ADS1115 analog gain signal module - how to run it with espruino?

Sure, I think your first port of call would be to try and replace the readRegister/writeRegister commands that were in arduino:

static void writeRegister(uint8_t i2cAddress, uint8_t reg, uint16_t value) {
  Wire.beginTransmission(i2cAddress);
  i2cwrite((uint8_t)reg);
  i2cwrite((uint8_t)(value>>8));
  i2cwrite((uint8_t)(value & 0xFF));
  Wire.endTransmission();
}

static uint16_t readRegister(uint8_t i2cAddress, uint8_t reg) {
  Wire.beginTransmission(i2cAddress);
  i2cwrite(ADS1015_REG_POINTER_CONVERT);
  Wire.endTransmission();
  Wire.requestFrom(i2cAddress, (uint8_t)2);
  return ((i2cread() << 8) | i2cread());  
}

In Espruino I reckon they should look like this:

var REG = {
   MASK : 3,
    CONVERT : 0,
    CONFIG : 1,
    LOWTHRESH : 2,
    HITHRESH : 3
};

function ADS1X15(i2c) {
  this.i2c = i2c;
  this.addr = 0x48;
}

ADS1X15.prototype.writeRegister = function(reg, value) {
  this.i2c.writeTo(this.addr, reg, value>>8, value);  
};

ADS1X15.prototype.readRegister = function(reg) {
  this.i2c.writeTo(this.addr, reg);  
  var d = this.i2c.readFrom(this.addr, 2);
  return (d[0] << 8) | d[1];  
};

// then try with
I2C1.setup({ scl : ..., sda: ...} );
var ads = new ADS1X15(I2C1);
console.log(ads.readRegister(REG.CONVERT));

That might actually print the conversion value... But for a fully working ADC you'll need to look at readADC_SingleEnded and copy what that's doing.

It does use a delay there, so I'd be tempted to use a callback to return the values instead, as it means Espruino can get on with other stuff in the mean time:

... getADC = function(callback) {
  // ..
  setTimeout(function() {
    var a = ...;
    callback(a);
  }, );
}

Maybe define a 'config' variable instead of all the #defines as well,

var CONFIG = {
OS_MASK      : (0x8000),
OS_SINGLE    : (0x8000),  // Write: Set to start a single-conversion
OS_BUSY      : (0x0000),  // Read: Bit = 0 when conversion is in progress
OS_NOTBUSY   : (0x8000),  // Read: Bit = 1 when device is not performing a conversion
            
MUX_MASK     : (0x7000),
MUX_DIFF_0_1 : (0x0000),  // Differential P = AIN0, N = AIN1 (default)
MUX_DIFF_0_3 : (0x1000),  // Differential P = AIN0, N = AIN3
MUX_DIFF_1_3 : (0x2000),  // Differential P = AIN1, N = AIN3
MUX_DIFF_2_3 : (0x3000),  // Differential P = AIN2, N = AIN3
MUX_SINGLE_0 : (0x4000),  // Single-ended AIN0
MUX_SINGLE_1 : (0x5000),  // Single-ended AIN1
MUX_SINGLE_2 : (0x6000),  // Single-ended AIN2
MUX_SINGLE_3 : (0x7000),  // Single-ended AIN3
            
PGA_MASK     : (0x0E00),
PGA_6_144V   : (0x0000),  // +/-6.144V range = Gain 2/3
PGA_4_096V   : (0x0200),  // +/-4.096V range = Gain 1
PGA_2_048V   : (0x0400),  // +/-2.048V range = Gain 2 (default)
PGA_1_024V   : (0x0600),  // +/-1.024V range = Gain 4
PGA_0_512V   : (0x0800),  // +/-0.512V range = Gain 8
PGA_0_256V   : (0x0A00),  // +/-0.256V range = Gain 16
            
MODE_MASK    : (0x0100),
MODE_CONTIN  : (0x0000),  // Continuous conversion mode
MODE_SINGLE  : (0x0100),  // Power-down single-shot mode (default)
          
DR_MASK      : (0x00E0),  
DR_128SPS    : (0x0000),  // 128 samples per second
DR_250SPS    : (0x0020),  // 250 samples per second
DR_490SPS    : (0x0040),  // 490 samples per second
DR_920SPS    : (0x0060),  // 920 samples per second
DR_1600SPS   : (0x0080),  // 1600 samples per second (default)
DR_2400SPS   : (0x00A0),  // 2400 samples per second
DR_3300SPS   : (0x00C0),  // 3300 samples per second
         
CMODE_MASK   : (0x0010),
CMODE_TRAD   : (0x0000),  // Traditional comparator with hysteresis (default)
CMODE_WINDOW : (0x0010),  // Window comparator
          
CPOL_MASK    : (0x0008),
CPOL_ACTVLOW : (0x0000),  // ALERT/RDY pin is low when active (default)
CPOL_ACTVHI  : (0x0008),  // ALERT/RDY pin is high when active
        
CLAT_MASK    : (0x0004),  // Determines if ALERT/RDY pin latches once asserted
CLAT_NONLAT  : (0x0000),  // Non-latching comparator (default)
CLAT_LATCH   : (0x0004),  // Latching comparator
           
CQUE_MASK    : (0x0003),
CQUE_1CONV   : (0x0000),  // Assert ALERT/RDY after one conversions
CQUE_2CONV   : (0x0001),  // Assert ALERT/RDY after two conversions
CQUE_4CONV   : (0x0002),  // Assert ALERT/RDY after four conversions
CQUE_NONE    : (0x0003),  // Disable the comparator and put ALERT/RDY in high state (default)
};

hope that helps!