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

1. One major function per file; CPU copies under matching asm CPU dirs.
2. 8085: stack-only; no EXX/IX/IY; legal (de) stores only (a/hl/post-inc).
3. Classic TIMER benches for math16: use z88dk-classic/*.c (parent sources may lack _Float16).
4. 8085 math16 often also needs -lmath32_8085 for higher helpers — match classic recipes.
5. 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).
6. 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.
7. 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).
8. 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.
9. --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).
10. 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/.
11. 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.
12. 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.
13. MPL v2 panel on asm/ cores only — not c/ glue, lm16 aliases, or C (some C is GPL).
14. 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