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-rw-r--r--lib/mlibc/options/ansi/generic/math-stubs.ignored-cpp1831
1 files changed, 1831 insertions, 0 deletions
diff --git a/lib/mlibc/options/ansi/generic/math-stubs.ignored-cpp b/lib/mlibc/options/ansi/generic/math-stubs.ignored-cpp
new file mode 100644
index 0000000..9be985f
--- /dev/null
+++ b/lib/mlibc/options/ansi/generic/math-stubs.ignored-cpp
@@ -0,0 +1,1831 @@
+
+#include <math.h>
+#include <immintrin.h>
+
+#include <bits/ensure.h>
+
+#include <stdint.h>
+
+#include <mlibc/debug.hpp>
+
+// Taken from musl. See musl for the license/copyright!
+#define FORCE_EVAL(x) do { \
+ if (sizeof(x) == sizeof(float)) { \
+ volatile float __x; \
+ __x = (x); \
+ } else if (sizeof(x) == sizeof(double)) { \
+ volatile double __x; \
+ __x = (x); \
+ } else { \
+ volatile long double __x; \
+ __x = (x); \
+ } \
+} while(0)
+
+namespace ieee754 {
+
+struct SoftDouble {
+ typedef uint64_t Bits;
+ typedef uint64_t Mantissa;
+ typedef int16_t Exp;
+
+ static constexpr int kMantissaBits = 52;
+ static constexpr int kExpBits = 11;
+ static constexpr int kBias = 1023;
+
+ // this exponent represents zeros (when mantissa = 0) and subnormals (when mantissa != 0)
+ static constexpr Exp kSubExp = -kBias;
+ // this exponent represents infinities (when mantissa = 0) and NaNs (when mantissa != 0)
+ static constexpr Exp kInfExp = ((Exp(1) << kExpBits) - 1) - kBias;
+
+ static constexpr Bits kMantissaMask = (Bits(1) << kMantissaBits) - 1;
+ static constexpr Bits kExpMask = ((Bits(1) << kExpBits) - 1) << kMantissaBits;
+ static constexpr Bits kSignMask = Bits(1) << (kMantissaBits + kExpBits);
+
+ SoftDouble(bool negative, Mantissa mantissa, Exp exp)
+ : negative(negative), mantissa(mantissa), exp(exp) {
+// mlibc::infoLogger.log() << "(" << (int)negative << ", " << (void *)mantissa
+// << ", " << exp << ")" << frg::end_log;
+ __ensure(mantissa < (Mantissa(1) << kMantissaBits));
+ __ensure((exp + kBias) >= 0);
+ __ensure((exp + kBias) < (Exp(1) << kExpBits));
+ }
+
+ const bool negative;
+ const Mantissa mantissa;
+ const Exp exp;
+};
+
+template<typename F>
+using Bits = typename F::Bits;
+
+template<typename F>
+using Mantissa = typename F::Mantissa;
+
+template<typename F>
+using Exp = typename F::Exp;
+
+template<typename F>
+bool isZero(F x) {
+ return x.exp == F::kSubExp && x.mantissa == 0;
+}
+
+template<typename F>
+bool isFinite(F x) {
+ return x.exp != F::kInfExp;
+}
+
+// --------------------------------------------------------
+// Soft float operations
+// --------------------------------------------------------
+
+template<typename F>
+F constZero(bool negative) {
+ return F(negative, 0, F::kSubExp);
+}
+
+template<typename F>
+F constOne(bool negative) {
+ return F(negative, 0, 0);
+}
+
+template<typename F>
+F floor(F x) {
+ if(!isFinite(x) || isZero(x)) // TODO: need exception for the not-finite case?
+ return x;
+
+ if(x.exp > F::kMantissaBits)
+ return x; // x is already integral
+
+ if(x.exp < 0) {
+ // TODO: raise inexact
+ // return -1 or +0
+ return x.negative ? constOne<F>(true) : constZero<F>(false);
+ }
+
+ Mantissa<F> mask = F::kMantissaMask >> x.exp;
+ if(!(x.mantissa & mask))
+ return x; // x is already integral
+
+ // TODO: raise inexact
+ Mantissa<F> integral_position = (Mantissa<F>(1) << F::kMantissaBits) >> x.exp;
+ if(x.negative)
+ return F(true, (x.mantissa + integral_position) & (~mask), x.exp);
+ return F(false, x.mantissa & (~mask), x.exp);
+}
+
+template<typename F>
+F ceil(F x) {
+ if(!isFinite(x) || isZero(x)) // TODO: need exception for the not-finite case?
