%g should not print 0 as infe-308 (#185)
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@ -490,21 +490,27 @@ static size_t _etoa(out_fct_type out, char *buffer, size_t idx, size_t maxlen, d
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} conv;
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conv.F = value;
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int exp2 = (int) ((conv.U >> 52U) & 0x07FFU) - 1023; // effectively log2
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conv.U = (conv.U & ((1ULL << 52U) - 1U)) | (1023ULL << 52U); // drop the exponent so conv.F is now in [1,2)
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// now approximate log10 from the log2 integer part and an expansion of ln around 1.5
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int expval = (int) (0.1760912590558 + exp2 * 0.301029995663981 + (conv.F - 1.5) * 0.289529654602168);
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// now we want to compute 10^expval but we want to be sure it won't overflow
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exp2 = (int) (expval * 3.321928094887362 + 0.5);
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const double z = expval * 2.302585092994046 - exp2 * 0.6931471805599453;
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const double z2 = z * z;
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conv.U = (uint64_t) (exp2 + 1023) << 52U;
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// compute exp(z) using continued fractions, see https://en.wikipedia.org/wiki/Exponential_function#Continued_fractions_for_ex
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conv.F *= 1 + 2 * z / (2 - z + (z2 / (6 + (z2 / (10 + z2 / 14)))));
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// correct for rounding errors
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if (value < conv.F) {
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expval--;
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conv.F /= 10;
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int expval;
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if (conv.U) {
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int exp2 = (int) ((conv.U >> 52U) & 0x07FFU) - 1023; // effectively log2
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conv.U = (conv.U & ((1ULL << 52U) - 1U)) | (1023ULL << 52U); // drop the exponent so conv.F is now in [1,2)
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// now approximate log10 from the log2 integer part and an expansion of ln around 1.5
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expval = (int) (0.1760912590558 + exp2 * 0.301029995663981 + (conv.F - 1.5) * 0.289529654602168);
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// now we want to compute 10^expval but we want to be sure it won't overflow
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exp2 = (int) (expval * 3.321928094887362 + 0.5);
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const double z = expval * 2.302585092994046 - exp2 * 0.6931471805599453;
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const double z2 = z * z;
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conv.U = (uint64_t) (exp2 + 1023) << 52U;
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// compute exp(z) using continued fractions, see https://en.wikipedia.org/wiki/Exponential_function#Continued_fractions_for_ex
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conv.F *= 1 + 2 * z / (2 - z + (z2 / (6 + (z2 / (10 + z2 / 14)))));
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// correct for rounding errors
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if (value < conv.F) {
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expval--;
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conv.F /= 10;
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}
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} else {
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expval = 0;
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conv.F = 1;
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}
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// the exponent format is "%+03d" and largest value is "307", so set aside 4-5 characters
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@ -513,7 +519,7 @@ static size_t _etoa(out_fct_type out, char *buffer, size_t idx, size_t maxlen, d
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// in "%g" mode, "prec" is the number of *significant figures* not decimals
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if (flags & FLAGS_ADAPT_EXP) {
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// do we want to fall-back to "%f" mode?
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if ((value >= 1e-4) && (value < 1e6)) {
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if ((value == 0.0) || ((value >= 1e-4) && (value < 1e6))) {
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if ((int) prec > expval) {
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prec = (unsigned) ((int) prec - expval - 1);
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} else {
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