extractFloatx80Sign(b);
|
|
|
|
int zSign = bSign ^ 1;
|
|
|
|
if (aExp == 0x7FFF) {
|
|
if ((uint64_t) (aSig<<1)
|
|
|| ((bExp == 0x7FFF) && (uint64_t) (bSig<<1)))
|
|
{
|
|
return propagateFloatx80NaN(a, b);
|
|
}
|
|
if (aSign)
|
|
{
|
|
invalid:
|
|
float_raise(float_flag_invalid);
|
|
return floatx80_default_nan;
|
|
}
|
|
else {
|
|
if (bExp == 0) {
|
|
if (bSig == 0) goto invalid;
|
|
float_raise(float_flag_denormal);
|
|
}
|
|
return packFloatx80(bSign, 0x7FFF, 0x8000000000000000U);
|
|
}
|
|
}
|
|
if (bExp == 0x7FFF)
|
|
{
|
|
if ((uint64_t) (bSig<<1)) return propagateFloatx80NaN(a, b);
|
|
if (aSign && (uint64_t)(aExp | aSig)) goto invalid;
|
|
if (aSig && (aExp == 0))
|
|
float_raise(float_flag_denormal);
|
|
if (aExp < 0x3FFF) {
|
|
return packFloatx80(zSign, 0x7FFF, 0x8000000000000000U);
|
|
}
|
|
if (aExp == 0x3FFF && ((uint64_t) (aSig<<1) == 0)) goto invalid;
|
|
return packFloatx80(bSign, 0x7FFF, 0x8000000000000000U);
|
|
}
|
|
if (aExp == 0) {
|
|
if (aSig == 0) {
|
|
if ((bExp | bSig) == 0) goto invalid;
|
|
float_raise(float_flag_divbyzero);
|
|
return packFloatx80(zSign, 0x7FFF, 0x8000000000000000U);
|
|
}
|
|
if (aSign) goto invalid;
|
|
float_raise(float_flag_denormal);
|
|
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
|
|
}
|
|
if (aSign) goto invalid;
|
|
if (bExp == 0) {
|
|
if (bSig == 0) {
|
|
if (aExp < 0x3FFF) return packFloatx80(zSign, 0, 0);
|
|
return packFloatx80(bSign, 0, 0);
|
|
}
|
|
float_raise(float_flag_denormal);
|
|
normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
|
|
}
|
|
if (aExp == 0x3FFF && ((uint64_t) (aSig<<1) == 0))
|
|
return packFloatx80(bSign, 0, 0);
|
|
|
|
float_raise(float_flag_inexact);
|
|
|
|
int ExpDiff = aExp - 0x3FFF;
|
|
aExp = 0;
|
|
if (aSig >= SQRT2_HALF_SIG) {
|
|
ExpDiff++;
|
|
aExp--;
|
|
}
|
|
|
|
/* ******************************** */
|
|
/* using float128 for approximation */
|
|
/* ******************************** */
|
|
|
|
uint64_t zSig0, zSig1;
|
|
shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1);
|
|
float128 x = packFloat128(0, aExp+0x3FFF, zSig0, zSig1);
|
|
x = poly_l2(x);
|
|
x = float128_add(x, int64_to_float128((int64_t) ExpDiff));
|
|
return floatx80_mul(b, float128_to_floatx80(x));
|
|
}
|
|
|
|
// =================================================
|
|
// FYL2XP1 Compute y * log (x + 1)
|
|
// 2
|
|
// =================================================
|
|
|
|
//
|
|
// Uses the following identities:
|
|
//
|
|
// 1. ----------------------------------------------------------
|
|
// ln(x)
|
|
// log (x) = -------
|
|
// 2 ln(2)
|
|
//
|
|
// 2. ----------------------------------------------------------
|
|
// 1+u x
|
|
// ln (x+1) = ln -----, when u = -----
|
|
// 1-u x+2
|
|
//
|
|
// 3. ----------------------------------------------------------
|
|
// 3 5 7 2n+1
|
|
// 1+u u u u u
|
|
// ln ----- = 2 [ u + --- + --- + --- + ... + ------ + ... ]
|
|
// 1-u 3 5 7 2n+1
|
|
//
|
|
|
|
floatx80 fyl2xp1(floatx80 a, floatx80 b)
|
|
{
|
|
int32_t aExp, bExp;
|
|
