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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;
+ }
+}