/* * fp_util.S * * Copyright Roman Zippel, 1997. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, and the entire permission notice in its entirety, * including the disclaimer of warranties. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. The name of the author may not be used to endorse or promote * products derived from this software without specific prior * written permission. * * ALTERNATIVELY, this product may be distributed under the terms of * the GNU General Public License, in which case the provisions of the GPL are * required INSTEAD OF the above restrictions. (This clause is * necessary due to a potential bad interaction between the GPL and * the restrictions contained in a BSD-style copyright.) * * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE * DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. */ #include "fp_emu.h" /* * Here are lots of conversion and normalization functions mainly * used by fp_scan.S * Note that these functions are optimized for "normal" numbers, * these are handled first and exit as fast as possible, this is * especially important for fp_normalize_ext/fp_conv_ext2ext, as * it's called very often. * The register usage is optimized for fp_scan.S and which register * is currently at that time unused, be careful if you want change * something here. %d0 and %d1 is always usable, sometimes %d2 (or * only the lower half) most function have to return the %a0 * unmodified, so that the caller can immediately reuse it. */ .globl fp_ill, fp_end | exits from fp_scan: | illegal instruction fp_ill: printf ,"fp_illegal\n" rts | completed instruction fp_end: tst.l (TASK_MM-8,%a2) jmi 1f tst.l (TASK_MM-4,%a2) jmi 1f tst.l (TASK_MM,%a2) jpl 2f 1: printf ,"oops:%p,%p,%p\n",3,%a2@(TASK_MM-8),%a2@(TASK_MM-4),%a2@(TASK_MM) 2: clr.l %d0 rts .globl fp_conv_long2ext, fp_conv_single2ext .globl fp_conv_double2ext, fp_conv_ext2ext .globl fp_normalize_ext, fp_normalize_double .globl fp_normalize_single, fp_normalize_single_fast .globl fp_conv_ext2double, fp_conv_ext2single .globl fp_conv_ext2long, fp_conv_ext2short .globl fp_conv_ext2byte .globl fp_finalrounding_single, fp_finalrounding_single_fast .globl fp_finalrounding_double .globl fp_finalrounding, fp_finaltest, fp_final /* * First several conversion functions from a source operand * into the extended format. Note, that only fp_conv_ext2ext * normalizes the number and is always called after the other * conversion functions, which only move the information into * fp_ext structure. */ | fp_conv_long2ext: | | args: %d0 = source (32-bit long) | %a0 = destination (ptr to struct fp_ext) fp_conv_long2ext: printf PCONV,"l2e: %p -> %p(",2,%d0,%a0 clr.l %d1 | sign defaults to zero tst.l %d0 jeq fp_l2e_zero | is source zero? jpl 1f | positive? moveq #1,%d1 neg.l %d0 1: swap %d1 move.w #0x3fff+31,%d1 move.l %d1,(%a0)+ | set sign / exp move.l %d0,(%a0)+ | set mantissa clr.l (%a0) subq.l #8,%a0 | restore %a0 printx PCONV,%a0@ printf PCONV,")\n" rts | source is zero fp_l2e_zero: clr.l (%a0)+ clr.l (%a0)+ clr.l (%a0) subq.l #8,%a0 printx PCONV,%a0@ printf PCONV,")\n" rts | fp_conv_single2ext | args: %d0 = source (single-precision fp value) | %a0 = dest (struct fp_ext *) fp_conv_single2ext: printf PCONV,"s2e: %p -> %p(",2,%d0,%a0 move.l %d0,%d1 lsl.l #8,%d0 | shift mantissa lsr.l #8,%d1 | exponent / sign lsr.l #7,%d1 lsr.w #8,%d1 jeq fp_s2e_small | zero / denormal? cmp.w #0xff,%d1 | NaN / Inf? jeq fp_s2e_large bset #31,%d0 | set explizit bit add.w #0x3fff-0x7f,%d1 | re-bias the exponent. 9: move.l %d1,(%a0)+ | fp_ext.sign, fp_ext.exp move.l %d0,(%a0)+ | high lword of fp_ext.mant clr.l (%a0) | low lword = 0 subq.l #8,%a0 printx PCONV,%a0@ printf PCONV,")\n" rts | zeros and denormalized fp_s2e_small: | exponent is zero, so explizit bit is already zero too tst.l %d0 jeq 9b move.w #0x4000-0x7f,%d1 jra 9b | infinities and NAN fp_s2e_large: bclr #31,%d0 | clear explizit bit move.w #0x7fff,%d1 jra 9b fp_conv_double2ext: #ifdef FPU_EMU_DEBUG getuser.l %a1@(0),%d0,fp_err_ua2,%a1 getuser.l %a1@(4),%d1,fp_err_ua2,%a1 printf PCONV,"d2e: %p%p -> %p(",3,%d0,%d1,%a0 #endif getuser.l (%a1)+,%d0,fp_err_ua2,%a1 move.l %d0,%d1 lsl.l #8,%d0 | shift high mantissa lsl.l #3,%d0 lsr.l #8,%d1 | exponent / sign lsr.l #7,%d1 lsr.w #5,%d1 jeq fp_d2e_small | zero / denormal? cmp.w #0x7ff,%d1 | NaN / Inf? jeq fp_d2e_large bset #31,%d0 | set explizit bit add.w #0x3fff-0x3ff,%d1 | re-bias the exponent. 