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Diffstat (limited to 'arch/i386/math-emu/poly_tan.c')
| -rw-r--r-- | arch/i386/math-emu/poly_tan.c | 213 |
1 files changed, 213 insertions, 0 deletions
diff --git a/arch/i386/math-emu/poly_tan.c b/arch/i386/math-emu/poly_tan.c new file mode 100644 index 000000000..d9b09e438 --- /dev/null +++ b/arch/i386/math-emu/poly_tan.c @@ -0,0 +1,213 @@ +/*---------------------------------------------------------------------------+ + | poly_tan.c | + | | + | Compute the tan of a FPU_REG, using a polynomial approximation. | + | | + | Copyright (C) 1992,1993,1994 | + | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, | + | Australia. E-mail billm@vaxc.cc.monash.edu.au | + | | + | | + +---------------------------------------------------------------------------*/ + +#include "exception.h" +#include "reg_constant.h" +#include "fpu_emu.h" +#include "control_w.h" +#include "poly.h" + + +#define HiPOWERop 3 /* odd poly, positive terms */ +static const unsigned long long oddplterm[HiPOWERop] = +{ + 0x0000000000000000LL, + 0x0051a1cf08fca228LL, + 0x0000000071284ff7LL +}; + +#define HiPOWERon 2 /* odd poly, negative terms */ +static const unsigned long long oddnegterm[HiPOWERon] = +{ + 0x1291a9a184244e80LL, + 0x0000583245819c21LL +}; + +#define HiPOWERep 2 /* even poly, positive terms */ +static const unsigned long long evenplterm[HiPOWERep] = +{ + 0x0e848884b539e888LL, + 0x00003c7f18b887daLL +}; + +#define HiPOWERen 2 /* even poly, negative terms */ +static const unsigned long long evennegterm[HiPOWERen] = +{ + 0xf1f0200fd51569ccLL, + 0x003afb46105c4432LL +}; + +static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL; + + +/*--- poly_tan() ------------------------------------------------------------+ + | | + +---------------------------------------------------------------------------*/ +void poly_tan(FPU_REG const *arg, FPU_REG *result) +{ + long int exponent; + int invert; + Xsig argSq, argSqSq, accumulatoro, accumulatore, accum, + argSignif, fix_up; + unsigned long adj; + + exponent = arg->exp - EXP_BIAS; + +#ifdef PARANOID + if ( arg->sign != 0 ) /* Can't hack a number < 0.0 */ + { arith_invalid(result); return; } /* Need a positive number */ +#endif PARANOID + + /* Split the problem into two domains, smaller and larger than pi/4 */ + if ( (exponent == 0) || ((exponent == -1) && (arg->sigh > 0xc90fdaa2)) ) + { + /* The argument is greater than (approx) pi/4 */ + invert = 1; + accum.lsw = 0; + XSIG_LL(accum) = significand(arg); + + if ( exponent == 0 ) + { + /* The argument is >= 1.0 */ + /* Put the binary point at the left. */ + XSIG_LL(accum) <<= 1; + } + /* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */ + XSIG_LL(accum) = 0x921fb54442d18469LL - XSIG_LL(accum); + + argSignif.lsw = accum.lsw; + XSIG_LL(argSignif) = XSIG_LL(accum); + exponent = -1 + norm_Xsig(&argSignif); + } + else + { + invert = 0; + argSignif.lsw = 0; + XSIG_LL(accum) = XSIG_LL(argSignif) = significand(arg); + + if ( exponent < -1 ) + { + /* shift the argument right by the required places */ + if ( shrx(&XSIG_LL(accum), -1-exponent) >= 0x80000000U ) + XSIG_LL(accum) ++; /* round up */ + } + } + + XSIG_LL(argSq) = XSIG_LL(accum); argSq.lsw = accum.lsw; + mul_Xsig_Xsig(&argSq, &argSq); + XSIG_LL(argSqSq) = XSIG_LL(argSq); argSqSq.lsw = argSq.lsw; + mul_Xsig_Xsig(&argSqSq, &argSqSq); + + /* Compute the negative terms for the numerator polynomial */ + accumulatoro.msw = accumulatoro.midw = accumulatoro.lsw = 0; + polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddnegterm, HiPOWERon-1); + mul_Xsig_Xsig(&accumulatoro, &argSq); + negate_Xsig(&accumulatoro); + /* Add the positive terms */ + polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddplterm, HiPOWERop-1); + + + /* Compute the positive terms for the denominator polynomial */ + accumulatore.msw = accumulatore.midw = accumulatore.lsw = 0; + polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evenplterm, HiPOWERep-1); + mul_Xsig_Xsig(&accumulatore, &argSq); + negate_Xsig(&accumulatore); + /* Add the negative terms */ + polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evennegterm, HiPOWERen-1); + /* Multiply by arg^2 */ + mul64_Xsig(&accumulatore, &XSIG_LL(argSignif)); + mul64_Xsig(&accumulatore, &XSIG_LL(argSignif)); + /* de-normalize and divide by 2 */ + shr_Xsig(&accumulatore, -2*(1+exponent) + 1); + negate_Xsig(&accumulatore); /* This does 1 - accumulator */ + + /* Now find the ratio. */ + if ( accumulatore.msw == 0 ) + { + /* accumulatoro must contain 1.0 here, (actually, 0) but it + really doesn't matter what value we use because it will + have negligible effect in later calculations + */ + XSIG_LL(accum) = 0x8000000000000000LL; + accum.lsw = 0; + } + else + { + div_Xsig(&accumulatoro, &accumulatore, &accum); + } + + /* Multiply by 1/3 * arg^3 */ + mul64_Xsig(&accum, &XSIG_LL(argSignif)); + mul64_Xsig(&accum, &XSIG_LL(argSignif)); + mul64_Xsig(&accum, &XSIG_LL(argSignif)); + mul64_Xsig(&accum, &twothirds); + shr_Xsig(&accum, -2*(exponent+1)); + + /* tan(arg) = arg + accum */ + add_two_Xsig(&accum, &argSignif, &exponent); + + if ( invert ) + { + /* We now have the value of tan(pi_2 - arg) where pi_2 is an + approximation for pi/2 + */ + /* The next step is to fix the answer to compensate for the + error due to the approximation used for pi/2 + */ + + /* This is (approx) delta, the error in our approx for pi/2 + (see above). It has an exponent of -65 + */ + XSIG_LL(fix_up) = 0x898cc51701b839a2LL; + fix_up.lsw = 0; + + if ( exponent == 0 ) + adj = 0xffffffff; /* We want approx 1.0 here, but + this is close enough. */ + else if ( exponent > -30 ) + { + adj = accum.msw >> -(exponent+1); /* tan */ + mul_32_32(adj, adj, &adj); /* tan^2 */ + } + else + adj = 0; + mul_32_32(0x898cc517, adj, &adj); /* delta * tan^2 */ + + fix_up.msw += adj; + if ( !(fix_up.msw & 0x80000000) ) /* did fix_up overflow ? */ + { + /* Yes, we need to add an msb */ + shr_Xsig(&fix_up, 1); + fix_up.msw |= 0x80000000; + shr_Xsig(&fix_up, 64 + exponent); + } + else + shr_Xsig(&fix_up, 65 + exponent); + + add_two_Xsig(&accum, &fix_up, &exponent); + + /* accum now contains tan(pi/2 - arg). + Use tan(arg) = 1.0 / tan(pi/2 - arg) + */ + accumulatoro.lsw = accumulatoro.midw = 0; + accumulatoro.msw = 0x80000000; + div_Xsig(&accumulatoro, &accum, &accum); + exponent = - exponent - 1; + } + + /* Transfer the result */ + round_Xsig(&accum); + *(short *)&(result->sign) = 0; + significand(result) = XSIG_LL(accum); + result->exp = EXP_BIAS + exponent; + +} |