diff options
Diffstat (limited to 'target/m68k/softfloat.c')
| -rw-r--r-- | target/m68k/softfloat.c | 1019 |
1 files changed, 1019 insertions, 0 deletions
diff --git a/target/m68k/softfloat.c b/target/m68k/softfloat.c index 9cb141900c..4bd5b9e6b7 100644 --- a/target/m68k/softfloat.c +++ b/target/m68k/softfloat.c @@ -21,6 +21,7 @@ #include "qemu/osdep.h" #include "softfloat.h" #include "fpu/softfloat-macros.h" +#include "softfloat_fpsp_tables.h" static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status) { @@ -247,3 +248,1021 @@ floatx80 floatx80_scale(floatx80 a, floatx80 b, float_status *status) return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, aExp, aSig, 0, status); } + +floatx80 floatx80_move(floatx80 a, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig; + + aSig = extractFloatx80Frac(a); + aExp = extractFloatx80Exp(a); + aSign = extractFloatx80Sign(a); + + if (aExp == 0x7FFF) { + if ((uint64_t)(aSig << 1)) { + return propagateFloatx80NaNOneArg(a, status); + } + return a; + } + if (aExp == 0) { + if (aSig == 0) { + return a; + } + normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision, + aSign, aExp, aSig, 0, status); + } + return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, + aExp, aSig, 0, status); +} + +/*---------------------------------------------------------------------------- +| Algorithms for transcendental functions supported by MC68881 and MC68882 +| mathematical coprocessors. The functions are derived from FPSP library. +*----------------------------------------------------------------------------*/ + +#define one_exp 0x3FFF +#define one_sig LIT64(0x8000000000000000) + +/*---------------------------------------------------------------------------- + | Function for compactifying extended double-precision floating point values. + *----------------------------------------------------------------------------*/ + +static int32_t floatx80_make_compact(int32_t aExp, uint64_t aSig) +{ + return (aExp << 16) | (aSig >> 48); +} + +/*---------------------------------------------------------------------------- + | Log base e of x plus 1 + *----------------------------------------------------------------------------*/ + +floatx80 floatx80_lognp1(floatx80 a, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig, fSig; + + int8_t user_rnd_mode, user_rnd_prec; + + int32_t compact, j, k; + floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu; + + aSig = extractFloatx80Frac(a); + aExp = extractFloatx80Exp(a); + aSign = extractFloatx80Sign(a); + + if (aExp == 0x7FFF) { + if ((uint64_t) (aSig << 1)) { + propagateFloatx80NaNOneArg(a, status); + } + if (aSign) { + float_raise(float_flag_invalid, status); + return floatx80_default_nan(status); + } + return packFloatx80(0, floatx80_infinity.high, floatx80_infinity.low); + } + + if (aExp == 0 && aSig == 0) { + return packFloatx80(aSign, 0, 0); + } + + if (aSign && aExp >= one_exp) { + if (aExp == one_exp && aSig == one_sig) { + float_raise(float_flag_divbyzero, status); + packFloatx80(aSign, floatx80_infinity.high, floatx80_infinity.low); + } + float_raise(float_flag_invalid, status); + return floatx80_default_nan(status); + } + + if (aExp < 0x3f99 || (aExp == 0x3f99 && aSig == one_sig)) { + /* <= min threshold */ + float_raise(float_flag_inexact, status); + return floatx80_move(a, status); + } + + user_rnd_mode = status->float_rounding_mode; + user_rnd_prec = status->floatx80_rounding_precision; + status->float_rounding_mode = float_round_nearest_even; + status->floatx80_rounding_precision = 80; + + compact = floatx80_make_compact(aExp, aSig); + + fp0 = a; /* Z */ + fp1 = a; + + fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), + status), status); /* X = (1+Z) */ + + aExp = extractFloatx80Exp(fp0); + aSig = extractFloatx80Frac(fp0); + + compact = floatx80_make_compact(aExp, aSig); + + if (compact < 0x3FFE8000 || compact > 0x3FFFC000) { + /* |X| < 1/2 or |X| > 3/2 */ + k = aExp - 0x3FFF; + fp1 = int32_to_floatx80(k, status); + + fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000); + j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */ + + f = packFloatx80(0, 0x3FFF, fSig); /* F */ + fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */ + + fp0 = floatx80_sub(fp0, f, status); /* Y-F */ + + lp1cont1: + /* LP1CONT1 */ + fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */ + logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); + klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */ + fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */ + + fp3 = fp2; + fp1 = fp2; + + fp1 = floatx80_mul(fp1, float64_to_floatx80( + make_float64(0x3FC2499AB5E4040B), status), + status); /* V*A6 */ + fp2 = floatx80_mul(fp2, float64_to_floatx80( + make_float64(0xBFC555B5848CB7DB), status), + status); /* V*A5 */ + fp1 = floatx80_add(fp1, float64_to_floatx80( + make_float64(0x3FC99999987D8730), status), + status); /* A4+V*A6 */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0xBFCFFFFFFF6F7E97), status), + status); /* A3+V*A5 */ + fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */ + fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */ + fp1 = floatx80_add(fp1, float64_to_floatx80( + make_float64(0x3FD55555555555A4), status), + status); /* A2+V*(A4+V*A6) */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0xBFE0000000000008), status), + status); /* A1+V*(A3+V*A5) */ + fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */ + fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */ + fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */ + fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */ + + fp1 = floatx80_add(fp1, log_tbl[j + 1], + status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */ + fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */ + + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_add(fp0, klog2, status); + + float_raise(float_flag_inexact, status); + + return a; + } else if (compact < 0x3FFEF07D || compact > 0x3FFF8841) { + /* |X| < 1/16 or |X| > -1/16 */ + /* LP1CARE */ + fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000); + f = packFloatx80(0, 0x3FFF, fSig); /* F */ + j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */ + + if (compact >= 0x3FFF8000) { /* 1+Z >= 1 */ + /* KISZERO */ + fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x3F800000), + status), f, status); /* 1-F */ + fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (1-F)+Z */ + fp1 = packFloatx80(0, 0, 0); /* K = 0 */ + } else { + /* KISNEG */ + fp0 = floatx80_sub(float32_to_floatx80(make_float32(0x40000000), + status), f, status); /* 2-F */ + fp1 = floatx80_add(fp1, fp1, status); /* 2Z */ + fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS Y-F = (2-F)+2Z */ + fp1 = packFloatx80(1, one_exp, one_sig); /* K = -1 */ + } + goto lp1cont1; + } else { + /* LP1ONE16 */ + fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2Z */ + fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), + status), status); /* FP0 IS 1+X */ + + /* LP1CONT2 */ + fp1 = floatx80_div(fp1, fp0, status); /* U */ + saveu = fp1; + fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */ + fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */ + + fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6), + status); /* B5 */ + fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0), + status); /* B4 */ + fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */ + fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */ + fp3 = floatx80_add(fp3, float64_to_floatx80( + make_float64(0x3F624924928BCCFF), status), + status); /* B3+W*B5 */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0x3F899999999995EC), status), + status); /* B2+W*B4 */ + fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */ + fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */ + fp1 = floatx80_add(fp1, float64_to_floatx80( + make_float64(0x3FB5555555555555), status), + status); /* B1+W*(B3+W*B5) */ + + fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */ + fp1 = floatx80_add(fp1, fp2, + status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */ + fp0 = floatx80_mul(fp0, fp1, + status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */ + + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_add(fp0, saveu, status); + + /*if (!floatx80_is_zero(a)) { */ + float_raise(float_flag_inexact, status); + /*} */ + + return a; + } +} + +/*---------------------------------------------------------------------------- + | Log base e + *----------------------------------------------------------------------------*/ + +floatx80 floatx80_logn(floatx80 a, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig, fSig; + + int8_t user_rnd_mode, user_rnd_prec; + + int32_t compact, j, k, adjk; + floatx80 fp0, fp1, fp2, fp3, f, logof2, klog2, saveu; + + aSig = extractFloatx80Frac(a); + aExp = extractFloatx80Exp(a); + aSign = extractFloatx80Sign(a); + + if (aExp == 0x7FFF) { + if ((uint64_t) (aSig << 1)) { + propagateFloatx80NaNOneArg(a, status); + } + if (aSign == 0) { + return packFloatx80(0, floatx80_infinity.high, + floatx80_infinity.low); + } + } + + adjk = 0; + + if (aExp == 0) { + if (aSig == 0) { /* zero */ + float_raise(float_flag_divbyzero, status); + return packFloatx80(1, floatx80_infinity.high, + floatx80_infinity.low); + } + if ((aSig & one_sig) == 0) { /* denormal */ + normalizeFloatx80Subnormal(aSig, &aExp, &aSig); + adjk = -100; + aExp += 100; + a = packFloatx80(aSign, aExp, aSig); + } + } + + if (aSign) { + float_raise(float_flag_invalid, status); + return floatx80_default_nan(status); + } + + user_rnd_mode = status->float_rounding_mode; + user_rnd_prec = status->floatx80_rounding_precision; + status->float_rounding_mode = float_round_nearest_even; + status->floatx80_rounding_precision = 80; + + compact = floatx80_make_compact(aExp, aSig); + + if (compact < 0x3FFEF07D || compact > 0x3FFF8841) { + /* |X| < 15/16 or |X| > 17/16 */ + k = aExp - 0x3FFF; + k += adjk; + fp1 = int32_to_floatx80(k, status); + + fSig = (aSig & LIT64(0xFE00000000000000)) | LIT64(0x0100000000000000); + j = (fSig >> 56) & 0x7E; /* DISPLACEMENT FOR 1/F */ + + f = packFloatx80(0, 0x3FFF, fSig); /* F */ + fp0 = packFloatx80(0, 0x3FFF, aSig); /* Y */ + + fp0 = floatx80_sub(fp0, f, status); /* Y-F */ + + /* LP1CONT1 */ + fp0 = floatx80_mul(fp0, log_tbl[j], status); /* FP0 IS U = (Y-F)/F */ + logof2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); + klog2 = floatx80_mul(fp1, logof2, status); /* FP1 IS K*LOG2 */ + fp2 = floatx80_mul(fp0, fp0, status); /* FP2 IS V=U*U */ + + fp3 = fp2; + fp1 = fp2; + + fp1 = floatx80_mul(fp1, float64_to_floatx80( + make_float64(0x3FC2499AB5E4040B), status), + status); /* V*A6 */ + fp2 = floatx80_mul(fp2, float64_to_floatx80( + make_float64(0xBFC555B5848CB7DB), status), + status); /* V*A5 */ + fp1 = floatx80_add(fp1, float64_to_floatx80( + make_float64(0x3FC99999987D8730), status), + status); /* A4+V*A6 */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0xBFCFFFFFFF6F7E97), status), + status); /* A3+V*A5 */ + fp1 = floatx80_mul(fp1, fp3, status); /* V*(A4+V*A6) */ + fp2 = floatx80_mul(fp2, fp3, status); /* V*(A3+V*A5) */ + fp1 = floatx80_add(fp1, float64_to_floatx80( + make_float64(0x3FD55555555555A4), status), + status); /* A2+V*(A4+V*A6) */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0xBFE0000000000008), status), + status); /* A1+V*(A3+V*A5) */ + fp1 = floatx80_mul(fp1, fp3, status); /* V*(A2+V*(A4+V*A6)) */ + fp2 = floatx80_mul(fp2, fp3, status); /* V*(A1+V*(A3+V*A5)) */ + fp1 = floatx80_mul(fp1, fp0, status); /* U*V*(A2+V*(A4+V*A6)) */ + fp0 = floatx80_add(fp0, fp2, status); /* U+V*(A1+V*(A3+V*A5)) */ + + fp1 = floatx80_add(fp1, log_tbl[j + 1], + status); /* LOG(F)+U*V*(A2+V*(A4+V*A6)) */ + fp0 = floatx80_add(fp0, fp1, status); /* FP0 IS LOG(F) + LOG(1+U) */ + + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_add(fp0, klog2, status); + + float_raise(float_flag_inexact, status); + + return a; + } else { /* |X-1| >= 1/16 */ + fp0 = a; + fp1 = a; + fp1 = floatx80_sub(fp1, float32_to_floatx80(make_float32(0x3F800000), + status), status); /* FP1 IS X-1 */ + fp0 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), + status), status); /* FP0 IS X+1 */ + fp1 = floatx80_add(fp1, fp1, status); /* FP1 IS 2(X-1) */ + + /* LP1CONT2 */ + fp1 = floatx80_div(fp1, fp0, status); /* U */ + saveu = fp1; + fp0 = floatx80_mul(fp1, fp1, status); /* FP0 IS V = U*U */ + fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS W = V*V */ + + fp3 = float64_to_floatx80(make_float64(0x3F175496ADD7DAD6), + status); /* B5 */ + fp2 = float64_to_floatx80(make_float64(0x3F3C71C2FE80C7E0), + status); /* B4 */ + fp3 = floatx80_mul(fp3, fp1, status); /* W*B5 */ + fp2 = floatx80_mul(fp2, fp1, status); /* W*B4 */ + fp3 = floatx80_add(fp3, float64_to_floatx80( + make_float64(0x3F624924928BCCFF), status), + status); /* B3+W*B5 */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0x3F899999999995EC), status), + status); /* B2+W*B4 */ + fp1 = floatx80_mul(fp1, fp3, status); /* W*(B3+W*B5) */ + fp2 = floatx80_mul(fp2, fp0, status); /* V*(B2+W*B4) */ + fp1 = floatx80_add(fp1, float64_to_floatx80( + make_float64(0x3FB5555555555555), status), + status); /* B1+W*(B3+W*B5) */ + + fp0 = floatx80_mul(fp0, saveu, status); /* FP0 IS U*V */ + fp1 = floatx80_add(fp1, fp2, status); /* B1+W*(B3+W*B5) + V*(B2+W*B4) */ + fp0 = floatx80_mul(fp0, fp1, + status); /* U*V*([B1+W*(B3+W*B5)] + [V*(B2+W*B4)]) */ + + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_add(fp0, saveu, status); + + /*if (!floatx80_is_zero(a)) { */ + float_raise(float_flag_inexact, status); + /*} */ + + return a; + } +} + +/*---------------------------------------------------------------------------- + | Log base 10 + *----------------------------------------------------------------------------*/ + +floatx80 floatx80_log10(floatx80 a, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig; + + int8_t user_rnd_mode, user_rnd_prec; + + floatx80 fp0, fp1; + + aSig = extractFloatx80Frac(a); + aExp = extractFloatx80Exp(a); + aSign = extractFloatx80Sign(a); + + if (aExp == 0x7FFF) { + if ((uint64_t) (aSig << 1)) { + propagateFloatx80NaNOneArg(a, status); + } + if (aSign == 0) { + return packFloatx80(0, floatx80_infinity.high, + floatx80_infinity.low); + } + } + + if (aExp == 0 && aSig == 0) { + float_raise(float_flag_divbyzero, status); + return packFloatx80(1, floatx80_infinity.high, + floatx80_infinity.low); + } + + if (aSign) { + float_raise(float_flag_invalid, status); + return floatx80_default_nan(status); + } + + user_rnd_mode = status->float_rounding_mode; + user_rnd_prec = status->floatx80_rounding_precision; + status->float_rounding_mode = float_round_nearest_even; + status->floatx80_rounding_precision = 80; + + fp0 = floatx80_logn(a, status); + fp1 = packFloatx80(0, 0x3FFD, LIT64(0xDE5BD8A937287195)); /* INV_L10 */ + + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L10 */ + + float_raise(float_flag_inexact, status); + + return a; +} + +/*---------------------------------------------------------------------------- + | Log base 2 + *----------------------------------------------------------------------------*/ + +floatx80 floatx80_log2(floatx80 a, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig; + + int8_t user_rnd_mode, user_rnd_prec; + + floatx80 