--- /dev/null
+/*
+ * C89 (+ long long) code to convert 64-bit IEEE 754 floating-point numbers to
+ * 16-bit floating-point numbers (OpenEXR et al), without any special hardware
+ * support for either format. Written from scratch by Steinar H. Gunderson
+ * <sgunderson@bigfoot.com>, put in the public domain.
+ */
+#include <stdio.h>
+#include <math.h>
+#include <stdlib.h>
+
+const int FP64_BIAS = 1023;
+const int FP64_MANTISSA_BITS = 52;
+const int FP64_EXPONENT_BITS = 11;
+const int FP64_MAX_EXPONENT = 0x7FF;
+
+#if 1
+const int FP16_BIAS = 15;
+const int FP16_MANTISSA_BITS = 10;
+const int FP16_EXPONENT_BITS = 5;
+const int FP16_MAX_EXPONENT = 0x1F;
+typedef unsigned short fp16_int_t;
+#else
+/* test using fp32, since we can verify against the FPU */
+const int FP16_BIAS = 127;
+const int FP16_MANTISSA_BITS = 23;
+const int FP16_EXPONENT_BITS = 8;
+typedef unsigned int fp16_int_t;
+#endif
+
+union fp64 {
+ double f;
+ unsigned long long ll;
+};
+union fp32 {
+ float f;
+ unsigned u;
+};
+
+double fromfp16(fp16_int_t x)
+{
+ int sign = x >> (FP16_MANTISSA_BITS + FP16_EXPONENT_BITS);
+ int exponent = (x & ((1ULL << (FP16_MANTISSA_BITS + FP16_EXPONENT_BITS)) - 1)) >> FP16_MANTISSA_BITS;
+ unsigned long long mantissa = x & ((1ULL << FP16_MANTISSA_BITS) - 1);
+
+ int sign64;
+ int exponent64;
+ unsigned long long mantissa64;
+
+ if (exponent == 0) {
+ /*
+ * Denormals, or zero. Zero is still zero, denormals become
+ * ordinary numbers.
+ */
+ if (mantissa == 0) {
+ sign64 = sign;
+ exponent64 = 0;
+ mantissa64 = 0;
+ } else {
+ sign64 = sign;
+ exponent64 = FP64_BIAS - FP16_BIAS;
+ mantissa64 = mantissa << (FP64_MANTISSA_BITS - FP16_MANTISSA_BITS + 1);
+
+ /* Normalize the number. */
+ while ((mantissa64 & (1ULL << FP64_MANTISSA_BITS)) == 0) {
+ --exponent64;
+ mantissa64 <<= 1;
+ }
+
+ /* Clear the now-implicit one-bit. */
+ mantissa64 &= ~(1ULL << FP64_MANTISSA_BITS);
+ }
+ } else if (exponent == FP16_MAX_EXPONENT) {
+ /*
+ * Infinities or NaN (mantissa=0 => infinity, otherwise NaN).
+ * We don't care much about NaNs, so let us just make sure we
+ * keep the first bit (which signals signalling/non-signalling
+ * in many implementations).
+ */
+ sign64 = sign;
+ exponent64 = FP64_MAX_EXPONENT;
+ mantissa64 = mantissa << (FP64_MANTISSA_BITS - FP16_MANTISSA_BITS);
+ } else {
+ sign64 = sign;
+
+ /* Up-conversion is simple. Just re-bias the exponent... */
+ exponent64 = exponent + FP64_BIAS - FP16_BIAS;
+
+ /* ...and convert the mantissa. */
+ mantissa64 = mantissa << (FP64_MANTISSA_BITS - FP16_MANTISSA_BITS);
+ }
+
+ union fp64 nx;
+ nx.ll = ((unsigned long long)sign64 << (FP64_MANTISSA_BITS + FP64_EXPONENT_BITS))
+ | ((unsigned long long)exponent64 << FP64_MANTISSA_BITS)
+ | mantissa64;
+ return nx.f;
+}
+
+unsigned long long shift_right_with_round(unsigned long long x, unsigned shift)
+{
+ /* shifts >= 64 need to be special-cased */
+ if (shift > 64) {
+ return 0;
+ } else if (shift == 64) {
+ if (x > (1ULL << 63)) {
+ return 1;
+ } else {
+ return 0;
+ }
+ }
+
+ unsigned long long round_part = x & ((1ULL << shift) - 1);
+ if (round_part < (1ULL << (shift - 1))) {
+ /* round down */
+ x >>= shift;
+ } else if (round_part > (1ULL << (shift - 1))) {
+ /* round up */
+ x >>= shift;
+ ++x;
+ } else {
+ /* round to nearest even number */
+ x >>= shift;
+ if ((x & 1) != 0) {
+ ++x;
+ }
+ }
+ return x;
+}
+
+fp16_int_t tofp16(double x)
+{
+ union fp64 nx;
+ nx.f = x;
+ unsigned long long f = nx.ll;
+ int sign = f >> (FP64_MANTISSA_BITS + FP64_EXPONENT_BITS);
+ int exponent = (f & ((1ULL << (FP64_MANTISSA_BITS + FP64_EXPONENT_BITS)) - 1)) >> FP64_MANTISSA_BITS;
+ unsigned long long mantissa = f & ((1ULL << FP64_MANTISSA_BITS) - 1);
+
+ int sign16;
+ int exponent16;
+ unsigned long long mantissa16;
+
+ if (exponent == 0) {
+ /*
+ * Denormals, or zero. The largest possible 64-bit
+ * denormal is about +- 2^-1022, and the smallest possible
+ * 16-bit denormal is +- 2^-24. Thus, we can safely
+ * just set all of these to zero (but keep the sign bit).
