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8179a84458
* New abbreviated types are in osd and util namespaces, and also in global namespace for things that #include "emu.h" * Get rid of import of cstdint types to global namespace (C99 does this anyway) * Remove the cstdint types from everything in emu * Get rid of U64/S64 macros * Fix a bug in dps16 caused by incorrect use of macro * Fix debugcon not checking for "do " prefix case-insensitively * Fix a lot of messed up tabulation * More constexpr * Fix up many __names
486 lines
15 KiB
C
486 lines
15 KiB
C
/*============================================================================
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This source file is an extension to the SoftFloat IEC/IEEE Floating-point
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Arithmetic Package, Release 2b, written for Bochs (x86 achitecture simulator)
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floating point emulation.
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float_raise(float_flag_invalid)
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THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
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been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
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RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
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AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
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COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
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EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
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INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
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OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
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Derivative works are acceptable, even for commercial purposes, so long as
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(1) the source code for the derivative work includes prominent notice that
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the work is derivative, and (2) the source code includes prominent notice with
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these four paragraphs for those parts of this code that are retained.
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=============================================================================*/
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/*============================================================================
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* Written for Bochs (x86 achitecture simulator) by
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* Stanislav Shwartsman [sshwarts at sourceforge net]
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* Adapted for lib/softfloat in MESS by Hans Ostermeyer (03/2012)
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* ==========================================================================*/
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#define FLOAT128
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#define USE_estimateDiv128To64
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#include "mamesf.h"
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#include "softfloat.h"
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//#include "softfloat-specialize"
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#include "fpu_constant.h"
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static const floatx80 floatx80_log10_2 = packFloatx80(0, 0x3ffd, 0x9a209a84fbcff798U);
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static const floatx80 floatx80_ln_2 = packFloatx80(0, 0x3ffe, 0xb17217f7d1cf79acU);
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static const floatx80 floatx80_one = packFloatx80(0, 0x3fff, 0x8000000000000000U);
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static const floatx80 floatx80_default_nan = packFloatx80(0, 0xffff, 0xffffffffffffffffU);
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#define packFloat_128(zHi, zLo) {(zHi), (zLo)}
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#define PACK_FLOAT_128(hi,lo) packFloat_128(LIT64(hi),LIT64(lo))
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#define EXP_BIAS 0x3FFF
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/*----------------------------------------------------------------------------
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| Returns the fraction bits of the extended double-precision floating-point
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| value `a'.
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*----------------------------------------------------------------------------*/
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INLINE bits64 extractFloatx80Frac( floatx80 a )
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{
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return a.low;
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}
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/*----------------------------------------------------------------------------
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| Returns the exponent bits of the extended double-precision floating-point
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| value `a'.
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*----------------------------------------------------------------------------*/
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INLINE int32 extractFloatx80Exp( floatx80 a )
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{
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return a.high & 0x7FFF;
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}
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/*----------------------------------------------------------------------------
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| Returns the sign bit of the extended double-precision floating-point value
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| `a'.
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*----------------------------------------------------------------------------*/
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INLINE flag extractFloatx80Sign( floatx80 a )
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{
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return a.high>>15;
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}
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#if 0
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/*----------------------------------------------------------------------------
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| Takes extended double-precision floating-point NaN `a' and returns the
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| appropriate NaN result. If `a' is a signaling NaN, the invalid exception
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| is raised.
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*----------------------------------------------------------------------------*/
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INLINE floatx80 propagateFloatx80NaNOneArg(floatx80 a)
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{
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if (floatx80_is_signaling_nan(a))
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float_raise(float_flag_invalid);
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a.low |= 0xC000000000000000U;
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return a;
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}
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#endif
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/*----------------------------------------------------------------------------
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| Normalizes the subnormal extended double-precision floating-point value
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| represented by the denormalized significand `aSig'. The normalized exponent
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| and significand are stored at the locations pointed to by `zExpPtr' and
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| `zSigPtr', respectively.
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*----------------------------------------------------------------------------*/
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INLINE void normalizeFloatx80Subnormal(uint64_t aSig, int32_t *zExpPtr, uint64_t *zSigPtr)
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{
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int shiftCount = countLeadingZeros64(aSig);
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*zSigPtr = aSig<<shiftCount;
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*zExpPtr = 1 - shiftCount;
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}
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/*----------------------------------------------------------------------------
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| Returns 1 if the extended double-precision floating-point value `a' is a
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| NaN; otherwise returns 0.