+ return x;
+
+ if(x.exp > F::kMantissaBits)
+ return x; // x is already integral
+
+ if(x.exp < 0) {
+ // TODO: raise inexact
+ // return -0 or +1
+ return x.negative ? constZero<F>(true) : constOne<F>(false);
+ }
+
+ Mantissa<F> mask = F::kMantissaMask >> x.exp;
+ if(!(x.mantissa & mask))
+ return x; // x is already integral
+
+ // TODO: raise inexact
+ Mantissa<F> integral_position = (Mantissa<F>(1) << F::kMantissaBits) >> x.exp;
+ if(x.negative)
+ return F(true, x.mantissa & (~mask), x.exp);
+ return F(false, (x.mantissa + integral_position) & (~mask), x.exp);
+}
+
+// --------------------------------------------------------
+// Soft float <-> bit string conversion functions
+// --------------------------------------------------------
+
+template<typename F>
+uint64_t compileBits(F soft) {
+ auto bits = Bits<F>(soft.mantissa) | ((Bits<F>(soft.exp) + F::kBias) << soft.kMantissaBits);
+ return soft.negative ? (F::kSignMask | bits) : bits;
+}
+
+SoftDouble extractBits(uint64_t bits) {
+ return SoftDouble(bits & SoftDouble::kSignMask, bits & SoftDouble::kMantissaMask,
+ ((bits & SoftDouble::kExpMask) >> SoftDouble::kMantissaBits) - SoftDouble::kBias);
+}
+
+// --------------------------------------------------------
+// Soft float -> native float conversion functions
+// --------------------------------------------------------
+
+union DoubleBits {
+ double fp;
+ uint64_t bits;
+};
+
+double compileNative(SoftDouble soft) {
+ DoubleBits word;
+ word.bits = compileBits(soft);
+ return word.fp;
+}
+
+SoftDouble extractNative(double native) {
+ DoubleBits word;
+ word.fp = native;
+ return extractBits(word.bits);
+}
+
+} // namespace ieee754
+
+int __mlibc_fpclassify(double x) {
+ return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x);
+}
+int __mlibc_fpclassifyf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+int __mlibc_fpclassifyl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double acos(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float acosf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double acosl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double asin(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float asinf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double asinl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double atan(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float atanf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double atanl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double atan2(double x, double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float atan2f(float x, float y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double atan2l(long double x, long double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+// Taken from musl. See musl for the license/copyright!
+float __sindf(double x) {
+ /* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */
+ static const double S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */
+ S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */
+ S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */
+ S4 = 0x16cd878c3b46a7.0p-71; /* 0.0000027183114939898219064 */
+
+ double r, s, w, z;
+
+ /* Try to optimize for parallel evaluation as in __tandf.c. */
+ z = x*x;
+ w = z*z;
+ r = S3 + z*S4;
+ s = z*x;
+ return (x + s*(S1 + z*S2)) + s*w*r;
+}
+
+// Taken from musl. See musl for the license/copyright!
+float __cosdf(double x) {
+ /* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */
+ static const double C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */
+ C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */
+ C2 = -0x16c087e80f1e27.0p-62, /* -0.00138867637746099294692 */
+ C3 = 0x199342e0ee5069.0p-68; /* 0.0000243904487962774090654 */
+
+ double r, w, z;
+
+ /* Try to optimize for parallel evaluation as in __tandf.c. */
+ z = x*x;
+ w = z*z;
+ r = C2+z*C3;
+ return ((1.0+z*C0) + w*C1) + (w*z)*r;
+}
+
+float __tandf(double x, int odd) {
+ /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
+ static const double T[] = {
+ 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
+ 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
+ 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
+ 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
+ 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
+ 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
+ };
+
+ double z,r,w,s,t,u;
+
+ z = x*x;
+ /*
+ * Split up the polynomial into small independent terms to give
+ * opportunities for parallel evaluation. The chosen splitting is
+ * micro-optimized for Athlons (XP, X64). It costs 2 multiplications
+ * relative to Horner's method on sequential machines.
+ *
+ * We add the small terms from lowest degree up for efficiency on
+ * non-sequential machines (the lowest degree terms tend to be ready
+ * earlier). Apart from this, we don't care about order of
+ * operations, and don't need to to care since we have precision to
+ * spare. However, the chosen splitting is good for accuracy too,
+ * and would give results as accurate as Horner's method if the
+ * small terms were added from highest degree down.
+ */
+ r = T[4] + z*T[5];
+ t = T[2] + z*T[3];
+ w = z*z;
+ s = z*x;
+ u = T[0] + z*T[1];
+ r = (x + s*u) + (s*w)*(t + w*r);
+ return odd ? -1.0/r : r;
+}
+
+#define DBL_EPSILON 2.22044604925031308085e-16
+#define EPS DBL_EPSILON
+
+/* Get a 32 bit int from a float. */
+#define GET_FLOAT_WORD(w,d) \
+do { \
+ union {float f; uint32_t i;} __u; \
+ __u.f = (d); \
+ (w) = __u.i; \
+} while (0)
+
+/* Get the more significant 32 bit int from a double. */
+#define GET_HIGH_WORD(hi,d) \
+do { \
+ union {double f; uint64_t i;} __u; \
+ __u.f = (d); \
+ (hi) = __u.i >> 32; \
+} while (0)
+
+/* Get the less significant 32 bit int from a double. */
+#define GET_LOW_WORD(lo,d) \
+do { \
+ union {double f; uint64_t i;} __u; \
+ __u.f = (d); \
+ (lo) = (uint32_t)__u.i; \
+} while (0)
+
+// Taken from musl. See musl for the license/copyright!