9: move.l %d1,(%a0)+ | fp_ext.sign, fp_ext.exp move.l %d0,(%a0)+ getuser.l (%a1)+,%d0,fp_err_ua2,%a1 move.l %d0,%d1 lsl.l #8,%d0 lsl.l #3,%d0 move.l %d0,(%a0) moveq #21,%d0 lsr.l %d0,%d1 or.l %d1,-(%a0) subq.l #4,%a0 printx PCONV,%a0@ printf PCONV,")\n" rts | zeros and denormalized fp_d2e_small: | exponent is zero, so explizit bit is already zero too tst.l %d0 jeq 9b move.w #0x4000-0x3ff,%d1 jra 9b | infinities and NAN fp_d2e_large: bclr #31,%d0 | clear explizit bit move.w #0x7fff,%d1 jra 9b | fp_conv_ext2ext: | originally used to get longdouble from userspace, now it's | called before arithmetic operations to make sure the number | is normalized [maybe rename it?]. | args: %a0 = dest (struct fp_ext *) | returns 0 in %d0 for a NaN, otherwise 1 fp_conv_ext2ext: printf PCONV,"e2e: %p(",1,%a0 printx PCONV,%a0@ printf PCONV,"), " move.l (%a0)+,%d0 cmp.w #0x7fff,%d0 | Inf / NaN? jeq fp_e2e_large move.l (%a0),%d0 jpl fp_e2e_small | zero / denorm? | The high bit is set, so normalization is irrelevant. fp_e2e_checkround: subq.l #4,%a0 #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC move.b (%a0),%d0 jne fp_e2e_round #endif printf PCONV,"%p(",1,%a0 printx PCONV,%a0@ printf PCONV,")\n" moveq #1,%d0 rts #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC fp_e2e_round: fp_set_sr FPSR_EXC_INEX2 clr.b (%a0) move.w (FPD_RND,FPDATA),%d2 jne fp_e2e_roundother | %d2 == 0, round to nearest tst.b %d0 | test guard bit jpl 9f | zero is closer btst #0,(11,%a0) | test lsb bit jne fp_e2e_doroundup | round to infinity lsl.b #1,%d0 | check low bits jeq 9f | round to zero fp_e2e_doroundup: addq.l #1,(8,%a0) jcc 9f addq.l #1,(4,%a0) jcc 9f move.w #0x8000,(4,%a0) addq.w #1,(2,%a0) 9: printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts fp_e2e_roundother: subq.w #2,%d2 jcs 9b | %d2 < 2, round to zero jhi 1f | %d2 > 2, round to +infinity tst.b (1,%a0) | to -inf jne fp_e2e_doroundup | negative, round to infinity jra 9b | positive, round to zero 1: tst.b (1,%a0) | to +inf jeq fp_e2e_doroundup | positive, round to infinity jra 9b | negative, round to zero #endif | zeros and subnormals: | try to normalize these anyway. fp_e2e_small: jne fp_e2e_small1 | high lword zero? move.l (4,%a0),%d0 jne fp_e2e_small2 #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC clr.l %d0 move.b (-4,%a0),%d0 jne fp_e2e_small3 #endif | Genuine zero. clr.w -(%a0) subq.l #2,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" moveq #1,%d0 rts | definitely subnormal, need to shift all 64 bits fp_e2e_small1: bfffo %d0{#0,#32},%d1 move.w -(%a0),%d2 sub.w %d1,%d2 jcc 1f | Pathologically small, denormalize. add.w %d2,%d1 clr.w %d2 1: move.w %d2,(%a0)+ move.w %d1,%d2 jeq fp_e2e_checkround | fancy 64-bit double-shift begins here lsl.l %d2,%d0 move.l %d0,(%a0)+ move.l (%a0),%d0 move.l %d0,%d1 lsl.l %d2,%d0 move.l %d0,(%a0) neg.w %d2 and.w #0x1f,%d2 lsr.l %d2,%d1 or.l %d1,-(%a0) #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC fp_e2e_extra1: clr.l %d0 move.b (-4,%a0),%d0 neg.w %d2 add.w #24,%d2 jcc 1f clr.b (-4,%a0) lsl.l %d2,%d0 or.l %d0,(4,%a0) jra fp_e2e_checkround 1: addq.w #8,%d2 lsl.l %d2,%d0 move.b %d0,(-4,%a0) lsr.l #8,%d0 or.l %d0,(4,%a0) #endif jra fp_e2e_checkround | pathologically small subnormal fp_e2e_small2: bfffo %d0{#0,#32},%d1 add.w #32,%d1 move.w -(%a0),%d2 sub.w %d1,%d2 jcc 1f | Beyond pathologically small, denormalize. add.w %d2,%d1 clr.w %d2 1: move.w %d2,(%a0)+ ext.l %d1 jeq fp_e2e_checkround clr.l (4,%a0) sub.w #32,%d2 jcs 1f lsl.l %d1,%d0 | lower lword needs only to be shifted move.l %d0,(%a0) | into the higher lword #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC clr.l %d0 move.b (-4,%a0),%d0 clr.b (-4,%a0) neg.w %d1 add.w #32,%d1 bfins %d0,(%a0){%d1,#8} #endif jra fp_e2e_checkround 1: neg.w %d1 | lower lword is splitted between bfins %d0,(%a0){%d1,#32} | higher and lower lword #ifndef CONFIG_M68KFPU_EMU_EXTRAPREC jra fp_e2e_checkround #else move.w %d1,%d2 jra fp_e2e_extra1 | These are extremely small numbers, that will