| /* |
| * 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; |
| } |
