169 lines
6.4 KiB
C++
Executable File
169 lines
6.4 KiB
C++
Executable File
/*============================================================================
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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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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 (gate at fidonet.org.il)
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* ==========================================================================*/
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#define FLOAT128
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#include "softfloatx80.h"
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#include "softfloat-round-pack.h"
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static const floatx80 floatx80_negone = packFloatx80(1, 0x3fff, BX_CONST64(0x8000000000000000));
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static const floatx80 floatx80_neghalf = packFloatx80(1, 0x3ffe, BX_CONST64(0x8000000000000000));
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static const float128 float128_ln2 =
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packFloat128(BX_CONST64(0x3ffe62e42fefa39e), BX_CONST64(0xf35793c7673007e6));
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#define LN2_SIG BX_CONST64(0xb17217f7d1cf79ac)
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#define EXP_ARR_SIZE 15
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static float128 exp_arr[EXP_ARR_SIZE] =
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{
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PACK_FLOAT_128(0x3fff000000000000, 0x0000000000000000), /* 1 */
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PACK_FLOAT_128(0x3ffe000000000000, 0x0000000000000000), /* 2 */
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PACK_FLOAT_128(0x3ffc555555555555, 0x5555555555555555), /* 3 */
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PACK_FLOAT_128(0x3ffa555555555555, 0x5555555555555555), /* 4 */
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PACK_FLOAT_128(0x3ff8111111111111, 0x1111111111111111), /* 5 */
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PACK_FLOAT_128(0x3ff56c16c16c16c1, 0x6c16c16c16c16c17), /* 6 */
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PACK_FLOAT_128(0x3ff2a01a01a01a01, 0xa01a01a01a01a01a), /* 7 */
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PACK_FLOAT_128(0x3fefa01a01a01a01, 0xa01a01a01a01a01a), /* 8 */
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PACK_FLOAT_128(0x3fec71de3a556c73, 0x38faac1c88e50017), /* 9 */
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PACK_FLOAT_128(0x3fe927e4fb7789f5, 0xc72ef016d3ea6679), /* 10 */
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PACK_FLOAT_128(0x3fe5ae64567f544e, 0x38fe747e4b837dc7), /* 11 */
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PACK_FLOAT_128(0x3fe21eed8eff8d89, 0x7b544da987acfe85), /* 12 */
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PACK_FLOAT_128(0x3fde6124613a86d0, 0x97ca38331d23af68), /* 13 */
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PACK_FLOAT_128(0x3fda93974a8c07c9, 0xd20badf145dfa3e5), /* 14 */
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PACK_FLOAT_128(0x3fd6ae7f3e733b81, 0xf11d8656b0ee8cb0) /* 15 */
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};
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extern float128 EvalPoly(float128 x, float128 *arr, unsigned n, float_status_t &status);
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/* required -1 < x < 1 */
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static float128 poly_exp(float128 x, float_status_t &status)
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{
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/*
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// 2 3 4 5 6 7 8 9
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// x x x x x x x x x
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// e - 1 ~ x + --- + --- + --- + --- + --- + --- + --- + --- + ...
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// 2! 3! 4! 5! 6! 7! 8! 9!
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//
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// 2 3 4 5 6 7 8
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// x x x x x x x x
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// = x [ 1 + --- + --- + --- + --- + --- + --- + --- + --- + ... ]
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// 2! 3! 4! 5! 6! 7! 8! 9!
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//
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// 8 8
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// -- 2k -- 2k+1
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// p(x) = > C * x q(x) = > C * x
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// -- 2k -- 2k+1
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// k=0 k=0
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//
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// x
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// e - 1 ~ x * [ p(x) + x * q(x) ]
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//
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*/
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float128 t = EvalPoly(x, exp_arr, EXP_ARR_SIZE, status);
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return float128_mul(t, x, status);
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}
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// =================================================
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// x
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// FX2P1 Compute 2 - 1
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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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// x x*ln(2)
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// 2 = e
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//
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// 2. ----------------------------------------------------------
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// 2 3 4 5 n
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// x x x x x x x
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// e = 1 + --- + --- + --- + --- + --- + ... + --- + ...
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// 1! 2! 3! 4! 5! n!
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//
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floatx80 f2xm1(floatx80 a, float_status_t &status)
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{
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Bit64u zSig0, zSig1;
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// handle unsupported extended double-precision floating encodings
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if (floatx80_is_unsupported(a))
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{
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float_raise(status, float_flag_invalid);
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return floatx80_default_nan;
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}
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Bit64u aSig = extractFloatx80Frac(a);
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Bit32s aExp = extractFloatx80Exp(a);
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int aSign = extractFloatx80Sign(a);
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if (aExp == 0x7FFF) {
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if ((Bit64u) (aSig<<1))
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return propagateFloatx80NaN(a, status);
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return (aSign) ? floatx80_negone : a;
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}
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if (aExp == 0) {
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if (aSig == 0) return a;
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float_raise(status, float_flag_denormal | float_flag_inexact);
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normalizeFloatx80Subnormal(aSig, &aExp, &aSig);
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tiny_argument:
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mul64To128(aSig, LN2_SIG, &zSig0, &zSig1);
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if (0 < (Bit64s) zSig0) {
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shortShift128Left(zSig0, zSig1, 1, &zSig0, &zSig1);
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--aExp;
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}
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return
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roundAndPackFloatx80(80, aSign, aExp, zSig0, zSig1, status);
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}
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float_raise(status, float_flag_inexact);
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if (aExp < 0x3FFF)
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{
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if (aExp < EXP_BIAS-68)
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goto tiny_argument;
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/* ******************************** */
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/* using float128 for approximation */
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/* ******************************** */
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float128 x = floatx80_to_float128(a, status);
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x = float128_mul(x, float128_ln2, status);
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x = poly_exp(x, status);
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return float128_to_floatx80(x, status);
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}
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else
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{
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if ((a.exp == 0xBFFF) && (! (aSig<<1)))
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return floatx80_neghalf;
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return a;
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}
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}
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