mostly end up as zero | anyway, so this is only important for correct rounding. fp_e2e_small3: bfffo %d0{#24,#8},%d1 add.w #40,%d1 move.w -(%a0),%d2 sub.w %d1,%d2 jcc 1f | Pathologically small, denormalize. add.w %d2,%d1 clr.w %d2 1: move.w %d2,(%a0)+ ext.l %d1 jeq fp_e2e_checkround cmp.w #8,%d1 jcs 2f 1: clr.b (-4,%a0) sub.w #64,%d1 jcs 1f add.w #24,%d1 lsl.l %d1,%d0 move.l %d0,(%a0) jra fp_e2e_checkround 1: neg.w %d1 bfins %d0,(%a0){%d1,#8} jra fp_e2e_checkround 2: lsl.l %d1,%d0 move.b %d0,(-4,%a0) lsr.l #8,%d0 move.b %d0,(7,%a0) jra fp_e2e_checkround #endif 1: move.l %d0,%d1 | lower lword is splitted between lsl.l %d2,%d0 | higher and lower lword move.l %d0,(%a0) move.l %d1,%d0 neg.w %d2 add.w #32,%d2 lsr.l %d2,%d0 move.l %d0,-(%a0) jra fp_e2e_checkround | Infinities and NaNs fp_e2e_large: move.l (%a0)+,%d0 jne 3f 1: tst.l (%a0) jne 4f moveq #1,%d0 2: subq.l #8,%a0 printf PCONV,"%p(",1,%a0 printx PCONV,%a0@ printf PCONV,")\n" rts | we have maybe a NaN, shift off the highest bit 3: lsl.l #1,%d0 jeq 1b | we have a NaN, clear the return value 4: clrl %d0 jra 2b /* * Normalization functions. Call these on the output of general * FP operators, and before any conversion into the destination * formats. fp_normalize_ext has always to be called first, the * following conversion functions expect an already normalized * number. */ | fp_normalize_ext: | normalize an extended in extended (unpacked) format, basically | it does the same as fp_conv_ext2ext, additionally it also does | the necessary postprocessing checks. | args: %a0 (struct fp_ext *) | NOTE: it does _not_ modify %a0/%a1 and the upper word of %d2 fp_normalize_ext: printf PNORM,"ne: %p(",1,%a0 printx PNORM,%a0@ printf PNORM,"), " move.l (%a0)+,%d0 cmp.w #0x7fff,%d0 | Inf / NaN? jeq fp_ne_large move.l (%a0),%d0 jpl fp_ne_small | zero / denorm? | The high bit is set, so normalization is irrelevant. fp_ne_checkround: subq.l #4,%a0 #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC move.b (%a0),%d0 jne fp_ne_round #endif printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC fp_ne_round: fp_set_sr FPSR_EXC_INEX2 clr.b (%a0) move.w (FPD_RND,FPDATA),%d2 jne fp_ne_roundother | %d2 == 0, round to nearest tst.b %d0 | test guard bit jpl 9f | zero is closer btst #0,(11,%a0) | test lsb bit jne fp_ne_doroundup | round to infinity lsl.b #1,%d0 | check low bits jeq 9f | round to zero fp_ne_doroundup: addq.l #1,(8,%a0) jcc 9f addq.l #1,(4,%a0) jcc 9f addq.w #1,(2,%a0) move.w #0x8000,(4,%a0) 9: printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts fp_ne_roundother: subq.w #2,%d2 jcs 9b | %d2 < 2, round to zero jhi 1f | %d2 > 2, round to +infinity tst.b (1,%a0) | to -inf jne fp_ne_doroundup | negative, round to infinity jra 9b | positive, round to zero 1: tst.b (1,%a0) | to +inf jeq fp_ne_doroundup | positive, round to infinity jra 9b | negative, round to zero #endif | Zeros and subnormal numbers | These are probably merely subnormal, rather than "denormalized" | numbers, so we will try to make them normal again. fp_ne_small: jne fp_ne_small1 | high lword zero? move.l (4,%a0),%d0 jne fp_ne_small2 #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC clr.l %d0 move.b (-4,%a0),%d0 jne fp_ne_small3 #endif | Genuine zero. clr.w -(%a0) subq.l #2,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | Subnormal. fp_ne_small1: bfffo %d0{#0,#32},%d1 move.w -(%a0),%d2 sub.w %d1,%d2 jcc 1f | Pathologically small, denormalize. add.w %d2,%d1 clr.w %d2 fp_set_sr FPSR_EXC_UNFL 1: move.w %d2,(%a0)+ move.w %d1,%d2 jeq fp_ne_checkround | This is exactly the same 64-bit double shift as seen above. lsl.l %d2,%d0 move.l %d0,(%a0)+ move.l (%a0),%d0 move.l %d0,%d1 lsl.l %d2,%d0 move.l %d0,(%a0) neg.w %d2 and.w #0x1f,%d2 lsr.l %d2,%d1 or.l %d1,-(%a0) #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC fp_ne_extra1: clr.l %d0 move.b (-4,%a0),%d0 neg.w %d2 add.w #24,%d2 jcc 1f clr.b (-4,%a0) lsl.l %d2,%d0 or.l %d0,(4,%a0) jra fp_ne_checkround 1: addq.w #8,%d2 lsl.l %d2,%d0 move.b %d0,(-4,%a0) lsr.l #8,%d0 or.l %d0,(4,%a0) #endif jra fp_ne_checkround | May or may not be subnormal, if so, only 32 bits to shift. fp_ne_small2: bfffo %d0{#0,#32},%d1 add.w #32,%d1 move.w -(%a0),%d2 sub.w %d1,%d2 jcc 1f | Beyond pathologically small, denormalize. add.w %d2,%d1 clr.w %d2 fp_set_sr FPSR_EXC_UNFL 1: move.w %d2,(%a0)+ ext.l %d1 jeq fp_ne_checkround clr.l (4,%a0) sub.w #32,%d1 jcs 1f lsl.l %d1,%d0 | lower lword needs only to be shifted move.l %d0,(%a0) | into the higher lword #ifdef CONFIG_M68KFPU_EMU_EXTRAPREC clr.l %d0 move.b (-4,%a0),%d0 clr.b (-4,%a0) neg.w %d1 add.w #32,%d1 bfins %d0,(%a0){%d1,#8} #endif jra fp_ne_checkround 1: neg.w %d1 | lower lword is splitted between bfins %d0,(%a0){%d1,#32} | higher and lower lword #ifndef CONFIG_M68KFPU_EMU_EXTRAPREC jra fp_ne_checkround #else move.w %d1,%d2 jra fp_ne_extra1 | These are extremely small numbers, that will mostly end up as zero | anyway, so this is only important for correct rounding. fp_ne_small3: bfffo %d0{#24,#8},%d1 add.w #40,%d1 move.w -(%a0),%d2 sub.w %d1,%d2 jcc 1f | Pathologically small, denormalize. add.w %d2,%d1 clr.w %d2 1: move.w %d2,(%a0)+ ext.l %d1 jeq fp_ne_checkround cmp.w #8,%d1 jcs 2f 1: clr.b (-4,%a0) sub.w #64,%d1 jcs 1f add.w #24,%d1 lsl.l %d1,%d0 move.l %d0,(%a0) jra fp_ne_checkround 1: neg.w %d1 bfins %d0,(%a0){%d1,#8} jra fp_ne_checkround 2: lsl.l %d1,%d0 move.b %d0,(-4,%a0) lsr.l #8,%d0 move.b %d0,(7,%a0) jra fp_ne_checkround #endif | Infinities and NaNs, again, same as above. fp_ne_large: move.l (%a0)+,%d0 jne 3f 1: tst.l (%a0) jne 4f 2: subq.l #8,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | we have maybe a NaN, shift off the highest bit 3: move.l %d0,%d1 lsl.l #1,%d1 jne 4f clr.l (-4,%a0) jra 1b | we have a NaN, test if it is signaling 4: bset #30,%d0 jne 2b fp_set_sr FPSR_EXC_SNAN move.l %d0,(-4,%a0) jra 2b | these next two do rounding as per the IEEE standard. | values for the rounding modes appear to be: | 0: Round to nearest | 1: Round to zero | 2: Round to -Infinity | 3: Round to +Infinity | both functions expect that fp_normalize was already | called (and extended argument is already normalized | as far as possible), these are used if there is different | rounding precision is selected and before converting | into single/double | fp_normalize_double: | normalize an extended with double (52-bit) precision | args: %a0 (struct fp_ext *) fp_normalize_double: printf PNORM,"nd: %p(",1,%a0 printx PNORM,%a0@ printf PNORM,"), " move.l (%a0)+,%d2 tst.w %d2 jeq fp_nd_zero | zero / denormalized cmp.w #0x7fff,%d2 jeq fp_nd_huge | NaN / infinitive. sub.w #0x4000-0x3ff,%d2 | will the exponent fit? jcs fp_nd_small | too small. cmp.w #0x7fe,%d2 jcc fp_nd_large | too big. addq.l #4,%a0 move.l (%a0),%d0 | low lword of mantissa | now, round off the low 11 bits. fp_nd_round: moveq #21,%d1 lsl.l %d1,%d0 | keep 11 low bits. jne fp_nd_checkround | Are they non-zero? | nothing to do here 9: subq.l #8,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | Be careful with the X bit! It contains the lsb | from the shift above, it is needed for round to nearest. fp_nd_checkround: fp_set_sr FPSR_EXC_INEX2 | INEX2 bit and.w #0xf800,(2,%a0) | clear bits 0-10 move.w (FPD_RND,FPDATA),%d2 | rounding mode jne 2f | %d2 == 0, round to nearest tst.l %d0 | test guard bit jpl 9b | zero is closer | here we test the X bit by adding it to %d2 clr.w %d2 | first set z bit, addx only clears it addx.w %d2,%d2 | test lsb bit | IEEE754-specified "round to even" behaviour. If the guard | bit is set, then the number is odd, so rounding works like | in grade-school arithmetic (i.e. 1.5 rounds to 2.0) | Otherwise, an equal distance rounds towards zero, so as not | to produce an odd number. This is strange, but it is what | the standard says. jne fp_nd_doroundup | round to infinity lsl.l #1,%d0 | check low bits jeq 9b | round to zero fp_nd_doroundup: | round (the mantissa, that is) towards infinity add.l #0x800,(%a0) jcc 9b | no overflow, good. addq.l #1,-(%a0) | extend to high lword jcc 1f | no overflow, good. | Yow! we have managed to overflow the mantissa. Since this | only happens when %d1 was 0xfffff800, it is now zero, so | reset the high bit, and increment the exponent. move.w #0x8000,(%a0) addq.w #1,-(%a0) cmp.w #0x43ff,(%a0)+ | exponent now overflown? jeq fp_nd_large | yes, so make it infinity. 