mirror of
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1da177e4c3
Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
1845 lines
41 KiB
C
1845 lines
41 KiB
C
/*---------------------------------------------------------------------------+
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| fpu_trig.c |
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| |
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| Implementation of the FPU "transcendental" functions. |
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| |
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| Copyright (C) 1992,1993,1994,1997,1999 |
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| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
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| Australia. E-mail billm@melbpc.org.au |
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+---------------------------------------------------------------------------*/
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#include "fpu_system.h"
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#include "exception.h"
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#include "fpu_emu.h"
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#include "status_w.h"
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#include "control_w.h"
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#include "reg_constant.h"
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static void rem_kernel(unsigned long long st0, unsigned long long *y,
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unsigned long long st1,
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unsigned long long q, int n);
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#define BETTER_THAN_486
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#define FCOS 4
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/* Used only by fptan, fsin, fcos, and fsincos. */
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/* This routine produces very accurate results, similar to
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using a value of pi with more than 128 bits precision. */
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/* Limited measurements show no results worse than 64 bit precision
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except for the results for arguments close to 2^63, where the
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precision of the result sometimes degrades to about 63.9 bits */
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static int trig_arg(FPU_REG *st0_ptr, int even)
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{
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FPU_REG tmp;
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u_char tmptag;
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unsigned long long q;
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int old_cw = control_word, saved_status = partial_status;
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int tag, st0_tag = TAG_Valid;
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if ( exponent(st0_ptr) >= 63 )
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{
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partial_status |= SW_C2; /* Reduction incomplete. */
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return -1;
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}
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control_word &= ~CW_RC;
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control_word |= RC_CHOP;
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setpositive(st0_ptr);
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tag = FPU_u_div(st0_ptr, &CONST_PI2, &tmp, PR_64_BITS | RC_CHOP | 0x3f,
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SIGN_POS);
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FPU_round_to_int(&tmp, tag); /* Fortunately, this can't overflow
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to 2^64 */
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q = significand(&tmp);
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if ( q )
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{
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rem_kernel(significand(st0_ptr),
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&significand(&tmp),
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significand(&CONST_PI2),
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q, exponent(st0_ptr) - exponent(&CONST_PI2));
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setexponent16(&tmp, exponent(&CONST_PI2));
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st0_tag = FPU_normalize(&tmp);
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FPU_copy_to_reg0(&tmp, st0_tag);
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}
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if ( (even && !(q & 1)) || (!even && (q & 1)) )
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{
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st0_tag = FPU_sub(REV|LOADED|TAG_Valid, (int)&CONST_PI2, FULL_PRECISION);
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#ifdef BETTER_THAN_486
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/* So far, the results are exact but based upon a 64 bit
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precision approximation to pi/2. The technique used
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now is equivalent to using an approximation to pi/2 which
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is accurate to about 128 bits. */
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if ( (exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64) || (q > 1) )
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{
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/* This code gives the effect of having pi/2 to better than
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128 bits precision. */
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significand(&tmp) = q + 1;
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setexponent16(&tmp, 63);
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FPU_normalize(&tmp);
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tmptag =
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FPU_u_mul(&CONST_PI2extra, &tmp, &tmp, FULL_PRECISION, SIGN_POS,
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exponent(&CONST_PI2extra) + exponent(&tmp));
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setsign(&tmp, getsign(&CONST_PI2extra));
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st0_tag = FPU_add(&tmp, tmptag, 0, FULL_PRECISION);
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if ( signnegative(st0_ptr) )
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{
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/* CONST_PI2extra is negative, so the result of the addition
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can be negative. This means that the argument is actually
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in a different quadrant. The correction is always < pi/2,
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so it can't overflow into yet another quadrant. */
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setpositive(st0_ptr);
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q++;
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}
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}
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#endif /* BETTER_THAN_486 */
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}
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#ifdef BETTER_THAN_486
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else
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{
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/* So far, the results are exact but based upon a 64 bit
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precision approximation to pi/2. The technique used
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now is equivalent to using an approximation to pi/2 which
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is accurate to about 128 bits. */
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if ( ((q > 0) && (exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64))
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|| (q > 1) )
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{
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/* This code gives the effect of having p/2 to better than
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128 bits precision. */
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significand(&tmp) = q;
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setexponent16(&tmp, 63);
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FPU_normalize(&tmp); /* This must return TAG_Valid */
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tmptag = FPU_u_mul(&CONST_PI2extra, &tmp, &tmp, FULL_PRECISION,
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SIGN_POS,
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exponent(&CONST_PI2extra) + exponent(&tmp));
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setsign(&tmp, getsign(&CONST_PI2extra));
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st0_tag = FPU_sub(LOADED|(tmptag & 0x0f), (int)&tmp,
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FULL_PRECISION);
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if ( (exponent(st0_ptr) == exponent(&CONST_PI2)) &&
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((st0_ptr->sigh > CONST_PI2.sigh)
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|| ((st0_ptr->sigh == CONST_PI2.sigh)
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&& (st0_ptr->sigl > CONST_PI2.sigl))) )
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{
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/* CONST_PI2extra is negative, so the result of the
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subtraction can be larger than pi/2. This means
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that the argument is actually in a different quadrant.
