diff options
Diffstat (limited to 'arch/x86/math-emu/fpu_trig.c')
| -rw-r--r-- | arch/x86/math-emu/fpu_trig.c | 1644 |
1 files changed, 1644 insertions, 0 deletions
diff --git a/arch/x86/math-emu/fpu_trig.c b/arch/x86/math-emu/fpu_trig.c new file mode 100644 index 000000000..4a9887851 --- /dev/null +++ b/arch/x86/math-emu/fpu_trig.c @@ -0,0 +1,1644 @@ +// SPDX-License-Identifier: GPL-2.0 +/*---------------------------------------------------------------------------+ + | fpu_trig.c | + | | + | Implementation of the FPU "transcendental" functions. | + | | + | Copyright (C) 1992,1993,1994,1997,1999 | + | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, | + | Australia. E-mail billm@melbpc.org.au | + | | + | | + +---------------------------------------------------------------------------*/ + +#include "fpu_system.h" +#include "exception.h" +#include "fpu_emu.h" +#include "status_w.h" +#include "control_w.h" +#include "reg_constant.h" + +static void rem_kernel(unsigned long long st0, unsigned long long *y, + unsigned long long st1, unsigned long long q, int n); + +#define BETTER_THAN_486 + +#define FCOS 4 + +/* Used only by fptan, fsin, fcos, and fsincos. */ +/* This routine produces very accurate results, similar to + using a value of pi with more than 128 bits precision. */ +/* Limited measurements show no results worse than 64 bit precision + except for the results for arguments close to 2^63, where the + precision of the result sometimes degrades to about 63.9 bits */ +static int trig_arg(FPU_REG *st0_ptr, int even) +{ + FPU_REG tmp; + u_char tmptag; + unsigned long long q; + int old_cw = control_word, saved_status = partial_status; + int tag, st0_tag = TAG_Valid; + + if (exponent(st0_ptr) >= 63) { + partial_status |= SW_C2; /* Reduction incomplete. */ + return -1; + } + + control_word &= ~CW_RC; + control_word |= RC_CHOP; + + setpositive(st0_ptr); + tag = FPU_u_div(st0_ptr, &CONST_PI2, &tmp, PR_64_BITS | RC_CHOP | 0x3f, + SIGN_POS); + + FPU_round_to_int(&tmp, tag); /* Fortunately, this can't overflow + to 2^64 */ + q = significand(&tmp); + if (q) { + rem_kernel(significand(st0_ptr), + &significand(&tmp), + significand(&CONST_PI2), + q, exponent(st0_ptr) - exponent(&CONST_PI2)); + setexponent16(&tmp, exponent(&CONST_PI2)); + st0_tag = FPU_normalize(&tmp); + FPU_copy_to_reg0(&tmp, st0_tag); + } + + if ((even && !(q & 1)) || (!even && (q & 1))) { + st0_tag = + FPU_sub(REV | LOADED | TAG_Valid, (int)&CONST_PI2, + FULL_PRECISION); + +#ifdef BETTER_THAN_486 + /* So far, the results are exact but based upon a 64 bit + precision approximation to pi/2. The technique used + now is equivalent to using an approximation to pi/2 which + is accurate to about 128 bits. */ + if ((exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64) + || (q > 1)) { + /* This code gives the effect of having pi/2 to better than + 128 bits precision. */ + + significand(&tmp) = q + 1; + setexponent16(&tmp, 63); + FPU_normalize(&tmp); + tmptag = + FPU_u_mul(&CONST_PI2extra, &tmp, &tmp, + FULL_PRECISION, SIGN_POS, + exponent(&CONST_PI2extra) + + exponent(&tmp)); + setsign(&tmp, getsign(&CONST_PI2extra)); + st0_tag = FPU_add(&tmp, tmptag, 0, FULL_PRECISION); + if (signnegative(st0_ptr)) { + /* CONST_PI2extra is negative, so the result of the addition + can be negative. This means that the argument is actually + in a different quadrant. The correction is always < pi/2, + so it can't overflow into yet another quadrant. */ + setpositive(st0_ptr); + q++; + } + } +#endif /* BETTER_THAN_486 */ + } +#ifdef BETTER_THAN_486 + else { + /* So far, the results are exact but based upon a 64 bit + precision approximation to pi/2. The technique used + now is equivalent to using an approximation to pi/2 which + is accurate to about 128 bits. */ + if (((q > 0) + && (exponent(st0_ptr) <= exponent(&CONST_PI2extra) + 64)) + || (q > 1)) { + /* This code gives the effect of having p/2 to better than + 128 bits precision. */ + + significand(&tmp) = q; + setexponent16(&tmp, 63); + FPU_normalize(&tmp); /* This must return TAG_Valid */ + tmptag = + FPU_u_mul(&CONST_PI2extra, &tmp, &tmp, + FULL_PRECISION, SIGN_POS, + exponent(&CONST_PI2extra) + + exponent(&tmp)); + setsign(&tmp, getsign(&CONST_PI2extra)); + st0_tag = FPU_sub(LOADED | (tmptag & 0x0f), (int)&tmp, + FULL_PRECISION); + if ((exponent(st0_ptr) == exponent(&CONST_PI2)) && + ((st0_ptr->sigh > CONST_PI2.sigh) + || ((st0_ptr->sigh == CONST_PI2.sigh) + && (st0_ptr->sigl > CONST_PI2.sigl)))) { + /* CONST_PI2extra is negative, so the result of the + subtraction can be larger than pi/2. This means + that the argument is actually in a different quadrant. + The correction is always < pi/2, so it can't overflow + into yet another quadrant. */ + st0_tag = + FPU_sub(REV | LOADED | TAG_Valid, + (int)&CONST_PI2, FULL_PRECISION); + q++; + } + } + } +#endif /* BETTER_THAN_486 */ + + FPU_settag0(st0_tag); + control_word = old_cw; + partial_status = saved_status & ~SW_C2; /* Reduction complete. */ + + return (q & 3) | even; +} + +/* Convert a long to register */ +static void convert_l2reg(long const *arg, int deststnr) +{ + int tag; + long num = *arg; + u_char sign; + FPU_REG *dest = &st(deststnr); + + if (num == 0) { + FPU_copy_to_regi(&CONST_Z, TAG_Zero, deststnr); + return; + } + + if (num > 0) { + sign = SIGN_POS; + } else { + num = -num; + sign = SIGN_NEG; + } + + dest->sigh = num; + dest->sigl = 0; + setexponent16(dest, 31); + tag = FPU_normalize(dest); + FPU_settagi(deststnr, tag); + setsign(dest, sign); + return; +} + +static void single_arg_error(FPU_REG *st0_ptr, u_char st0_tag) +{ + if (st0_tag == TAG_Empty) + FPU_stack_underflow(); /* Puts a QNaN in st(0) */ + else if (st0_tag == TW_NaN) + real_1op_NaN(st0_ptr); /* return with a NaN in st(0) */ +#ifdef PARANOID + else + EXCEPTION(EX_INTERNAL | 0x0112); +#endif /* PARANOID */ +} + +static void single_arg_2_error(FPU_REG *st0_ptr, u_char st0_tag) +{ + int isNaN; + + switch (st0_tag) { + case TW_NaN: + isNaN = (exponent(st0_ptr) == EXP_OVER) + && (st0_ptr->sigh & 0x80000000); + if (isNaN && !(st0_ptr->sigh & 0x40000000)) { /* Signaling ? */ + EXCEPTION(EX_Invalid); + if (control_word & CW_Invalid) { + /* The masked response */ + /* Convert to a QNaN */ + st0_ptr->sigh |= 0x40000000; + push(); + FPU_copy_to_reg0(st0_ptr, TAG_Special); + } + } else if (isNaN) { + /* A QNaN */ + push(); + FPU_copy_to_reg0(st0_ptr, TAG_Special); + } else { + /* pseudoNaN or other unsupported */ + EXCEPTION(EX_Invalid); + if (control_word & CW_Invalid) { + /* The masked response */ + FPU_copy_to_reg0(&CONST_QNaN, TAG_Special); + push(); + FPU_copy_to_reg0(&CONST_QNaN, TAG_Special); + } + } + break; /* return with a NaN in st(0) */ +#ifdef PARANOID + default: + EXCEPTION(EX_INTERNAL | 0x0112); +#endif /* PARANOID */ + } +} + +/*---------------------------------------------------------------------------*/ + +static void f2xm1(FPU_REG *st0_ptr, u_char tag) +{ + FPU_REG a; + + clear_C1(); + + if (tag == TAG_Valid) { + /* For an 80486 FPU, the result is undefined if the arg is >= 1.0 */ + if (exponent(st0_ptr) < 0) { + denormal_arg: + + FPU_to_exp16(st0_ptr, &a); + + /* poly_2xm1(x) requires 0 < st(0) < 1. */ + poly_2xm1(getsign(st0_ptr), &a, st0_ptr); + } + set_precision_flag_up(); /* 80486 appears to always do this */ + return; + } + + if (tag == TAG_Zero) + return; + + if (tag == TAG_Special) + tag = FPU_Special(st0_ptr); + + switch (tag) { + case TW_Denormal: + if (denormal_operand() < 0) + return; + goto denormal_arg; + case TW_Infinity: + if (signnegative(st0_ptr)) { + /* -infinity gives -1 (p16-10) */ + FPU_copy_to_reg0(&CONST_1, TAG_Valid); + setnegative(st0_ptr); + } + return; + default: + single_arg_error(st0_ptr, tag); + } +} + +static void fptan(FPU_REG *st0_ptr, u_char st0_tag) +{ + FPU_REG *st_new_ptr; + int q; + u_char arg_sign = getsign(st0_ptr); + + /* 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_Valid) { + if (exponent(st0_ptr) > -40) { + if ((q = trig_arg(st0_ptr, 0)) == -1) { + /* Operand is out of range */ + return; + } + + poly_tan(st0_ptr); + setsign(st0_ptr, (q & 1) ^ (arg_sign != 0)); + set_precision_flag_up(); /* We do not really know if up or down */ + } else { + /* For a small arg, the result == the argument */ + /* Underflow may happen */ + + denormal_arg: + + FPU_to_exp16(st0_ptr, st0_ptr); + + st0_tag = + FPU_round(st0_ptr, 1, 0, FULL_PRECISION, arg_sign); + FPU_settag0(st0_tag); + } + push(); + FPU_copy_to_reg0(&CONST_1, TAG_Valid); + return; + } + + if (st0_tag == TAG_Zero) { + push(); + FPU_copy_to_reg0(&CONST_1, TAG_Valid); + setcc(0); + return; + } + + if (st0_tag == TAG_Special) + st0_tag = FPU_Special(st0_ptr); + + if (st0_tag == TW_Denormal) { + if (denormal_operand() < 0) + return; + + goto denormal_arg; + } + + if (st0_tag == TW_Infinity) { + /* The 80486 treats infinity as an invalid operand */ + if (arith_invalid(0) >= 0) { + st_new_ptr = &st(-1); + push(); + arith_invalid(0); + } + return; + } + + single_arg_2_error(st0_ptr, st0_tag); +} + +static void fxtract(FPU_REG *st0_ptr, u_char st0_tag) +{ + FPU_REG *st_new_ptr; + u_char sign; + register FPU_REG *st1_ptr = st0_ptr; /* anticipate */ + + if (STACK_OVERFLOW) { + FPU_stack_overflow(); + return; + } + + clear_C1(); + + if (st0_tag == TAG_Valid) { + long e; + + push(); + sign = getsign(st1_ptr); + reg_copy(st1_ptr, st_new_ptr); + setexponent16(st_new_ptr, exponent(st_new_ptr)); + + denormal_arg: + + e = exponent16(st_new_ptr); + convert_l2reg(&e, 1); + setexponentpos(st_new_ptr, 0); + setsign(st_new_ptr, sign); + FPU_settag0(TAG_Valid); /* Needed if arg was a denormal */ + return; + } else if (st0_tag == TAG_Zero) { + sign = getsign(st0_ptr); + + if (FPU_divide_by_zero(0, SIGN_NEG) < 0) + return; + + push(); + FPU_copy_to_reg0(&CONST_Z, TAG_Zero); + setsign(st_new_ptr, sign); + return; + } + + if (st0_tag == TAG_Special) + st0_tag = FPU_Special(st0_ptr); + + if (st0_tag == TW_Denormal) { + if (denormal_operand() < 0) + return; + + push(); + sign = getsign(st1_ptr); + FPU_to_exp16(st1_ptr, st_new_ptr); + goto denormal_arg; + } else if (st0_tag == TW_Infinity) { + sign = getsign(st0_ptr); + setpositive(st0_ptr); + push(); + FPU_copy_to_reg0(&CONST_INF, TAG_Special); + setsign(st_new_ptr, sign); + return; + } else if (st0_tag == TW_NaN) { + if (real_1op_NaN(st0_ptr) < 0) + 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; + fallthrough; + 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()); +} |