352 lines
12 KiB
C++
Executable File
352 lines
12 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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#include "fpu_constant.h"
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static const floatx80 floatx80_one =
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packFloatx80(0, 0x3fff, BX_CONST64(0x8000000000000000));
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static const float128 float128_one =
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packFloat128(BX_CONST64(0x3fff000000000000), BX_CONST64(0x0000000000000000));
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static const float128 float128_two =
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packFloat128(BX_CONST64(0x4000000000000000), BX_CONST64(0x0000000000000000));
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static const float128 float128_ln2inv2 =
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packFloat128(BX_CONST64(0x400071547652b82f), BX_CONST64(0xe1777d0ffda0d23a));
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#define SQRT2_HALF_SIG BX_CONST64(0xb504f333f9de6484)
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extern float128 OddPoly(float128 x, float128 *arr, unsigned n, float_status_t &status);
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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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packFloat128(BX_CONST64(0x3fff000000000000), BX_CONST64(0x0000000000000000)), /* 1 */
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packFloat128(BX_CONST64(0x3ffd555555555555), BX_CONST64(0x5555555555555555)), /* 3 */
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packFloat128(BX_CONST64(0x3ffc999999999999), BX_CONST64(0x999999999999999a)), /* 5 */
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packFloat128(BX_CONST64(0x3ffc249249249249), BX_CONST64(0x2492492492492492)), /* 7 */
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packFloat128(BX_CONST64(0x3ffbc71c71c71c71), BX_CONST64(0xc71c71c71c71c71c)), /* 9 */
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packFloat128(BX_CONST64(0x3ffb745d1745d174), BX_CONST64(0x5d1745d1745d1746)), /* 11 */
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packFloat128(BX_CONST64(0x3ffb3b13b13b13b1), BX_CONST64(0x3b13b13b13b13b14)), /* 13 */
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packFloat128(BX_CONST64(0x3ffb111111111111), BX_CONST64(0x1111111111111111)), /* 15 */
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packFloat128(BX_CONST64(0x3ffae1e1e1e1e1e1), BX_CONST64(0xe1e1e1e1e1e1e1e2)) /* 17 */
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};
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static float128 poly_ln(float128 x1, float_status_t &status)
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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, status);
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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, float_status_t &status)
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{
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/* using float128 for approximation */
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float128 x_p1 = float128_add(x, float128_one, status);
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float128 x_m1 = float128_sub(x, float128_one, status);
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x = float128_div(x_m1, x_p1, status);
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x = poly_ln(x, status);
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x = float128_mul(x, float128_ln2inv2, status);
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return x;
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}
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static float128 poly_l2p1(float128 x, float_status_t &status)
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{
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/* using float128 for approximation */
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float128 x_p2 = float128_add(x, float128_two, status);
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x = float128_div(x, x_p2, status);
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x = poly_ln(x, status);
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x = float128_mul(x, float128_ln2inv2, status);
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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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floatx80 fyl2x(floatx80 a, floatx80 b, float_status_t &status)
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{
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// handle unsupported extended double-precision floating encodings
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if (floatx80_is_unsupported(a)) {
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invalid:
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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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Bit64u bSig = extractFloatx80Frac(b);
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Bit32s 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 ((Bit64u) (aSig<<1)
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|| ((bExp == 0x7FFF) && (Bit64u) (bSig<<1)))
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{
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return propagateFloatx80NaN(a, b, status);
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}
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if (aSign) goto invalid;
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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(status, float_flag_denormal);
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}
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return packFloatx80(bSign, 0x7FFF, BX_CONST64(0x8000000000000000));
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}
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}
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if (bExp == 0x7FFF)
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{
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if ((Bit64u) (bSig<<1)) return propagateFloatx80NaN(a, b, status);
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if (aSign && (Bit64u)(aExp | aSig)) goto invalid;
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if (aSig && (aExp == 0))
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float_raise(status, float_flag_denormal);
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if (aExp < 0x3FFF) {
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return packFloatx80(zSign, 0x7FFF, BX_CONST64(0x8000000000000000));
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}
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if (aExp == 0x3FFF && ((Bit64u) (aSig<<1) == 0)) goto invalid;
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return packFloatx80(bSign, 0x7FFF, BX_CONST64(0x8000000000000000));
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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(status, float_flag_divbyzero);
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return packFloatx80(zSign, 0x7FFF, BX_CONST64(0x8000000000000000));
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}
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if (aSign) goto invalid;
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float_raise(status, 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(status, float_flag_denormal);
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normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
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}
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if (aExp == 0x3FFF && ((Bit64u) (aSig<<1) == 0))
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return packFloatx80(bSign, 0, 0);
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float_raise(status, 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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float128 x = normalizeRoundAndPackFloat128(0, aExp+0x3FEF, aSig, 0, status);
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x = poly_l2(x, status);
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x = float128_add(x, floatx80_to_float128(int32_to_floatx80(ExpDiff), status), status);
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return floatx80_mul(b, x, status);
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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, float_status_t &status)
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{
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Bit64u aSig, bSig;
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Bit32s aExp, bExp;
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int aSign, bSign;
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// handle unsupported extended double-precision floating encodings
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if (floatx80_is_unsupported(a)) {
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invalid:
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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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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 ((Bit64u) (aSig<<1)
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|| ((bExp == 0x7FFF) && (Bit64u) (bSig<<1)))
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{
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return propagateFloatx80NaN(a, b, status);
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}
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if (aSign) goto invalid;
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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(status, float_flag_denormal);
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}
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return packFloatx80(bSign, 0x7FFF, BX_CONST64(0x8000000000000000));
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}
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}
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if (bExp == 0x7FFF)
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{
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if ((Bit64u) (bSig<<1))
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return propagateFloatx80NaN(a, b, status);
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if (aExp == 0) {
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if (aSig == 0) goto invalid;
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float_raise(status, float_flag_denormal);
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}
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return packFloatx80(zSign, 0x7FFF, BX_CONST64(0x8000000000000000));
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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(status, float_flag_denormal);
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return packFloatx80(zSign, 0, 0);
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}
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float_raise(status, 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(status, float_flag_denormal);
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normalizeFloatx80Subnormal(bSig, &bExp, &bSig);
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}
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float_raise(status, 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, status), b, status);
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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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Bit64u zSig0, zSig1, zSig2;
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Bit32s 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 < (Bit64s) 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 < (Bit64s) 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, status);
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}
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/* ******************************** */
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/* using float128 for approximation */
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/* ******************************** */
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float128 x = normalizeRoundAndPackFloat128(aSign, aExp-0x10, aSig, 0, status);
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x = poly_l2p1(x, status);
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return floatx80_mul(b, x, status);
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}
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