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The correction is always < pi/2, so it can't overflow
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into yet another quadrant. */
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st0_tag = FPU_sub(REV|LOADED|TAG_Valid, (int)&CONST_PI2,
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FULL_PRECISION);
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q++;
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}
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}
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}
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#endif /* BETTER_THAN_486 */
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FPU_settag0(st0_tag);
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control_word = old_cw;
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partial_status = saved_status & ~SW_C2; /* Reduction complete. */
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return (q & 3) | even;
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}
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/* Convert a long to register */
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static void convert_l2reg(long const *arg, int deststnr)
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{
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int tag;
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long num = *arg;
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u_char sign;
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FPU_REG *dest = &st(deststnr);
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if (num == 0)
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{
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FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr);
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return;
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}
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if (num > 0)
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{ sign = SIGN_POS; }
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else
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{ num = -num; sign = SIGN_NEG; }
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dest->sigh = num;
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dest->sigl = 0;
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setexponent16(dest, 31);
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tag = FPU_normalize(dest);
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FPU_settagi(deststnr, tag);
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setsign(dest, sign);
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return;
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}
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static void single_arg_error(FPU_REG *st0_ptr, u_char st0_tag)
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{
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if ( st0_tag == TAG_Empty )
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FPU_stack_underflow(); /* Puts a QNaN in st(0) */
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else if ( st0_tag == TW_NaN )
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real_1op_NaN(st0_ptr); /* return with a NaN in st(0) */
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#ifdef PARANOID
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else
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EXCEPTION(EX_INTERNAL|0x0112);
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#endif /* PARANOID */
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}
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static void single_arg_2_error(FPU_REG *st0_ptr, u_char st0_tag)
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{
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int isNaN;
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switch ( st0_tag )
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{
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case TW_NaN:
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isNaN = (exponent(st0_ptr) == EXP_OVER) && (st0_ptr->sigh & 0x80000000);
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if ( isNaN && !(st0_ptr->sigh & 0x40000000) ) /* Signaling ? */
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{
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EXCEPTION(EX_Invalid);
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if ( control_word & CW_Invalid )
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{
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/* The masked response */
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/* Convert to a QNaN */
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st0_ptr->sigh |= 0x40000000;
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push();
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FPU_copy_to_reg0(st0_ptr, TAG_Special);
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}
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}
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else if ( isNaN )
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{
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/* A QNaN */
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push();
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FPU_copy_to_reg0(st0_ptr, TAG_Special);
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}
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else
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{
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/* pseudoNaN or other unsupported */
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EXCEPTION(EX_Invalid);
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if ( control_word & CW_Invalid )
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{
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/* The masked response */
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FPU_copy_to_reg0(&CONST_QNaN, TAG_Special);
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push();
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FPU_copy_to_reg0(&CONST_QNaN, TAG_Special);
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}
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}
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break; /* return with a NaN in st(0) */
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#ifdef PARANOID
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default:
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EXCEPTION(EX_INTERNAL|0x0112);
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#endif /* PARANOID */
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}
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}
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/*---------------------------------------------------------------------------*/
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static void f2xm1(FPU_REG *st0_ptr, u_char tag)
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{
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FPU_REG a;
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clear_C1();
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if ( tag == TAG_Valid )
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{
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/* For an 80486 FPU, the result is undefined if the arg is >= 1.0 */
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if ( exponent(st0_ptr) < 0 )
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{
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denormal_arg:
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FPU_to_exp16(st0_ptr, &a);
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/* poly_2xm1(x) requires 0 < st(0) < 1. */
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poly_2xm1(getsign(st0_ptr), &a, st0_ptr);
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}
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set_precision_flag_up(); /* 80486 appears to always do this */
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return;
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}
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if ( tag == TAG_Zero )
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return;
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if ( tag == TAG_Special )
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tag = FPU_Special(st0_ptr);
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switch ( tag )
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{
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case TW_Denormal:
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if ( denormal_operand() < 0 )
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return;
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goto denormal_arg;
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case TW_Infinity:
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if ( signnegative(st0_ptr) )
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{
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/* -infinity gives -1 (p16-10) */
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FPU_copy_to_reg0(&CONST_1, TAG_Valid);
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setnegative(st0_ptr);
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}
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return;
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default:
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single_arg_error(st0_ptr, tag);
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}
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}
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static void fptan(FPU_REG *st0_ptr, u_char st0_tag)
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{
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FPU_REG *st_new_ptr;
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int q;
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u_char arg_sign = getsign(st0_ptr);
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/* Stack underflow has higher priority */
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if ( st0_tag == TAG_Empty )