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*----------------------------------------------------------------------------*/
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INLINE int floatx80_is_nan(floatx80 a)
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{
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return ((a.high & 0x7FFF) == 0x7FFF) && (int64_t) (a.low<<1);
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}
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/*----------------------------------------------------------------------------
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| Takes two extended double-precision floating-point values `a' and `b', one
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| of which is a NaN, and returns the appropriate NaN result. If either `a' or
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| `b' is a signaling NaN, the invalid exception is raised.
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*----------------------------------------------------------------------------*/
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static floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b)
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{
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int aIsNaN = floatx80_is_nan(a);
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int aIsSignalingNaN = floatx80_is_signaling_nan(a);
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int bIsNaN = floatx80_is_nan(b);
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int bIsSignalingNaN = floatx80_is_signaling_nan(b);
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a.low |= 0xC000000000000000U;
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b.low |= 0xC000000000000000U;
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if (aIsSignalingNaN | bIsSignalingNaN) float_raise(float_flag_invalid);
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if (aIsSignalingNaN) {
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if (bIsSignalingNaN) goto returnLargerSignificand;
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return bIsNaN ? b : a;
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}
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else if (aIsNaN) {
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if (bIsSignalingNaN | ! bIsNaN) return a;
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returnLargerSignificand:
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if (a.low < b.low) return b;
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if (b.low < a.low) return a;
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return (a.high < b.high) ? a : b;
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}
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else {
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return b;
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}
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}
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static const float128 float128_one =
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packFloat_128(0x3fff000000000000U, 0x0000000000000000U);
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static const float128 float128_two =
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packFloat_128(0x4000000000000000U, 0x0000000000000000U);
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static const float128 float128_ln2inv2 =
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packFloat_128(0x400071547652b82fU, 0xe1777d0ffda0d23aU);
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#define SQRT2_HALF_SIG 0xb504f333f9de6484U
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extern float128 OddPoly(float128 x, float128 *arr, unsigned n);
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#define L2_ARR_SIZE 9
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static float128 ln_arr[L2_ARR_SIZE] =
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{
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PACK_FLOAT_128(0x3fff000000000000, 0x0000000000000000), /* 1 */
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PACK_FLOAT_128(0x3ffd555555555555, 0x5555555555555555), /* 3 */
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PACK_FLOAT_128(0x3ffc999999999999, 0x999999999999999a), /* 5 */
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PACK_FLOAT_128(0x3ffc249249249249, 0x2492492492492492), /* 7 */
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PACK_FLOAT_128(0x3ffbc71c71c71c71, 0xc71c71c71c71c71c), /* 9 */
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PACK_FLOAT_128(0x3ffb745d1745d174, 0x5d1745d1745d1746), /* 11 */
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PACK_FLOAT_128(0x3ffb3b13b13b13b1, 0x3b13b13b13b13b14), /* 13 */
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PACK_FLOAT_128(0x3ffb111111111111, 0x1111111111111111), /* 15 */
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PACK_FLOAT_128(0x3ffae1e1e1e1e1e1, 0xe1e1e1e1e1e1e1e2) /* 17 */
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};
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static float128 poly_ln(float128 x1)
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{
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/*
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//
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// 3 5 7 9 11 13 15
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// 1+u u u u u u u u
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// 1/2 ln --- ~ u + --- + --- + --- + --- + ---- + ---- + ---- =
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// 1-u 3 5 7 9 11 13 15
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//
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// 2 4 6 8 10 12 14
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// u u u u u u u
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// = u * [ 1 + --- + --- + --- + --- + ---- + ---- + ---- ] =
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// 3 5 7 9 11 13 15
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//
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// 3 3
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// -- 4k -- 4k+2
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// p(u) = > C * u q(u) = > C * u
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// -- 2k -- 2k+1
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// k=0 k=0
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//
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// 1+u 2
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// 1/2 ln --- ~ u * [ p(u) + u * q(u) ]
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// 1-u
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//
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*/
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return OddPoly(x1, ln_arr, L2_ARR_SIZE);
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}
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/* required sqrt(2)/2 < x < sqrt(2) */
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static float128 poly_l2(float128 x)
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{
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/* using float128 for approximation */
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float128 x_p1 = float128_add(x, float128_one);
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float128 x_m1 = float128_sub(x, float128_one);
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x = float128_div(x_m1, x_p1);
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x = poly_ln(x);
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x = float128_mul(x, float128_ln2inv2);
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return x;
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}
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static float128 poly_l2p1(float128 x)
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{
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/* using float128 for approximation */
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float128 x_p2 = float128_add(x, float128_two);
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x = float128_div(x, x_p2);
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x = poly_ln(x);
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x = float128_mul(x, float128_ln2inv2);
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return x;
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}
