Library — math16
Home under classic/newlib float trees (see libsrc/math/float/ math16 paths and
--math16 on zcc). Policy mirrors math32:
| Op |
Algorithm |
div / asm_f16_div |
Restoring |
inv / asm_f16_inv |
Newton–Raphson |
In C higher functions (c/*.c):
| Need |
Write |
Do not write |
Reciprocal 1/n |
1.0/x (restoring div) |
invf16(x) |
| Inverse square root |
invsqrtf16(x) |
1.0/sqrtf16(x) |
Square x*x |
sqrf16(x) (fastcall, always +) |
mulf16(x,x) / a sqrf16 macro |
| IEEE bits |
union float16_int from c/math16.h |
a local uint16_t union |
pow(x, -0.5) keeps invsqrtf16. Packed-half hi byte after abs: |x|>=128 iff m16_ieee_hi >= 0x58. Do not fmod for |x|<128.
Agent rules
- One major function per file; CPU copies under matching asm CPU dirs.
- 8085: stack-only; no EXX/IX/IY; legal
(de) stores only (a/hl/post-inc).
- Classic TIMER benches for math16: use
z88dk-classic/*.c (parent sources may lack _Float16).
- 8085 math16 often also needs
-lmath32_8085 for higher helpers — match classic recipes.
- Suite:
make -C test/suites/math test_math16.bin test_math16_z180.bin test_math16_ez80_z80.bin test_math16_z80n.bin test_math16_r2ka.bin test_math16_r4k.bin test_math16_r6k.bin test_math16_kc160.bin test_math16_8085.bin test_math16_8080.bin test_math16_gbz80.bin. Newlib: +rc2014 -clib=new with -lmath16 -lmath32 (mirror math32 rc2014 recipe).
- Higher funcs layout:
c/z80/ (sccz80 +new), c/8085/, c/8080/, c/gbz80/. c/Makefile clean: only remove C-derived *.asm in those dirs ($(AFILES8085) / $(AFILES8080) / $(AFILESGBZ80)); keep hand-written cm16_sccz80_*.asm.
- Cores:
asm/{z80,8085,8080,gbz80}/. Packed * / sqrf16 = 11×11 (asm_f16_mul_callee / asm_f16_sqr). Poly, inv, sqrt NR, hypot, fma = f24 16×16 (asm_f24_mul_f24).
- Unrolled 11×11 / 16×16 mulu is
IF __CPU_Z80__ only. z80n / z180 / ez80 / kc160 / rabbit call l_mulu_32_16x16 (HW integer). Do not assemble the unrolled body into those products.
--math16 is adjunct (no conflict with math32/math48). Classic: math16.lib + math16_{8085,8080,gbz80,…}.lib. Newlib sccz80 bakes math16 into lib/clibs/sccz80/z80.lib. After core edits: delete *math16* .o under libsrc/newlib/target/{math16,z80}/obj, then make -C libsrc/newlib math16 z80. Prove cm16_sccz80_mul_callee is G = onto asm_f16_mul_callee (stale is G A at a later line).- Classic 8085/8080/gbz80 Makefile targets have no OBJECTS deps.
rm obj/<cpu>/…/asm_f16_*.o and libsrc/math16*.lib, then make -C libsrc math16.lib and cp into lib/clibs/.
- Specials stay off the finite path. Classify Inf/NaN on overflow / zero / equal-exp 255 (packed exp 31) only.
inc r / jp Z tests exp==255 (8-bit inc sets Z, not C). Pack underflow is unsigned jp C after sub 112 (not jp M: d=255 → 143 looks minus). Packed Inf × tiny finite (sum−15 < 31) may not be Inf.
- gbz80: no cheap
ex (sp),hl (148c helper). Open-code: park DE, ld hl,sp+n, swap through (hl), restore DE; BC is often the return. No jp P / ret m (no S): bit 7,h.
- MPL v2 panel on
asm/ cores only — not c/ glue, lm16 aliases, or C (some C is GPL).
- Restoring f24 div: z80 uses
exx + djnz (count in B'). 8085 / 8080 / gbz80 have no spare count register (B is the divisor). After prenorm, DE is free: stacked ret — push div_pack, 15× div_bit, jp div_bit; div_bit ends in ret. Do not call div_bit 16 times. 8080/gbz80 inner push de/push af sit above those words. z80 keeps the djnz loop.
Calling vs math32
Many half API symbols are plain defc sinf16 = _m16_sinf (true DEHL) even with
-D__CLASSIC — not the math32 stack-bridge trap. Still prefer map proof
(sinf16 / sqrtf16 / invsqrtf16) after link. Fair n-body: math16 may keep
invsqrtf16; math32 TIMER source should use 1.0/sqrt on both classic and newlib.