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{
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FPU_stack_underflow(); /* Puts a QNaN in st(0) */
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if ( control_word & CW_Invalid )
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{
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st_new_ptr = &st(-1);
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push();
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FPU_stack_underflow(); /* Puts a QNaN in the new st(0) */
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}
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return;
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}
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if ( STACK_OVERFLOW )
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{ FPU_stack_overflow(); return; }
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if ( st0_tag == TAG_Valid )
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{
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if ( exponent(st0_ptr) > -40 )
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{
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if ( (q = trig_arg(st0_ptr, 0)) == -1 )
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{
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/* Operand is out of range */
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return;
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}
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poly_tan(st0_ptr);
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setsign(st0_ptr, (q & 1) ^ (arg_sign != 0));
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set_precision_flag_up(); /* We do not really know if up or down */
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}
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else
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{
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/* For a small arg, the result == the argument */
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/* Underflow may happen */
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denormal_arg:
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FPU_to_exp16(st0_ptr, st0_ptr);
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st0_tag = FPU_round(st0_ptr, 1, 0, FULL_PRECISION, arg_sign);
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FPU_settag0(st0_tag);
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}
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push();
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FPU_copy_to_reg0(&CONST_1, TAG_Valid);
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return;
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}
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if ( st0_tag == TAG_Zero )
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{
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push();
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FPU_copy_to_reg0(&CONST_1, TAG_Valid);
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setcc(0);
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return;
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}
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if ( st0_tag == TAG_Special )
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st0_tag = FPU_Special(st0_ptr);
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if ( st0_tag == TW_Denormal )
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{
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if ( denormal_operand() < 0 )
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return;
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goto denormal_arg;
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}
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if ( st0_tag == TW_Infinity )
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{
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/* The 80486 treats infinity as an invalid operand */
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if ( arith_invalid(0) >= 0 )
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{
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st_new_ptr = &st(-1);
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push();
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arith_invalid(0);
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}
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return;
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}
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single_arg_2_error(st0_ptr, st0_tag);
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}
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static void fxtract(FPU_REG *st0_ptr, u_char st0_tag)
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{
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FPU_REG *st_new_ptr;
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u_char sign;
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register FPU_REG *st1_ptr = st0_ptr; /* anticipate */
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|
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if ( STACK_OVERFLOW )
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{ FPU_stack_overflow(); return; }
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clear_C1();
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|
|
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if ( st0_tag == TAG_Valid )
|
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{
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long e;
|
|
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push();
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sign = getsign(st1_ptr);
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reg_copy(st1_ptr, st_new_ptr);
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setexponent16(st_new_ptr, exponent(st_new_ptr));
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denormal_arg:
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|
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e = exponent16(st_new_ptr);
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convert_l2reg(&e, 1);
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setexponentpos(st_new_ptr, 0);
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setsign(st_new_ptr, sign);
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FPU_settag0(TAG_Valid); /* Needed if arg was a denormal */
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return;
|
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}
|
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else if ( st0_tag == TAG_Zero )
|
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{
|
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sign = getsign(st0_ptr);
|
|
|
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if ( FPU_divide_by_zero(0, SIGN_NEG) < 0 )
|
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return;
|
|
|
|
push();
|
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FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
|
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setsign(st_new_ptr, sign);
|
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return;
|
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}
|
|
|
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if ( st0_tag == TAG_Special )
|
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st0_tag = FPU_Special(st0_ptr);
|
|
|
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if ( st0_tag == TW_Denormal )
|
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{
|
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if (denormal_operand() < 0 )
|
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return;
|
|
|
|
push();
|
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sign = getsign(st1_ptr);
|
|
FPU_to_exp16(st1_ptr, st_new_ptr);
|
|
goto denormal_arg;
|
|
}
|
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else if ( st0_tag == TW_Infinity )
|
|
{
|
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sign = getsign(st0_ptr);
|
|
setpositive(st0_ptr);
|
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push();
|
|
FPU_copy_to_reg0(&CONST_INF, TAG_Special);
|
|
setsign(st_new_ptr, sign);
|
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return;
|
|
}
|
|
else if ( st0_tag == TW_NaN )
|
|
{
|
|
if ( real_1op_NaN(st0_ptr) < 0 )
|
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return;
|
|
|
|
push();
|
|
FPU_copy_to_reg0(st0_ptr, TAG_Special);
|
|
return;
|
|
}
|
|
else if ( st0_tag == TAG_Empty )
|
|
{
|
|
/* Is this the correct behaviour? */
|
|
if ( control_word & EX_Invalid )
|
|
{
|
|
FPU_stack_underflow();
|
|
push();
|
|
FPU_stack_underflow();
|
|
}
|
|
else
|
|
EXCEPTION(EX_StackUnder);
|
|
}
|
|
#ifdef PARANOID
|
|
else
|
|
EXCEPTION(EX_INTERNAL | 0x119);
|
|
#endif /* PARANOID */
|
|
}
|
|
|
|
|
|
static void fdecstp(void)
|
|
{
|
|
clear_C1();
|
|
top--;
|
|
}
|
|
|
|
static void fincstp(void)
|
|
{
|
|
clear_C1();
|
|
top++;
|
|
}
|
|
|
|
|
|
static void fsqrt_(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
int expon;
|
|
|
|
clear_C1();
|
|
|
|
if ( st0_tag == TAG_Valid )
|
|
{
|
|
u_char tag;
|
|
|
|
if (signnegative(st0_ptr))
|
|
{
|
|
arith_invalid(0); /* sqrt(negative) is invalid */
|
|
return;
|
|
}
|
|
|
|
/* make st(0) in [1.0 .. 4.0) */
|
|
expon = exponent(st0_ptr);
|
|
|
|
denormal_arg:
|
|
|
|
setexponent16(st0_ptr, (expon & 1));
|
|
|
|
/* Do the computation, the sign of the result will be positive. */
|
|
tag = wm_sqrt(st0_ptr, 0, 0, control_word, SIGN_POS);
|
|
addexponent(st0_ptr, expon >> 1);
|
|
FPU_settag0(tag);
|
|
return;
|
|
}
|
|
|
|
if ( st0_tag == TAG_Zero )
|
|
return;
|
|
|
|
if ( st0_tag == TAG_Special )
|
|
st0_tag = FPU_Special(st0_ptr);
|
|
|
|
if ( st0_tag == TW_Infinity )
|
|
{
|
|
if ( signnegative(st0_ptr) )
|
|
arith_invalid(0); /* sqrt(-Infinity) is invalid */
|
|
return;
|
|
}
|
|
else if ( st0_tag == TW_Denormal )
|
|
{
|
|
if (signnegative(st0_ptr))
|
|
{
|
|
arith_invalid(0); /* sqrt(negative) is invalid */
|
|
return;
|
|
}
|
|
|
|
if ( denormal_operand() < 0 )
|
|
return;
|
|
|
|
FPU_to_exp16(st0_ptr, st0_ptr);
|
|
|
|