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// =================================================
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// FYL2X Compute y * log (x)
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// 2
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// =================================================
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//
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// Uses the following identities:
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//
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// 1. ----------------------------------------------------------
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// ln(x)
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// log (x) = -------, ln (x*y) = ln(x) + ln(y)
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// 2 ln(2)
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//
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// 2. ----------------------------------------------------------
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// 1+u x-1
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// ln (x) = ln -----, when u = -----
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// 1-u x+1
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//
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// 3. ----------------------------------------------------------
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// 3 5 7 2n+1
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// 1+u u u u u
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// ln ----- = 2 [ u + --- + --- + --- + ... + ------ + ... ]
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// 1-u 3 5 7 2n+1
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//
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static floatx80 fyl2x(floatx80 a, floatx80 b)
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{
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uint64_t aSig = extractFloatx80Frac(a);
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int32_t aExp = extractFloatx80Exp(a);
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int aSign = extractFloatx80Sign(a);
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uint64_t bSig = extractFloatx80Frac(b);
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int32_t bExp = extractFloatx80Exp(b);
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int bSign = extractFloatx80Sign(b);
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int zSign = bSign ^ 1;
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if (aExp == 0x7FFF) {
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if ((uint64_t) (aSig<<1)
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|| ((bExp == 0x7FFF) && (uint64_t) (bSig<<1)))
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{
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return propagateFloatx80NaN(a, b);
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}
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if (aSign)
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{
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invalid:
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float_raise(float_flag_invalid);
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return floatx80_default_nan;
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}
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else {
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if (bExp == 0) {
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if (bSig == 0) goto invalid;
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float_raise(float_flag_denormal);
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}
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return packFloatx80(bSign, 0x7FFF, 0x8000000000000000U);
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}
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}
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if (bExp == 0x7FFF)
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{
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if ((uint64_t) (bSig<<1)) return propagateFloatx80NaN(a, b);
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if (aSign && (uint64_t)(aExp | aSig)) goto invalid;
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if (aSig && (aExp == 0))
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float_raise(float_flag_denormal);
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if (aExp < 0x3FFF) {
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return packFloatx80(zSign, 0x7FFF, 0x8000000000000000U);
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}
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if (aExp == 0x3FFF && ((uint64_t) (aSig<<1) == 0)) goto invalid;
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return packFloatx80(bSign, 0x7FFF, 0x8000000000000000U);
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}
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if (aExp == 0) {
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if (aSig == 0) {
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if ((bExp | bSig) == 0) goto invalid;
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float_raise(float_flag_divbyzero);
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return packFloatx80(zSign, 0x7FFF, 0x8000000000000000U);
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}
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if (aSign) goto invalid;
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float_raise(float_flag_denormal);
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normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
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}
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if (aSign) goto invalid;
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if (bExp == 0) {
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if (bSig == 0) {
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if (aExp < 0x3FFF) return packFloatx80(zSign, 0, 0);
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return packFloatx80(bSign, 0, 0);
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}
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float_raise(float_flag_denormal);
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normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
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}
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if (aExp == 0x3FFF && ((uint64_t) (aSig<<1) == 0))
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return packFloatx80(bSign, 0, 0);
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float_raise(float_flag_inexact);
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int ExpDiff = aExp - 0x3FFF;
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aExp = 0;
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if (aSig >= SQRT2_HALF_SIG) {
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ExpDiff++;
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aExp--;
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}
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/* ******************************** */
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/* using float128 for approximation */
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/* ******************************** */
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uint64_t zSig0, zSig1;
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shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1);
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float128 x = packFloat128(0, aExp+0x3FFF, zSig0, zSig1);
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x = poly_l2(x);
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x = float128_add(x, int64_to_float128((int64_t) ExpDiff));
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return floatx80_mul(b, float128_to_floatx80(x));
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}
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// =================================================
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// FYL2XP1 Compute y * log (x + 1)
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// 2
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// =================================================
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//
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// Uses the following identities:
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//
