700 lines
14 KiB
C
700 lines
14 KiB
C
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// SPDX-License-Identifier: GPL-2.0-or-later
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/*
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fp_arith.c: floating-point math routines for the Linux-m68k
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floating point emulator.
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Copyright (c) 1998-1999 David Huggins-Daines.
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Somewhat based on the AlphaLinux floating point emulator, by David
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Mosberger-Tang.
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*/
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#include "fp_emu.h"
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#include "multi_arith.h"
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#include "fp_arith.h"
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const struct fp_ext fp_QNaN =
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{
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.exp = 0x7fff,
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.mant = { .m64 = ~0 }
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};
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const struct fp_ext fp_Inf =
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{
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.exp = 0x7fff,
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};
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/* let's start with the easy ones */
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struct fp_ext *
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fp_fabs(struct fp_ext *dest, struct fp_ext *src)
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{
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dprint(PINSTR, "fabs\n");
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fp_monadic_check(dest, src);
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dest->sign = 0;
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return dest;
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}
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struct fp_ext *
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fp_fneg(struct fp_ext *dest, struct fp_ext *src)
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{
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dprint(PINSTR, "fneg\n");
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fp_monadic_check(dest, src);
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dest->sign = !dest->sign;
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return dest;
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}
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/* Now, the slightly harder ones */
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/* fp_fadd: Implements the kernel of the FADD, FSADD, FDADD, FSUB,
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FDSUB, and FCMP instructions. */
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struct fp_ext *
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fp_fadd(struct fp_ext *dest, struct fp_ext *src)
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{
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int diff;
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dprint(PINSTR, "fadd\n");
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fp_dyadic_check(dest, src);
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if (IS_INF(dest)) {
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/* infinity - infinity == NaN */
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if (IS_INF(src) && (src->sign != dest->sign))
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fp_set_nan(dest);
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return dest;
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}
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if (IS_INF(src)) {
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fp_copy_ext(dest, src);
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return dest;
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}
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if (IS_ZERO(dest)) {
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if (IS_ZERO(src)) {
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if (src->sign != dest->sign) {
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if (FPDATA->rnd == FPCR_ROUND_RM)
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dest->sign = 1;
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else
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dest->sign = 0;
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}
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} else
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fp_copy_ext(dest, src);
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return dest;
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}
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dest->lowmant = src->lowmant = 0;
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if ((diff = dest->exp - src->exp) > 0)
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fp_denormalize(src, diff);
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else if ((diff = -diff) > 0)
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fp_denormalize(dest, diff);
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if (dest->sign == src->sign) {
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if (fp_addmant(dest, src))
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if (!fp_addcarry(dest))
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return dest;
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} else {
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if (dest->mant.m64 < src->mant.m64) {
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fp_submant(dest, src, dest);
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dest->sign = !dest->sign;
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} else
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fp_submant(dest, dest, src);
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}
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return dest;
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}
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/* fp_fsub: Implements the kernel of the FSUB, FSSUB, and FDSUB
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instructions.