expon = exponent16(st0_ptr);
|
|
|
|
goto denormal_arg;
|
|
}
|
|
|
|
single_arg_error(st0_ptr, st0_tag);
|
|
|
|
}
|
|
|
|
|
|
static void frndint_(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
int flags, tag;
|
|
|
|
if ( st0_tag == TAG_Valid )
|
|
{
|
|
u_char sign;
|
|
|
|
denormal_arg:
|
|
|
|
sign = getsign(st0_ptr);
|
|
|
|
if (exponent(st0_ptr) > 63)
|
|
return;
|
|
|
|
if ( st0_tag == TW_Denormal )
|
|
{
|
|
if (denormal_operand() < 0 )
|
|
return;
|
|
}
|
|
|
|
/* Fortunately, this can't overflow to 2^64 */
|
|
if ( (flags = FPU_round_to_int(st0_ptr, st0_tag)) )
|
|
set_precision_flag(flags);
|
|
|
|
setexponent16(st0_ptr, 63);
|
|
tag = FPU_normalize(st0_ptr);
|
|
setsign(st0_ptr, sign);
|
|
FPU_settag0(tag);
|
|
return;
|
|
}
|
|
|
|
if ( st0_tag == TAG_Zero )
|
|
return;
|
|
|
|
if ( st0_tag == TAG_Special )
|
|
st0_tag = FPU_Special(st0_ptr);
|
|
|
|
if ( st0_tag == TW_Denormal )
|
|
goto denormal_arg;
|
|
else if ( st0_tag == TW_Infinity )
|
|
return;
|
|
else
|
|
single_arg_error(st0_ptr, st0_tag);
|
|
}
|
|
|
|
|
|
static int fsin(FPU_REG *st0_ptr, u_char tag)
|
|
{
|
|
u_char arg_sign = getsign(st0_ptr);
|
|
|
|
if ( tag == TAG_Valid )
|
|
{
|
|
int q;
|
|
|
|
if ( exponent(st0_ptr) > -40 )
|
|
{
|
|
if ( (q = trig_arg(st0_ptr, 0)) == -1 )
|
|
{
|
|
/* Operand is out of range */
|
|
return 1;
|
|
}
|
|
|
|
poly_sine(st0_ptr);
|
|
|
|
if (q & 2)
|
|
changesign(st0_ptr);
|
|
|
|
setsign(st0_ptr, getsign(st0_ptr) ^ arg_sign);
|
|
|
|
/* We do not really know if up or down */
|
|
set_precision_flag_up();
|
|
return 0;
|
|
}
|
|
else
|
|
{
|
|
/* For a small arg, the result == the argument */
|
|
set_precision_flag_up(); /* Must be up. */
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
if ( tag == TAG_Zero )
|
|
{
|
|
setcc(0);
|
|
return 0;
|
|
}
|
|
|
|
if ( tag == TAG_Special )
|
|
tag = FPU_Special(st0_ptr);
|
|
|
|
if ( tag == TW_Denormal )
|
|
{
|
|
if ( denormal_operand() < 0 )
|
|
return 1;
|
|
|
|
/* For a small arg, the result == the argument */
|
|
/* Underflow may happen */
|
|
FPU_to_exp16(st0_ptr, st0_ptr);
|
|
|
|
tag = FPU_round(st0_ptr, 1, 0, FULL_PRECISION, arg_sign);
|
|
|
|
FPU_settag0(tag);
|
|
|
|
return 0;
|
|
}
|
|
else if ( tag == TW_Infinity )
|
|
{
|
|
/* The 80486 treats infinity as an invalid operand */
|
|
arith_invalid(0);
|
|
return 1;
|
|
}
|
|
else
|
|
{
|
|
single_arg_error(st0_ptr, tag);
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
|
|
static int f_cos(FPU_REG *st0_ptr, u_char tag)
|
|
{
|
|
u_char st0_sign;
|
|
|
|
st0_sign = getsign(st0_ptr);
|
|
|
|
if ( tag == TAG_Valid )
|
|
{
|
|
int q;
|
|
|
|
if ( exponent(st0_ptr) > -40 )
|
|
{
|
|
if ( (exponent(st0_ptr) < 0)
|
|
|| ((exponent(st0_ptr) == 0)
|
|
&& (significand(st0_ptr) <= 0xc90fdaa22168c234LL)) )
|
|
{
|
|
poly_cos(st0_ptr);
|
|
|
|
/* We do not really know if up or down */
|
|
set_precision_flag_down();
|
|
|
|
return 0;
|
|
}
|
|
else if ( (q = trig_arg(st0_ptr, FCOS)) != -1 )
|
|
{
|
|
poly_sine(st0_ptr);
|
|
|
|
if ((q+1) & 2)
|
|
changesign(st0_ptr);
|
|
|
|
/* We do not really know if up or down */
|
|
set_precision_flag_down();
|
|
|
|
return 0;
|
|
}
|
|
else
|
|
{
|
|
/* Operand is out of range */
|
|
return 1;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
denormal_arg:
|
|
|
|
setcc(0);
|
|
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
|
|
#ifdef PECULIAR_486
|
|
set_precision_flag_down(); /* 80486 appears to do this. */
|
|
#else
|
|
set_precision_flag_up(); /* Must be up. */
|
|
#endif /* PECULIAR_486 */
|
|
return 0;
|
|
}
|
|
}
|
|
else if ( tag == TAG_Zero )
|
|
{
|
|
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
|
|
setcc(0);
|
|
return 0;
|
|
}
|
|
|
|
if ( tag == TAG_Special )
|
|
tag = FPU_Special(st0_ptr);
|
|
|
|
if ( tag == TW_Denormal )
|
|
{
|
|
if ( denormal_operand() < 0 )
|
|
return 1;
|
|
|
|
goto denormal_arg;
|
|
}
|
|
else if ( tag == TW_Infinity )
|
|
{
|
|
/* The 80486 treats infinity as an invalid operand */
|
|
arith_invalid(0);
|
|
return 1;
|
|
}
|
|
else
|
|
{
|
|
single_arg_error(st0_ptr, tag); /* requires st0_ptr == &st(0) */
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
|
|
static void fcos(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
f_cos(st0_ptr, st0_tag);
|
|
}
|
|
|
|
|
|
static void fsincos(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
FPU_REG *st_new_ptr;
|
|
FPU_REG arg;
|
|
u_char tag;
|
|
|
|
/* Stack underflow has higher priority */
|
|
if ( st0_tag == TAG_Empty )
|
|
{
|
|
FPU_stack_underflow(); /* Puts a QNaN in st(0) */
|
|
if ( control_word & CW_Invalid )
|
|
{
|
|
st_new_ptr = &st(-1);
|
|
push();
|
|
FPU_stack_underflow(); /* Puts a QNaN in the new st(0) */
|
|
}
|
|
return;
|
|
}
|
|
|
|
if ( STACK_OVERFLOW )
|
|
{ FPU_stack_overflow(); return; }
|
|
|
|
if ( st0_tag == TAG_Special )
|
|
tag = FPU_Special(st0_ptr);
|
|
else
|
|
tag = st0_tag;
|
|
|
|
if ( tag == TW_NaN )
|
|
{
|
|
single_arg_2_error(st0_ptr, TW_NaN);
|
|
return;
|
|
}
|
|
else if ( tag == TW_Infinity )
|
|
{
|
|
/* The 80486 treats infinity as an invalid operand */
|
|
if ( arith_invalid(0) >= 0 )
|
|
{
|
|
/* Masked response */
|
|
push();
|
|
arith_invalid(0);
|
|
}
|
|
return;
|
|
}
|
|
|
|
reg_copy(st0_ptr, &arg);
|
|
if ( !fsin(st0_ptr, st0_tag) )
|
|
{
|
|
push();
|
|
FPU_copy_to_reg0(&arg, st0_tag);
|
|
f_cos(&st(0), st0_tag);
|
|
}
|
|
else
|
|
{
|
|
/* An error, so restore st(0) */
|
|
FPU_copy_to_reg0(&arg, st0_tag);
|
|
}
|
|
}
|
|
|
|
|
|
/*---------------------------------------------------------------------------*/
|
|
/* The following all require two arguments: st(0) and st(1) */
|
|
|
|
/* A lean, mean kernel for the fprem instructions. This relies upon
|
|
the division and rounding to an integer in do_fprem giving an
|
|
exact result. Because of this, rem_kernel() needs to deal only with
|
|
the least significant 64 bits, the more significant bits of the
|
|
result must be zero.
|
|
*/
|
|
static void rem_kernel(unsigned long long st0, unsigned long long *y,
|
|
unsigned long long st1,
|
|
unsigned long long q, int n)
|
|
{
|
|
int dummy;
|
|
unsigned long long x;
|
|
|
|
x = st0 << n;
|
|
|
|
/* Do the required multiplication and subtraction in the one operation */
|
|
|
|
/* lsw x -= lsw st1 * lsw q */
|
|
asm volatile ("mull %4; subl %%eax,%0; sbbl %%edx,%1"
|
|
:"=m" (((unsigned *)&x)[0]), "=m" (((unsigned *)&x)[1]),
|
|
"=a" (dummy)
|
|
:"2" (((unsigned *)&st1)[0]), "m" (((unsigned *)&q)[0])
|
|
:"%dx");
|
|
/* msw x -= msw st1 * lsw q */
|
|
asm volatile ("mull %3; subl %%eax,%0"
|
|
:"=m" (((unsigned *)&x)[1]), "=a" (dummy)
|
|
:"1" (((unsigned *)&st1)[1]), "m" (((unsigned *)&q)[0])
|
|
:"%dx");
|
|
/* msw x -= lsw st1 * msw q */
|
|
asm volatile ("mull %3; subl %%eax,%0"
|
|
:"=m" (((unsigned *)&x)[1]), "=a" (dummy)
|
|
:"1" (((unsigned *)&st1)[0]), "m" (((unsigned *)&q)[1])
|
|
:"%dx");
|
|
|
|
*y = x;
|
|
}
|
|
|
|
|
|
/* Remainder of st(0) / st(1) */
|
|
/* This routine produces exact results, i.e. there is never any
|
|
rounding or truncation, etc of the result. */
|
|
static void do_fprem(FPU_REG *st0_ptr, u_char st0_tag, int round)
|
|
{
|
|
FPU_REG *st1_ptr = &st(1);
|
|
u_char st1_tag = FPU_gettagi(1);
|
|
|
|
if ( !((st0_tag ^ TAG_Valid) | (st1_tag ^ TAG_Valid)) )
|
|
{
|
|
FPU_REG tmp, st0, st1;
|
|
u_char st0_sign, st1_sign;
|
|
u_char tmptag;
|
|
int tag;
|
|
int old_cw;
|
|
int expdif;
|
|
long long q;
|
|
unsigned short saved_status;
|
|
int cc;
|
|
|
|
fprem_valid:
|
|
/* Convert registers for internal use. */
|
|
st0_sign = FPU_to_exp16(st0_ptr, &st0);
|
|
st1_sign = FPU_to_exp16(st1_ptr, &st1);
|
|
expdif = exponent16(&st0) - exponent16(&st1);
|
|
|
|
old_cw = control_word;
|
|
cc = 0;
|
|
|
|
/* We want the status following the denorm tests, but don't want
|
|
the status changed by the arithmetic operations. */
|
|
saved_status = partial_status;
|
|
control_word &= ~CW_RC;
|
|
control_word |= RC_CHOP;
|
|
|
|
if ( expdif < 64 )
|
|
{
|
|
/* This should be the most common case */
|
|
|
|
if ( expdif > -2 )
|
|
{
|
|
u_char sign = st0_sign ^ st1_sign;
|
|
tag = FPU_u_div(&st0, &st1, &tmp,
|
|
PR_64_BITS | RC_CHOP | 0x3f,
|
|
sign);
|
|
setsign(&tmp, sign);
|
|
|
|
if ( exponent(&tmp) >= 0 )
|
|
{
|
|
FPU_round_to_int(&tmp, tag); /* Fortunately, this can't
|
|
overflow to 2^64 */
|
|
q = significand(&tmp);
|
|
|
|
rem_kernel(significand(&st0),
|
|
&significand(&tmp),
|
|
significand(&st1),
|
|
q, expdif);
|
|
|
|
setexponent16(&tmp, exponent16(&st1));
|
|
}
|
|
else
|
|
{
|
|
reg_copy(&st0, &tmp);
|
|
q = 0;
|
|
}
|
|
|
|
if ( (round == RC_RND) && (tmp.sigh & 0xc0000000) )
|
|
{
|
|
/* We may need to subtract st(1) once more,
|
|
to get a result <= 1/2 of st(1). */
|
|
unsigned long long x;
|
|
expdif = exponent16(&st1) - exponent16(&tmp);
|
|
if ( expdif <= 1 )
|
|
{
|
|
if ( expdif == 0 )
|
|
x = significand(&st1) - significand(&tmp);
|
|
else /* expdif is 1 */
|
|
x = (significand(&st1) << 1) - significand(&tmp);
|
|
if ( (x < significand(&tmp)) ||
|
|
/* or equi-distant (from 0 & st(1)) and q is odd */
|
|
((x == significand(&tmp)) && (q & 1) ) )
|
|
{
|
|
st0_sign = ! st0_sign;
|
|
significand(&tmp) = x;
|
|
q++;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (q & 4) cc |= SW_C0;
|
|
if (q & 2) cc |= SW_C3;
|
|
if (q & 1) cc |= SW_C1;
|
|
}
|
|
else
|
|
{
|
|
control_word = old_cw;
|
|
setcc(0);
|
|
return;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* There is a large exponent difference ( >= 64 ) */
|
|
/* To make much sense, the code in this section should
|
|
be done at high precision. */
|
|
int exp_1, N;
|
|
u_char sign;
|
|
|
|
/* prevent overflow here */
|
|
/* N is 'a number between 32 and 63' (p26-113) */
|
|
reg_copy(&st0, &tmp);
|
|
tmptag = st0_tag;
|
|
N = (expdif & 0x0000001f) + 32; /* This choice gives results
|
|
identical to an AMD 486 */
|
|
setexponent16(&tmp, N);
|
|
exp_1 = exponent16(&st1);
|
|
setexponent16(&st1, 0);
|
|
expdif -= N;
|
|
|
|
sign = getsign(&tmp) ^ st1_sign;
|
|
tag = FPU_u_div(&tmp, &st1, &tmp, PR_64_BITS | RC_CHOP | 0x3f,
|
|
sign);
|
|
setsign(&tmp, sign);
|
|
|
|
FPU_round_to_int(&tmp, tag); /* Fortunately, this can't
|
|
overflow to 2^64 */
|
|
|
|
rem_kernel(significand(&st0),
|
|
&significand(&tmp),
|
|
significand(&st1),
|
|
significand(&tmp),
|
|
exponent(&tmp)
|
|
);
|
|
setexponent16(&tmp, exp_1 + expdif);
|
|
|
|
/* It is possible for the operation to be complete here.
