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/*============================================================================
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.
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]
* ==========================================================================*/
#define FLOAT128
#define USE_estimateDiv128To64
#include "mamesf.h"
#include "softfloat.h"
#include "fpu_constant.h"
#define packFloat_128(zHi, zLo) {(zHi), (zLo)}
#define PACK_FLOAT_128(hi,lo) packFloat_128(LIT64(hi),LIT64(lo))
static const floatx80 floatx80_negone = packFloatx80(1, 0x3fff, 0x8000000000000000U);
static const floatx80 floatx80_neghalf = packFloatx80(1, 0x3ffe, 0x8000000000000000U);
static const float128 float128_ln2 =
packFloat_128(0x3ffe62e42fefa39eU, 0xf35793c7673007e6U);
#define LN2_SIG_HI 0xb17217f7d1cf79abU
#define LN2_SIG_LO 0xc000000000000000U /* 67-bit precision */
#define EXP_ARR_SIZE 15
static float128 exp_arr[EXP_ARR_SIZE] =
{
PACK_FLOAT_128(0x3fff000000000000, 0x0000000000000000), /* 1 */
PACK_FLOAT_128(0x3ffe000000000000, 0x0000000000000000), /* 2 */
PACK_FLOAT_128(0x3ffc555555555555, 0x5555555555555555), /* 3 */
PACK_FLOAT_128(0x3ffa555555555555, 0x5555555555555555), /* 4 */
PACK_FLOAT_128(0x3ff8111111111111, 0x1111111111111111), /* 5 */
PACK_FLOAT_128(0x3ff56c16c16c16c1, 0x6c16c16c16c16c17), /* 6 */
PACK_FLOAT_128(0x3ff2a01a01a01a01, 0xa01a01a01a01a01a), /* 7 */
PACK_FLOAT_128(0x3fefa01a01a01a01, 0xa01a01a01a01a01a), /* 8 */
PACK_FLOAT_128(0x3fec71de3a556c73, 0x38faac1c88e50017), /* 9 */
PACK_FLOAT_128(0x3fe927e4fb7789f5, 0xc72ef016d3ea6679), /* 10 */
PACK_FLOAT_128(0x3fe5ae64567f544e, 0x38fe747e4b837dc7), /* 11 */
PACK_FLOAT_128(0x3fe21eed8eff8d89, 0x7b544da987acfe85), /* 12 */
PACK_FLOAT_128(0x3fde6124613a86d0, 0x97ca38331d23af68), /* 13 */
PACK_FLOAT_128(0x3fda93974a8c07c9, 0xd20badf145dfa3e5), /* 14 */
PACK_FLOAT_128(0x3fd6ae7f3e733b81, 0xf11d8656b0ee8cb0) /* 15 */
};
#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;
}
/*----------------------------------------------------------------------------
| 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;
}
/*----------------------------------------------------------------------------
| 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 propagateFloatx80NaN(floatx80 a)
{
if (floatx80_is_signaling_nan(a))
float_raise(float_flag_invalid);
a.low |= 0xC000000000000000U;
return a;
}
// 2 3 4 n
// f(x) ~ C + (C * x) + (C * x) + (C * x) + (C * x) + ... + (C * x)
// 0 1 2 3 4 n
//
// -- 2k -- 2k+1
// p(x) = > C * x q(x) = > C * x
// -- 2k -- 2k+1
//
// f(x) ~ [ p(x) + x * q(x) ]
//
static float128 EvalPoly(float128 x, float128 *arr, unsigned n)
{
float128 x2 = float128_mul(x, x);
unsigned i;
assert(n > 1);
float128 r1 = arr[--n];
i = n;
while(i >= 2) {
r1 = float128_mul(r1, x2);
i -= 2;
r1 = float128_add(r1, arr[i]);
}
if (i) r1 = float128_mul(r1, x);
float128 r2 = arr[--n];
i = n;
while(i >= 2) {
r2 = float128_mul(r2, x2);
i -= 2;
r2 = float128_add(r2, arr[i]);
}
if (i) r2 = float128_mul(r2, x);
return float128_add(r1, r2);
}
/* required -1 < x < 1 */
static float128 poly_exp(float128 x)
{
/*
// 2 3 4 5 6 7 8 9
// x x x x x x x x x
// e - 1 ~ x + --- + --- + --- + --- + --- + --- + --- + --- + ...
// 2! 3! 4! 5! 6! 7! 8! 9!
//
// 2 3 4 5 6 7 8
// x x x x x x x x
// = x [ 1 + --- + --- + --- + --- + --- + --- + --- + --- + ... ]
// 2! 3! 4! 5! 6! 7! 8! 9!
//
// 8 8
// -- 2k -- 2k+1
// p(x) = > C * x q(x) = > C * x
// -- 2k -- 2k+1
// k=0 k=0
//
// x
// e - 1 ~ x * [ p(x) + x * q(x) ]
//
*/
float128 t = EvalPoly(x, exp_arr, EXP_ARR_SIZE);
return float128_mul(t, x);
}
// =================================================
// x
// FX2M1 Compute 2 - 1
// =================================================
//
// Uses the following identities:
//
// 1. ----------------------------------------------------------
// x x*ln(2)
// 2 = e
//
// 2. ----------------------------------------------------------
// 2 3 4 5 n
// x x x x x x x
// e = 1 + --- + --- + --- + --- + --- + ... + --- + ...
// 1! 2! 3! 4! 5! n!
//
floatx80 f2xm1(floatx80 a)
{
bits64 zSig0, zSig1, zSig2;
bits64 aSig = extractFloatx80Frac(a);
sbits32 aExp = extractFloatx80Exp(a);
int aSign = extractFloatx80Sign(a);
if (aExp == 0x7FFF) {
if ((bits64) (aSig<<1))
return propagateFloatx80NaN(a);
return (aSign) ? floatx80_negone : a;
}
if (aExp == 0) {
if (aSig == 0) return a;
float_raise(float_flag_denormal | float_flag_inexact);
normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
tiny_argument:
mul128By64To192(LN2_SIG_HI, LN2_SIG_LO, aSig, &zSig0, &zSig1, &zSig2);
if (0 < (sbits64) zSig0) {
shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
--aExp;
}
return
roundAndPackFloatx80(80, aSign, aExp, zSig0, zSig1);
}
float_raise(float_flag_inexact);
if (aExp < 0x3FFF)
{
if (aExp < EXP_BIAS-68)
goto tiny_argument;
/* ******************************** */
/* using float128 for approximation */
/* ******************************** */
float128 x = floatx80_to_float128(a);
x = float128_mul(x, float128_ln2);
x = poly_exp(x);
return float128_to_floatx80(x);
}
else
{
if (a.high == 0xBFFF && ! (aSig<<1))
return floatx80_neghalf;
return a;
}
}
|