1: subq.l #4,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts 2: subq.w #2,%d2 jcs 9b | %d2 < 2, round to zero jhi 3f | %d2 > 2, round to +infinity | Round to +Inf or -Inf. High word of %d2 contains the | sign of the number, by the way. swap %d2 | to -inf tst.b %d2 jne fp_nd_doroundup | negative, round to infinity jra 9b | positive, round to zero 3: swap %d2 | to +inf tst.b %d2 jeq fp_nd_doroundup | positive, round to infinity jra 9b | negative, round to zero | Exponent underflow. Try to make a denormal, and set it to | the smallest possible fraction if this fails. fp_nd_small: fp_set_sr FPSR_EXC_UNFL | set UNFL bit move.w #0x3c01,(-2,%a0) | 2**-1022 neg.w %d2 | degree of underflow cmp.w #32,%d2 | single or double shift? jcc 1f | Again, another 64-bit double shift. move.l (%a0),%d0 move.l %d0,%d1 lsr.l %d2,%d0 move.l %d0,(%a0)+ move.l (%a0),%d0 lsr.l %d2,%d0 neg.w %d2 add.w #32,%d2 lsl.l %d2,%d1 or.l %d1,%d0 move.l (%a0),%d1 move.l %d0,(%a0) | Check to see if we shifted off any significant bits lsl.l %d2,%d1 jeq fp_nd_round | Nope, round. bset #0,%d0 | Yes, so set the "sticky bit". jra fp_nd_round | Now, round. | Another 64-bit single shift and store 1: sub.w #32,%d2 cmp.w #32,%d2 | Do we really need to shift? jcc 2f | No, the number is too small. move.l (%a0),%d0 clr.l (%a0)+ move.l %d0,%d1 lsr.l %d2,%d0 neg.w %d2 add.w #32,%d2 | Again, check to see if we shifted off any significant bits. tst.l (%a0) jeq 1f bset #0,%d0 | Sticky bit. 1: move.l %d0,(%a0) lsl.l %d2,%d1 jeq fp_nd_round bset #0,%d0 jra fp_nd_round | Sorry, the number is just too small. 2: clr.l (%a0)+ clr.l (%a0) moveq #1,%d0 | Smallest possible fraction, jra fp_nd_round | round as desired. | zero and denormalized fp_nd_zero: tst.l (%a0)+ jne 1f tst.l (%a0) jne 1f subq.l #8,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | zero. nothing to do. | These are not merely subnormal numbers, but true denormals, | i.e. pathologically small (exponent is 2**-16383) numbers. | It is clearly impossible for even a normal extended number | with that exponent to fit into double precision, so just | write these ones off as "too darn small". 1: fp_set_sr FPSR_EXC_UNFL | Set UNFL bit clr.l (%a0) clr.l -(%a0) move.w #0x3c01,-(%a0) | i.e. 2**-1022 addq.l #6,%a0 moveq #1,%d0 jra fp_nd_round | round. | Exponent overflow. Just call it infinity. fp_nd_large: move.w #0x7ff,%d0 and.w (6,%a0),%d0 jeq 1f fp_set_sr FPSR_EXC_INEX2 1: fp_set_sr FPSR_EXC_OVFL move.w (FPD_RND,FPDATA),%d2 jne 3f | %d2 = 0 round to nearest 1: move.w #0x7fff,(-2,%a0) clr.l (%a0)+ clr.l (%a0) 2: subq.l #8,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts 3: subq.w #2,%d2 jcs 5f | %d2 < 2, round to zero jhi 4f | %d2 > 2, round to +infinity tst.b (-3,%a0) | to -inf jne 1b jra 5f 4: tst.b (-3,%a0) | to +inf jeq 1b 5: move.w #0x43fe,(-2,%a0) moveq #-1,%d0 move.l %d0,(%a0)+ move.w #0xf800,%d0 move.l %d0,(%a0) jra 2b | Infinities or NaNs fp_nd_huge: subq.l #4,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | fp_normalize_single: | normalize an extended with single (23-bit) precision | args: %a0 (struct fp_ext *) fp_normalize_single: printf PNORM,"ns: %p(",1,%a0 printx PNORM,%a0@ printf PNORM,") " addq.l #2,%a0 move.w (%a0)+,%d2 jeq fp_ns_zero | zero / denormalized cmp.w #0x7fff,%d2 jeq fp_ns_huge | NaN / infinitive. sub.w #0x4000-0x7f,%d2 | will the exponent fit? jcs fp_ns_small | too small. cmp.w #0xfe,%d2 jcc fp_ns_large | too big. move.l (%a0)+,%d0 | get high lword of mantissa fp_ns_round: tst.l (%a0) | check the low lword jeq 1f | Set a sticky bit if it is non-zero. This should only | affect the rounding in what would otherwise be equal- | distance situations, which is what we want it to do. bset #0,%d0 1: clr.l (%a0) | zap it from memory. | now, round off the low 8 bits of the hi lword. tst.b %d0 | 8 low bits. jne fp_ns_checkround | Are they non-zero? | nothing to do here subq.l #8,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts fp_ns_checkround: fp_set_sr FPSR_EXC_INEX2 | INEX2 bit clr.b -(%a0) | clear low byte of high lword subq.l #3,%a0 move.w (FPD_RND,FPDATA),%d2 | rounding mode jne 2f | %d2 == 0, round to nearest tst.b %d0 | test guard bit jpl 9f | zero is closer btst #8,%d0 | test lsb bit | round to even behaviour, see above. jne fp_ns_doroundup | round to infinity lsl.b #1,%d0 | check low bits jeq 9f | round to zero fp_ns_doroundup: | round (the mantissa, that is) towards infinity add.l #0x100,(%a0) jcc 9f | no overflow, good. | Overflow. This means that the %d1 was 0xffffff00, so it | is now zero. We will set the mantissa to reflect this, and | increment the exponent (checking for overflow there too) move.w #0x8000,(%a0) addq.w #1,-(%a0) cmp.w #0x407f,(%a0)+ | exponent now overflown? jeq fp_ns_large | yes, so make it infinity. 