|
|
What does the IEEE standard say? The Intel 80486 manual
|
|
implies that the operation will never be completed at this
|
|
point, and the behaviour of a real 80486 confirms this.
|
|
*/
|
|
if ( !(tmp.sigh | tmp.sigl) )
|
|
{
|
|
/* The result is zero */
|
|
control_word = old_cw;
|
|
partial_status = saved_status;
|
|
FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
|
|
setsign(&st0, st0_sign);
|
|
#ifdef PECULIAR_486
|
|
setcc(SW_C2);
|
|
#else
|
|
setcc(0);
|
|
#endif /* PECULIAR_486 */
|
|
return;
|
|
}
|
|
cc = SW_C2;
|
|
}
|
|
|
|
control_word = old_cw;
|
|
partial_status = saved_status;
|
|
tag = FPU_normalize_nuo(&tmp);
|
|
reg_copy(&tmp, st0_ptr);
|
|
|
|
/* The only condition to be looked for is underflow,
|
|
and it can occur here only if underflow is unmasked. */
|
|
if ( (exponent16(&tmp) <= EXP_UNDER) && (tag != TAG_Zero)
|
|
&& !(control_word & CW_Underflow) )
|
|
{
|
|
setcc(cc);
|
|
tag = arith_underflow(st0_ptr);
|
|
setsign(st0_ptr, st0_sign);
|
|
FPU_settag0(tag);
|
|
return;
|
|
}
|
|
else if ( (exponent16(&tmp) > EXP_UNDER) || (tag == TAG_Zero) )
|
|
{
|
|
stdexp(st0_ptr);
|
|
setsign(st0_ptr, st0_sign);
|
|
}
|
|
else
|
|
{
|
|
tag = FPU_round(st0_ptr, 0, 0, FULL_PRECISION, st0_sign);
|
|
}
|
|
FPU_settag0(tag);
|
|
setcc(cc);
|
|
|
|
return;
|
|
}
|
|
|
|
if ( st0_tag == TAG_Special )
|
|
st0_tag = FPU_Special(st0_ptr);
|
|
if ( st1_tag == TAG_Special )
|
|
st1_tag = FPU_Special(st1_ptr);
|
|
|
|
if ( ((st0_tag == TAG_Valid) && (st1_tag == TW_Denormal))
|
|
|| ((st0_tag == TW_Denormal) && (st1_tag == TAG_Valid))
|
|
|| ((st0_tag == TW_Denormal) && (st1_tag == TW_Denormal)) )
|
|
{
|
|
if ( denormal_operand() < 0 )
|
|
return;
|
|
goto fprem_valid;
|
|
}
|
|
else if ( (st0_tag == TAG_Empty) || (st1_tag == TAG_Empty) )
|
|
{
|
|
FPU_stack_underflow();
|
|
return;
|
|
}
|
|
else if ( st0_tag == TAG_Zero )
|
|
{
|
|
if ( st1_tag == TAG_Valid )
|
|
{
|
|
setcc(0); return;
|
|
}
|
|
else if ( st1_tag == TW_Denormal )
|
|
{
|
|
if ( denormal_operand() < 0 )
|
|
return;
|
|
setcc(0); return;
|
|
}
|
|
else if ( st1_tag == TAG_Zero )
|
|
{ arith_invalid(0); return; } /* fprem(?,0) always invalid */
|
|
else if ( st1_tag == TW_Infinity )
|
|
{ setcc(0); return; }
|
|
}
|
|
else if ( (st0_tag == TAG_Valid) || (st0_tag == TW_Denormal) )
|
|
{
|
|
if ( st1_tag == TAG_Zero )
|
|
{
|
|
arith_invalid(0); /* fprem(Valid,Zero) is invalid */
|
|
return;
|
|
}
|
|
else if ( st1_tag != TW_NaN )
|
|
{
|
|
if ( ((st0_tag == TW_Denormal) || (st1_tag == TW_Denormal))
|
|
&& (denormal_operand() < 0) )
|
|
return;
|
|
|
|
if ( st1_tag == TW_Infinity )
|
|
{
|
|
/* fprem(Valid,Infinity) is o.k. */
|
|
setcc(0); return;
|
|
}
|
|
}
|
|
}
|
|
else if ( st0_tag == TW_Infinity )
|
|
{
|
|
if ( st1_tag != TW_NaN )
|
|
{
|
|
arith_invalid(0); /* fprem(Infinity,?) is invalid */
|
|
return;
|
|
}
|
|
}
|
|
|
|
/* One of the registers must contain a NaN if we got here. */
|
|
|
|
#ifdef PARANOID
|
|
if ( (st0_tag != TW_NaN) && (st1_tag != TW_NaN) )
|
|
EXCEPTION(EX_INTERNAL | 0x118);
|
|
#endif /* PARANOID */
|
|
|
|
real_2op_NaN(st1_ptr, st1_tag, 0, st1_ptr);
|
|
|
|
}
|
|
|
|
|
|
/* ST(1) <- ST(1) * log ST; pop ST */
|
|
static void fyl2x(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
FPU_REG *st1_ptr = &st(1), exponent;
|
|
u_char st1_tag = FPU_gettagi(1);
|
|
u_char sign;
|
|
int e, tag;
|
|
|
|
clear_C1();
|
|
|
|
if ( (st0_tag == TAG_Valid) && (st1_tag == TAG_Valid) )
|
|
{
|
|
both_valid:
|
|
/* Both regs are Valid or Denormal */
|
|
if ( signpositive(st0_ptr) )
|
|
{
|
|
if ( st0_tag == TW_Denormal )
|
|
FPU_to_exp16(st0_ptr, st0_ptr);
|
|
else
|
|
/* Convert st(0) for internal use. */
|
|
setexponent16(st0_ptr, exponent(st0_ptr));
|
|
|
|
if ( (st0_ptr->sigh == 0x80000000) && (st0_ptr->sigl == 0) )
|
|
{
|
|
/* Special case. The result can be precise. */
|
|
u_char esign;
|
|
e = exponent16(st0_ptr);
|
|
if ( e >= 0 )
|
|
{
|
|
exponent.sigh = e;
|
|
esign = SIGN_POS;
|
|
}
|
|
else
|
|
{
|
|
exponent.sigh = -e;
|
|
esign = SIGN_NEG;
|
|
}
|
|
exponent.sigl = 0;
|
|
setexponent16(&exponent, 31);
|
|
tag = FPU_normalize_nuo(&exponent);
|
|
stdexp(&exponent);
|
|
setsign(&exponent, esign);
|
|
tag = FPU_mul(&exponent, tag, 1, FULL_PRECISION);
|
|
if ( tag >= 0 )
|
|
FPU_settagi(1, tag);
|
|
}
|
|
else
|
|
{
|
|
/* The usual case */
|
|
sign = getsign(st1_ptr);
|
|
if ( st1_tag == TW_Denormal )
|
|
FPU_to_exp16(st1_ptr, st1_ptr);
|
|
else
|
|
/* Convert st(1) for internal use. */
|
|
setexponent16(st1_ptr, exponent(st1_ptr));
|
|
poly_l2(st0_ptr, st1_ptr, sign);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* negative */
|
|
if ( arith_invalid(1) < 0 )
|
|
return;
|
|
}
|
|
|
|
FPU_pop();
|
|
|
|
return;
|
|
}
|
|
|
|
if ( st0_tag == TAG_Special )
|
|
st0_tag = FPU_Special(st0_ptr);
|
|
