--- /dev/null
+/*============================================================================
+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 "m68kcpu.h" // which includes softfloat.h after defining the basic types
+
+//#include "softfloat-specialize"
+#include "fpu_constant.h"
+
+#define floatx80_log10_2 packFloatx80(0, 0x3ffd, 0x9a209a84fbcff798U)
+#define floatx80_ln_2 packFloatx80(0, 0x3ffe, 0xb17217f7d1cf79acU)
+#define floatx80_one packFloatx80(0, 0x3fff, 0x8000000000000000U)
+#define 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'.
+*----------------------------------------------------------------------------*/
+
+static inline bits64 extractFloatx80Frac( floatx80 a )
+{
+ return a.low;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the exponent bits of the extended double-precision floating-point
+| value `a'.
+*----------------------------------------------------------------------------*/
+
+static inline int32 extractFloatx80Exp( floatx80 a )
+{
+ return a.high & 0x7FFF;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the sign bit of the extended double-precision floating-point value
+| `a'.
+*----------------------------------------------------------------------------*/
+
+static 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.
+*----------------------------------------------------------------------------*/
+
+static 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.
+*----------------------------------------------------------------------------*/
+
+static 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.
+*----------------------------------------------------------------------------*/
+
+static 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
+//
+
+static 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);
+}
projects / pistorm / blobdiff