fp0, fp1; + + aSig = extractFloatx80Frac(a); + aExp = extractFloatx80Exp(a); + aSign = extractFloatx80Sign(a); + + if (aExp == 0x7FFF) { + if ((uint64_t) (aSig << 1)) { + propagateFloatx80NaNOneArg(a, status); + } + if (aSign == 0) { + return packFloatx80(0, floatx80_infinity.high, + floatx80_infinity.low); + } + } + + if (aExp == 0) { + if (aSig == 0) { + float_raise(float_flag_divbyzero, status); + return packFloatx80(1, floatx80_infinity.high, + floatx80_infinity.low); + } + normalizeFloatx80Subnormal(aSig, &aExp, &aSig); + } + + if (aSign) { + float_raise(float_flag_invalid, status); + return floatx80_default_nan(status); + } + + user_rnd_mode = status->float_rounding_mode; + user_rnd_prec = status->floatx80_rounding_precision; + status->float_rounding_mode = float_round_nearest_even; + status->floatx80_rounding_precision = 80; + + if (aSig == one_sig) { /* X is 2^k */ + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = int32_to_floatx80(aExp - 0x3FFF, status); + } else { + fp0 = floatx80_logn(a, status); + fp1 = packFloatx80(0, 0x3FFF, LIT64(0xB8AA3B295C17F0BC)); /* INV_L2 */ + + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_mul(fp0, fp1, status); /* LOGN(X)*INV_L2 */ + } + + float_raise(float_flag_inexact, status); + + return a; +} + +/*---------------------------------------------------------------------------- + | e to x + *----------------------------------------------------------------------------*/ + +floatx80 floatx80_etox(floatx80 a, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig; + + int8_t user_rnd_mode, user_rnd_prec; + + int32_t compact, n, j, k, m, m1; + floatx80 fp0, fp1, fp2, fp3, l2, scale, adjscale; + flag adjflag; + + aSig = extractFloatx80Frac(a); + aExp = extractFloatx80Exp(a); + aSign = extractFloatx80Sign(a); + + if (aExp == 0x7FFF) { + if ((uint64_t) (aSig << 1)) { + return propagateFloatx80NaNOneArg(a, status); + } + if (aSign) { + return packFloatx80(0, 0, 0); + } + return packFloatx80(0, floatx80_infinity.high, + floatx80_infinity.low); + } + + if (aExp == 0 && aSig == 0) { + return packFloatx80(0, one_exp, one_sig); + } + + user_rnd_mode = status->float_rounding_mode; + user_rnd_prec = status->floatx80_rounding_precision; + status->float_rounding_mode = float_round_nearest_even; + status->floatx80_rounding_precision = 80; + + adjflag = 0; + + if (aExp >= 0x3FBE) { /* |X| >= 2^(-65) */ + compact = floatx80_make_compact(aExp, aSig); + + if (compact < 0x400CB167) { /* |X| < 16380 log2 */ + fp0 = a; + fp1 = a; + fp0 = floatx80_mul(fp0, float32_to_floatx80( + make_float32(0x42B8AA3B), status), + status); /* 64/log2 * X */ + adjflag = 0; + n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */ + fp0 = int32_to_floatx80(n, status); + + j = n & 0x3F; /* J = N mod 64 */ + m = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ + if (n < 0 && j) { + /* arithmetic right shift is division and + * round towards minus infinity + */ + m--; + } + m += 0x3FFF; /* biased exponent of 2^(M) */ + + expcont1: + fp2 = fp0; /* N */ + fp0 = floatx80_mul(fp0, float32_to_floatx80( + make_float32(0xBC317218), status), + status); /* N * L1, L1 = lead(-log2/64) */ + l2 = packFloatx80(0, 0x3FDC, LIT64(0x82E308654361C4C6)); + fp2 = floatx80_mul(fp2, l2, status); /* N * L2, L1+L2 = -log2/64 */ + fp0 = floatx80_add(fp0, fp1, status); /* X + N*L1 */ + fp0 = floatx80_add(fp0, fp2, status); /* R */ + + fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ + fp2 = float32_to_floatx80(make_float32(0x3AB60B70), + status); /* A5 */ + fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A5 */ + fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3C088895), + status), fp1, + status); /* fp3 is S*A4 */ + fp2 = floatx80_add(fp2, float64_to_floatx80(make_float64( + 0x3FA5555555554431), status), + status); /* fp2 is A3+S*A5 */ + fp3 = floatx80_add(fp3, float64_to_floatx80(make_float64( + 0x3FC5555555554018), status), + status); /* fp3 is A2+S*A4 */ + fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*(A3+S*A5) */ + fp3 = floatx80_mul(fp3, fp1, status); /* fp3 is S*(A2+S*A4) */ + fp2 = floatx80_add(fp2, float32_to_floatx80( + make_float32(0x3F000000), status), + status); /* fp2 is A1+S*(A3+S*A5) */ + fp3 = floatx80_mul(fp3, fp0, status); /* fp3 IS R*S*(A2+S*A4) */ + fp2 = floatx80_mul(fp2, fp1, + status); /* fp2 IS S*(A1+S*(A3+S*A5)) */ + fp0 = floatx80_add(fp0, fp3, status); /* fp0 IS R+R*S*(A2+S*A4) */ + fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */ + + fp1 = exp_tbl[j]; + fp0 = floatx80_mul(fp0, fp1, status); /* 2^(J/64)*(Exp(R)-1) */ + fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status), + status); /* accurate 2^(J/64) */ + fp0 = floatx80_add(fp0, fp1, + status); /* 2^(J/64) + 2^(J/64)*(Exp(R)-1) */ + + scale = packFloatx80(0, m, one_sig); + if (adjflag) { + adjscale = packFloatx80(0, m1, one_sig); + fp0 = floatx80_mul(fp0, adjscale, status); + } + + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_mul(fp0, scale, status); + + float_raise(float_flag_inexact, status); + + return a; + } else { /* |X| >= 16380 log2 */ + if (compact > 0x400CB27C) { /* |X| >= 16480 log2 */ + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + if (aSign) { + a = roundAndPackFloatx80( + status->floatx80_rounding_precision, + 0, -0x1000, aSig, 0, status); + } else { + a = roundAndPackFloatx80( + status->floatx80_rounding_precision, + 0, 0x8000, aSig, 0, status); + } + float_raise(float_flag_inexact, status); + + return a; + } else { + fp0 = a; + fp1 = a; + fp0 = floatx80_mul(fp0, float32_to_floatx80( + make_float32(0x42B8AA3B), status), + status); /* 64/log2 * X */ + adjflag = 1; + n = floatx80_to_int32(fp0, status); /* int(64/log2*X) */ + fp0 = int32_to_floatx80(n, status); + + j = n & 0x3F; /* J = N mod 64 */ + /* NOTE: this is really arithmetic right shift by 6 */ + k = n / 64; + if (n < 0 && j) { + /* arithmetic right shift is division and + * round towards minus infinity + */ + k--; + } + /* NOTE: this is really arithmetic right shift by 1 */ + m1 = k / 2; + if (k < 0 && (k & 1)) { + /* arithmetic right shift is division and + * round towards minus infinity + */ + m1--; + } + m = k - m1; + m1 += 0x3FFF; /* biased exponent of 2^(M1) */ + m += 0x3FFF; /* biased exponent of 2^(M) */ + + goto expcont1; + } + } + } else { /* |X| < 2^(-65) */ + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_add(a, float32_to_floatx80(make_float32(0x3F800000), + status), status); /* 1 + X */ + + float_raise(float_flag_inexact, status); + + return a; + } +} + +/*---------------------------------------------------------------------------- + | 2 to x + *----------------------------------------------------------------------------*/ + +floatx80 floatx80_twotox(floatx80 a, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig; + + int8_t user_rnd_mode, user_rnd_prec; + + int32_t compact, n, j, l, m, m1; + floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2; + + aSig = extractFloatx80Frac(a); + aExp = extractFloatx80Exp(a); + aSign = extractFloatx80Sign(a); + + if (aExp == 0x7FFF) { + if ((uint64_t) (aSig << 1)) { + return propagateFloatx80NaNOneArg(a, status); + } + if (aSign) { + return packFloatx80(0, 0, 0); + } + return packFloatx80(0, floatx80_infinity.high, + floatx80_infinity.low); + } + + if (aExp == 0 && aSig == 0) { + return packFloatx80(0, one_exp, one_sig); + } + + user_rnd_mode = status->float_rounding_mode; + user_rnd_prec = status->floatx80_rounding_precision; + status->float_rounding_mode = float_round_nearest_even; + status->floatx80_rounding_precision = 80; + + fp0 = a; + + compact = floatx80_make_compact(aExp, aSig); + + if (compact < 0x3FB98000 || compact > 0x400D80C0) { + /* |X| > 