if ( st1_tag == TAG_Special )
|
|
st1_tag = FPU_Special(st1_ptr);
|
|
|
|
if ( (st0_tag == TAG_Empty) || (st1_tag == TAG_Empty) )
|
|
{
|
|
FPU_stack_underflow_pop(1);
|
|
return;
|
|
}
|
|
else if ( (st0_tag <= TW_Denormal) && (st1_tag <= TW_Denormal) )
|
|
{
|
|
if ( st0_tag == TAG_Zero )
|
|
{
|
|
if ( st1_tag == TAG_Zero )
|
|
{
|
|
/* Both args zero is invalid */
|
|
if ( arith_invalid(1) < 0 )
|
|
return;
|
|
}
|
|
else
|
|
{
|
|
u_char sign;
|
|
sign = getsign(st1_ptr)^SIGN_NEG;
|
|
if ( FPU_divide_by_zero(1, sign) < 0 )
|
|
return;
|
|
|
|
setsign(st1_ptr, sign);
|
|
}
|
|
}
|
|
else if ( st1_tag == TAG_Zero )
|
|
{
|
|
/* st(1) contains zero, st(0) valid <> 0 */
|
|
/* Zero is the valid answer */
|
|
sign = getsign(st1_ptr);
|
|
|
|
if ( signnegative(st0_ptr) )
|
|
{
|
|
/* log(negative) */
|
|
if ( arith_invalid(1) < 0 )
|
|
return;
|
|
}
|
|
else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
else
|
|
{
|
|
if ( exponent(st0_ptr) < 0 )
|
|
sign ^= SIGN_NEG;
|
|
|
|
FPU_copy_to_reg1(&CONST_Z, TAG_Zero);
|
|
setsign(st1_ptr, sign);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* One or both operands are denormals. */
|
|
if ( denormal_operand() < 0 )
|
|
return;
|
|
goto both_valid;
|
|
}
|
|
}
|
|
else if ( (st0_tag == TW_NaN) || (st1_tag == TW_NaN) )
|
|
{
|
|
if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
|
|
return;
|
|
}
|
|
/* One or both arg must be an infinity */
|
|
else if ( st0_tag == TW_Infinity )
|
|
{
|
|
if ( (signnegative(st0_ptr)) || (st1_tag == TAG_Zero) )
|
|
{
|
|
/* log(-infinity) or 0*log(infinity) */
|
|
if ( arith_invalid(1) < 0 )
|
|
return;
|
|
}
|
|
else
|
|
{
|
|
u_char sign = getsign(st1_ptr);
|
|
|
|
if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
|
|
FPU_copy_to_reg1(&CONST_INF, TAG_Special);
|
|
setsign(st1_ptr, sign);
|
|
}
|
|
}
|
|
/* st(1) must be infinity here */
|
|
else if ( ((st0_tag == TAG_Valid) || (st0_tag == TW_Denormal))
|
|
&& ( signpositive(st0_ptr) ) )
|
|
{
|
|
if ( exponent(st0_ptr) >= 0 )
|
|
{
|
|
if ( (exponent(st0_ptr) == 0) &&
|
|
(st0_ptr->sigh == 0x80000000) &&
|
|
(st0_ptr->sigl == 0) )
|
|
{
|
|
/* st(0) holds 1.0 */
|
|
/* infinity*log(1) */
|
|
if ( arith_invalid(1) < 0 )
|
|
return;
|
|
}
|
|
/* else st(0) is positive and > 1.0 */
|
|
}
|
|
else
|
|
{
|
|
/* st(0) is positive and < 1.0 */
|
|
|
|
if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
|
|
changesign(st1_ptr);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* st(0) must be zero or negative */
|
|
if ( st0_tag == TAG_Zero )
|
|
{
|
|
/* This should be invalid, but a real 80486 is happy with it. */
|
|
|
|
#ifndef PECULIAR_486
|
|
sign = getsign(st1_ptr);
|
|
if ( FPU_divide_by_zero(1, sign) < 0 )
|
|
return;
|
|
#endif /* PECULIAR_486 */
|
|
|
|
changesign(st1_ptr);
|
|
}
|
|
else if ( arith_invalid(1) < 0 ) /* log(negative) */
|
|
return;
|
|
}
|
|
|
|
FPU_pop();
|
|
}
|
|
|
|
|
|
static void fpatan(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
FPU_REG *st1_ptr = &st(1);
|
|
u_char st1_tag = FPU_gettagi(1);
|
|
int tag;
|
|
|
|
clear_C1();
|
|
if ( !((st0_tag ^ TAG_Valid) | (st1_tag ^ TAG_Valid)) )
|
|
{
|
|
valid_atan:
|
|
|
|
poly_atan(st0_ptr, st0_tag, st1_ptr, st1_tag);
|
|
|
|
FPU_pop();
|
|
|
|
return;
|
|
}
|
|
|
|
if ( st0_tag == TAG_Special )
|
|
st0_tag = FPU_Special(st0_ptr);
|
|
if ( st1_tag == TAG_Special )
|
|
st1_tag = FPU_Special(st1_ptr);
|
|
|
|
if ( ((st0_tag == TAG_Valid) && (st1_tag == TW_Denormal))
|
|
|| ((st0_tag == TW_Denormal) && (st1_tag == TAG_Valid))
|
|
|| ((st0_tag == TW_Denormal) && (st1_tag == TW_Denormal)) )
|
|
{
|
|
if ( denormal_operand() < 0 )
|
|
return;
|
|
|
|
goto valid_atan;
|
|
}
|
|
else if ( (st0_tag == TAG_Empty) || (st1_tag == TAG_Empty) )
|
|
{
|
|
FPU_stack_underflow_pop(1);
|
|
return;
|
|
}
|
|
else if ( (st0_tag == TW_NaN) || (st1_tag == TW_NaN) )
|
|
{
|
|
if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) >= 0 )
|
|
FPU_pop();
|
|
return;
|
|
}
|
|
else if ( (st0_tag == TW_Infinity) || (st1_tag == TW_Infinity) )
|
|
{
|
|
u_char sign = getsign(st1_ptr);
|
|
if ( st0_tag == TW_Infinity )
|
|
{
|
|
if ( st1_tag == TW_Infinity )
|
|
{
|
|
if ( signpositive(st0_ptr) )
|
|
{
|
|
FPU_copy_to_reg1(&CONST_PI4, TAG_Valid);
|
|
}
|
|
else
|
|
{
|
|
setpositive(st1_ptr);
|
|
tag = FPU_u_add(&CONST_PI4, &CONST_PI2, st1_ptr,
|
|
FULL_PRECISION, SIGN_POS,
|
|
exponent(&CONST_PI4), exponent(&CONST_PI2));
|
|
if ( tag >= 0 )
|
|
FPU_settagi(1, tag);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
|
|
if ( signpositive(st0_ptr) )
|
|
{
|
|
FPU_copy_to_reg1(&CONST_Z, TAG_Zero);
|
|
setsign(st1_ptr, sign); /* An 80486 preserves the sign */
|
|
FPU_pop();
|
|
return;
|
|
}
|
|
else
|
|
{
|
|
FPU_copy_to_reg1(&CONST_PI, TAG_Valid);
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* st(1) is infinity, st(0) not infinity */