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// 1. ----------------------------------------------------------
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// ln(x)
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// log (x) = -------
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// 2 ln(2)
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//
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// 2. ----------------------------------------------------------
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// 1+u x
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// ln (x+1) = ln -----, when u = -----
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// 1-u x+2
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//
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// 3. ----------------------------------------------------------
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// 3 5 7 2n+1
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// 1+u u u u u
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// ln ----- = 2 [ u + --- + --- + --- + ... + ------ + ... ]
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// 1-u 3 5 7 2n+1
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//
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floatx80 fyl2xp1(floatx80 a, floatx80 b)
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{
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int32_t aExp, bExp;
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uint64_t aSig, bSig, zSig0, zSig1, zSig2;
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int aSign, bSign;
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aSig = extractFloatx80Frac(a);
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aExp = extractFloatx80Exp(a);
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aSign = extractFloatx80Sign(a);
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bSig = extractFloatx80Frac(b);
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bExp = extractFloatx80Exp(b);
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bSign = extractFloatx80Sign(b);
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int zSign = aSign ^ bSign;
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if (aExp == 0x7FFF) {
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if ((uint64_t) (aSig<<1)
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|| ((bExp == 0x7FFF) && (uint64_t) (bSig<<1)))
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{
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return propagateFloatx80NaN(a, b);
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}
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if (aSign)
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{
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invalid:
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float_raise(float_flag_invalid);
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return floatx80_default_nan;
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}
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else {
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if (bExp == 0) {
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if (bSig == 0) goto invalid;
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float_raise(float_flag_denormal);
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}
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return packFloatx80(bSign, 0x7FFF, 0x8000000000000000U);
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}
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}
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if (bExp == 0x7FFF)
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{
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if ((uint64_t) (bSig<<1))
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return propagateFloatx80NaN(a, b);
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if (aExp == 0) {
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if (aSig == 0) goto invalid;
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float_raise(float_flag_denormal);
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}
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return packFloatx80(zSign, 0x7FFF, 0x8000000000000000U);
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}
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if (aExp == 0) {
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if (aSig == 0) {
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if (bSig && (bExp == 0)) float_raise(float_flag_denormal);
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return packFloatx80(zSign, 0, 0);
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}
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float_raise(float_flag_denormal);
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normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
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}
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if (bExp == 0) {
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if (bSig == 0) return packFloatx80(zSign, 0, 0);
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float_raise(float_flag_denormal);
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normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
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}
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float_raise(float_flag_inexact);
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if (aSign && aExp >= 0x3FFF)
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return a;
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if (aExp >= 0x3FFC) // big argument
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{
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return fyl2x(floatx80_add(a, floatx80_one), b);
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}
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// handle tiny argument
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if (aExp < EXP_BIAS-70)
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{
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// first order approximation, return (a*b)/ln(2)
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int32_t zExp = aExp + FLOAT_LN2INV_EXP - 0x3FFE;
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mul128By64To192(FLOAT_LN2INV_HI, FLOAT_LN2INV_LO, aSig, &zSig0, &zSig1, &zSig2);
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if (0 < (int64_t) zSig0) {
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shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
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--zExp;
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}
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zExp = zExp + bExp - 0x3FFE;
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mul128By64To192(zSig0, zSig1, bSig, &zSig0, &zSig1, &zSig2);
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if (0 < (int64_t) zSig0) {
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shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
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--zExp;
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}
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return
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roundAndPackFloatx80(80, aSign ^ bSign, zExp, zSig0, zSig1);
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}
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/* ******************************** */
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/* using float128 for approximation */
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/* ******************************** */
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shift128Right(aSig<<1, 0, 16, &zSig0, &zSig1);
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float128 x = packFloat128(aSign, aExp, zSig0, zSig1);
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x = poly_l2p1(x);
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return floatx80_mul(b, float128_to_floatx80(x));
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}
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floatx80 floatx80_flognp1(floatx80 a)
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{
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return fyl2xp1(a, floatx80_ln_2);
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}
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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);
|
|
}
|