diff options
Diffstat (limited to 'arch/m68k/math-emu/fp_arith.c')
| -rw-r--r-- | arch/m68k/math-emu/fp_arith.c | 699 |
1 files changed, 699 insertions, 0 deletions
diff --git a/arch/m68k/math-emu/fp_arith.c b/arch/m68k/math-emu/fp_arith.c new file mode 100644 index 000000000..d9033238d --- /dev/null +++ b/arch/m68k/math-emu/fp_arith.c @@ -0,0 +1,699 @@ +// SPDX-License-Identifier: GPL-2.0-or-later +/* + + fp_arith.c: floating-point math routines for the Linux-m68k + floating point emulator. + + Copyright (c) 1998-1999 David Huggins-Daines. + + Somewhat based on the AlphaLinux floating point emulator, by David + Mosberger-Tang. + + */ + +#include "fp_emu.h" +#include "multi_arith.h" +#include "fp_arith.h" + +const struct fp_ext fp_QNaN = +{ + .exp = 0x7fff, + .mant = { .m64 = ~0 } +}; + +const struct fp_ext fp_Inf = +{ + .exp = 0x7fff, +}; + +/* let's start with the easy ones */ + +struct fp_ext * +fp_fabs(struct fp_ext *dest, struct fp_ext *src) +{ + dprint(PINSTR, "fabs\n"); + + fp_monadic_check(dest, src); + + dest->sign = 0; + + return dest; +} + +struct fp_ext * +fp_fneg(struct fp_ext *dest, struct fp_ext *src) +{ + dprint(PINSTR, "fneg\n"); + + fp_monadic_check(dest, src); + + dest->sign = !dest->sign; + + return dest; +} + +/* Now, the slightly harder ones */ + +/* fp_fadd: Implements the kernel of the FADD, FSADD, FDADD, FSUB, + FDSUB, and FCMP instructions. */ + +struct fp_ext * +fp_fadd(struct fp_ext *dest, struct fp_ext *src) +{ + int diff; + + dprint(PINSTR, "fadd\n"); + + fp_dyadic_check(dest, src); + + if (IS_INF(dest)) { + /* infinity - infinity == NaN */ + if (IS_INF(src) && (src->sign != dest->sign)) + fp_set_nan(dest); + return dest; + } + if (IS_INF(src)) { + fp_copy_ext(dest, src); + return dest; + } + + if (IS_ZERO(dest)) { + if (IS_ZERO(src)) { + if (src->sign != dest->sign) { + if (FPDATA->rnd == FPCR_ROUND_RM) + dest->sign = 1; + else + dest->sign = 0; + } + } else + fp_copy_ext(dest, src); + return dest; + } + + dest->lowmant = src->lowmant = 0; + + if ((diff = dest->exp - src->exp) > 0) + fp_denormalize(src, diff); + else if ((diff = -diff) > 0) + fp_denormalize(dest, diff); + + if (dest->sign == src->sign) { + if (fp_addmant(dest, src)) + if (!fp_addcarry(dest)) + return dest; + } else { + if (dest->mant.m64 < src->mant.m64) { + fp_submant(dest, src, dest); + dest->sign = !dest->sign; + } else + fp_submant(dest, dest, src); + } + + return dest; +} + +/* fp_fsub: Implements the kernel of the FSUB, FSSUB, and FDSUB + instructions. + + Remember that the arguments are in assembler-syntax order! */ + +struct fp_ext * +fp_fsub(struct fp_ext *dest, struct fp_ext *src) +{ + dprint(PINSTR, "fsub "); + + src->sign = !src->sign; + return fp_fadd(dest, src); +} + + +struct fp_ext * +fp_fcmp(struct fp_ext *dest, struct fp_ext *src) +{ + dprint(PINSTR, "fcmp "); + + FPDATA->temp[1] = *dest; + src->sign = !src->sign; + return fp_fadd(&FPDATA->temp[1], src); +} + +struct fp_ext * +fp_ftst(struct fp_ext *dest, struct fp_ext *src) +{ + dprint(PINSTR, "ftst\n"); + + (void)dest; + + return src; +} + +struct fp_ext * +fp_fmul(struct fp_ext *dest, struct fp_ext *src) +{ + union fp_mant128 temp; + int exp; + + dprint(PINSTR, "fmul\n"); + + fp_dyadic_check(dest, src); + + /* calculate the correct sign now, as it's necessary for infinities */ + dest->sign = src->sign ^ dest->sign; + + /* Handle infinities */ + if (IS_INF(dest)) { + if (IS_ZERO(src)) + fp_set_nan(dest); + return dest; + } + if (IS_INF(src)) { + if (IS_ZERO(dest)) + fp_set_nan(dest); + else + fp_copy_ext(dest, src); + return dest; + } + + /* Of course, as we all know, zero * anything = zero. You may + not have known that it might be a positive or negative + zero... */ + if (IS_ZERO(dest) || IS_ZERO(src)) { + dest->exp = 0; + dest->mant.m64 = 0; + dest->lowmant = 0; + + return dest; + } + + exp = dest->exp + src->exp - 0x3ffe; + + /* shift up the mantissa for denormalized numbers, + so that the highest bit is set, this makes the + shift of the result below easier */ + if ((long)dest->mant.m32[0] >= 0) + exp -= fp_overnormalize(dest); + if ((long)src->mant.m32[0] >= 0) + exp -= fp_overnormalize(src); + + /* now, do a 64-bit multiply