/* * Ported from a work by Andreas Grabher for Previous, NeXT Computer Emulator, * derived from NetBSD M68040 FPSP functions, * derived from release 2a of the SoftFloat IEC/IEEE Floating-point Arithmetic * Package. Those parts of the code (and some later contributions) are * provided under that license, as detailed below. * It has subsequently been modified by contributors to the QEMU Project, * so some portions are provided under: * the SoftFloat-2a license * the BSD license * GPL-v2-or-later * * Any future contributions to this file will be taken to be licensed under * the Softfloat-2a license unless specifically indicated otherwise. */ /* * Portions of this work are licensed under the terms of the GNU GPL, * version 2 or later. See the COPYING file in the top-level directory. */ #include "qemu/osdep.h" #include "softfloat.h" #include "fpu/softfloat-macros.h" #include "softfloat_fpsp_tables.h" #define pi_exp 0x4000 #define piby2_exp 0x3FFF #define pi_sig UINT64_C(0xc90fdaa22168c235) static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status) { if (floatx80_is_signaling_nan(a, status)) { float_raise(float_flag_invalid, status); a = floatx80_silence_nan(a, status); } if (status->default_nan_mode) { return floatx80_default_nan(status); } return a; } /* * Returns the modulo remainder of the extended double-precision floating-point * value `a' with respect to the corresponding value `b'. */ floatx80 floatx80_mod(floatx80 a, floatx80 b, float_status *status) { flag aSign, zSign; int32_t aExp, bExp, expDiff; uint64_t aSig0, aSig1, bSig; uint64_t qTemp, term0, term1; aSig0 = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); bSig = extractFloatx80Frac(b); bExp = extractFloatx80Exp(b); if (aExp == 0x7FFF) { if ((uint64_t) (aSig0 << 1) || ((bExp == 0x7FFF) && (uint64_t) (bSig << 1))) { return propagateFloatx80NaN(a, b, status); } goto invalid; } if (bExp == 0x7FFF) { if ((uint64_t) (bSig << 1)) { return propagateFloatx80NaN(a, b, status); } return a; } if (bExp == 0) { if (bSig == 0) { invalid: float_raise(float_flag_invalid, status); return floatx80_default_nan(status); } normalizeFloatx80Subnormal(bSig, &bExp, &bSig); } if (aExp == 0) { if ((uint64_t) (aSig0 << 1) == 0) { return a; } normalizeFloatx80Subnormal(aSig0, &aExp, &aSig0); } bSig |= UINT64_C(0x8000000000000000); zSign = aSign; expDiff = aExp - bExp; aSig1 = 0; if (expDiff < 0) { return a; } qTemp = (bSig <= aSig0); if (qTemp) { aSig0 -= bSig; } expDiff -= 64; while (0 < expDiff) { qTemp = estimateDiv128To64(aSig0, aSig1, bSig); qTemp = (2 < qTemp) ? qTemp - 2 : 0; mul64To128(bSig, qTemp, &term0, &term1); sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1); shortShift128Left(aSig0, aSig1, 62, &aSig0, &aSig1); expDiff -= 62; } expDiff += 64; if (0 < expDiff) { qTemp = estimateDiv128To64(aSig0, aSig1, bSig); qTemp = (2 < qTemp) ? qTemp - 2 : 0; qTemp >>= 64 - expDiff; mul64To128(bSig, qTemp << (64 - expDiff), &term0, &term1); sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1); shortShift128Left(0, bSig, 64 - expDiff, &term0, &term1); while (le128(term0, term1, aSig0, aSig1)) { ++qTemp; sub128(aSig0, aSig1, term0, term1, &aSig0, &aSig1); } } return normalizeRoundAndPackFloatx80( 80, zSign, bExp + expDiff, aSig0, aSig1, status); } /* * Returns the mantissa of the extended double-precision floating-point * value `a'. */ floatx80 floatx80_getman(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); } float_raise(float_flag_invalid , status); return floatx80_default_nan(status); } if (aExp == 0) { if (aSig == 0) { return packFloatx80(aSign, 0, 0); } normalizeFloatx80Subnormal(aSig, &aExp, &aSig); } return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, 0x3FFF, aSig, 0, status); } /* * Returns the exponent of the extended double-precision floating-point * value `a' as an extended double-precision value. */ floatx80 floatx80_getexp(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); } float_raise(float_flag_invalid , status); return floatx80_default_nan(status); } if (aExp == 0) { if (aSig == 0) { return packFloatx80(aSign, 0, 0); } normalizeFloatx80Subnormal(aSig, &aExp, &aSig); } return int32_to_floatx80(aExp - 0x3FFF, status); } /* * Scales extended double-precision floating-point value in operand `a' by * value `b'. The function truncates the value in the second operand 'b' to * an integral value and adds that value to the exponent of the operand 'a'. * The operation performed according to the IEC/IEEE Standard for Binary * Floating-Point Arithmetic. */ floatx80 floatx80_scale(floatx80 a, floatx80 b, float_status *status) { flag aSign, bSign; int32_t aExp, bExp, shiftCount; uint64_t aSig, bSig; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); bSig = extractFloatx80Frac(b); bExp = extractFloatx80Exp(b); bSign = extractFloatx80Sign(b); if (bExp == 0x7FFF) { if ((uint64_t) (bSig << 1) || ((aExp == 0x7FFF) && (uint64_t) (aSig << 1))) { return propagateFloatx80NaN(a, b, status); } float_raise(float_flag_invalid , status); return floatx80_default_nan(status); } if (aExp == 0x7FFF) { if ((uint64_t) (aSig << 1)) { return propagateFloatx80NaN(a, b, status); } return packFloatx80(aSign, floatx80_infinity.high, floatx80_infinity.low); } if (aExp == 0) { if (aSig == 0) { return packFloatx80(aSign, 0, 0); } if (bExp < 0x3FFF) { return a; } normalizeFloatx80Subnormal(aSig, &aExp, &aSig); } if (bExp < 0x3FFF) { return a; } if (0x400F < bExp) { aExp = bSign ? -0x6001 : 0xE000; return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, aExp, aSig, 0, status); } shiftCount = 0x403E - bExp; bSig >>= shiftCount; aExp = bSign ? (aExp - bSig) : (aExp + bSig); 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 UINT64_C(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); return 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 & UINT64_C(0xFE00000000000000)) | UINT64_C(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, UINT64_C(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 & UINT64_C(0xFE00000000000000)) | UINT64_C(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 & UINT64_C(0xFE00000000000000)) | UINT64_C(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, UINT64_C(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, UINT64_C(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, UINT64_C(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, UINT64_C(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, UINT64_C(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, UINT64_C(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, UINT64_C(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; } } /* * Tangent */ floatx80 floatx80_tan(floatx80 a, float_status *status) { flag aSign, xSign; int32_t aExp, xExp; uint64_t aSig, xSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact, l, n, j; floatx80 fp0, fp1, fp2, fp3, fp4, fp5, invtwopi, twopi1, twopi2; float32 twoto63; flag endflag; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); if (aExp == 0x7FFF) { if ((uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } float_raise(float_flag_invalid, status); return floatx80_default_nan(status); } if (aExp == 0 && aSig == 0) { return packFloatx80(aSign, 0, 0); } 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; if (compact < 0x3FD78000 || compact > 0x4004BC7E) { /* 2^(-40) > |X| > 15 PI */ if (compact > 0x3FFF8000) { /* |X| >= 15 PI */ /* REDUCEX */ fp1 = packFloatx80(0, 0, 0); if (compact == 0x7FFEFFFF) { twopi1 = packFloatx80(aSign ^ 1, 0x7FFE, UINT64_C(0xC90FDAA200000000)); twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, UINT64_C(0x85A308D300000000)); fp0 = floatx80_add(fp0, twopi1, status); fp1 = fp0; fp0 = floatx80_add(fp0, twopi2, status); fp1 = floatx80_sub(fp1, fp0, status); fp1 = floatx80_add(fp1, twopi2, status); } loop: xSign = extractFloatx80Sign(fp0); xExp = extractFloatx80Exp(fp0); xExp -= 0x3FFF; if (xExp <= 28) { l = 0; endflag = 1; } else { l = xExp - 27; endflag = 0; } invtwopi = packFloatx80(0, 0x3FFE - l, UINT64_C(0xA2F9836E4E44152A)); /* INVTWOPI */ twopi1 = packFloatx80(0, 0x3FFF + l, UINT64_C(0xC90FDAA200000000)); twopi2 = packFloatx80(0, 0x3FDD + l, UINT64_C(0x85A308D300000000)); /* SIGN(INARG)*2^63 IN SGL */ twoto63 = packFloat32(xSign, 0xBE, 0); fp2 = floatx80_mul(fp0, invtwopi, status); fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), status); /* THE FRACT PART OF FP2 IS ROUNDED */ fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status), status); /* FP2 is N */ fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */ fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */ fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */ fp4 = floatx80_sub(fp4, fp3, status); /* W-P */ fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */ fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */ fp3 = fp0; /* FP3 is A */ fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */ fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */ if (endflag > 0) { n = floatx80_to_int32(fp2, status); goto tancont; } fp3 = floatx80_sub(fp3, fp0, status); /* A-R */ fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */ goto loop; } else { status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_move(a, status); float_raise(float_flag_inexact, status); return a; } } else { fp1 = floatx80_mul(fp0, float64_to_floatx80( make_float64(0x3FE45F306DC9C883), status), status); /* X*2/PI */ n = floatx80_to_int32(fp1, status); j = 32 + n; fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */ fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status), status); /* FP0 IS R = (X-Y1)-Y2 */ tancont: if (n & 1) { /* NODD */ fp1 = fp0; /* R */ fp0 = floatx80_mul(fp0, fp0, status); /* S = R*R */ fp3 = float64_to_floatx80(make_float64(0x3EA0B759F50F8688), status); /* Q4 */ fp2 = float64_to_floatx80(make_float64(0xBEF2BAA5A8924F04), status); /* P3 */ fp3 = floatx80_mul(fp3, fp0, status); /* SQ4 */ fp2 = floatx80_mul(fp2, fp0, status); /* SP3 */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBF346F59B39BA65F), status), status); /* Q3+SQ4 */ fp4 = packFloatx80(0, 0x3FF6, UINT64_C(0xE073D3FC199C4A00)); fp2 = floatx80_add(fp2, fp4, status); /* P2+SP3 */ fp3 = floatx80_mul(fp3, fp0, status); /* S(Q3+SQ4) */ fp2 = floatx80_mul(fp2, fp0, status); /* S(P2+SP3) */ fp4 = packFloatx80(0, 0x3FF9, UINT64_C(0xD23CD68415D95FA1)); fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */ fp4 = packFloatx80(1, 0x3FFC, UINT64_C(0x8895A6C5FB423BCA)); fp2 = floatx80_add(fp2, fp4, status); /* P1+S(P2+SP3) */ fp3 = floatx80_mul(fp3, fp0, status); /* S(Q2+S(Q3+SQ4)) */ fp2 = floatx80_mul(fp2, fp0, status); /* S(P1+S(P2+SP3)) */ fp4 = packFloatx80(1, 0x3FFD, UINT64_C(0xEEF57E0DA84BC8CE)); fp3 = floatx80_add(fp3, fp4, status); /* Q1+S(Q2+S(Q3+SQ4)) */ fp2 = floatx80_mul(fp2, fp1, status); /* RS(P1+S(P2+SP3)) */ fp0 = floatx80_mul(fp0, fp3, status); /* S(Q1+S(Q2+S(Q3+SQ4))) */ fp1 = floatx80_add(fp1, fp2, status); /* R+RS(P1+S(P2+SP3)) */ fp0 = floatx80_add(fp0, float32_to_floatx80( make_float32(0x3F800000), status), status); /* 1+S(Q1+S(Q2+S(Q3+SQ4))) */ xSign = extractFloatx80Sign(fp1); xExp = extractFloatx80Exp(fp1); xSig = extractFloatx80Frac(fp1); xSign ^= 1; fp1 = packFloatx80(xSign, xExp, xSig); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_div(fp0, fp1, status); float_raise(float_flag_inexact, status); return a; } else { fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ fp3 = float64_to_floatx80(make_float64(0x3EA0B759F50F8688), status); /* Q4 */ fp2 = float64_to_floatx80(make_float64(0xBEF2BAA5A8924F04), status); /* P3 */ fp3 = floatx80_mul(fp3, fp1, status); /* SQ4 */ fp2 = floatx80_mul(fp2, fp1, status); /* SP3 */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBF346F59B39BA65F), status), status); /* Q3+SQ4 */ fp4 = packFloatx80(0, 0x3FF6, UINT64_C(0xE073D3FC199C4A00)); fp2 = floatx80_add(fp2, fp4, status); /* P2+SP3 */ fp3 = floatx80_mul(fp3, fp1, status); /* S(Q3+SQ4) */ fp2 = floatx80_mul(fp2, fp1, status); /* S(P2+SP3) */ fp4 = packFloatx80(0, 0x3FF9, UINT64_C(0xD23CD68415D95FA1)); fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */ fp4 = packFloatx80(1, 0x3FFC, UINT64_C(0x8895A6C5FB423BCA)); fp2 = floatx80_add(fp2, fp4, status); /* P1+S(P2+SP3) */ fp3 = floatx80_mul(fp3, fp1, status); /* S(Q2+S(Q3+SQ4)) */ fp2 = floatx80_mul(fp2, fp1, status); /* S(P1+S(P2+SP3)) */ fp4 = packFloatx80(1, 0x3FFD, UINT64_C(0xEEF57E0DA84BC8CE)); fp3 = floatx80_add(fp3, fp4, status); /* Q1+S(Q2+S(Q3+SQ4)) */ fp2 = floatx80_mul(fp2, fp0, status); /* RS(P1+S(P2+SP3)) */ fp1 = floatx80_mul(fp1, fp3, status); /* S(Q1+S(Q2+S(Q3+SQ4))) */ fp0 = floatx80_add(fp0, fp2, status); /* R+RS(P1+S(P2+SP3)) */ fp1 = floatx80_add(fp1, float32_to_floatx80( make_float32(0x3F800000), status), status); /* 1+S(Q1+S(Q2+S(Q3+SQ4))) */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_div(fp0, fp1, status); float_raise(float_flag_inexact, status); return a; } } } /* * Sine */ floatx80 floatx80_sin(floatx80 a, float_status *status) { flag aSign, xSign; int32_t aExp, xExp; uint64_t aSig, xSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact, l, n, j; floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2; float32 posneg1, twoto63; flag endflag; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); if (aExp == 0x7FFF) { if ((uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } float_raise(float_flag_invalid, status); return floatx80_default_nan(status); } if (aExp == 0 && aSig == 0) { return packFloatx80(aSign, 0, 0); } 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; if (compact < 0x3FD78000 || compact > 0x4004BC7E) { /* 2^(-40) > |X| > 15 PI */ if (compact > 0x3FFF8000) { /* |X| >= 15 PI */ /* REDUCEX */ fp1 = packFloatx80(0, 0, 0); if (compact == 0x7FFEFFFF) { twopi1 = packFloatx80(aSign ^ 1, 0x7FFE, UINT64_C(0xC90FDAA200000000)); twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, UINT64_C(0x85A308D300000000)); fp0 = floatx80_add(fp0, twopi1, status); fp1 = fp0; fp0 = floatx80_add(fp0, twopi2, status); fp1 = floatx80_sub(fp1, fp0, status); fp1 = floatx80_add(fp1, twopi2, status); } loop: xSign = extractFloatx80Sign(fp0); xExp = extractFloatx80Exp(fp0); xExp -= 0x3FFF; if (xExp <= 28) { l = 0; endflag = 1; } else { l = xExp - 27; endflag = 0; } invtwopi = packFloatx80(0, 0x3FFE - l, UINT64_C(0xA2F9836E4E44152A)); /* INVTWOPI */ twopi1 = packFloatx80(0, 0x3FFF + l, UINT64_C(0xC90FDAA200000000)); twopi2 = packFloatx80(0, 0x3FDD + l, UINT64_C(0x85A308D300000000)); /* SIGN(INARG)*2^63 IN SGL */ twoto63 = packFloat32(xSign, 0xBE, 0); fp2 = floatx80_mul(fp0, invtwopi, status); fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), status); /* THE FRACT PART OF FP2 IS ROUNDED */ fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status), status); /* FP2 is N */ fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */ fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */ fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */ fp4 = floatx80_sub(fp4, fp3, status); /* W-P */ fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */ fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */ fp3 = fp0; /* FP3 is A */ fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */ fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */ if (endflag > 0) { n = floatx80_to_int32(fp2, status); goto sincont; } fp3 = floatx80_sub(fp3, fp0, status); /* A-R */ fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */ goto loop; } else { /* SINSM */ fp0 = float32_to_floatx80(make_float32(0x3F800000), status); /* 1 */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; /* SINTINY */ a = floatx80_move(a, status); float_raise(float_flag_inexact, status); return a; } } else { fp1 = floatx80_mul(fp0, float64_to_floatx80( make_float64(0x3FE45F306DC9C883), status), status); /* X*2/PI */ n = floatx80_to_int32(fp1, status); j = 32 + n; fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */ fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status), status); /* FP0 IS R = (X-Y1)-Y2 */ sincont: if (n & 1) { /* COSPOLY */ fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */ fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */ fp2 = float64_to_floatx80(make_float64(0x3D2AC4D0D6011EE3), status); /* B8 */ fp3 = float64_to_floatx80(make_float64(0xBDA9396F9F45AC19), status); /* B7 */ xSign = extractFloatx80Sign(fp0); /* X IS S */ xExp = extractFloatx80Exp(fp0); xSig = extractFloatx80Frac(fp0); if ((n >> 1) & 1) { xSign ^= 1; posneg1 = make_float32(0xBF800000); /* -1 */ } else { xSign ^= 0; posneg1 = make_float32(0x3F800000); /* 1 */ } /* X IS NOW R'= SGN*R */ fp2 = floatx80_mul(fp2, fp1, status); /* TB8 */ fp3 = floatx80_mul(fp3, fp1, status); /* TB7 */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3E21EED90612C972), status), status); /* B6+TB8 */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBE927E4FB79D9FCF), status), status); /* B5+TB7 */ fp2 = floatx80_mul(fp2, fp1, status); /* T(B6+TB8) */ fp3 = floatx80_mul(fp3, fp1, status); /* T(B5+TB7) */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3EFA01A01A01D423), status), status); /* B4+T(B6+TB8) */ fp4 = packFloatx80(1, 0x3FF5, UINT64_C(0xB60B60B60B61D438)); fp3 = floatx80_add(fp3, fp4, status); /* B3+T(B5+TB7) */ fp2 = floatx80_mul(fp2, fp1, status); /* T(B4+T(B6+TB8)) */ fp1 = floatx80_mul(fp1, fp3, status); /* T(B3+T(B5+TB7)) */ fp4 = packFloatx80(0, 0x3FFA, UINT64_C(0xAAAAAAAAAAAAAB5E)); fp2 = floatx80_add(fp2, fp4, status); /* B2+T(B4+T(B6+TB8)) */ fp1 = floatx80_add(fp1, float32_to_floatx80( make_float32(0xBF000000), status), status); /* B1+T(B3+T(B5+TB7)) */ fp0 = floatx80_mul(fp0, fp2, status); /* S(B2+T(B4+T(B6+TB8))) */ fp0 = floatx80_add(fp0, fp1, status); /* [B1+T(B3+T(B5+TB7))]+ * [S(B2+T(B4+T(B6+TB8)))] */ x = packFloatx80(xSign, xExp, xSig); fp0 = floatx80_mul(fp0, x, status); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status); float_raise(float_flag_inexact, status); return