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NoLongerBreathedIn
NoLongerBreathedIn
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MMIX, 36 bytes (9 instrs)

3FFF0001 F60100FF 3B00003F E0FFB5D4 E5FFF333 E6FFF9DE E7FF6484 1E0000FF F8010000

Explanation

3FFF0001: SRU $255,$0,1
F60100FF: PUT rD,$255 Put input / 2 in hidiv register.
3B00003F: SLU $0,$0,1 Multiply input by \$2^{63}\$ (mod \$2^{64}\$).
E0FFB5D4: SETH $255,#B5D4
E5FFF333: INCMH $255,#F333
E6FFF9DE: INCML $255,#F9DE
E7FF6484: INCL $255,#6484 Set temp to \$\lfloor\sqrt2\mathop\cdot2^{63}\rfloor\$.
1E0000FF: DIVU $0,$0,$255 Divide \$2^{63}\$ times input by temp.¹
F8010000: POP 1,0 Return one register

The value of 0xb5d4f333f9de6484 I used for \$\sqrt2\mathop\cdot2^{63}\$ was hand-calculated by bisecting search.

  1. DIVU $X,$Y,$Z sets $X to the quotient of rD * 2^64 + $Y divided by $Z, rounding down (and rR to the remainder, though it isn't used).

MMIX, 36 bytes

3FFF0001 F60100FF 3B00003F E0FFB5D4 E5FFF333 E6FFF9DE E7FF6484 1E0000FF F8010000

Explanation

3FFF0001: SRU $255,$0,1
F60100FF: PUT rD,$255 Put input / 2 in hidiv register.
3B00003F: SLU $0,$0,1 Multiply input by \$2^{63}\$ (mod \$2^{64}\$).
E0FFB5D4: SETH $255,#B5D4
E5FFF333: INCMH $255,#F333
E6FFF9DE: INCML $255,#F9DE
E7FF6484: INCL $255,#6484 Set temp to \$\lfloor\sqrt2\mathop\cdot2^{63}\rfloor\$.
1E0000FF: DIVU $0,$0,$255 Divide \$2^{63}\$ times input by temp.¹
F8010000: POP 1,0 Return one register

The value of 0xb5d4f333f9de6484 I used for \$\sqrt2\mathop\cdot2^{63}\$ was hand-calculated by bisecting search.

  1. DIVU $X,$Y,$Z sets $X to the quotient of rD * 2^64 + $Y divided by $Z, rounding down (and rR to the remainder, though it isn't used).

MMIX, 36 bytes (9 instrs)

3FFF0001 F60100FF 3B00003F E0FFB5D4 E5FFF333 E6FFF9DE E7FF6484 1E0000FF F8010000

Explanation

3FFF0001: SRU $255,$0,1
F60100FF: PUT rD,$255 Put input / 2 in hidiv register.
3B00003F: SLU $0,$0,1 Multiply input by \$2^{63}\$ (mod \$2^{64}\$).
E0FFB5D4: SETH $255,#B5D4
E5FFF333: INCMH $255,#F333
E6FFF9DE: INCML $255,#F9DE
E7FF6484: INCL $255,#6484 Set temp to \$\lfloor\sqrt2\mathop\cdot2^{63}\rfloor\$.
1E0000FF: DIVU $0,$0,$255 Divide \$2^{63}\$ times input by temp.¹
F8010000: POP 1,0 Return one register

The value of 0xb5d4f333f9de6484 I used for \$\sqrt2\mathop\cdot2^{63}\$ was hand-calculated by bisecting search.

  1. DIVU $X,$Y,$Z sets $X to the quotient of rD * 2^64 + $Y divided by $Z, rounding down (and rR to the remainder, though it isn't used).
Clarified my calculation method.
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NoLongerBreathedIn
NoLongerBreathedIn
  • 1.9k
  • 9
  • 11

MMIX, 36 bytes

3FFF0001 F60100FF 3B00003F E0FFB5D4 E5FFF333 E6FFF9DE E7FF6484 1E0000FF F8010000

Explanation

3FFF0001: SRU $255,$0,1
F60100FF: PUT rD,$255 Put input / 2 in hidiv register.
3B00003F: SLU $0,$0,1 Multiply input by \$2^{63}\$ (mod \$2^{64}\$).
E0FFB5D4: SETH $255,#B5D4
E5FFF333: INCMH $255,#F333
E6FFF9DE: INCML $255,#F9DE
E7FF6484: INCL $255,#6484 Set temp to \$\lfloor\sqrt2\mathop\cdot2^{63}\rfloor\$.
1E0000FF: DIVU $0,$0,$255 Divide \$2^{63}\$ times input by temp.¹
F8010000: POP 1,0 Return one register

The value of 0xb5d4f333f9de6484 I used for \$\sqrt2\mathop\cdot2^{63}\$ was hand-calculated by bisecting search.

