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target/m68k: implement fatan
Using a local m68k floatx80_atan() [copied from previous: Written by Andreas Grabher for Previous, NeXT Computer Emulator.] Signed-off-by: Laurent Vivier <laurent@vivier.eu> Message-Id: <20180312202728.23790-6-laurent@vivier.eu>
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Laurent Vivier
parent
47446c9ce3
commit
8c992abc89
6 changed files with 341 additions and 0 deletions
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@ -23,6 +23,9 @@
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#include "fpu/softfloat-macros.h"
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#include "softfloat_fpsp_tables.h"
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#define piby2_exp 0x3FFF
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#define pi_sig LIT64(0xc90fdaa22168c235)
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static floatx80 propagateFloatx80NaNOneArg(floatx80 a, float_status *status)
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{
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if (floatx80_is_signaling_nan(a, status)) {
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@ -1967,3 +1970,200 @@ floatx80 floatx80_cos(floatx80 a, float_status *status)
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}
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}
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}
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/*----------------------------------------------------------------------------
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| Arc tangent
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*----------------------------------------------------------------------------*/
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floatx80 floatx80_atan(floatx80 a, float_status *status)
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{
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flag aSign;
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int32_t aExp;
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uint64_t aSig;
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int8_t user_rnd_mode, user_rnd_prec;
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int32_t compact, tbl_index;
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floatx80 fp0, fp1, fp2, fp3, xsave;
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aSig = extractFloatx80Frac(a);
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aExp = extractFloatx80Exp(a);
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aSign = extractFloatx80Sign(a);
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if (aExp == 0x7FFF) {
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if ((uint64_t) (aSig << 1)) {
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return propagateFloatx80NaNOneArg(a, status);
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}
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a = packFloatx80(aSign, piby2_exp, pi_sig);
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float_raise(float_flag_inexact, status);
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return floatx80_move(a, status);
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}
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if (aExp == 0 && aSig == 0) {
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return packFloatx80(aSign, 0, 0);
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}
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compact = floatx80_make_compact(aExp, aSig);
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user_rnd_mode = status->float_rounding_mode;
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user_rnd_prec = status->floatx80_rounding_precision;
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status->float_rounding_mode = float_round_nearest_even;
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status->floatx80_rounding_precision = 80;
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if (compact < 0x3FFB8000 || compact > 0x4002FFFF) {
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/* |X| >= 16 or |X| < 1/16 */
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if (compact > 0x3FFF8000) { /* |X| >= 16 */
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if (compact > 0x40638000) { /* |X| > 2^(100) */
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fp0 = packFloatx80(aSign, piby2_exp, pi_sig);
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fp1 = packFloatx80(aSign, 0x0001, one_sig);
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status->float_rounding_mode = user_rnd_mode;
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status->floatx80_rounding_precision = user_rnd_prec;
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a = floatx80_sub(fp0, fp1, status);
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float_raise(float_flag_inexact, status);
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return a;
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} else {
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fp0 = a;
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fp1 = packFloatx80(1, one_exp, one_sig); /* -1 */
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fp1 = floatx80_div(fp1, fp0, status); /* X' = -1/X */
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xsave = fp1;
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fp0 = floatx80_mul(fp1, fp1, status); /* Y = X'*X' */
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fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */
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fp3 = float64_to_floatx80(make_float64(0xBFB70BF398539E6A),
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status); /* C5 */
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fp2 = float64_to_floatx80(make_float64(0x3FBC7187962D1D7D),
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status); /* C4 */
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fp3 = floatx80_mul(fp3, fp1, status); /* Z*C5 */
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fp2 = floatx80_mul(fp2, fp1, status); /* Z*C4 */
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fp3 = floatx80_add(fp3, float64_to_floatx80(
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make_float64(0xBFC24924827107B8), status),
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status); /* C3+Z*C5 */
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fp2 = floatx80_add(fp2, float64_to_floatx80(
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make_float64(0x3FC999999996263E), status),
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status); /* C2+Z*C4 */
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fp1 = floatx80_mul(fp1, fp3, status); /* Z*(C3+Z*C5) */
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fp2 = floatx80_mul(fp2, fp0, status); /* Y*(C2+Z*C4) */
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fp1 = floatx80_add(fp1, float64_to_floatx80(
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make_float64(0xBFD5555555555536), status),
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status); /* C1+Z*(C3+Z*C5) */
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fp0 = floatx80_mul(fp0, xsave, status); /* X'*Y */
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/* [Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)] */
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fp1 = floatx80_add(fp1, fp2, status);
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/* X'*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) ?? */
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fp0 = floatx80_mul(fp0, fp1, status);
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fp0 = floatx80_add(fp0, xsave, status);
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fp1 = packFloatx80(aSign, piby2_exp, pi_sig);
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status->float_rounding_mode = user_rnd_mode;