9: subq.l #4,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | check nondefault rounding modes 2: subq.w #2,%d2 jcs 9b | %d2 < 2, round to zero jhi 3f | %d2 > 2, round to +infinity tst.b (-3,%a0) | to -inf jne fp_ns_doroundup | negative, round to infinity jra 9b | positive, round to zero 3: tst.b (-3,%a0) | to +inf jeq fp_ns_doroundup | positive, round to infinity jra 9b | negative, round to zero | Exponent underflow. Try to make a denormal, and set it to | the smallest possible fraction if this fails. fp_ns_small: fp_set_sr FPSR_EXC_UNFL | set UNFL bit move.w #0x3f81,(-2,%a0) | 2**-126 neg.w %d2 | degree of underflow cmp.w #32,%d2 | single or double shift? jcc 2f | a 32-bit shift. move.l (%a0),%d0 move.l %d0,%d1 lsr.l %d2,%d0 move.l %d0,(%a0)+ | Check to see if we shifted off any significant bits. neg.w %d2 add.w #32,%d2 lsl.l %d2,%d1 jeq 1f bset #0,%d0 | Sticky bit. | Check the lower lword 1: tst.l (%a0) jeq fp_ns_round clr (%a0) bset #0,%d0 | Sticky bit. jra fp_ns_round | Sorry, the number is just too small. 2: clr.l (%a0)+ clr.l (%a0) moveq #1,%d0 | Smallest possible fraction, jra fp_ns_round | round as desired. | Exponent overflow. Just call it infinity. fp_ns_large: tst.b (3,%a0) jeq 1f fp_set_sr FPSR_EXC_INEX2 1: fp_set_sr FPSR_EXC_OVFL move.w (FPD_RND,FPDATA),%d2 jne 3f | %d2 = 0 round to nearest 1: move.w #0x7fff,(-2,%a0) clr.l (%a0)+ clr.l (%a0) 2: subq.l #8,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts 3: subq.w #2,%d2 jcs 5f | %d2 < 2, round to zero jhi 4f | %d2 > 2, round to +infinity tst.b (-3,%a0) | to -inf jne 1b jra 5f 4: tst.b (-3,%a0) | to +inf jeq 1b 5: move.w #0x407e,(-2,%a0) move.l #0xffffff00,(%a0)+ clr.l (%a0) jra 2b | zero and denormalized fp_ns_zero: tst.l (%a0)+ jne 1f tst.l (%a0) jne 1f subq.l #8,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | zero. nothing to do. | These are not merely subnormal numbers, but true denormals, | i.e. pathologically small (exponent is 2**-16383) numbers. | It is clearly impossible for even a normal extended number | with that exponent to fit into single precision, so just | write these ones off as "too darn small". 1: fp_set_sr FPSR_EXC_UNFL | Set UNFL bit clr.l (%a0) clr.l -(%a0) move.w #0x3f81,-(%a0) | i.e. 2**-126 addq.l #6,%a0 moveq #1,%d0 jra fp_ns_round | round. | Infinities or NaNs fp_ns_huge: subq.l #4,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | fp_normalize_single_fast: | normalize an extended with single (23-bit) precision | this is only used by fsgldiv/fsgdlmul, where the | operand is not completly normalized. | args: %a0 (struct fp_ext *) fp_normalize_single_fast: printf PNORM,"nsf: %p(",1,%a0 printx PNORM,%a0@ printf PNORM,") " addq.l #2,%a0 move.w (%a0)+,%d2 cmp.w #0x7fff,%d2 jeq fp_nsf_huge | NaN / infinitive. move.l (%a0)+,%d0 | get high lword of mantissa fp_nsf_round: tst.l (%a0) | check the low lword jeq 1f | Set a sticky bit if it is non-zero. This should only | affect the rounding in what would otherwise be equal- | distance situations, which is what we want it to do. bset #0,%d0 1: clr.l (%a0) | zap it from memory. | now, round off the low 8 bits of the hi lword. tst.b %d0 | 8 low bits. jne fp_nsf_checkround | Are they non-zero? | nothing to do here subq.l #8,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts fp_nsf_checkround: fp_set_sr FPSR_EXC_INEX2 | INEX2 bit clr.b -(%a0) | clear low byte of high lword subq.l #3,%a0 move.w (FPD_RND,FPDATA),%d2 | rounding mode jne 2f | %d2 == 0, round to nearest tst.b %d0 | test guard bit jpl 9f | zero is closer btst #8,%d0 | test lsb bit | round to even behaviour, see above. jne fp_nsf_doroundup | round to infinity lsl.b #1,%d0 | check low bits jeq 9f | round to zero fp_nsf_doroundup: | round (the mantissa, that is) towards infinity add.l #0x100,(%a0) jcc 9f | no overflow, good. | Overflow. This means that the %d1 was 0xffffff00, so it | is now zero. We will set the mantissa to reflect this, and | increment the exponent (checking for overflow there too) move.w #0x8000,(%a0) addq.w #1,-(%a0) cmp.w #0x407f,(%a0)+ | exponent now overflown? jeq fp_nsf_large | yes, so make it infinity. 