a; } else { /* SINPOLY */ xSign = extractFloatx80Sign(fp0); /* X IS R */ xExp = extractFloatx80Exp(fp0); xSig = extractFloatx80Frac(fp0); xSign ^= (n >> 1) & 1; /* X IS NOW R'= SGN*R */ fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */ fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */ fp3 = float64_to_floatx80(make_float64(0xBD6AAA77CCC994F5), status); /* A7 */ fp2 = float64_to_floatx80(make_float64(0x3DE612097AAE8DA1), status); /* A6 */ fp3 = floatx80_mul(fp3, fp1, status); /* T*A7 */ fp2 = floatx80_mul(fp2, fp1, status); /* T*A6 */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBE5AE6452A118AE4), status), status); /* A5+T*A7 */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3EC71DE3A5341531), status), status); /* A4+T*A6 */ fp3 = floatx80_mul(fp3, fp1, status); /* T(A5+TA7) */ fp2 = floatx80_mul(fp2, fp1, status); /* T(A4+TA6) */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBF2A01A01A018B59), status), status); /* A3+T(A5+TA7) */ fp4 = packFloatx80(0, 0x3FF8, UINT64_C(0x88888888888859AF)); fp2 = floatx80_add(fp2, fp4, status); /* A2+T(A4+TA6) */ fp1 = floatx80_mul(fp1, fp3, status); /* T(A3+T(A5+TA7)) */ fp2 = floatx80_mul(fp2, fp0, status); /* S(A2+T(A4+TA6)) */ fp4 = packFloatx80(1, 0x3FFC, UINT64_C(0xAAAAAAAAAAAAAA99)); fp1 = floatx80_add(fp1, fp4, status); /* A1+T(A3+T(A5+TA7)) */ fp1 = floatx80_add(fp1, fp2, status); /* [A1+T(A3+T(A5+TA7))]+ * [S(A2+T(A4+TA6))] */ x = packFloatx80(xSign, xExp, xSig); fp0 = floatx80_mul(fp0, x, status); /* R'*S */ fp0 = floatx80_mul(fp0, fp1, status); /* SIN(R')-R' */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, x, status); float_raise(float_flag_inexact, status); return a; } } } /* * Cosine */ floatx80 floatx80_cos(floatx80 a, float_status *status) { flag aSign, xSign; int32_t aExp, xExp; uint64_t aSig, xSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact, l, n, j; floatx80 fp0, fp1, fp2, fp3, fp4, fp5, x, invtwopi, twopi1, twopi2; float32 posneg1, twoto63; flag endflag; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); if (aExp == 0x7FFF) { if ((uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } float_raise(float_flag_invalid, status); return floatx80_default_nan(status); } 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; compact = floatx80_make_compact(aExp, aSig); fp0 = a; if (compact < 0x3FD78000 || compact > 0x4004BC7E) { /* 2^(-40) > |X| > 15 PI */ if (compact > 0x3FFF8000) { /* |X| >= 15 PI */ /* REDUCEX */ fp1 = packFloatx80(0, 0, 0); if (compact == 0x7FFEFFFF) { twopi1 = packFloatx80(aSign ^ 1, 0x7FFE, UINT64_C(0xC90FDAA200000000)); twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, UINT64_C(0x85A308D300000000)); fp0 = floatx80_add(fp0, twopi1, status); fp1 = fp0; fp0 = floatx80_add(fp0, twopi2, status); fp1 = floatx80_sub(fp1, fp0, status); fp1 = floatx80_add(fp1, twopi2, status); } loop: xSign = extractFloatx80Sign(fp0); xExp = extractFloatx80Exp(fp0); xExp -= 0x3FFF; if (xExp <= 28) { l = 0; endflag = 1; } else { l = xExp - 27; endflag = 0; } invtwopi = packFloatx80(0, 0x3FFE - l, UINT64_C(0xA2F9836E4E44152A)); /* INVTWOPI */ twopi1 = packFloatx80(0, 0x3FFF + l, UINT64_C(0xC90FDAA200000000)); twopi2 = packFloatx80(0, 0x3FDD + l, UINT64_C(0x85A308D300000000)); /* SIGN(INARG)*2^63 IN SGL */ twoto63 = packFloat32(xSign, 0xBE, 0); fp2 = floatx80_mul(fp0, invtwopi, status); fp2 = floatx80_add(fp2, float32_to_floatx80(twoto63, status), status); /* THE FRACT PART OF FP2 IS ROUNDED */ fp2 = floatx80_sub(fp2, float32_to_floatx80(twoto63, status), status); /* FP2 is N */ fp4 = floatx80_mul(twopi1, fp2, status); /* W = N*P1 */ fp5 = floatx80_mul(twopi2, fp2, status); /* w = N*P2 */ fp3 = floatx80_add(fp4, fp5, status); /* FP3 is P */ fp4 = floatx80_sub(fp4, fp3, status); /* W-P */ fp0 = floatx80_sub(fp0, fp3, status); /* FP0 is A := R - P */ fp4 = floatx80_add(fp4, fp5, status); /* FP4 is p = (W-P)+w */ fp3 = fp0; /* FP3 is A */ fp1 = floatx80_sub(fp1, fp4, status); /* FP1 is a := r - p */ fp0 = floatx80_add(fp0, fp1, status); /* FP0 is R := A+a */ if (endflag > 0) { n = floatx80_to_int32(fp2, status); goto sincont; } fp3 = floatx80_sub(fp3, fp0, status); /* A-R */ fp1 = floatx80_add(fp1, fp3, status); /* FP1 is r := (A-R)+a */ goto loop; } else { /* SINSM */ fp0 = float32_to_floatx80(make_float32(0x3F800000), status); /* 1 */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; /* COSTINY */ a = floatx80_sub(fp0, float32_to_floatx80( make_float32(0x00800000), status), status); float_raise(float_flag_inexact, status); return a; } } else { fp1 = floatx80_mul(fp0, float64_to_floatx80( make_float64(0x3FE45F306DC9C883), status), status); /* X*2/PI */ n = floatx80_to_int32(fp1, status); j = 32 + n; fp0 = floatx80_sub(fp0, pi_tbl[j], status); /* X-Y1 */ fp0 = floatx80_sub(fp0, float32_to_floatx80(pi_tbl2[j], status), status); /* FP0 IS R = (X-Y1)-Y2 */ sincont: if ((n + 1) & 1) { /* COSPOLY */ fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */ fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */ fp2 = float64_to_floatx80(make_float64(0x3D2AC4D0D6011EE3), status); /* B8 */ fp3 = float64_to_floatx80(make_float64(0xBDA9396F9F45AC19), status); /* B7 */ xSign = extractFloatx80Sign(fp0); /* X IS S */ xExp = extractFloatx80Exp(fp0); xSig = extractFloatx80Frac(fp0); if (((n + 1) >> 1) & 1) { xSign ^= 1; posneg1 = make_float32(0xBF800000); /* -1 */ } else { xSign ^= 0; posneg1 = make_float32(0x3F800000); /* 1 */ } /* X IS NOW R'= SGN*R */ fp2 = floatx80_mul(fp2, fp1, status); /* TB8 */ fp3 = floatx80_mul(fp3, fp1, status); /* TB7 */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3E21EED90612C972), status), status); /* B6+TB8 */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBE927E4FB79D9FCF), status), status); /* B5+TB7 */ fp2 = floatx80_mul(fp2, fp1, status); /* T(B6+TB8) */ fp3 = floatx80_mul(fp3, fp1, status); /* T(B5+TB7) */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3EFA01A01A01D423), status), status); /* B4+T(B6+TB8) */ fp4 = packFloatx80(1, 0x3FF5, UINT64_C(0xB60B60B60B61D438)); fp3 = floatx80_add(fp3, fp4, status); /* B3+T(B5+TB7) */ fp2 = floatx80_mul(fp2, fp1, status); /* T(B4+T(B6+TB8)) */ fp1 = floatx80_mul(fp1, fp3, status); /* T(B3+T(B5+TB7)) */ fp4 = packFloatx80(0, 0x3FFA, UINT64_C(0xAAAAAAAAAAAAAB5E)); fp2 = floatx80_add(fp2, fp4, status); /* B2+T(B4+T(B6+TB8)) */ fp1 = floatx80_add(fp1, float32_to_floatx80( make_float32(0xBF000000), status), status); /* B1+T(B3+T(B5+TB7)) */ fp0 = floatx80_mul(fp0, fp2, status); /* S(B2+T(B4+T(B6+TB8))) */ fp0 = floatx80_add(fp0, fp1, status); /* [B1+T(B3+T(B5+TB7))]+[S(B2+T(B4+T(B6+TB8)))] */ x = packFloatx80(xSign, xExp, xSig); fp0 = floatx80_mul(fp0, x, status); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, float32_to_floatx80(posneg1, status), status); float_raise(float_flag_inexact, status); return a; } else { /* SINPOLY */ xSign = extractFloatx80Sign(fp0); /* X IS R */ xExp = extractFloatx80Exp(fp0); xSig = extractFloatx80Frac(fp0); xSign ^= ((n + 1) >> 1) & 1; /* X IS NOW R'= SGN*R */ fp0 = floatx80_mul(fp0, fp0, status); /* FP0 IS S */ fp1 = floatx80_mul(fp0, fp0, status); /* FP1 IS T */ fp3 = float64_to_floatx80(make_float64(0xBD6AAA77CCC994F5), status); /* A7 */ fp2 = float64_to_floatx80(make_float64(0x3DE612097AAE8DA1), status); /* A6 */ fp3 = floatx80_mul(fp3, fp1, status); /* T*A7 */ fp2 = floatx80_mul(fp2, fp1, status); /* T*A6 */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBE5AE6452A118AE4), status), status); /* A5+T*A7 */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3EC71DE3A5341531), status), status); /* A4+T*A6 */ fp3 = floatx80_mul(fp3, fp1, status); /* T(A5+TA7) */ fp2 = floatx80_mul(fp2, fp1, status); /* T(A4+TA6) */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBF2A01A01A018B59), status), status); /* A3+T(A5+TA7) */ fp4 = packFloatx80(0, 0x3FF8, UINT64_C(0x88888888888859AF)); fp2 = floatx80_add(fp2, fp4, status); /* A2+T(A4+TA6) */ fp1 = floatx80_mul(fp1, fp3, status); /* T(A3+T(A5+TA7)) */ fp2 = floatx80_mul(fp2, fp0, status); /* S(A2+T(A4+TA6)) */ fp4 = packFloatx80(1, 0x3FFC, UINT64_C(0xAAAAAAAAAAAAAA99)); fp1 = floatx80_add(fp1, fp4, status); /* A1+T(A3+T(A5+TA7)) */ fp1 = floatx80_add(fp1, fp2, status); /* [A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))] */ x = packFloatx80(xSign, xExp, xSig); fp0 = floatx80_mul(fp0, x, status); /* R'*S */ fp0 = floatx80_mul(fp0, fp1, status); /* SIN(R')-R' */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, x, status); float_raise(float_flag_inexact, status); return a; } } } /* * Arc tangent */ floatx80 floatx80_atan(floatx80 a, float_status *status) { flag aSign; int32_t aExp; uint64_t aSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact, tbl_index; floatx80 fp0, fp1, fp2, fp3, xsave; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); if (aExp == 0x7FFF) { if ((uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } a = packFloatx80(aSign, piby2_exp, pi_sig); float_raise(float_flag_inexact, status); return floatx80_move(a, status); } if (aExp == 0 && aSig == 0) { return packFloatx80(aSign, 0, 0); } compact = floatx80_make_compact(aExp, aSig); 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 (compact < 0x3FFB8000 || compact > 0x4002FFFF) { /* |X| >= 16 or |X| < 1/16 */ if (compact > 0x3FFF8000) { /* |X| >= 16 */ if (compact > 0x40638000) { /* |X| > 2^(100) */ fp0 = packFloatx80(aSign, piby2_exp, pi_sig); fp1 = packFloatx80(aSign, 0x0001, one_sig); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_sub(fp0, fp1, status); float_raise(float_flag_inexact, status); return a; } else { fp0 = a; fp1 = packFloatx80(1, one_exp, one_sig); /* -1 */ fp1 = floatx80_div(fp1, fp0, status); /* X' = -1/X */ xsave = fp1; fp0 = floatx80_mul(fp1, fp1, status); /* Y = X'*X' */ fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */ fp3 = float64_to_floatx80(make_float64(0xBFB70BF398539E6A), status); /* C5 */ fp2 = float64_to_floatx80(make_float64(0x3FBC7187962D1D7D), status); /* C4 */ fp3 = floatx80_mul(fp3, fp1, status); /* Z*C5 */ fp2 = floatx80_mul(fp2, fp1, status); /* Z*C4 */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBFC24924827107B8), status), status); /* C3+Z*C5 */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3FC999999996263E), status), status); /* C2+Z*C4 */ fp1 = floatx80_mul(fp1, fp3, status); /* Z*(C3+Z*C5) */ fp2 = floatx80_mul(fp2, fp0, status); /* Y*(C2+Z*C4) */ fp1 = floatx80_add(fp1, float64_to_floatx80( make_float64(0xBFD5555555555536), status), status); /* C1+Z*(C3+Z*C5) */ fp0 = floatx80_mul(fp0, xsave, status); /* X'*Y */ /* [Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)] */ fp1 = floatx80_add(fp1, fp2, status); /* X'*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) ?? */ fp0 = floatx80_mul(fp0, fp1, status); fp0 = floatx80_add(fp0, xsave, status); fp1 = packFloatx80(aSign, piby2_exp, pi_sig); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, fp1, status); float_raise(float_flag_inexact, status); return a; } } else { /* |X| < 1/16 */ if (compact < 0x3FD78000) { /* |X| < 2^(-40) */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_move(a, status); float_raise(float_flag_inexact, status); return a; } else { fp0 = a; xsave = a; fp0 = floatx80_mul(fp0, fp0, status); /* Y = X*X */ fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */ fp2 = float64_to_floatx80(make_float64(0x3FB344447F876989), status); /* B6 */ fp3 = float64_to_floatx80(make_float64(0xBFB744EE7FAF45DB), status); /* B5 */ fp2 = floatx80_mul(fp2, fp1, status); /* Z*B6 */ fp3 = floatx80_mul(fp3, fp1, status); /* Z*B5 */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3FBC71C646940220), status), status); /* B4+Z*B6 */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0xBFC24924921872F9), status), status); /* B3+Z*B5 */ fp2 = floatx80_mul(fp2, fp1, status); /* Z*(B4+Z*B6) */ fp1 = floatx80_mul(fp1, fp3, status); /* Z*(B3+Z*B5) */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3FC9999999998FA9), status), status); /* B2+Z*(B4+Z*B6) */ fp1 = floatx80_add(fp1, float64_to_floatx80( make_float64(0xBFD5555555555555), status), status); /* B1+Z*(B3+Z*B5) */ fp2 = floatx80_mul(fp2, fp0, status); /* Y*(B2+Z*(B4+Z*B6)) */ fp0 = floatx80_mul(fp0, xsave, status); /* X*Y */ /* [B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))] */ fp1 = floatx80_add(fp1, fp2, status); /* X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) */ fp0 = floatx80_mul(fp0, fp1, status); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, xsave, status); float_raise(float_flag_inexact, status); return a; } } } else { aSig &= UINT64_C(0xF800000000000000); aSig |= UINT64_C(0x0400000000000000); xsave = packFloatx80(aSign, aExp, aSig); /* F */ fp0 = a; fp1 = a; /* X */ fp2 = packFloatx80(0, one_exp, one_sig); /* 1 */ fp1 = floatx80_mul(fp1, xsave, status); /* X*F */ fp0 = floatx80_sub(fp0, xsave, status); /* X-F */ fp1 = floatx80_add(fp1, fp2, status); /* 1 + X*F */ fp0 = floatx80_div(fp0, fp1, status); /* U = (X-F)/(1+X*F) */ tbl_index = compact; tbl_index &= 0x7FFF0000; tbl_index -= 0x3FFB0000; tbl_index >>= 1; tbl_index += compact & 0x00007800; tbl_index >>= 11; fp3 = atan_tbl[tbl_index]; fp3.high |= aSign ? 0x8000 : 0; /* ATAN(F) */ fp1 = floatx80_mul(fp0, fp0, status); /* V = U*U */ fp2 = float64_to_floatx80(make_float64(0xBFF6687E314987D8), status); /* A3 */ fp2 = floatx80_add(fp2, fp1, status); /* A3+V */ fp2 = floatx80_mul(fp2, fp1, status); /* V*(A3+V) */ fp1 = floatx80_mul(fp1, fp0, status); /* U*V */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x4002AC6934A26DB3), status), status); /* A2+V*(A3+V) */ fp1 = floatx80_mul(fp1, float64_to_floatx80( make_float64(0xBFC2476F4E1DA28E), status), status); /* A1+U*V */ fp1 = floatx80_mul(fp1, fp2, status); /* A1*U*V*(A2+V*(A3+V)) */ fp0 = floatx80_add(fp0, fp1, status); /* ATAN(U) */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, fp3, status); /* ATAN(X) */ float_raise(float_flag_inexact, status); return a; } } /* * Arc sine */ floatx80 floatx80_asin(floatx80 a, float_status *status) { flag aSign; int32_t aExp; uint64_t aSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact; floatx80 fp0, fp1, fp2, one; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } if (aExp == 0 && aSig == 0) { return packFloatx80(aSign, 0, 0); } compact = floatx80_make_compact(aExp, aSig); if (compact >= 0x3FFF8000) { /* |X| >= 1 */ if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */ float_raise(float_flag_inexact, status); a = packFloatx80(aSign, piby2_exp, pi_sig); return floatx80_move(a, status); } else { /* |X| > 1 */ float_raise(float_flag_invalid, status); return floatx80_default_nan(status); } } /* |X| < 1 */ 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; one = packFloatx80(0, one_exp, one_sig); fp0 = a; fp1 = floatx80_sub(one, fp0, status); /* 1 - X */ fp2 = floatx80_add(one, fp0, status); /* 1 + X */ fp1 = floatx80_mul(fp2, fp1, status); /* (1+X)*(1-X) */ fp1 = floatx80_sqrt(fp1, status); /* SQRT((1+X)*(1-X)) */ fp0 = floatx80_div(fp0, fp1, status); /* X/SQRT((1+X)*(1-X)) */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_atan(fp0, status); /* ATAN(X/SQRT((1+X)*(1-X))) */ float_raise(float_flag_inexact, status); return a; } /* * Arc cosine */ floatx80 floatx80_acos(floatx80 a, float_status *status) { flag aSign; int32_t aExp; uint64_t aSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact; floatx80 fp0, fp1, one; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } if (aExp == 0 && aSig == 0) { float_raise(float_flag_inexact, status); return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, piby2_exp, pi_sig, 0, status); } compact = floatx80_make_compact(aExp, aSig); if (compact >= 0x3FFF8000) { /* |X| >= 1 */ if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */ if (aSign) { /* X == -1 */ a = packFloatx80(0, pi_exp, pi_sig); float_raise(float_flag_inexact, status); return floatx80_move(a, status); } else { /* X == +1 */ return packFloatx80(0, 0, 0); } } else { /* |X| > 1 */ float_raise(float_flag_invalid, status); return floatx80_default_nan(status); } } /* |X| < 1 */ 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; one = packFloatx80(0, one_exp, one_sig); fp0 = a; fp1 = floatx80_add(one, fp0, status); /* 1 + X */ fp0 = floatx80_sub(one, fp0, status); /* 1 - X */ fp0 = floatx80_div(fp0, fp1, status); /* (1-X)/(1+X) */ fp0 = floatx80_sqrt(fp0, status); /* SQRT((1-X)/(1+X)) */ fp0 = floatx80_atan(fp0, status); /* ATAN(SQRT((1-X)/(1+X))) */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, fp0, status); /* 2 * ATAN(SQRT((1-X)/(1+X))) */ float_raise(float_flag_inexact, status); return a; } /* * Hyperbolic arc tangent */ floatx80 floatx80_atanh(floatx80 a, float_status *status) { flag aSign; int32_t aExp; uint64_t aSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact; floatx80 fp0, fp1, fp2, one; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); if (aExp == 0x7FFF && (uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } if (aExp == 0 && aSig == 0) { return packFloatx80(aSign, 0, 0); } compact = floatx80_make_compact(aExp, aSig); if (compact >= 0x3FFF8000) { /* |X| >= 1 */ if (aExp == one_exp && aSig == one_sig) { /* |X| == 1 */ float_raise(float_flag_divbyzero, status); return packFloatx80(aSign, floatx80_infinity.high, floatx80_infinity.low); } else { /* |X| > 1 */ float_raise(float_flag_invalid, status); return floatx80_default_nan(status); } } /* |X| < 1 */ 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; one = packFloatx80(0, one_exp, one_sig); fp2 = packFloatx80(aSign, 0x3FFE, one_sig); /* SIGN(X) * (1/2) */ fp0 = packFloatx80(0, aExp, aSig); /* Y = |X| */ fp1 = packFloatx80(1, aExp, aSig); /* -Y */ fp0 = floatx80_add(fp0, fp0, status); /* 2Y */ fp1 = floatx80_add(fp1, one, status); /* 1-Y */ fp0 = floatx80_div(fp0, fp1, status); /* Z = 2Y/(1-Y) */ fp0 = floatx80_lognp1(fp0, status); /* LOG1P(Z) */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_mul(fp0, fp2, status); /* ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z) */ float_raise(float_flag_inexact, status); return a; } /* * e to x minus 1 */ floatx80 floatx80_etoxm1(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, m, m1; floatx80 fp0, fp1, fp2, fp3, l2, sc, onebysc; 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(aSign, one_exp, one_sig); } return packFloatx80(0, floatx80_infinity.high, floatx80_infinity.low); } if (aExp == 0 && aSig == 0) { return packFloatx80(aSign, 0, 0); } 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 (aExp >= 0x3FFD) { /* |X| >= 1/4 */ compact = floatx80_make_compact(aExp, aSig); if (compact <= 0x4004C215) { /* |X| <= 70 log2 */ fp0 = a; fp1 = a; fp0 = floatx80_mul(fp0, float32_to_floatx80( make_float32(0x42B8AA3B), status), status); /* 64/log2 * X */ 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--; } m1 = -m; /*m += 0x3FFF; // biased exponent of 2^(M) */ /*m1 += 0x3FFF; // biased exponent of -2^(-M) */ 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, UINT64_C(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(0x3950097B), status); /* A6 */ fp2 = floatx80_mul(fp2, fp1, status); /* fp2 is S*A6 */ fp3 = floatx80_mul(float32_to_floatx80(make_float32(0x3AB60B6A), status), fp1, status); /* fp3 is S*A5 */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3F81111111174385), status), status); /* fp2 IS A4+S*A6 */ fp3 = floatx80_add(fp3, float64_to_floatx80( make_float64(0x3FA5555555554F5A), status), status); /* fp3 is A3+S*A5 */ fp2 = floatx80_mul(fp2, fp1, status); /* fp2 IS S*(A4+S*A6) */ fp3 = floatx80_mul(fp3, fp1, status); /* fp3 IS S*(A3+S*A5) */ fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3FC5555555555555), status), status); /* fp2 IS A2+S*(A4+S*A6) */ fp3 = floatx80_add(fp3, float32_to_floatx80( make_float32(0x3F000000), status), status); /* fp3 IS A1+S*(A3+S*A5) */ fp2 = floatx80_mul(fp2, fp1, status); /* fp2 IS S*(A2+S*(A4+S*A6)) */ fp1 = floatx80_mul(fp1, fp3, status); /* fp1 IS S*(A1+S*(A3+S*A5)) */ fp2 = floatx80_mul(fp2, fp0, status); /* fp2 IS R*S*(A2+S*(A4+S*A6)) */ fp0 = floatx80_add(fp0, fp1, status); /* fp0 IS R+S*(A1+S*(A3+S*A5)) */ fp0 = floatx80_add(fp0, fp2, status); /* fp0 IS EXP(R) - 1 */ fp0 = floatx80_mul(fp0, exp_tbl[j], status); /* 2^(J/64)*(Exp(R)-1) */ if (m >= 64) { fp1 = float32_to_floatx80(exp_tbl2[j], status); onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */ fp1 = floatx80_add(fp1, onebysc, status); fp0 = floatx80_add(fp0, fp1, status); fp0 = floatx80_add(fp0, exp_tbl[j], status); } else if (m < -3) { fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status), status); fp0 = floatx80_add(fp0, exp_tbl[j], status); onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */ fp0 = floatx80_add(fp0, onebysc, status); } else { /* -3 <= m <= 63 */ fp1 = exp_tbl[j]; fp0 = floatx80_add(fp0, float32_to_floatx80(exp_tbl2[j], status), status); onebysc = packFloatx80(1, m1 + 0x3FFF, one_sig); /* -2^(-M) */ fp1 = floatx80_add(fp1, onebysc, status); fp0 = floatx80_add(fp0, fp1, status); } sc = packFloatx80(0, m + 0x3FFF, one_sig); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_mul(fp0, sc, status); float_raise(float_flag_inexact, status); return a; } else { /* |X| > 70 log2 */ if (aSign) { fp0 = float32_to_floatx80(make_float32(0xBF800000), status); /* -1 */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, float32_to_floatx80( make_float32(0x00800000), status), status); /* -1 + 2^(-126) */ float_raise(float_flag_inexact, status); return a; } else { status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; return floatx80_etox(a, status); } } } else { /* |X| < 1/4 */ if (aExp >= 0x3FBE) { fp0 = a; fp0 = floatx80_mul(fp0, fp0, status); /* S = X*X */ fp1 = float32_to_floatx80(make_float32(0x2F30CAA8), status); /* B12 */ fp1 = floatx80_mul(fp1, fp0, status); /* S * B12 */ fp2 = float32_to_floatx80(make_float32(0x310F8290), status); /* B11 */ fp1 = floatx80_add(fp1, float32_to_floatx80( make_float32(0x32D73220), status), status); /* B10 */ fp2 = floatx80_mul(fp2, fp0, status); fp1 = floatx80_mul(fp1, fp0, status); fp2 = floatx80_add(fp2, float32_to_floatx80( make_float32(0x3493F281), status), status); /* B9 */ fp1 = floatx80_add(fp1, float64_to_floatx80( make_float64(0x3EC71DE3A5774682), status), status); /* B8 */ fp2 = floatx80_mul(fp2, fp0, status); fp1 = floatx80_mul(fp1, fp0, status); fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3EFA01A019D7CB68), status), status); /* B7 */ fp1 = floatx80_add(fp1, float64_to_floatx80( make_float64(0x3F2A01A01A019DF3), status), status); /* B6 */ fp2 = floatx80_mul(fp2, fp0, status); fp1 = floatx80_mul(fp1, fp0, status); fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3F56C16C16C170E2), status), status); /* B5 */ fp1 = floatx80_add(fp1, float64_to_floatx80( make_float64(0x3F81111111111111), status), status); /* B4 */ fp2 = floatx80_mul(fp2, fp0, status); fp1 = floatx80_mul(fp1, fp0, status); fp2 = floatx80_add(fp2, float64_to_floatx80( make_float64(0x3FA5555555555555), status), status); /* B3 */ fp3 = packFloatx80(0, 0x3FFC, UINT64_C(0xAAAAAAAAAAAAAAAB)); fp1 = floatx80_add(fp1, fp3, status); /* B2 */ fp2 = floatx80_mul(fp2, fp0, status); fp1 = floatx80_mul(fp1, fp0, status); fp2 = floatx80_mul(fp2, fp0, status); fp1 = floatx80_mul(fp1, a, status); fp0 = floatx80_mul(fp0, float32_to_floatx80( make_float32(0x3F000000), status), status); /* S*B1 */ fp1 = floatx80_add(fp1, fp2, status); /* Q */ fp0 = floatx80_add(fp0, fp1, status); /* S*B1+Q */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, a, status); float_raise(float_flag_inexact, status); return a; } else { /* |X| < 2^(-65) */ sc = packFloatx80(1, 1, one_sig); fp0 = a; if (aExp < 0x0033) { /* |X| < 2^(-16382) */ fp0 = floatx80_mul(fp0, float64_to_floatx80( make_float64(0x48B0000000000000), status), status); fp0 = floatx80_add(fp0, sc, status); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_mul(fp0, float64_to_floatx80( make_float64(0x3730000000000000), status), status); } else { status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, sc, status); } float_raise(float_flag_inexact, status); return a; } } } /* * Hyperbolic tangent */ floatx80 floatx80_tanh(floatx80 a, float_status *status) { flag aSign, vSign; int32_t aExp, vExp; uint64_t aSig, vSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact; floatx80 fp0, fp1; uint32_t sign; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); if (aExp == 0x7FFF) { if ((uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } return packFloatx80(aSign, one_exp, one_sig); } if (aExp == 0 && aSig == 0) { return packFloatx80(aSign, 0, 0); } 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 < 0x3FD78000 || compact > 0x3FFFDDCE) { /* TANHBORS */ if (compact < 0x3FFF8000) { /* TANHSM */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_move(a, status); float_raise(float_flag_inexact, status); return a; } else { if (compact > 0x40048AA1) { /* TANHHUGE */ sign = 0x3F800000; sign |= aSign ? 0x80000000 : 0x00000000; fp0 = float32_to_floatx80(make_float32(sign), status); sign &= 0x80000000; sign ^= 0x80800000; /* -SIGN(X)*EPS */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, float32_to_floatx80(make_float32(sign), status), status); float_raise(float_flag_inexact, status); return a; } else { fp0 = packFloatx80(0, aExp + 1, aSig); /* Y = 2|X| */ fp0 = floatx80_etox(fp0, status); /* FP0 IS EXP(Y) */ fp0 = floatx80_add(fp0, float32_to_floatx80( make_float32(0x3F800000), status), status); /* EXP(Y)+1 */ sign = aSign ? 0x80000000 : 0x00000000; fp1 = floatx80_div(float32_to_floatx80(make_float32( sign ^ 0xC0000000), status), fp0, status); /* -SIGN(X)*2 / [EXP(Y)+1] */ fp0 = float32_to_floatx80(make_float32(sign | 0x3F800000), status); /* SIGN */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp1, fp0, status); float_raise(float_flag_inexact, status); return a; } } } else { /* 2**(-40) < |X| < (5/2)LOG2 */ fp0 = packFloatx80(0, aExp + 1, aSig); /* Y = 2|X| */ fp0 = floatx80_etoxm1(fp0, status); /* FP0 IS Z = EXPM1(Y) */ fp1 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x40000000), status), status); /* Z+2 */ vSign = extractFloatx80Sign(fp1); vExp = extractFloatx80Exp(fp1); vSig = extractFloatx80Frac(fp1); fp1 = packFloatx80(vSign ^ aSign, vExp, vSig); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_div(fp0, fp1, status); float_raise(float_flag_inexact, status); return a; } } /* * Hyperbolic sine */ floatx80 floatx80_sinh(floatx80 a, float_status *status) { flag aSign; int32_t aExp; uint64_t aSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact; floatx80 fp0, fp1, fp2; float32 fact; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); aSign = extractFloatx80Sign(a); if (aExp == 0x7FFF) { if ((uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } return packFloatx80(aSign, floatx80_infinity.high, floatx80_infinity.low); } if (aExp == 0 && aSig == 0) { return packFloatx80(aSign, 0, 0); } 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 > 0x400CB167) { /* SINHBIG */ if (compact > 0x400CB2B3) { status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; return roundAndPackFloatx80(status->floatx80_rounding_precision, aSign, 0x8000, aSig, 0, status); } else { fp0 = floatx80_abs(a); /* Y = |X| */ fp0 = floatx80_sub(fp0, float64_to_floatx80( make_float64(0x40C62D38D3D64634), status), status); /* (|X|-16381LOG2_LEAD) */ fp0 = floatx80_sub(fp0, float64_to_floatx80( make_float64(0x3D6F90AEB1E75CC7), status), status); /* |X| - 16381 LOG2, ACCURATE */ fp0 = floatx80_etox(fp0, status); fp2 = packFloatx80(aSign, 0x7FFB, one_sig); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_mul(fp0, fp2, status); float_raise(float_flag_inexact, status); return a; } } else { /* |X| < 16380 LOG2 */ fp0 = floatx80_abs(a); /* Y = |X| */ fp0 = floatx80_etoxm1(fp0, status); /* FP0 IS Z = EXPM1(Y) */ fp1 = floatx80_add(fp0, float32_to_floatx80(make_float32(0x3F800000), status), status); /* 1+Z */ fp2 = fp0; fp0 = floatx80_div(fp0, fp1, status); /* Z/(1+Z) */ fp0 = floatx80_add(fp0, fp2, status); fact = packFloat32(aSign, 0x7E, 0); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_mul(fp0, float32_to_floatx80(fact, status), status); float_raise(float_flag_inexact, status); return a; } } /* * Hyperbolic cosine */ floatx80 floatx80_cosh(floatx80 a, float_status *status) { int32_t aExp; uint64_t aSig; int8_t user_rnd_mode, user_rnd_prec; int32_t compact; floatx80 fp0, fp1; aSig = extractFloatx80Frac(a); aExp = extractFloatx80Exp(a); if (aExp == 0x7FFF) { if ((uint64_t) (aSig << 1)) { return propagateFloatx80NaNOneArg(a, status); } 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; compact = floatx80_make_compact(aExp, aSig); if (compact > 0x400CB167) { if (compact > 0x400CB2B3) { status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; return roundAndPackFloatx80(status->floatx80_rounding_precision, 0, 0x8000, one_sig, 0, status); } else { fp0 = packFloatx80(0, aExp, aSig); fp0 = floatx80_sub(fp0, float64_to_floatx80( make_float64(0x40C62D38D3D64634), status), status); fp0 = floatx80_sub(fp0, float64_to_floatx80( make_float64(0x3D6F90AEB1E75CC7), status), status); fp0 = floatx80_etox(fp0, status); fp1 = packFloatx80(0, 0x7FFB, one_sig); status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_mul(fp0, fp1, status); float_raise(float_flag_inexact, status); return a; } } fp0 = packFloatx80(0, aExp, aSig); /* |X| */ fp0 = floatx80_etox(fp0, status); /* EXP(|X|) */ fp0 = floatx80_mul(fp0, float32_to_floatx80(make_float32(0x3F000000), status), status); /* (1/2)*EXP(|X|) */ fp1 = float32_to_floatx80(make_float32(0x3E800000), status); /* 1/4 */ fp1 = floatx80_div(fp1, fp0, status); /* 1/(2*EXP(|X|)) */ status->float_rounding_mode = user_rnd_mode; status->floatx80_rounding_precision = user_rnd_prec; a = floatx80_add(fp0, fp1, status); float_raise(float_flag_inexact, status); return a; }