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Remember that the arguments are in assembler-syntax order! */
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struct fp_ext *
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fp_fsub(struct fp_ext *dest, struct fp_ext *src)
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{
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dprint(PINSTR, "fsub ");
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src->sign = !src->sign;
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return fp_fadd(dest, src);
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}
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struct fp_ext *
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fp_fcmp(struct fp_ext *dest, struct fp_ext *src)
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{
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dprint(PINSTR, "fcmp ");
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FPDATA->temp[1] = *dest;
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src->sign = !src->sign;
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return fp_fadd(&FPDATA->temp[1], src);
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}
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struct fp_ext *
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fp_ftst(struct fp_ext *dest, struct fp_ext *src)
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{
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dprint(PINSTR, "ftst\n");
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(void)dest;
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return src;
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}
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struct fp_ext *
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fp_fmul(struct fp_ext *dest, struct fp_ext *src)
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{
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union fp_mant128 temp;
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int exp;
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dprint(PINSTR, "fmul\n");
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fp_dyadic_check(dest, src);
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/* calculate the correct sign now, as it's necessary for infinities */
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dest->sign = src->sign ^ dest->sign;
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/* Handle infinities */
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if (IS_INF(dest)) {
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if (IS_ZERO(src))
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fp_set_nan(dest);
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return dest;
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}
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if (IS_INF(src)) {
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if (IS_ZERO(dest))
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fp_set_nan(dest);
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else
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fp_copy_ext(dest, src);
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return dest;
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}
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/* Of course, as we all know, zero * anything = zero. You may
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not have known that it might be a positive or negative
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zero... */
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if (IS_ZERO(dest) || IS_ZERO(src)) {
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dest->exp = 0;
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dest->mant.m64 = 0;
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dest->lowmant = 0;
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return dest;
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}
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exp = dest->exp + src->exp - 0x3ffe;
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/* shift up the mantissa for denormalized numbers,
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so that the highest bit is set, this makes the
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shift of the result below easier */
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if ((long)dest->mant.m32[0] >= 0)
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exp -= fp_overnormalize(dest);
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if ((long)src->mant.m32[0] >= 0)
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exp -= fp_overnormalize(src);
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/* now, do a 64-bit multiply with expansion */
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fp_multiplymant(&temp, dest, src);
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/* normalize it back to 64 bits and stuff it back into the
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destination struct */
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if ((long)temp.m32[0] > 0) {
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exp--;
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fp_putmant128(dest, &temp, 1);
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} else
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fp_putmant128(dest, &temp, 0);
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if (exp >= 0x7fff) {
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fp_set_ovrflw(dest);
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return dest;
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}
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dest->exp = exp;
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if (exp < 0) {
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fp_set_sr(FPSR_EXC_UNFL);
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fp_denormalize(dest, -exp);
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}
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return dest;
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}
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/* fp_fdiv: Implements the "kernel" of the FDIV, FSDIV, FDDIV and
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FSGLDIV instructions.
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Note that the order of the operands is counter-intuitive: instead
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of src / dest, the result is actually dest / src. */
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struct fp_ext *
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fp_fdiv(struct fp_ext *dest, struct fp_ext *src)
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{
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union fp_mant128 temp;
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int exp;
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dprint(PINSTR, "fdiv\n");
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fp_dyadic_check(dest, src);
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/* calculate the correct sign now, as it's necessary for infinities */
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dest->sign = src->sign ^ dest->sign;
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/* Handle infinities */
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if (IS_INF(dest)) {
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/* infinity / infinity = NaN (quiet, as always) */
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if (IS_INF(src))
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fp_set_nan(dest);
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/* infinity / anything else = infinity (with approprate sign) */
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return dest;
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}
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if (IS_INF(src)) {
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/* anything / infinity = zero (with appropriate sign) */
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dest->exp = 0;
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dest->mant.m64 = 0;
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dest->lowmant = 0;
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return dest;
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}
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/* zeroes */
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if (IS_ZERO(dest)) {
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/* zero / zero = NaN */
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if (IS_ZERO(src))
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fp_set_nan(dest);
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/* zero / anything else = zero */
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return dest;
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}
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if (IS_ZERO(src)) {
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/* anything / zero = infinity (with appropriate sign) */
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fp_set_sr(FPSR_EXC_DZ);
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dest->exp = 0x7fff;
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dest->mant.m64 = 0;
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return dest;
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}