with expansion */ + fp_multiplymant(&temp, dest, src); + + /* normalize it back to 64 bits and stuff it back into the + destination struct */ + if ((long)temp.m32[0] > 0) { + exp--; + fp_putmant128(dest, &temp, 1); + } else + fp_putmant128(dest, &temp, 0); + + 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_fdiv: Implements the "kernel" of the FDIV, FSDIV, FDDIV and + FSGLDIV instructions. + + Note that the order of the operands is counter-intuitive: instead + of src / dest, the result is actually dest / src. */ + +struct fp_ext * +fp_fdiv(struct fp_ext *dest, struct fp_ext *src) +{ + union fp_mant128 temp; + int exp; + + dprint(PINSTR, "fdiv\n"); + + fp_dyadic_check(dest, src); + + /* calculate the correct sign now, as it's necessary for infinities */ + dest->sign = src->sign ^ dest->sign; + + /* Handle infinities */ + if (IS_INF(dest)) { + /* infinity / infinity = NaN (quiet, as always) */ + if (IS_INF(src)) + fp_set_nan(dest); + /* infinity / anything else = infinity (with approprate sign) */ + return dest; + } + if (IS_INF(src)) { + /* anything / infinity = zero (with appropriate sign) */ + dest->exp = 0; + dest->mant.m64 = 0; + dest->lowmant = 0; + + return dest; + } + + /* zeroes */ + if (IS_ZERO(dest)) { + /* zero / zero = NaN */ + if (IS_ZERO(src)) + fp_set_nan(dest); + /* zero / anything else = zero */ + return dest; + } + if (IS_ZERO(src)) { + /* anything / zero = infinity (with appropriate sign) */ + fp_set_sr(FPSR_EXC_DZ); + dest->exp = 0x7fff; + dest->mant.m64 = 0; + + return dest; + } + + exp = dest->exp - src->exp + 0x3fff; + + /* shift up the mantissa for denormalized numbers, + so that the highest bit is set, this makes lots + of things below easier */ + if ((long)dest->mant.m32[0] >= 0) + exp -= fp_overnormalize(dest); + if ((long)src->mant.m32[0] >= 0) + exp -= fp_overnormalize(src); + + /* now, do the 64-bit divide */ + fp_dividemant(&temp, dest, src); + + /* normalize it back to 64 bits and stuff it back into the + destination struct */ + if (!temp.m32[0]) { + exp--; + fp_putmant128(dest, &temp, 32); + } else + fp_putmant128(dest, &temp, 31); + + 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; +} + +struct fp_ext * +fp_fsglmul(struct fp_ext *dest, struct fp_ext *src) +{ + int exp; + + dprint(PINSTR, "fsglmul\n"); + + fp_dyadic_check(dest, src); + + /* calculate the correct sign now, as it's necessary for infinities */ + dest->sign = src->sign ^ dest->sign; + + /* Handle infinities */ + if (IS_INF(dest)) { + if (IS_ZERO(src)) + fp_set_nan(dest); + return dest; + } + if (IS_INF(src)) { + if (IS_ZERO(dest)) + fp_set_nan(dest); + else + fp_copy_ext(dest, src); + return dest; + } + + /* Of course, as we all know, zero * anything = zero. You may + not have known that it might be a positive or negative + zero... */ + if (IS_ZERO(dest) || IS_ZERO(src)) { + dest->exp = 0; + dest->mant.m64 = 0; + dest->lowmant = 0; + + return dest; + } + + exp = dest->exp + src->exp - 0x3ffe; + + /* do a 32-bit multiply */ + fp_mul64(dest->mant.m32[0], dest->mant.m32[1], + dest->mant.m32[0] & 0xffffff00, + src->mant.m32[0] & 0xffffff00); + + 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; +} + +struct fp_ext * +fp_fsgldiv(struct fp_ext *dest, struct fp_ext *src) +{ + int exp; + unsigned long quot, rem; + + dprint(PINSTR, "fsgldiv\n"); + + fp_dyadic_check(dest, src); + + /* calculate the correct sign now, as it's necessary for infinities */ + dest->sign = src->sign ^ dest->sign; + + /* Handle infinities */ + if (IS_INF(dest)) { + /* infinity / infinity = NaN (quiet, as always) */ + if (IS_INF(src)) + fp_set_nan(dest); + /* infinity / anything else = infinity (with approprate sign) */ + return dest; + } + if (IS_INF(src)) { + /* anything / infinity = zero (with appropriate sign) */ + dest->exp = 0; + dest->mant.m64 = 0; + dest->lowmant = 0; + + return dest; + } + + /* zeroes */ + if (IS_ZERO(dest)) { + /* zero / zero = NaN */ + if (IS_ZERO(src)) + fp_set_nan(dest); + /* zero / anything else = zero */ + return dest; + } + if (IS_ZERO(src)) { + /* anything / zero = infinity (with appropriate sign) */ + fp_set_sr(FPSR_EXC_DZ); + 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; +} + |