  1. DIVU $X,$Y,$Z sets $X to the quotient of rD * 2^64 + $Y divided by $Z, rounding down (and rR to the remainder, though it isn't used).

MMIX, 36 bytes

3FFF0001 F60100FF 3B00003F E0FFB5D4 E5FFF333 E6FFF9DE E7FF6484 1E0000FF F8010000

Explanation

3FFF0001: SRU $255,$0,1
F60100FF: PUT rD,$255 Put input / 2 in hidiv register.
3B00003F: SLU $0,$0,1 Multiply input by \$2^{63}\$ (mod \$2^{64}\$).
E0FFB5D4: SETH $255,#B5D4
E5FFF333: INCMH $255,#F333
E6FFF9DE: INCML $255,#F9DE
E7FF6484: INCL $255,#6484 Set temp to \$\lfloor\sqrt2\mathop\cdot2^{63}\rfloor\$.
1E0000FF: DIVU $0,$0,$255 Divide \$2^{63}\$ times input by temp.¹
F8010000: POP 1,0 Return one register

The value of 0xb5d4f333f9de6484 I used for \$\sqrt2\mathop\cdot2^{63}\$ was hand-calculated.

  1. DIVU $X,$Y,$Z sets $X to the quotient of rD * 2^64 + $Y divided by $Z, rounding down (and rR to the remainder, though it isn't used).

MMIX, 36 bytes

3FFF0001 F60100FF 3B00003F E0FFB5D4 E5FFF333 E6FFF9DE E7FF6484 1E0000FF F8010000

Explanation

3FFF0001: SRU $255,$0,1
F60100FF: PUT rD,$255 Put input / 2 in hidiv register.
3B00003F: SLU $0,$0,1 Multiply input by \$2^{63}\$ (mod \$2^{64}\$).
E0FFB5D4: SETH $255,#B5D4
E5FFF333: INCMH $255,#F333
E6FFF9DE: INCML $255,#F9DE
E7FF6484: INCL $255,#6484 Set temp to \$\lfloor\sqrt2\mathop\cdot2^{63}\rfloor\$.
1E0000FF: DIVU $0,$0,$255 Divide \$2^{63}\$ times input by temp.¹
F8010000: POP 1,0 Return one register

The value of 0xb5d4f333f9de6484 I used for \$\sqrt2\mathop\cdot2^{63}\$ was hand-calculated by bisecting search.

  1. DIVU $X,$Y,$Z sets $X to the quotient of rD * 2^64 + $Y divided by $Z, rounding down (and rR to the remainder, though it isn't used).
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NoLongerBreathedIn
NoLongerBreathedIn
  • 1.9k
  • 9
  • 11

MMIX, 36 bytes

3FFF0001 F60100FF 3B00003F E0FFB5D4 E5FFF333 E6FFF9DE E7FF6484 1E0000FF F8010000

Explanation

3FFF0001: SRU $255,$0,1
F60100FF: PUT rD,$255 Put input / 2 in hidiv register.
3B00003F: SLU $0,$0,1 Multiply input by \$2^{63}\$ (mod \$2^{64}\$).
E0FFB5D4: SETH $255,#B5D4
E5FFF333: INCMH $255,#F333
E6FFF9DE: INCML $255,#F9DE
E7FF6484: INCL $255,#6484 Set temp to \$\lfloor\sqrt2\mathop\cdot2^{63}\rfloor\$.
1E0000FF: DIVU $0,$0,$255 Divide \$2^{63}\$ times input by temp.¹
F8010000: POP 1,0 Return one register

The value of 0xb5d4f333f9de6484 I used for \$\sqrt2\mathop\cdot2^{63}\$ was hand-calculated.

  1. DIVU $X,$Y,$Z sets $X to the quotient of rD * 2^64 + $Y divided by $Z, rounding down (and rR to the remainder, though it isn't used).