How do I calculate the SPI CRC-16 in C?

Ross N. Williams's article is the go-to:

http://www.ross.net/crc/download/crc_v3.txt

via: https://blog.mbedded.ninja/programming/general/crcs-cyclic-redundancy-checks/

Is the polynomial X1+X3 same as x^16+x^3+x^1. And what about initial value? What byte order should I input the 16-bit data? Should I reverse the bits?

To get the CRC samples, just set up that SPI as master, and then play with it in the debugger:

(gdb) set SPI2->CRCPR=0x5 // is this the poly you are after?
(gdb) set SPI2->CR1=0x2b44 // LSB bit = 0, i.e. MSB first, master 16-bit, CRC enabled
(gdb) p /x *SPI2 // checking - note TXCRCR = 0, that's the initial value
$37 = {CR1 = 0x2b44, CR2 = 0x0, SR = 0x2, DR = 0xffff, CRCPR = 0x5,
 RXCRCR = 0x0, TXCRCR = 0x0, I2SCFGR = 0x0, I2SPR = 0x2}
(gdb) set SPI2->DR=0x1234 // just Tx something
(gdb) p /x *SPI2
$38 = {CR1 = 0x2b44, CR2 = 0x0, SR = 0x3, DR = 0xffff, CRCPR = 0x5,
 RXCRCR = 0xc, TXCRCR = 0x5ae4, I2SCFGR = 0x0, I2SPR = 0x2}

compare TXCRC=0x5ae4 to calculation on web calculator:

Now let's try the same thing just LSB first:

(gdb) set SPI2->CR1=0 // switch off SPI
(gdb) p /x *SPI2
$39 = {CR1 = 0x0, CR2 = 0x0, SR = 0x2, DR = 0xffff, CRCPR = 0x5,
 RXCRCR = 0xc, TXCRCR = 0x5ae4, I2SCFGR = 0x0, I2SPR = 0x2}
(gdb) set SPI2->CR1=0x2bc4 // same setup except LSB set
(gdb) p /x *SPI2
$40 = {CR1 = 0x2bc4, CR2 = 0x0, SR = 0x2, DR = 0xffff, CRCPR = 0x5,
 RXCRCR = 0x0, TXCRCR = 0x0, I2SCFGR = 0x0, I2SPR = 0x2}
(gdb) set SPI2->DR=0x1234 // same data
(gdb) p /x *SPI2
$41 = {CR1 = 0x2bc4, CR2 = 0x0, SR = 0x3, DR = 0xffff, CRCPR = 0x5,
 RXCRCR = 0xc, TXCRCR = 0x9d68, I2SCFGR = 0x0, I2SPR = 0x2}
(gdb)

Note, that now we had to reverse both bit order and bytes order (the web-calculator feeds byte-wise):

JW