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exp = dest->exp - src->exp + 0x3fff;
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/* shift up the mantissa for denormalized numbers,
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so that the highest bit is set, this makes lots
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of things below easier */
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if ((long)dest->mant.m32[0] >= 0)
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exp -= fp_overnormalize(dest);
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if ((long)src->mant.m32[0] >= 0)
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exp -= fp_overnormalize(src);
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/* now, do the 64-bit divide */
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fp_dividemant(&temp, dest, src);
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/* normalize it back to 64 bits and stuff it back into the
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destination struct */
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if (!temp.m32[0]) {
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exp--;
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fp_putmant128(dest, &temp, 32);
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} else
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fp_putmant128(dest, &temp, 31);
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if (exp >= 0x7fff) {
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fp_set_ovrflw(dest);
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return dest;
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}
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dest->exp = exp;
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if (exp < 0) {
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fp_set_sr(FPSR_EXC_UNFL);
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fp_denormalize(dest, -exp);
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}
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return dest;
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}
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struct fp_ext *
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fp_fsglmul(struct fp_ext *dest, struct fp_ext *src)
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{
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int exp;
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dprint(PINSTR, "fsglmul\n");
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fp_dyadic_check(dest, src);
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/* calculate the correct sign now, as it's necessary for infinities */
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dest->sign = src->sign ^ dest->sign;
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/* Handle infinities */
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if (IS_INF(dest)) {
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if (IS_ZERO(src))
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fp_set_nan(dest);
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return dest;
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}
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if (IS_INF(src)) {
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if (IS_ZERO(dest))
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fp_set_nan(dest);
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else
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fp_copy_ext(dest, src);
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return dest;
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}
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/* Of course, as we all know, zero * anything = zero. You may
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not have known that it might be a positive or negative
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zero... */
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if (IS_ZERO(dest) || IS_ZERO(src)) {
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dest->exp = 0;
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dest->mant.m64 = 0;
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dest->lowmant = 0;
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return dest;
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}
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exp = dest->exp + src->exp - 0x3ffe;
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/* do a 32-bit multiply */
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fp_mul64(dest->mant.m32[0], dest->mant.m32[1],
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dest->mant.m32[0] & 0xffffff00,
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src->mant.m32[0] & 0xffffff00);
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if (exp >= 0x7fff) {
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fp_set_ovrflw(dest);
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return dest;
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}
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dest->exp = exp;
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if (exp < 0) {
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fp_set_sr(FPSR_EXC_UNFL);
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fp_denormalize(dest, -exp);
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}
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return dest;
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}
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struct fp_ext *
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fp_fsgldiv(struct fp_ext *dest, struct fp_ext *src)
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{
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int exp;
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unsigned long quot, rem;
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dprint(PINSTR, "fsgldiv\n");
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fp_dyadic_check(dest, src);
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/* calculate the correct sign now, as it's necessary for infinities */
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dest->sign = src->sign ^ dest->sign;
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/* Handle infinities */
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if (IS_INF(dest)) {
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/* infinity / infinity = NaN (quiet, as always) */
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if (IS_INF(src))
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fp_set_nan(dest);
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/* infinity / anything else = infinity (with approprate sign) */
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return dest;
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}
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if (IS_INF(src)) {
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/* anything / infinity = zero (with appropriate sign) */
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dest->exp = 0;
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dest->mant.m64 = 0;
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dest->lowmant = 0;
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return dest;
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}
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/* zeroes */
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if (IS_ZERO(dest)) {
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/* zero / zero = NaN */
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if (IS_ZERO(src))
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fp_set_nan(dest);
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/* zero / anything else = zero */
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return dest;
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}
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if (IS_ZERO(src)) {
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/* anything / zero = infinity (with appropriate sign) */
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fp_set_sr(FPSR_EXC_DZ);
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|
|
dest->exp = 0x7fff;
|
||
|
|
dest->mant.m64 = 0;
|
||
|
|
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
|
||
|
|
exp = dest->exp - src->exp + 0x3fff;
|
||
|
|
|
||
|
|
dest->mant.m32[0] &= 0xffffff00;
|
||
|
|
src->mant.m32[0] &= 0xffffff00;
|
||
|
|
|
||
|
|
/* do the 32-bit divide */
|
||
|
|
if (dest->mant.m32[0] >= src->mant.m32[0]) {
|
||
|
|
fp_sub64(dest->mant, src->mant);
|
||
|
|
fp_div64(quot, rem, dest->mant.m32[0], 0, src->mant.m32[0]);
|
||
|
|
dest->mant.m32[0] = 0x80000000 | (quot >> 1);
|
||
|
|
dest->mant.m32[1] = (quot & 1) | rem; /* only for rounding */
|
||
|
|
} else {
|
||
|
|
fp_div64(quot, rem, dest->mant.m32[0], 0, src->mant.m32[0]);
|
||
|
|
dest->mant.m32[0] = quot;
|
||
|
|
dest->mant.m32[1] = rem; /* only for rounding */
|
||
|
|
exp--;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (exp >= 0x7fff) {
|
||
|
|
fp_set_ovrflw(dest);
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
dest->exp = exp;
|
||
|
|
if (exp < 0) {
|
||
|
|
fp_set_sr(FPSR_EXC_UNFL);
|
||
|
|
fp_denormalize(dest, -exp);
|
||
|
|
}
|
||
|
|
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* fp_roundint: Internal rounding function for use by several of these
|
||
|
|
emulated instructions.