+ */
+ sign16 = sign;
+ exponent16 = 0;
+ mantissa16 = 0;
+ } else if (exponent == FP64_MAX_EXPONENT) {
+ /*
+ * Infinities or NaN (mantissa=0 => infinity, otherwise NaN).
+ * We don't care much about NaNs, so let us just keep the first
+ * bit (which signals signalling/ non-signalling) and make sure
+ * that we don't coerce NaNs down to infinities.
+ */
+ if (mantissa == 0) {
+ sign16 = sign;
+ exponent16 = FP16_MAX_EXPONENT;
+ mantissa16 = 0;
+ } else {
+ sign16 = sign; /* undefined */
+ exponent16 = FP16_MAX_EXPONENT;
+ mantissa16 = mantissa >> (FP64_MANTISSA_BITS - FP16_MANTISSA_BITS);
+ if (mantissa16 == 0) {
+ mantissa16 = 1;
+ }
+ }
+ } else {
+ /* Re-bias the exponent, and check if we will create a denormal. */
+ exponent16 = exponent + FP16_BIAS - FP64_BIAS;
+ if (exponent16 <= 0) {
+ int shift_amount = FP64_MANTISSA_BITS - FP16_MANTISSA_BITS - exponent16 + 1;
+ sign16 = sign;
+ exponent16 = 0;
+ mantissa16 = shift_right_with_round(mantissa | (1ULL << FP64_MANTISSA_BITS), shift_amount);
+
+ /*
+ * We could actually have rounded back into the lowest possible non-denormal
+ * here, so check for that.
+ */
+ if (mantissa16 == (1ULL << FP16_MANTISSA_BITS)) {
+ exponent16 = 1;
+ mantissa16 = 0;
+ }
+ } else {
+ /*
+ * First, round off the mantissa, since that could change
+ * the exponent. We use standard IEEE 754r roundTiesToEven
+ * mode.
+ */
+ sign16 = sign;
+ mantissa16 = shift_right_with_round(mantissa, FP64_MANTISSA_BITS - FP16_MANTISSA_BITS);
+
+ /* Check if we overflowed and need to increase the exponent. */
+ if (mantissa16 == (1ULL << FP16_MANTISSA_BITS)) {
+ ++exponent16;
+ mantissa16 = 0;
+ }
+
+ /* Finally, check for overflow, and create +- inf if we need to. */
+ if (exponent16 >= FP16_MAX_EXPONENT) {
+ exponent16 = FP16_MAX_EXPONENT;
+ mantissa16 = 0;
+ }
+ }
+ }
+
+ return (sign16 << (FP16_MANTISSA_BITS + FP16_EXPONENT_BITS))
+ | (exponent16 << FP16_MANTISSA_BITS)
+ | mantissa16;
+}
+
+int main(void)
+{
+#if 1
+ printf("%.9f\n", fromfp16(0x34aa));
+ printf("%.9f = %04x => %.9f\n\n", 1.0, tofp16(1.0), fromfp16(tofp16(1.0)));
+ printf("%.9f = %04x => %.9f\n\n", 1.0/3.0, tofp16(1.0/3.0), fromfp16(tofp16(1.0/3.0)));
+ printf("%.9f = %04x => %.9f\n\n", 0.0, tofp16(0.0), fromfp16(tofp16(0.0)));
+
+ {
+ int i;
+ double t = 7.999;
+ for (i = 0; i < 2800; ++i) {
+ t *= 3.0;
+ printf("%.9f = %04x => %.9f\n\n", t, tofp16(t), fromfp16(tofp16(t)));
+ }
+ }
+#else
+ /*
+ * Randomly test a large number of fp64 -> fp32 conversions, comparing
+ * against the FPU.
+ */
+ unsigned long long num = 0;
+ srand((time_t)time(NULL));
+
+ for ( ;; ) {
+ unsigned r1 = rand();
+ unsigned r2 = rand();
+ unsigned r3 = rand();
+ union fp64 f;
+ union fp32 fs;
+
+ f.ll = (((unsigned long long)r1) << 33) ^ ((unsigned long long)r2 << 16) ^ r3;
+ fs.f = (float)f.f;
+
+ if (tofp16(f.f) != fs.u) {
+ printf("%llx (%.15f): FPU says %x, our code says %x\n", f.ll, f.f, fs.u, tofp16(f.f));
+ }
+
+ if (++num % 1048576 == 0) {
+ printf("%lluM checked, last: %llx -> %x\n", num / 1048576, f.ll, fs.u);
+ }
+ }
+#endif
+ exit(0);
+}
projects / fp-downconvert / commitdiff