diff options
Diffstat (limited to 'target/m68k/softfloat.c')
| -rw-r--r-- | target/m68k/softfloat.c | 1637 |
1 files changed, 1637 insertions, 0 deletions
diff --git a/target/m68k/softfloat.c b/target/m68k/softfloat.c index 4bd5b9e6b7..dffb371c71 100644 --- a/target/m68k/softfloat.c +++ b/target/m68k/softfloat.c @@ -23,6 +23,10 @@ #include "fpu/softfloat-macros.h" #include "softfloat_fpsp_tables.h" +#define pi_exp 0x4000 +#define piby2_exp 0x3FFF +#define pi_sig LIT64(0xc90fdaa22168c235) + static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status) { if (floatx80_is_signaling_nan(a, status)) { @@ -1266,3 +1270,1636 @@ floatx80 floatx80_tentox(floatx80 a, float_status *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, + LIT64(0xC90FDAA200000000)); + twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, + LIT64(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, + LIT64(0xA2F9836E4E44152A)); /* INVTWOPI */ + twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000)); + twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(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, LIT64(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, LIT64(0xD23CD68415D95FA1)); + fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */ + fp4 = packFloatx80(1, 0x3FFC, LIT64(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, LIT64(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, LIT64(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, LIT64(0xD23CD68415D95FA1)); + fp3 = floatx80_add(fp3, fp4, status); /* Q2+S(Q3+SQ4) */ + fp4 = packFloatx80(1, 0x3FFC, LIT64(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, LIT64(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 adjn, 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); + } + + adjn = 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, + LIT64(0xC90FDAA200000000)); + twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, + LIT64(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, + LIT64(0xA2F9836E4E44152A)); /* INVTWOPI */ + twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000)); + twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(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; + + if (adjn) { + /* COSTINY */ + a = floatx80_sub(fp0, float32_to_floatx80( + make_float32(0x00800000), status), status); + } else { + /* 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 + adjn) & 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 + adjn) >> 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, LIT64(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, LIT64(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 + adjn) >> 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, LIT64(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, LIT64(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 adjn, 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); + } + + adjn = 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; + + 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, + LIT64(0xC90FDAA200000000)); + twopi2 = packFloatx80(aSign ^ 1, 0x7FDC, + LIT64(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, + LIT64(0xA2F9836E4E44152A)); /* INVTWOPI */ + twopi1 = packFloatx80(0, 0x3FFF + l, LIT64(0xC90FDAA200000000)); + twopi2 = packFloatx80(0, 0x3FDD + l, LIT64(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; + + if (adjn) { + /* COSTINY */ + a = floatx80_sub(fp0, float32_to_floatx80( + make_float32(0x00800000), status), + status); + } else { + /* 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 + adjn) & 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 + adjn) >> 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, LIT64(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, LIT64(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 + adjn) >> 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, LIT64(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, LIT64(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 &= LIT64(0xF800000000000000); + aSig |= LIT64(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, LIT64(0x82E308654361C4C6)); + fp2 = floatx80_mul(fp2, l2, status); /* N * L2, L1+L2 = -log2/64 */ + fp0 = floatx80_add(fp0, fp1, status); /* X + N*L1 */ + fp0 = floatx80_add(fp0, fp2, status); /* R */ + + fp1 = floatx80_mul(fp0, fp0, status); /* S = R*R */ + fp2 = float32_to_floatx80(make_float32(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, LIT64(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; +} |