|
||
|
|
|
||
|
|
This one rounds off the fractional part using the rounding mode
|
||
|
|
specified. */
|
||
|
|
|
||
|
|
static void fp_roundint(struct fp_ext *dest, int mode)
|
||
|
|
{
|
||
|
|
union fp_mant64 oldmant;
|
||
|
|
unsigned long mask;
|
||
|
|
|
||
|
|
if (!fp_normalize_ext(dest))
|
||
|
|
return;
|
||
|
|
|
||
|
|
/* infinities and zeroes */
|
||
|
|
if (IS_INF(dest) || IS_ZERO(dest))
|
||
|
|
return;
|
||
|
|
|
||
|
|
/* first truncate the lower bits */
|
||
|
|
oldmant = dest->mant;
|
||
|
|
switch (dest->exp) {
|
||
|
|
case 0 ... 0x3ffe:
|
||
|
|
dest->mant.m64 = 0;
|
||
|
|
break;
|
||
|
|
case 0x3fff ... 0x401e:
|
||
|
|
dest->mant.m32[0] &= 0xffffffffU << (0x401e - dest->exp);
|
||
|
|
dest->mant.m32[1] = 0;
|
||
|
|
if (oldmant.m64 == dest->mant.m64)
|
||
|
|
return;
|
||
|
|
break;
|
||
|
|
case 0x401f ... 0x403e:
|
||
|
|
dest->mant.m32[1] &= 0xffffffffU << (0x403e - dest->exp);
|
||
|
|
if (oldmant.m32[1] == dest->mant.m32[1])
|
||
|
|
return;
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
fp_set_sr(FPSR_EXC_INEX2);
|
||
|
|
|
||
|
|
/* We might want to normalize upwards here... however, since
|
||
|
|
we know that this is only called on the output of fp_fdiv,
|
||
|
|
or with the input to fp_fint or fp_fintrz, and the inputs
|
||
|
|
to all these functions are either normal or denormalized
|
||
|
|
(no subnormals allowed!), there's really no need.