uint64_t aSig, bSig, zSig0, zSig1, zSig2;
|
|
int aSign, bSign;
|
|
|
|
aSig = extractFloatx80Frac(a);
|
|
aExp = extractFloatx80Exp(a);
|
|
aSign = extractFloatx80Sign(a);
|
|
bSig = extractFloatx80Frac(b);
|
|
bExp = extractFloatx80Exp(b);
|
|
bSign = extractFloatx80Sign(b);
|
|
int zSign = aSign ^ bSign;
|
|
|
|
if (aExp == 0x7FFF) {
|
|
if ((uint64_t) (aSig<<1)
|
|
|| ((bExp == 0x7FFF) && (uint64_t) (bSig<<1)))
|
|
{
|
|
return propagateFloatx80NaN(a, b);
|
|
}
|
|
if (aSign)
|
|
{
|
|
invalid:
|
|
float_raise(float_flag_invalid);
|
|
return floatx80_default_nan;
|
|
}
|
|
else {
|
|
if (bExp == 0) {
|
|
if (bSig == 0) goto invalid;
|
|
float_raise(float_flag_denormal);
|
|
}
|
|
return packFloatx80(bSign, 0x7FFF, 0x8000000000000000U);
|
|
}
|
|
}
|
|
if (bExp == 0x7FFF)
|
|
{
|
|
if ((uint64_t) (bSig<<1))
|
|
return propagateFloatx80NaN(a, b);
|
|
|
|
if (aExp == 0) {
|
|
if (aSig == 0) goto invalid;
|
|
float_raise(float_flag_denormal);
|
|
}
|
|
|
|
return packFloatx80(zSign, 0x7FFF, 0x8000000000000000U);
|
|
}
|
|
if (aExp == 0) {
|
|
if (aSig == 0) {
|
|
if (bSig && (bExp == 0)) float_raise(float_flag_denormal);
|
|
return packFloatx80(zSign, 0, 0);
|
|
}
|
|
float_raise(float_flag_denormal);
|
|
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
|
|
}
|
|
if (bExp == 0) {
|
|
if (bSig == 0) return packFloatx80(zSign, 0, 0);
|
|
float_raise(float_flag_denormal);
|
|
normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
|
|
}
|
|
|
|
float_raise(float_flag_inexact);
|
|
|
|
if (aSign && aExp >= 0x3FFF)
|
|
return a;
|
|
|
|
if (aExp >= 0x3FFC) // big argument
|
|
{
|
|
return fyl2x(floatx80_add(a, floatx80_one), b);
|
|
}
|
|
|
|
// handle tiny argument
|
|
if (aExp < EXP_BIAS-70)
|
|
{
|
|
// first order approximation, return (a*b)/ln(2)
|
|
int32_t zExp = aExp + FLOAT_LN2INV_EXP - 0x3FFE;
|
|
|
|
mul128By64To192(FLOAT_LN2INV_HI, FLOAT_LN2INV_LO, aSig, &zSig0, &zSig1, &zSig2);
|
|
if (0 < (int64_t) zSig0) {
|
|
shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
|
|
--zExp;
|
|
}
|
|
|
|
zExp = zExp + bExp - 0x3FFE;
|
|
mul128By64To192(zSig0, zSig1, bSig, &zSig0, &zSig1, &zSig2);
|
|
if (0 < (int64_t) zSig0) {
|
|
shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
|
|
--zExp;
|
|
}
|
|
|
|
return
|
|
roundAndPackFloatx80(80, aSign ^ bSign, zExp, zSig0, zSig1);
|
|
}
|
|
|
|
/* ******************************** */
|
|
/* using float128 for approximation */
|
|
/* ******************************** */
|
|
|
|
shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1);
|
|
float128 x = packFloat128(aSign, aExp, zSig0, zSig1);
|
|
x = poly_l2p1(x);
|
|
return floatx80_mul(b, float128_to_floatx80(x));
|
|
}
|
|
|
|
floatx80 floatx80_flognp1(floatx80 a)
|
|
{
|
|
return fyl2xp1(a, floatx80_ln_2);
|
|
}
|
|
|
|
floatx80 floatx80_flogn(floatx80 a)
|
|
{
|
|
return fyl2x(a, floatx80_ln_2);
|
|
}
|
|
|
|
floatx80 floatx80_flog2(floatx80 a)
|
|
{
|
|
return fyl2x(a, floatx80_one);
|
|
}
|
|
|
|
floatx80 floatx80_flog10(floatx80 a)
|
|
{
|
|
return fyl2x(a, floatx80_log10_2);
|
|
}
|