9: subq.l #4,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | check nondefault rounding modes 2: subq.w #2,%d2 jcs 9b | %d2 < 2, round to zero jhi 3f | %d2 > 2, round to +infinity tst.b (-3,%a0) | to -inf jne fp_nsf_doroundup | negative, round to infinity jra 9b | positive, round to zero 3: tst.b (-3,%a0) | to +inf jeq fp_nsf_doroundup | positive, round to infinity jra 9b | negative, round to zero | Exponent overflow. Just call it infinity. fp_nsf_large: tst.b (3,%a0) jeq 1f fp_set_sr FPSR_EXC_INEX2 1: fp_set_sr FPSR_EXC_OVFL move.w (FPD_RND,FPDATA),%d2 jne 3f | %d2 = 0 round to nearest 1: move.w #0x7fff,(-2,%a0) clr.l (%a0)+ clr.l (%a0) 2: subq.l #8,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts 3: subq.w #2,%d2 jcs 5f | %d2 < 2, round to zero jhi 4f | %d2 > 2, round to +infinity tst.b (-3,%a0) | to -inf jne 1b jra 5f 4: tst.b (-3,%a0) | to +inf jeq 1b 5: move.w #0x407e,(-2,%a0) move.l #0xffffff00,(%a0)+ clr.l (%a0) jra 2b | Infinities or NaNs fp_nsf_huge: subq.l #4,%a0 printf PNORM,"%p(",1,%a0 printx PNORM,%a0@ printf PNORM,")\n" rts | conv_ext2int (macro): | Generates a subroutine that converts an extended value to an | integer of a given size, again, with the appropriate type of | rounding. | Macro arguments: | s: size, as given in an assembly instruction. | b: number of bits in that size. | Subroutine arguments: | %a0: source (struct fp_ext *) | Returns the integer in %d0 (like it should) .macro conv_ext2int s,b .set inf,(1<<(\b-1))-1 | i.e. MAXINT printf PCONV,"e2i%d: %p(",2,#\b,%a0 printx PCONV,%a0@ printf PCONV,") " addq.l #2,%a0 move.w (%a0)+,%d2 | exponent jeq fp_e2i_zero\b | zero / denorm (== 0, here) cmp.w #0x7fff,%d2 jeq fp_e2i_huge\b | Inf / NaN sub.w #0x3ffe,%d2 jcs fp_e2i_small\b cmp.w #\b,%d2 jhi fp_e2i_large\b move.l (%a0),%d0 move.l %d0,%d1 lsl.l %d2,%d1 jne fp_e2i_round\b tst.l (4,%a0) jne fp_e2i_round\b neg.w %d2 add.w #32,%d2 lsr.l %d2,%d0 9: tst.w (-4,%a0) jne 1f tst.\s %d0 jmi fp_e2i_large\b printf PCONV,"-> %p\n",1,%d0 rts 1: neg.\s %d0 jeq 1f jpl fp_e2i_large\b 1: printf PCONV,"-> %p\n",1,%d0 rts fp_e2i_round\b: fp_set_sr FPSR_EXC_INEX2 | INEX2 bit neg.w %d2 add.w #32,%d2 .if \b>16 jeq 5f .endif lsr.l %d2,%d0 move.w (FPD_RND,FPDATA),%d2 | rounding mode jne 2f | %d2 == 0, round to nearest tst.l %d1 | test guard bit jpl 9b | zero is closer btst %d2,%d0 | test lsb bit (%d2 still 0) jne fp_e2i_doroundup\b lsl.l #1,%d1 | check low bits jne fp_e2i_doroundup\b tst.l (4,%a0) jeq 9b fp_e2i_doroundup\b: addq.l #1,%d0 jra 9b | check nondefault rounding modes 2: subq.w #2,%d2 jcs 9b | %d2 < 2, round to zero jhi 3f | %d2 > 2, round to +infinity tst.w (-4,%a0) | to -inf jne fp_e2i_doroundup\b | negative, round to infinity jra 9b | positive, round to zero 3: tst.w (-4,%a0) | to +inf jeq fp_e2i_doroundup\b | positive, round to infinity jra 9b | negative, round to zero | we are only want -2**127 get correctly rounded here, | since the guard bit is in the lower lword. | everything else ends up anyway as overflow. .if \b>16 5: move.w (FPD_RND,FPDATA),%d2 | rounding mode jne 2b | %d2 == 0, round to nearest move.l (4,%a0),%d1 | test guard bit jpl 9b | zero is closer lsl.l #1,%d1 | check low bits jne fp_e2i_doroundup\b jra 9b .endif fp_e2i_zero\b: clr.l %d0 tst.l (%a0)+ jne 1f tst.l (%a0) jeq 3f 1: subq.l #4,%a0 fp_clr_sr FPSR_EXC_UNFL | fp_normalize_ext has set this bit fp_e2i_small\b: fp_set_sr FPSR_EXC_INEX2 clr.l %d0 move.w (FPD_RND,FPDATA),%d2 | rounding mode subq.w #2,%d2 jcs 3f | %d2 < 2, round to nearest/zero jhi 2f | %d2 > 2, round to +infinity tst.w (-4,%a0) | to -inf jeq 3f subq.\s #1,%d0 jra 3f 2: tst.w (-4,%a0) | to +inf jne 3f addq.\s #1,%d0 3: printf PCONV,"-> %p\n",1,%d0 rts fp_e2i_large\b: fp_set_sr FPSR_EXC_OPERR move.\s #inf,%d0 tst.w (-4,%a0) jeq 1f addq.\s #1,%d0 1: printf PCONV,"-> %p\n",1,%d0 rts fp_e2i_huge\b: move.