|
||
|
|
|
||
|
|
In the case of fp_fdiv, observe that 0x80000000 / 0xffff =
|
||
|
|
0xffff8000, and the same holds for 128-bit / 64-bit. (i.e. the
|
||
|
|
smallest possible normal dividend and the largest possible normal
|
||
|
|
divisor will still produce a normal quotient, therefore, (normal
|
||
|
|
<< 64) / normal is normal in all cases) */
|
||
|
|
|
||
|
|
switch (mode) {
|
||
|
|
case FPCR_ROUND_RN:
|
||
|
|
switch (dest->exp) {
|
||
|
|
case 0 ... 0x3ffd:
|
||
|
|
return;
|
||
|
|
case 0x3ffe:
|
||
|
|
/* As noted above, the input is always normal, so the
|
||
|
|
guard bit (bit 63) is always set. therefore, the
|
||
|
|
only case in which we will NOT round to 1.0 is when
|
||
|
|
the input is exactly 0.5. */
|
||
|
|
if (oldmant.m64 == (1ULL << 63))
|
||
|
|
return;
|
||
|
|
break;
|
||
|
|
case 0x3fff ... 0x401d:
|
||
|
|
mask = 1 << (0x401d - dest->exp);
|
||
|
|
if (!(oldmant.m32[0] & mask))
|
||
|
|
return;
|
||
|
|
if (oldmant.m32[0] & (mask << 1))
|
||
|
|
break;
|
||
|
|
if (!(oldmant.m32[0] << (dest->exp - 0x3ffd)) &&
|
||
|
|
!oldmant.m32[1])
|
||
|
|
return;
|
||
|
|
break;
|
||
|
|
case 0x401e:
|
||
|
|
if (oldmant.m32[1] & 0x80000000)
|
||
|
|
return;
|
||
|
|
if (oldmant.m32[0] & 1)
|
||
|
|
break;
|
||
|
|
if (!(oldmant.m32[1] << 1))
|
||
|
|
return;
|
||
|
|
break;
|
||
|
|
case 0x401f ... 0x403d:
|
||
|
|
mask = 1 << (0x403d - dest->exp);
|
||
|
|
if (!(oldmant.m32[1] & mask))
|
||
|
|
return;
|
||
|
|
if (oldmant.m32[1] & (mask << 1))
|
||
|
|
break;
|
||
|
|
if (!(oldmant.m32[1] << (dest->exp - 0x401d)))
|
||
|
|
return;
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
case FPCR_ROUND_RZ:
|
||
|
|
return;
|
||
|
|
default:
|
||
|
|
if (dest->sign ^ (mode - FPCR_ROUND_RM))
|
||
|
|
break;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
switch (dest->exp) {
|
||
|
|
case 0 ... 0x3ffe:
|
||
|
|
dest->exp = 0x3fff;
|
||
|
|
dest->mant.m64 = 1ULL << 63;
|
||
|
|
break;
|
||
|
|
case 0x3fff ... 0x401e:
|
||
|
|
mask = 1 << (0x401e - dest->exp);
|
||
|
|
if (dest->mant.m32[0] += mask)
|
||
|
|
break;
|
||
|
|
dest->mant.m32[0] = 0x80000000;
|
||
|
|
dest->exp++;
|
||
|
|
break;
|
||
|
|
case 0x401f ... 0x403e:
|
||
|
|
mask = 1 << (0x403e - dest->exp);
|
||
|
|
if (dest->mant.m32[1] += mask)
|
||
|
|
break;
|
||
|
|
if (dest->mant.m32[0] += 1)
|
||
|
|
break;
|
||
|
|
dest->mant.m32[0] = 0x80000000;
|
||
|
|
dest->exp++;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* modrem_kernel: Implementation of the FREM and FMOD instructions
|
||
|
|
(which are exactly the same, except for the rounding used on the
|
||
|
|
intermediate value) */
|
||
|
|
|
||
|
|
static struct fp_ext *
|
||
|
|
modrem_kernel(struct fp_ext *dest, struct fp_ext *src, int mode)
|
||
|
|
{
|
||
|
|
struct fp_ext tmp;
|
||
|
|
|
||
|
|
fp_dyadic_check(dest, src);
|
||
|
|
|
||
|
|
/* Infinities and zeros */
|
||
|
|
if (IS_INF(dest) || IS_ZERO(src)) {
|
||
|
|
fp_set_nan(dest);
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
if (IS_ZERO(dest) || IS_INF(src))
|
||
|
|
return dest;
|
||
|
|
|
||
|
|
/* FIXME: there is almost certainly a smarter way to do this */
|
||
|
|
fp_copy_ext(&tmp, dest);
|
||
|
|
fp_fdiv(&tmp, src); /* NOTE: src might be modified */
|
||
|
|
fp_roundint(&tmp, mode);
|
||
|
|
fp_fmul(&tmp, src);
|
||
|
|
fp_fsub(dest, &tmp);
|
||
|
|
|
||
|
|
/* set the quotient byte */
|
||
|
|
fp_set_quotient((dest->mant.m64 & 0x7f) | (dest->sign << 7));
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* fp_fmod: Implements the kernel of the FMOD instruction.