|
|
if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
|
|
FPU_copy_to_reg1(&CONST_PI2, TAG_Valid);
|
|
}
|
|
setsign(st1_ptr, sign);
|
|
}
|
|
else if ( st1_tag == TAG_Zero )
|
|
{
|
|
/* st(0) must be valid or zero */
|
|
u_char sign = getsign(st1_ptr);
|
|
|
|
if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
|
|
if ( signpositive(st0_ptr) )
|
|
{
|
|
/* An 80486 preserves the sign */
|
|
FPU_pop();
|
|
return;
|
|
}
|
|
|
|
FPU_copy_to_reg1(&CONST_PI, TAG_Valid);
|
|
setsign(st1_ptr, sign);
|
|
}
|
|
else if ( st0_tag == TAG_Zero )
|
|
{
|
|
/* st(1) must be TAG_Valid here */
|
|
u_char sign = getsign(st1_ptr);
|
|
|
|
if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
|
|
FPU_copy_to_reg1(&CONST_PI2, TAG_Valid);
|
|
setsign(st1_ptr, sign);
|
|
}
|
|
#ifdef PARANOID
|
|
else
|
|
EXCEPTION(EX_INTERNAL | 0x125);
|
|
#endif /* PARANOID */
|
|
|
|
FPU_pop();
|
|
set_precision_flag_up(); /* We do not really know if up or down */
|
|
}
|
|
|
|
|
|
static void fprem(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
do_fprem(st0_ptr, st0_tag, RC_CHOP);
|
|
}
|
|
|
|
|
|
static void fprem1(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
do_fprem(st0_ptr, st0_tag, RC_RND);
|
|
}
|
|
|
|
|
|
static void fyl2xp1(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
u_char sign, sign1;
|
|
FPU_REG *st1_ptr = &st(1), a, b;
|
|
u_char st1_tag = FPU_gettagi(1);
|
|
|
|
clear_C1();
|
|
if ( !((st0_tag ^ TAG_Valid) | (st1_tag ^ TAG_Valid)) )
|
|
{
|
|
valid_yl2xp1:
|
|
|
|
sign = getsign(st0_ptr);
|
|
sign1 = getsign(st1_ptr);
|
|
|
|
FPU_to_exp16(st0_ptr, &a);
|
|
FPU_to_exp16(st1_ptr, &b);
|
|
|
|
if ( poly_l2p1(sign, sign1, &a, &b, st1_ptr) )
|
|
return;
|
|
|
|
FPU_pop();
|
|
return;
|
|
}
|
|
|
|
if ( st0_tag == TAG_Special )
|
|
st0_tag = FPU_Special(st0_ptr);
|
|
if ( st1_tag == TAG_Special )
|
|
st1_tag = FPU_Special(st1_ptr);
|
|
|
|
if ( ((st0_tag == TAG_Valid) && (st1_tag == TW_Denormal))
|
|
|| ((st0_tag == TW_Denormal) && (st1_tag == TAG_Valid))
|
|
|| ((st0_tag == TW_Denormal) && (st1_tag == TW_Denormal)) )
|
|
{
|
|
if ( denormal_operand() < 0 )
|
|
return;
|
|
|
|
goto valid_yl2xp1;
|
|
}
|
|
else if ( (st0_tag == TAG_Empty) | (st1_tag == TAG_Empty) )
|
|
{
|
|
FPU_stack_underflow_pop(1);
|
|
return;
|
|
}
|
|
else if ( st0_tag == TAG_Zero )
|
|
{
|
|
switch ( st1_tag )
|
|
{
|
|
case TW_Denormal:
|
|
if ( denormal_operand() < 0 )
|
|
return;
|
|
|
|
case TAG_Zero:
|
|
case TAG_Valid:
|
|
setsign(st0_ptr, getsign(st0_ptr) ^ getsign(st1_ptr));
|
|
FPU_copy_to_reg1(st0_ptr, st0_tag);
|
|
break;
|
|
|
|
case TW_Infinity:
|
|
/* Infinity*log(1) */
|
|
if ( arith_invalid(1) < 0 )
|
|
return;
|
|
break;
|
|
|
|
case TW_NaN:
|
|
if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
|
|
return;
|
|
break;
|
|
|
|
default:
|
|
#ifdef PARANOID
|
|
EXCEPTION(EX_INTERNAL | 0x116);
|
|
return;
|
|
#endif /* PARANOID */
|
|
break;
|
|
}
|
|
}
|
|
else if ( (st0_tag == TAG_Valid) || (st0_tag == TW_Denormal) )
|
|
{
|
|
switch ( st1_tag )
|
|
{
|
|
case TAG_Zero:
|
|
if ( signnegative(st0_ptr) )
|
|
{
|
|
if ( exponent(st0_ptr) >= 0 )
|
|
{
|
|
/* st(0) holds <= -1.0 */
|
|
#ifdef PECULIAR_486 /* Stupid 80486 doesn't worry about log(negative). */
|
|
changesign(st1_ptr);
|
|
#else
|
|
if ( arith_invalid(1) < 0 )
|
|
return;
|
|
#endif /* PECULIAR_486 */
|
|
}
|
|
else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
else
|
|
changesign(st1_ptr);
|
|
}
|
|
else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
break;
|
|
|
|
case TW_Infinity:
|
|
if ( signnegative(st0_ptr) )
|
|
{
|
|
if ( (exponent(st0_ptr) >= 0) &&
|
|
!((st0_ptr->sigh == 0x80000000) &&
|
|
(st0_ptr->sigl == 0)) )
|
|
{
|
|
/* st(0) holds < -1.0 */
|
|
#ifdef PECULIAR_486 /* Stupid 80486 doesn't worry about log(negative). */
|
|
changesign(st1_ptr);
|
|
#else
|
|
if ( arith_invalid(1) < 0 ) return;
|
|
#endif /* PECULIAR_486 */
|
|
}
|
|
else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
else
|
|
changesign(st1_ptr);
|
|
}
|
|
else if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
break;
|
|
|
|
case TW_NaN:
|
|
if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
|
|
return;
|
|
}
|
|
|
|
}
|
|
else if ( st0_tag == TW_NaN )
|
|
{
|
|
if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
|
|
return;
|
|
}
|
|
else if ( st0_tag == TW_Infinity )
|
|
{
|
|
if ( st1_tag == TW_NaN )
|
|
{
|
|
if ( real_2op_NaN(st0_ptr, st0_tag, 1, st0_ptr) < 0 )
|
|
return;
|
|
}
|
|
else if ( signnegative(st0_ptr) )
|
|
{
|
|
#ifndef PECULIAR_486
|
|
/* This should have higher priority than denormals, but... */
|
|
if ( arith_invalid(1) < 0 ) /* log(-infinity) */
|
|
return;
|
|
#endif /* PECULIAR_486 */
|
|
if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
#ifdef PECULIAR_486
|
|