\s (%a0),%d0 tst.l (%a0) jne 1f tst.l (%a0) jeq fp_e2i_large\b | fp_normalize_ext has set this bit already | and made the number nonsignaling 1: fp_tst_sr FPSR_EXC_SNAN jne 1f fp_set_sr FPSR_EXC_OPERR 1: printf PCONV,"-> %p\n",1,%d0 rts .endm fp_conv_ext2long: conv_ext2int l,32 fp_conv_ext2short: conv_ext2int w,16 fp_conv_ext2byte: conv_ext2int b,8 fp_conv_ext2double: jsr fp_normalize_double printf PCONV,"e2d: %p(",1,%a0 printx PCONV,%a0@ printf PCONV,"), " move.l (%a0)+,%d2 cmp.w #0x7fff,%d2 jne 1f move.w #0x7ff,%d2 move.l (%a0)+,%d0 jra 2f 1: sub.w #0x3fff-0x3ff,%d2 move.l (%a0)+,%d0 jmi 2f clr.w %d2 2: lsl.w #5,%d2 lsl.l #7,%d2 lsl.l #8,%d2 move.l %d0,%d1 lsl.l #1,%d0 lsr.l #4,%d0 lsr.l #8,%d0 or.l %d2,%d0 putuser.l %d0,(%a1)+,fp_err_ua2,%a1 moveq #21,%d0 lsl.l %d0,%d1 move.l (%a0),%d0 lsr.l #4,%d0 lsr.l #7,%d0 or.l %d1,%d0 putuser.l %d0,(%a1),fp_err_ua2,%a1 #ifdef FPU_EMU_DEBUG getuser.l %a1@(-4),%d0,fp_err_ua2,%a1 getuser.l %a1@(0),%d1,fp_err_ua2,%a1 printf PCONV,"%p(%08x%08x)\n",3,%a1,%d0,%d1 #endif rts fp_conv_ext2single: jsr fp_normalize_single printf PCONV,"e2s: %p(",1,%a0 printx PCONV,%a0@ printf PCONV,"), " move.l (%a0)+,%d1 cmp.w #0x7fff,%d1 jne 1f move.w #0xff,%d1 move.l (%a0)+,%d0 jra 2f 1: sub.w #0x3fff-0x7f,%d1 move.l (%a0)+,%d0 jmi 2f clr.w %d1 2: lsl.w #8,%d1 lsl.l #7,%d1 lsl.l #8,%d1 bclr #31,%d0 lsr.l #8,%d0 or.l %d1,%d0 printf PCONV,"%08x\n",1,%d0 rts | special return addresses for instr that | encode the rounding precision in the opcode | (e.g. fsmove,fdmove) fp_finalrounding_single: addq.l #8,%sp jsr fp_normalize_ext jsr fp_normalize_single jra fp_finaltest fp_finalrounding_single_fast: addq.l #8,%sp jsr fp_normalize_ext jsr fp_normalize_single_fast jra fp_finaltest fp_finalrounding_double: addq.l #8,%sp jsr fp_normalize_ext jsr fp_normalize_double jra fp_finaltest | fp_finaltest: | set the emulated status register based on the outcome of an | emulated instruction. fp_finalrounding: addq.l #8,%sp | printf ,"f: %p\n",1,%a0 jsr fp_normalize_ext move.w (FPD_PREC,FPDATA),%d0 subq.w #1,%d0 jcs fp_finaltest jne 1f jsr fp_normalize_single jra 2f 1: jsr fp_normalize_double 2:| printf ,"f: %p\n",1,%a0 fp_finaltest: | First, we do some of the obvious tests for the exception | status byte and condition code bytes of fp_sr here, so that | they do not have to be handled individually by every | emulated instruction. clr.l %d0 addq.l #1,%a0 tst.b (%a0)+ | sign jeq 1f bset #FPSR_CC_NEG-24,%d0 | N bit 1: cmp.w #0x7fff,(%a0)+ | exponent jeq 2f | test for zero moveq #FPSR_CC_Z-24,%d1 tst.l (%a0)+ jne 9f tst.l (%a0) jne 9f jra 8f | infinitiv and NAN 2: moveq #FPSR_CC_NAN-24,%d1 move.l (%a0)+,%d2 lsl.l #1,%d2 | ignore high bit jne 8f tst.l (%a0) jne 8f moveq #FPSR_CC_INF-24,%d1 8: bset %d1,%d0 9: move.b %d0,(FPD_FPSR+0,FPDATA) | set condition test result | move instructions enter here | Here, we test things in the exception status byte, and set | other things in the accrued exception byte accordingly. | Emulated instructions can set various things in the former, | as defined in fp_emu.h. fp_final: move.l (FPD_FPSR,FPDATA),%d0 #if 0 btst #FPSR_EXC_SNAN,%d0 | EXC_SNAN jne 1f btst #FPSR_EXC_OPERR,%d0 | EXC_OPERR jeq 2f 1: bset #FPSR_AEXC_IOP,%d0 | set IOP bit 2: btst #FPSR_EXC_OVFL,%d0 | EXC_OVFL jeq 1f bset #FPSR_AEXC_OVFL,%d0 | set OVFL bit 1: btst #FPSR_EXC_UNFL,%d0 | EXC_UNFL jeq 1f btst #FPSR_EXC_INEX2,%d0 | EXC_INEX2 jeq 1f bset #FPSR_AEXC_UNFL,%d0 | set UNFL bit 1: btst #FPSR_EXC_DZ,%d0 | EXC_INEX1 jeq 1f bset #FPSR_AEXC_DZ,%d0 | set DZ bit 1: btst #FPSR_EXC_OVFL,%d0 | EXC_OVFL jne 1f btst #FPSR_EXC_INEX2,%d0 | EXC_INEX2 jne 1f btst #FPSR_EXC_INEX1,%d0 | EXC_INEX1 jeq 2f 1: bset #FPSR_AEXC_INEX,%d0 | set INEX bit 2: move.l %d0,(FPD_FPSR,FPDATA) #else | same as above, greatly optimized, but untested (yet) move.l %d0,%d2 lsr.l #5,%d0 move.l %d0,%d1 lsr.l #4,%d1 or.l %d0,%d1 and.b #0x08,%d1 move.l %d2,%d0 lsr.l #6,%d0 or.l %d1,%d0 move.l %d2,%d1 lsr.l #4,%d1 or.b #0xdf,%d1 and.b %d1,%d0 move.l %d2,%d1 lsr.l #7,%d1 and.b #0x80,%d1 or.b %d1,%d0 and.b #0xf8,%d0 or.b %d0,%d2 move.l %d2,(FPD_FPSR,FPDATA) #endif move.b (FPD_FPSR+2,FPDATA),%d0 and.b (FPD_FPCR+2,FPDATA),%d0 jeq 1f printf ,"send signal!!!\n" 1: jra fp_end