Related
library-math32, cpu-8085, methodology-measure, library-newlib (header regen)- Product readme: math16
README.md under the float tree
1---2name: library-math163description: math16 half-float library for z88dk: f16/f24 cores, restoring div vs NR inv, classic +test recipes need z88dk-classic sources. Use when editing libsrc math16 or measuring half-float.4---56# Library — math1678Home under classic/newlib float trees (see `libsrc/math/float/` math16 paths and9`--math16` on `zcc`). Policy mirrors math32:1011| Op | Algorithm |12|----|-----------|13| **div** / `asm_f16_div` | **Restoring** |14| **inv** / `asm_f16_inv` | Newton–Raphson |1516In **C higher functions** (`c/*.c`):1718| Need | Write | Do not write |19|------|--------|----------------|20| Reciprocal `1/n` | `1.0/x` (restoring `div`) | `invf16(x)` |21| Inverse square root | `invsqrtf16(x)` | `1.0/sqrtf16(x)` |22| Square `x*x` | `sqrf16(x)` (fastcall, always +) | `mulf16(x,x)` / a `sqrf16` macro |23| IEEE bits | `union float16_int` from `c/math16.h` | a local `uint16_t` union |2425`pow(x, -0.5)` keeps `invsqrtf16`. Packed-half hi byte after abs: `|x|>=128` iff `m16_ieee_hi >= 0x58`. Do not fmod for `|x|<128`.2627## Agent rules28291. One major function per file; CPU copies under matching asm CPU dirs.302. 8085: stack-only; no EXX/IX/IY; legal `(de)` stores only (`a`/`hl`/post-inc).313. Classic TIMER benches for math16: use **`z88dk-classic/*.c`** (parent sources may lack `_Float16`).324. 8085 math16 often also needs `-lmath32_8085` for higher helpers — match classic recipes.335. Suite: `make -C test/suites/math test_math16.bin test_math16_z180.bin test_math16_ez80_z80.bin test_math16_z80n.bin test_math16_r2ka.bin test_math16_r4k.bin test_math16_r6k.bin test_math16_kc160.bin test_math16_8085.bin test_math16_8080.bin test_math16_gbz80.bin`. Newlib: `+rc2014 -clib=new` with `-lmath16 -lmath32` (mirror math32 rc2014 recipe).346. Higher funcs layout: `c/z80/` (sccz80 +new), `c/8085/`, `c/8080/`, `c/gbz80/`. **`c/Makefile` clean:** only remove C-derived `*.asm` in those dirs (`$(AFILES8085)` / `$(AFILES8080)` / `$(AFILESGBZ80)`); keep hand-written `cm16_sccz80_*.asm`.357. Cores: `asm/{z80,8085,8080,gbz80}/`. Packed `*` / `sqrf16` = 11×11 (`asm_f16_mul_callee` / `asm_f16_sqr`). Poly, inv, sqrt NR, hypot, fma = f24 16×16 (`asm_f24_mul_f24`).368. Unrolled 11×11 / 16×16 mulu is **`IF __CPU_Z80__` only**. z80n / z180 / ez80 / kc160 / rabbit call **`l_mulu_32_16x16`** (HW integer). Do not assemble the unrolled body into those products.379. `--math16` is **adjunct** (no conflict with math32/math48). Classic: `math16.lib` + `math16_{8085,8080,gbz80,…}.lib`. Newlib sccz80 **bakes math16 into `lib/clibs/sccz80/z80.lib`**. After core edits: delete `*math16*` `.o` under `libsrc/newlib/target/{math16,z80}/obj`, then `make -C libsrc/newlib math16 z80`. Prove `cm16_sccz80_mul_callee` is `G =` onto `asm_f16_mul_callee` (stale is `G A` at a later line).3810. Classic 8085/8080/gbz80 Makefile targets have **no OBJECTS deps**. `rm` `obj/<cpu>/…/asm_f16_*.o` and `libsrc/math16*.lib`, then `make -C libsrc math16.lib` and `cp` into `lib/clibs/`.3911. Specials stay off the finite path. Classify Inf/NaN on overflow / zero / equal-exp 255 (packed exp 31) only. `inc r` / `jp Z` tests exp==255 (8-bit inc sets Z, not C). Pack underflow is unsigned `jp C` after `sub 112` (not `jp M`: d=255 → 143 looks minus). Packed Inf × tiny finite (sum−15 < 31) may not be Inf.4012. gbz80: no cheap `ex (sp),hl` (148c helper). Open-code: park DE, `ld hl,sp+n`, swap through `(hl)`, restore DE; **BC is often the return**. No `jp P` / `ret m` (no S): `bit 7,h`.4113. MPL v2 panel on **`asm/`** cores only — not `c/` glue, lm16 aliases, or C (some C is GPL).4214. Restoring f24 div: z80 uses `exx` + `djnz` (count in `B'`). 8085 / 8080 / gbz80 have no spare count register (B is the divisor). After prenorm, DE is free: **stacked ret** — push `div_pack`, 15× `div_bit`, `jp div_bit`; `div_bit` ends in `ret`. Do **not** `call div_bit` 16 times. 8080/gbz80 inner `push de`/`push af` sit above those words. z80 keeps the `djnz` loop.4344### Calling vs math324546Many half API symbols are plain `defc sinf16 = _m16_sinf` (true DEHL) even with47`-D__CLASSIC` — **not** the math32 stack-bridge trap. Still prefer map proof48(`sinf16` / `sqrtf16` / `invsqrtf16`) after link. Fair n-body: math16 may keep49`invsqrtf16`; math32 TIMER source should use `1.0/sqrt` on both classic and newlib.5051## Related5253- `library-math32`, `cpu-8085`, `methodology-measure`, `library-newlib` (header regen)54- Product readme: math16 `README.md` under the float tree
z88dk