16480 or |X| < 2^(-70) */ + if (compact > 0x3FFF8000) { /* |X| > 16480 */ + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + if (aSign) { + return roundAndPackFloatx80(status->floatx80_rounding_precision, + 0, -0x1000, aSig, 0, status); + } else { + return roundAndPackFloatx80(status->floatx80_rounding_precision, + 0, 0x8000, aSig, 0, status); + } + } else { /* |X| < 2^(-70) */ + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_add(fp0, float32_to_floatx80( + make_float32(0x3F800000), status), + status); /* 1 + X */ + + float_raise(float_flag_inexact, status); + + return a; + } + } else { /* 2^(-70) <= |X| <= 16480 */ + fp1 = fp0; /* X */ + fp1 = floatx80_mul(fp1, float32_to_floatx80( + make_float32(0x42800000), status), + status); /* X * 64 */ + n = floatx80_to_int32(fp1, status); + fp1 = int32_to_floatx80(n, status); + j = n & 0x3F; + l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ + if (n < 0 && j) { + /* arithmetic right shift is division and + * round towards minus infinity + */ + l--; + } + m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */ + if (l < 0 && (l & 1)) { + /* arithmetic right shift is division and + * round towards minus infinity + */ + m--; + } + m1 = l - m; + m1 += 0x3FFF; /* ADJFACT IS 2^(M') */ + + adjfact = packFloatx80(0, m1, one_sig); + fact1 = exp2_tbl[j]; + fact1.high += m; + fact2.high = exp2_tbl2[j] >> 16; + fact2.high += m; + fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF); + fact2.low <<= 48; + + fp1 = floatx80_mul(fp1, float32_to_floatx80( + make_float32(0x3C800000), status), + status); /* (1/64)*N */ + fp0 = floatx80_sub(fp0, fp1, status); /* X - (1/64)*INT(64 X) */ + fp2 = packFloatx80(0, 0x3FFE, LIT64(0xB17217F7D1CF79AC)); /* LOG2 */ + fp0 = floatx80_mul(fp0, fp2, status); /* R */ + + /* EXPR */ + fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ + fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2), + status); /* A5 */ + fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C), + status); /* A4 */ + fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */ + fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0x3FA5555555554CC1), status), + status); /* A3+S*A5 */ + fp3 = floatx80_add(fp3, float64_to_floatx80( + make_float64(0x3FC5555555554A54), status), + status); /* A2+S*A4 */ + fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */ + fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0x3FE0000000000000), status), + status); /* A1+S*(A3+S*A5) */ + fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */ + + fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */ + fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */ + fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */ + + fp0 = floatx80_mul(fp0, fact1, status); + fp0 = floatx80_add(fp0, fact2, status); + fp0 = floatx80_add(fp0, fact1, status); + + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_mul(fp0, adjfact, status); + + float_raise(float_flag_inexact, status); + + return a; + } +} + +/*---------------------------------------------------------------------------- + | 10 to x + *----------------------------------------------------------------------------*/ + +floatx80 floatx80_tentox(floatx80 a, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig; + + int8_t user_rnd_mode, user_rnd_prec; + + int32_t compact, n, j, l, m, m1; + floatx80 fp0, fp1, fp2, fp3, adjfact, fact1, fact2; + + aSig = extractFloatx80Frac(a); + aExp = extractFloatx80Exp(a); + aSign = extractFloatx80Sign(a); + + if (aExp == 0x7FFF) { + if ((uint64_t) (aSig << 1)) { + return propagateFloatx80NaNOneArg(a, status); + } + if (aSign) { + return packFloatx80(0, 0, 0); + } + return packFloatx80(0, floatx80_infinity.high, + floatx80_infinity.low); + } + + if (aExp == 0 && aSig == 0) { + return packFloatx80(0, one_exp, one_sig); + } + + user_rnd_mode = status->float_rounding_mode; + user_rnd_prec = status->floatx80_rounding_precision; + status->float_rounding_mode = float_round_nearest_even; + status->floatx80_rounding_precision = 80; + + fp0 = a; + + compact = floatx80_make_compact(aExp, aSig); + + if (compact < 0x3FB98000 || compact > 0x400B9B07) { + /* |X| > 16480 LOG2/LOG10 or |X| < 2^(-70) */ + if (compact > 0x3FFF8000) { /* |X| > 16480 */ + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + if (aSign) { + return roundAndPackFloatx80(status->floatx80_rounding_precision, + 0, -0x1000, aSig, 0, status); + } else { + return roundAndPackFloatx80(status->floatx80_rounding_precision, + 0, 0x8000, aSig, 0, status); + } + } else { /* |X| < 2^(-70) */ + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_add(fp0, float32_to_floatx80( + make_float32(0x3F800000), status), + status); /* 1 + X */ + + float_raise(float_flag_inexact, status); + + return a; + } + } else { /* 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10 */ + fp1 = fp0; /* X */ + fp1 = floatx80_mul(fp1, float64_to_floatx80( + make_float64(0x406A934F0979A371), + status), status); /* X*64*LOG10/LOG2 */ + n = floatx80_to_int32(fp1, status); /* N=INT(X*64*LOG10/LOG2) */ + fp1 = int32_to_floatx80(n, status); + + j = n & 0x3F; + l = n / 64; /* NOTE: this is really arithmetic right shift by 6 */ + if (n < 0 && j) { + /* arithmetic right shift is division and + * round towards minus infinity + */ + l--; + } + m = l / 2; /* NOTE: this is really arithmetic right shift by 1 */ + if (l < 0 && (l & 1)) { + /* arithmetic right shift is division and + * round towards minus infinity + */ + m--; + } + m1 = l - m; + m1 += 0x3FFF; /* ADJFACT IS 2^(M') */ + + adjfact = packFloatx80(0, m1, one_sig); + fact1 = exp2_tbl[j]; + fact1.high += m; + fact2.high = exp2_tbl2[j] >> 16; + fact2.high += m; + fact2.low = (uint64_t)(exp2_tbl2[j] & 0xFFFF); + fact2.low <<= 48; + + fp2 = fp1; /* N */ + fp1 = floatx80_mul(fp1, float64_to_floatx80( + make_float64(0x3F734413509F8000), status), + status); /* N*(LOG2/64LOG10)_LEAD */ + fp3 = packFloatx80(1, 0x3FCD, LIT64(0xC0219DC1DA994FD2)); + fp2 = floatx80_mul(fp2, fp3, status); /* N*(LOG2/64LOG10)_TRAIL */ + fp0 = floatx80_sub(fp0, fp1, status); /* X - N L_LEAD */ + fp0 = floatx80_sub(fp0, fp2, status); /* X - N L_TRAIL */ + fp2 = packFloatx80(0, 0x4000, LIT64(0x935D8DDDAAA8AC17)); /* LOG10 */ + fp0 = floatx80_mul(fp0, fp2, status); /* R */ + + /* EXPR */ + fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ + fp2 = float64_to_floatx80(make_float64(0x3F56C16D6F7BD0B2), + status); /* A5 */ + fp3 = float64_to_floatx80(make_float64(0x3F811112302C712C), + status); /* A4 */ + fp2 = floatx80_mul(fp2, fp1, status); /* S*A5 */ + fp3 = floatx80_mul(fp3, fp1, status); /* S*A4 */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0x3FA5555555554CC1), status), + status); /* A3+S*A5 */ + fp3 = floatx80_add(fp3, float64_to_floatx80( + make_float64(0x3FC5555555554A54), status), + status); /* A2+S*A4 */ + fp2 = floatx80_mul(fp2, fp1, status); /* S*(A3+S*A5) */ + fp3 = floatx80_mul(fp3, fp1, status); /* S*(A2+S*A4) */ + fp2 = floatx80_add(fp2, float64_to_floatx80( + make_float64(0x3FE0000000000000), status), + status); /* A1+S*(A3+S*A5) */ + fp3 = floatx80_mul(fp3, fp0, status); /* R*S*(A2+S*A4) */ + + fp2 = floatx80_mul(fp2, fp1, status); /* S*(A1+S*(A3+S*A5)) */ + fp0 = floatx80_add(fp0, fp3, status); /* R+R*S*(A2+S*A4) */ + fp0 = floatx80_add(fp0, fp2, status); /* EXP(R) - 1 */ + + fp0 = floatx80_mul(fp0, fact1, status); + fp0 = floatx80_add(fp0, fact2, status); + fp0 = floatx80_add(fp0, fact1, status); + + status->float_rounding_mode = user_rnd_mode; + status->floatx80_rounding_precision = user_rnd_prec; + + a = floatx80_mul(fp0, adjfact, status); + + float_raise(float_flag_inexact, status); + + return a; + } +} |