179 lines
6.8 KiB
C++
179 lines
6.8 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.
|
|
|
|
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
|
|
|
|
#include "fpu_trans.h"
|
|
#include "softfloat-helpers.h"
|
|
|
|
static const floatx80 floatx80_negone = packFloatx80(1, 0x3fff, BX_CONST64(0x8000000000000000));
|
|
static const floatx80 floatx80_neghalf = packFloatx80(1, 0x3ffe, BX_CONST64(0x8000000000000000));
|
|
static const float128_t float128_ln2 =
|
|
packFloat128(BX_CONST64(0x3ffe62e42fefa39e), BX_CONST64(0xf35793c7673007e6));
|
|
|
|
#ifdef BETTER_THAN_PENTIUM
|
|
|
|
#define LN2_SIG_HI BX_CONST64(0xb17217f7d1cf79ab)
|
|
#define LN2_SIG_LO BX_CONST64(0xc9e3b39800000000) /* 96 bit precision */
|
|
|
|
#else
|
|
|
|
#define LN2_SIG_HI BX_CONST64(0xb17217f7d1cf79ab)
|
|
#define LN2_SIG_LO BX_CONST64(0xc000000000000000) /* 67-bit precision */
|
|
|
|
#endif
|
|
|
|
#define EXP_ARR_SIZE 15
|
|
|
|
static float128_t 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 */
|
|
};
|
|
|
|
extern float128_t EvalPoly(float128_t x, const float128_t *arr, int n, softfloat_status_t &status);
|
|
|
|
/* required -1 < x < 1 */
|
|
static float128_t poly_exp(float128_t x, softfloat_status_t &status)
|
|
{
|
|
/*
|
|
// 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 t = EvalPoly(x, (const float128_t*) exp_arr, EXP_ARR_SIZE, status);
|
|
return f128_mul(t, x, &status);
|
|
}
|
|
|
|
// =================================================
|
|
// 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, softfloat_status_t &status)
|
|
{
|
|
Bit64u zSig0, zSig1, zSig2;
|
|
struct exp32_sig64 normExpSig;
|
|
|
|
// handle unsupported extended double-precision floating encodings
|
|
if (extF80_isUnsupported(a)) {
|
|
softfloat_raiseFlags(&status, softfloat_flag_invalid);
|
|
return floatx80_default_nan;
|
|
}
|
|
|
|
Bit64u aSig = extF80_fraction(a);
|
|
Bit32s aExp = extF80_exp(a);
|
|
int aSign = extF80_sign(a);
|
|
|
|
if (aExp == 0x7FFF) {
|
|
if (aSig << 1)
|
|
return softfloat_propagateNaNExtF80UI(a.signExp, aSig, 0, 0, &status);
|
|
|
|
return (aSign) ? floatx80_negone : a;
|
|
}
|
|
|
|
if (! aExp) {
|
|
if (! aSig) return a;
|
|
softfloat_raiseFlags(&status, softfloat_flag_denormal | softfloat_flag_inexact);
|
|
normExpSig = softfloat_normSubnormalExtF80Sig(aSig);
|
|
aExp = normExpSig.exp + 1;
|
|
aSig = normExpSig.sig;
|
|
|
|
tiny_argument:
|
|
mul128By64To192(LN2_SIG_HI, LN2_SIG_LO, aSig, &zSig0, &zSig1, &zSig2);
|
|
if (0 < (Bit64s) zSig0) {
|
|
shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
|
|
--aExp;
|
|
}
|
|
return softfloat_roundPackToExtF80(aSign, aExp, zSig0, zSig1, 80, &status);
|
|
}
|
|
|
|
softfloat_raiseFlags(&status, softfloat_flag_inexact);
|
|
|
|
if (aExp < 0x3FFF)
|
|
{
|
|
if (aExp < FLOATX80_EXP_BIAS-68)
|
|
goto tiny_argument;
|
|
|
|
/* ******************************** */
|
|
/* using float128 for approximation */
|
|
/* ******************************** */
|
|
|
|
float128_t x = extF80_to_f128(a, &status);
|
|
x = f128_mul(x, float128_ln2, &status);
|
|
x = poly_exp(x, status);
|
|
return f128_to_extF80(x, &status);
|
|
}
|
|
else
|
|
{
|
|
if (a.signExp == 0xBFFF && ! (aSig<<1))
|
|
return floatx80_neghalf;
|
|
|
|
return a;
|
|
}
|
|
}
|