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status->floatx80_rounding_precision = user_rnd_prec;
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a = floatx80_add(fp0, fp1, status);
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float_raise(float_flag_inexact, status);
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return a;
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}
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} else { /* |X| < 1/16 */
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if (compact < 0x3FD78000) { /* |X| < 2^(-40) */
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status->float_rounding_mode = user_rnd_mode;
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status->floatx80_rounding_precision = user_rnd_prec;
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a = floatx80_move(a, status);
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float_raise(float_flag_inexact, status);
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return a;
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} else {
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fp0 = a;
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xsave = a;
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fp0 = floatx80_mul(fp0, fp0, status); /* Y = X*X */
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fp1 = floatx80_mul(fp0, fp0, status); /* Z = Y*Y */
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fp2 = float64_to_floatx80(make_float64(0x3FB344447F876989),
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status); /* B6 */
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fp3 = float64_to_floatx80(make_float64(0xBFB744EE7FAF45DB),
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status); /* B5 */
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fp2 = floatx80_mul(fp2, fp1, status); /* Z*B6 */
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fp3 = floatx80_mul(fp3, fp1, status); /* Z*B5 */
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fp2 = floatx80_add(fp2, float64_to_floatx80(
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make_float64(0x3FBC71C646940220), status),
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status); /* B4+Z*B6 */
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fp3 = floatx80_add(fp3, float64_to_floatx80(
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make_float64(0xBFC24924921872F9),
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status), status); /* B3+Z*B5 */
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fp2 = floatx80_mul(fp2, fp1, status); /* Z*(B4+Z*B6) */
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fp1 = floatx80_mul(fp1, fp3, status); /* Z*(B3+Z*B5) */
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fp2 = floatx80_add(fp2, float64_to_floatx80(
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make_float64(0x3FC9999999998FA9), status),
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status); /* B2+Z*(B4+Z*B6) */
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fp1 = floatx80_add(fp1, float64_to_floatx80(
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make_float64(0xBFD5555555555555), status),
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status); /* B1+Z*(B3+Z*B5) */
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fp2 = floatx80_mul(fp2, fp0, status); /* Y*(B2+Z*(B4+Z*B6)) */
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fp0 = floatx80_mul(fp0, xsave, status); /* X*Y */
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/* [B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))] */
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fp1 = floatx80_add(fp1, fp2, status);
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/* X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]) */
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fp0 = floatx80_mul(fp0, fp1, status);
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status->float_rounding_mode = user_rnd_mode;
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status->floatx80_rounding_precision = user_rnd_prec;
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a = floatx80_add(fp0, xsave, status);
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float_raise(float_flag_inexact, status);
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return a;
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}
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}
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} else {
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aSig &= LIT64(0xF800000000000000);
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aSig |= LIT64(0x0400000000000000);
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xsave = packFloatx80(aSign, aExp, aSig); /* F */
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fp0 = a;
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fp1 = a; /* X */
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fp2 = packFloatx80(0, one_exp, one_sig); /* 1 */
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fp1 = floatx80_mul(fp1, xsave, status); /* X*F */
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fp0 = floatx80_sub(fp0, xsave, status); /* X-F */
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fp1 = floatx80_add(fp1, fp2, status); /* 1 + X*F */
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fp0 = floatx80_div(fp0, fp1, status); /* U = (X-F)/(1+X*F) */
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tbl_index = compact;
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tbl_index &= 0x7FFF0000;
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tbl_index -= 0x3FFB0000;
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tbl_index >>= 1;
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tbl_index += compact & 0x00007800;
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tbl_index >>= 11;
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fp3 = atan_tbl[tbl_index];
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fp3.high |= aSign ? 0x8000 : 0; /* ATAN(F) */
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fp1 = floatx80_mul(fp0, fp0, status); /* V = U*U */
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fp2 = float64_to_floatx80(make_float64(0xBFF6687E314987D8),
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status); /* A3 */
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fp2 = floatx80_add(fp2, fp1, status); /* A3+V */
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fp2 = floatx80_mul(fp2, fp1, status); /* V*(A3+V) */
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fp1 = floatx80_mul(fp1, fp0, status); /* U*V */
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fp2 = floatx80_add(fp2, float64_to_floatx80(
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make_float64(0x4002AC6934A26DB3), status),
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status); /* A2+V*(A3+V) */
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fp1 = floatx80_mul(fp1, float64_to_floatx80(
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make_float64(0xBFC2476F4E1DA28E), status),
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status); /* A1+U*V */
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fp1 = floatx80_mul(fp1, fp2, status); /* A1*U*V*(A2+V*(A3+V)) */
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fp0 = floatx80_add(fp0, fp1, status); /* ATAN(U) */
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status->float_rounding_mode = user_rnd_mode;
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status->floatx80_rounding_precision = user_rnd_prec;
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a = floatx80_add(fp0, fp3, status); /* ATAN(X) */
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float_raise(float_flag_inexact, status);
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return a;
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}
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}
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