/* Denormal operands actually get higher priority */
|
|
if ( arith_invalid(1) < 0 ) /* log(-infinity) */
|
|
return;
|
|
#endif /* PECULIAR_486 */
|
|
}
|
|
else if ( st1_tag == TAG_Zero )
|
|
{
|
|
/* log(infinity) */
|
|
if ( arith_invalid(1) < 0 )
|
|
return;
|
|
}
|
|
|
|
/* st(1) must be valid here. */
|
|
|
|
else if ( (st1_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
|
|
/* The Manual says that log(Infinity) is invalid, but a real
|
|
80486 sensibly says that it is o.k. */
|
|
else
|
|
{
|
|
u_char sign = getsign(st1_ptr);
|
|
FPU_copy_to_reg1(&CONST_INF, TAG_Special);
|
|
setsign(st1_ptr, sign);
|
|
}
|
|
}
|
|
#ifdef PARANOID
|
|
else
|
|
{
|
|
EXCEPTION(EX_INTERNAL | 0x117);
|
|
return;
|
|
}
|
|
#endif /* PARANOID */
|
|
|
|
FPU_pop();
|
|
return;
|
|
|
|
}
|
|
|
|
|
|
static void fscale(FPU_REG *st0_ptr, u_char st0_tag)
|
|
{
|
|
FPU_REG *st1_ptr = &st(1);
|
|
u_char st1_tag = FPU_gettagi(1);
|
|
int old_cw = control_word;
|
|
u_char sign = getsign(st0_ptr);
|
|
|
|
clear_C1();
|
|
if ( !((st0_tag ^ TAG_Valid) | (st1_tag ^ TAG_Valid)) )
|
|
{
|
|
long scale;
|
|
FPU_REG tmp;
|
|
|
|
/* Convert register for internal use. */
|
|
setexponent16(st0_ptr, exponent(st0_ptr));
|
|
|
|
valid_scale:
|
|
|
|
if ( exponent(st1_ptr) > 30 )
|
|
{
|
|
/* 2^31 is far too large, would require 2^(2^30) or 2^(-2^30) */
|
|
|
|
if ( signpositive(st1_ptr) )
|
|
{
|
|
EXCEPTION(EX_Overflow);
|
|
FPU_copy_to_reg0(&CONST_INF, TAG_Special);
|
|
}
|
|
else
|
|
{
|
|
EXCEPTION(EX_Underflow);
|
|
FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
|
|
}
|
|
setsign(st0_ptr, sign);
|
|
return;
|
|
}
|
|
|
|
control_word &= ~CW_RC;
|
|
control_word |= RC_CHOP;
|
|
reg_copy(st1_ptr, &tmp);
|
|
FPU_round_to_int(&tmp, st1_tag); /* This can never overflow here */
|
|
control_word = old_cw;
|
|
scale = signnegative(st1_ptr) ? -tmp.sigl : tmp.sigl;
|
|
scale += exponent16(st0_ptr);
|
|
|
|
setexponent16(st0_ptr, scale);
|
|
|
|
/* Use FPU_round() to properly detect under/overflow etc */
|
|
FPU_round(st0_ptr, 0, 0, control_word, sign);
|
|
|
|
return;
|
|
}
|
|
|
|
if ( st0_tag == TAG_Special )
|
|
st0_tag = FPU_Special(st0_ptr);
|
|
if ( st1_tag == TAG_Special )
|
|
st1_tag = FPU_Special(st1_ptr);
|
|
|
|
if ( (st0_tag == TAG_Valid) || (st0_tag == TW_Denormal) )
|
|
{
|
|
switch ( st1_tag )
|
|
{
|
|
case TAG_Valid:
|
|
/* st(0) must be a denormal */
|
|
if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
|
|
FPU_to_exp16(st0_ptr, st0_ptr); /* Will not be left on stack */
|
|
goto valid_scale;
|
|
|
|
case TAG_Zero:
|
|
if ( st0_tag == TW_Denormal )
|
|
denormal_operand();
|
|
return;
|
|
|
|
case TW_Denormal:
|
|
denormal_operand();
|
|
return;
|
|
|
|
case TW_Infinity:
|
|
if ( (st0_tag == TW_Denormal) && (denormal_operand() < 0) )
|
|
return;
|
|
|
|
if ( signpositive(st1_ptr) )
|
|
FPU_copy_to_reg0(&CONST_INF, TAG_Special);
|
|
else
|
|
FPU_copy_to_reg0(&CONST_Z, TAG_Zero);
|
|
setsign(st0_ptr, sign);
|
|
return;
|
|
|
|
case TW_NaN:
|
|
real_2op_NaN(st1_ptr, st1_tag, 0, st0_ptr);
|
|
return;
|
|
}
|
|
}
|
|
else if ( st0_tag == TAG_Zero )
|
|
{
|
|
switch ( st1_tag )
|
|
{
|
|
case TAG_Valid:
|
|
case TAG_Zero:
|
|
return;
|
|
|
|
case TW_Denormal:
|
|
denormal_operand();
|
|
return;
|
|
|
|
case TW_Infinity:
|
|
if ( signpositive(st1_ptr) )
|
|
arith_invalid(0); /* Zero scaled by +Infinity */
|
|
return;
|
|
|
|
case TW_NaN:
|
|
real_2op_NaN(st1_ptr, st1_tag, 0, st0_ptr);
|
|
return;
|
|
}
|
|
}
|
|
else if ( st0_tag == TW_Infinity )
|
|
{
|
|
switch ( st1_tag )
|
|
{
|
|
case TAG_Valid:
|
|
case TAG_Zero:
|
|
return;
|
|
|
|
case TW_Denormal:
|
|
denormal_operand();
|
|
return;
|
|
|
|
case TW_Infinity:
|
|
if ( signnegative(st1_ptr) )
|
|
arith_invalid(0); /* Infinity scaled by -Infinity */
|
|
return;
|
|
|
|
case TW_NaN:
|
|
real_2op_NaN(st1_ptr, st1_tag, 0, st0_ptr);
|
|
return;
|
|
}
|
|
}
|
|
else if ( st0_tag == TW_NaN )
|
|
{
|
|
if ( st1_tag != TAG_Empty )
|
|
{ real_2op_NaN(st1_ptr, st1_tag, 0, st0_ptr); return; }
|
|
}
|
|
|
|
#ifdef PARANOID
|
|
if ( !((st0_tag == TAG_Empty) || (st1_tag == TAG_Empty)) )
|
|
{
|
|
EXCEPTION(EX_INTERNAL | 0x115);
|
|
return;
|
|
}
|
|
#endif
|
|
|
|
/* At least one of st(0), st(1) must be empty */
|
|
FPU_stack_underflow();
|
|
|
|
}
|
|
|
|
|
|
/*---------------------------------------------------------------------------*/
|
|
|
|
static FUNC_ST0 const trig_table_a[] = {
|
|
f2xm1, fyl2x, fptan, fpatan,
|
|
fxtract, fprem1, (FUNC_ST0)fdecstp, (FUNC_ST0)fincstp
|
|
};
|
|
|
|
void FPU_triga(void)
|
|
{
|
|
(trig_table_a[FPU_rm])(&st(0), FPU_gettag0());
|
|
}
|
|
|
|
|
|
static FUNC_ST0 const trig_table_b[] =
|
|
{
|
|
fprem, fyl2xp1, fsqrt_, fsincos, frndint_, fscale, (FUNC_ST0)fsin, fcos
|
|
};
|
|
|
|
void FPU_trigb(void)
|
|
{
|
|
(trig_table_b[FPU_rm])(&st(0), FPU_gettag0());
|
|
}
|