|
||
|
|
|
||
|
|
Again, the argument order is backwards. The result, as defined in
|
||
|
|
the Motorola manuals, is:
|
||
|
|
|
||
|
|
fmod(src,dest) = (dest - (src * floor(dest / src))) */
|
||
|
|
|
||
|
|
struct fp_ext *
|
||
|
|
fp_fmod(struct fp_ext *dest, struct fp_ext *src)
|
||
|
|
{
|
||
|
|
dprint(PINSTR, "fmod\n");
|
||
|
|
return modrem_kernel(dest, src, FPCR_ROUND_RZ);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* fp_frem: Implements the kernel of the FREM instruction.
|
||
|
|
|
||
|
|
frem(src,dest) = (dest - (src * round(dest / src)))
|
||
|
|
*/
|
||
|
|
|
||
|
|
struct fp_ext *
|
||
|
|
fp_frem(struct fp_ext *dest, struct fp_ext *src)
|
||
|
|
{
|
||
|
|
dprint(PINSTR, "frem\n");
|
||
|
|
return modrem_kernel(dest, src, FPCR_ROUND_RN);
|
||
|
|
}
|
||
|
|
|
||
|
|
struct fp_ext *
|
||
|
|
fp_fint(struct fp_ext *dest, struct fp_ext *src)
|
||
|
|
{
|
||
|
|
dprint(PINSTR, "fint\n");
|
||
|
|
|
||
|
|
fp_copy_ext(dest, src);
|
||
|
|
|
||
|
|
fp_roundint(dest, FPDATA->rnd);
|
||
|
|
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
|
||
|
|
struct fp_ext *
|
||
|
|
fp_fintrz(struct fp_ext *dest, struct fp_ext *src)
|
||
|
|
{
|
||
|
|
dprint(PINSTR, "fintrz\n");
|
||
|
|
|
||
|
|
fp_copy_ext(dest, src);
|
||
|
|
|
||
|
|
fp_roundint(dest, FPCR_ROUND_RZ);
|
||
|
|
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
|
||
|
|
struct fp_ext *
|
||
|
|
fp_fscale(struct fp_ext *dest, struct fp_ext *src)
|
||
|
|
{
|
||
|
|
int scale, oldround;
|
||
|
|
|
||
|
|
dprint(PINSTR, "fscale\n");
|
||
|
|
|
||
|
|
fp_dyadic_check(dest, src);
|
||
|
|
|
||
|
|
/* Infinities */
|
||
|
|
if (IS_INF(src)) {
|
||
|
|
fp_set_nan(dest);
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
if (IS_INF(dest))
|
||
|
|
return dest;
|
||
|
|
|
||
|
|
/* zeroes */
|
||
|
|
if (IS_ZERO(src) || IS_ZERO(dest))
|
||
|
|
return dest;
|
||
|
|
|
||
|
|
/* Source exponent out of range */
|
||
|
|
if (src->exp >= 0x400c) {
|
||
|
|
fp_set_ovrflw(dest);
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* src must be rounded with round to zero. */
|
||
|
|
oldround = FPDATA->rnd;
|
||
|
|
FPDATA->rnd = FPCR_ROUND_RZ;
|
||
|
|
scale = fp_conv_ext2long(src);
|
||
|
|
FPDATA->rnd = oldround;
|
||
|
|
|
||
|
|
/* new exponent */
|
||
|
|
scale += dest->exp;
|
||
|
|
|
||
|
|
if (scale >= 0x7fff) {
|
||
|
|
fp_set_ovrflw(dest);
|
||
|
|
} else if (scale <= 0) {
|
||
|
|
fp_set_sr(FPSR_EXC_UNFL);
|
||
|
|
fp_denormalize(dest, -scale);
|
||
|
|
} else
|
||
|
|
dest->exp = scale;
|
||
|
|
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
|