How is the carry flag being set in this assembly code?

Question

Given the following assembly code for a 16-bit PRNG function,

$80/8111 E2 20       SEP #$20   ; set 8-bit mode accumulator
$80/8113 AD E5 05    LDA $05E5  ; load low byte of last random number
$80/8116 8D 02 42    STA $4202
$80/8119 A9 05       LDA #$05   ; multiply it by 5
$80/811B 8D 03 42    STA $4203
$80/811E EA          NOP
$80/811F C2 20       REP #$20   ; set 16-bit mode accumulator
$80/8121 AD 16 42    LDA $4216  ; load the resultant product
$80/8124 48          PHA        ; push it onto the stack
$80/8125 E2 20       SEP #$20   ; 8-bit
$80/8127 AD E6 05    LDA $05E6  ; load high byte of last random number
$80/812A 8D 02 42    STA $4202
$80/812D A9 05       LDA #$05   ; multiply by 5
$80/812F 8D 03 42    STA $4203
$80/8132 EB          XBA        ; exchange high and low bytes of accumulator
$80/8133 EA          NOP
$80/8134 AD 16 42    LDA $4216  ; load low byte of product
$80/8137 38          SEC
$80/8138 63 02       ADC $02,s  ; add to it the high byte of the original product
$80/813A 83 02       STA $02,s  ; save it to the high byte of the original product
$80/813C C2 20       REP #$20   ; 16-bit
$80/813E 68          PLA        ; pull it from the stack
$80/813F 69 11 00    ADC #$0011 ; add 11
$80/8142 8D E5 05    STA $05E5  ; save as new random number
$80/8145 6B          RTL

a user by the name of @sagara translated the code to C:

#define LOW(exp)  ((exp) & 0x00FF)
#define HIGH(exp) (((exp) & 0xFF00) >> 8)

uint16_t prng(uint16_t v) {

    uint16_t low  = LOW(v);
    uint16_t high = HIGH(v);

    uint16_t mul_low  = low  * 5;
    uint16_t mul_high = high * 5;

    // need to check for overflow, since final addition is adc as well
    uint16_t v1    = LOW(mul_high) + HIGH(mul_low) + 1;
    uint8_t  carry = HIGH(v1) ? 1 : 0;

    uint16_t v2 = (LOW(v1) << 8) + LOW(mul_low);

    return (v2 + 0x11 + carry);
}

I'm confused by two things.

1. In this line...

   uint16_t v1    = LOW(mul_high) + HIGH(mul_low) + 1;
   

   Why is there a + 1? I think it's because of the ADC operation, but how can we be sure that the carry flag is set to 1? What previous operation would guarantee this? The XBC? I read a few posts such as Assembly ADC (Add with carry) to C++ and Overflow and Carry flags on Z80 but it's not clear to me because the instruction set appears to be different I'm not familiar with 65C816 assembly. (This is from a popular 1994 SNES game whose NA release anniversary recently passed; free upvote to the correct guess :-)

2. In the next line...

   uint8_t  carry = HIGH(v1) ? 1 : 0;
   

   Why would it work this way? I read this as, "Set the carry flag if and only if the high byte is non-zero." But wouldn't the indication of an overflow be only if the high byte is zero? (I'm probably misinterpreting what the line is doing.)

Thanks in advance for any insights.

Answer 1

1. but how can we be sure that the carry flag is set to 1? What previous operation would guarantee this?

$80/8137 38          SEC   ; SEt Carry flag

---

2. uint8_t carry = HIGH(v1) ? 1 : 0;
   Why would it work this way? I read this as, "Set the carry flag if and only if the high byte is non-zero." But wouldn't the indication of an overflow be only if the high byte is zero?

The addition ADC #$0011 is using the carry from ADC $02,s. When ADC $02,s is performed, the accumulator is set to 8-bit (because of SEP #$20), so the carry flag will be set if the result of ADC $02,s would've exceeded 8 bits (i.e. if you would've got something >= $100 in 16-bit mode).
In the C version you've got a 16-bit variable (v1) to hold the result, so your carry will be in bit 8 of v1, which you can test with HIGH(v1) == 1, or simply HIGH(v1) since it will either be 1 or 0.

Answer 2

1) The line

$80/8137 38     SEC

is explicity setting the carry just before an ADC add-with-carry instruction, that's why the +1 in the C code.

2) The processor has an 8-bit accumulator, and the addition will overflow to the carry, ready for the next ADC instruction. However, the C code is using a 16-bit variable v1, and the carry remains in the upper 8 bits. Hence the test of those upper 8 bits to extract the so-called "carry".