+int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec)
+{
+ static const int init_jk[] = {3,4,4,6}; /* initial value for jk */
+
+ /*
+ * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
+ *
+ * integer array, contains the (24*i)-th to (24*i+23)-th
+ * bit of 2/pi after binary point. The corresponding
+ * floating value is
+ *
+ * ipio2[i] * 2^(-24(i+1)).
+ *
+ * NB: This table must have at least (e0-3)/24 + jk terms.
+ * For quad precision (e0 <= 16360, jk = 6), this is 686.
+ */
+ static const int32_t ipio2[] = {
+ 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
+ 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
+ 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
+ 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
+ 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
+ 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
+ 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
+ 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
+ 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
+ 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
+ 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
+
+ #if LDBL_MAX_EXP > 1024
+ 0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6,
+ 0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2,
+ 0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35,
+ 0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30,
+ 0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C,
+ 0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4,
+ 0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770,
+ 0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7,
+ 0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19,
+ 0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522,
+ 0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16,
+ 0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6,
+ 0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E,
+ 0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48,
+ 0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3,
+ 0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF,
+ 0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55,
+ 0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612,
+ 0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929,
+ 0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC,
+ 0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B,
+ 0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C,
+ 0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4,
+ 0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB,
+ 0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC,
+ 0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C,
+ 0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F,
+ 0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5,
+ 0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437,
+ 0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B,
+ 0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA,
+ 0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD,
+ 0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3,
+ 0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3,
+ 0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717,
+ 0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F,
+ 0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61,
+ 0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB,
+ 0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51,
+ 0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0,
+ 0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C,
+ 0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6,
+ 0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC,
+ 0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED,
+ 0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328,
+ 0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D,
+ 0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0,
+ 0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B,
+ 0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4,
+ 0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3,
+ 0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F,
+ 0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD,
+ 0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B,
+ 0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4,
+ 0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761,
+ 0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31,
+ 0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30,
+ 0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262,
+ 0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E,
+ 0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1,
+ 0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C,
+ 0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4,
+ 0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08,
+ 0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196,
+ 0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9,
+ 0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4,
+ 0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC,
+ 0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C,
+ 0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0,
+ 0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C,
+ 0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0,
+ 0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC,
+ 0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22,
+ 0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893,
+ 0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7,
+ 0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5,
+ 0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F,
+ 0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4,
+ 0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF,
+ 0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B,
+ 0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2,
+ 0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138,
+ 0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E,
+ 0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569,
+ 0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34,
+ 0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9,
+ 0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D,
+ 0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F,
+ 0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855,
+ 0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569,
+ 0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B,
+ 0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE,
+ 0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41,
+ 0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49,
+ 0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F,
+ 0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110,
+ 0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8,
+ 0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365,
+ 0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A,
+ 0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270,
+ 0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5,
+ 0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616,
+ 0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B,
+ 0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0,
+ #endif
+ };
+
+ static const double PIo2[] = {
+ 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
+ 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
+ 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
+ 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
+ 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
+ 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
+ 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
+ 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
+ };
+
+ int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
+ double z,fw,f[20],fq[20],q[20];
+
+ /* initialize jk*/
+ jk = init_jk[prec];
+ jp = jk;
+
+ /* determine jx,jv,q0, note that 3>q0 */
+ jx = nx-1;
+ jv = (e0-3)/24; if(jv<0) jv=0;
+ q0 = e0-24*(jv+1);
+
+ /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
+ j = jv-jx; m = jx+jk;
+ for (i=0; i<=m; i++,j++)
+ f[i] = j<0 ? 0.0 : (double)ipio2[j];
+
+ /* compute q[0],q[1],...q[jk] */
+ for (i=0; i<=jk; i++) {
+ for (j=0,fw=0.0; j<=jx; j++)
+ fw += x[j]*f[jx+i-j];
+ q[i] = fw;
+ }
+
+ jz = jk;
+recompute:
+ /* distill q[] into iq[] reversingly */
+ for (i=0,j=jz,z=q[jz]; j>0; i++,j--) {
+ fw = (double)(int32_t)(0x1p-24*z);
+ iq[i] = (int32_t)(z - 0x1p24*fw);
+ z = q[j-1]+fw;
+ }
+
+ /* compute n */
+ z = scalbn(z,q0); /* actual value of z */
+ z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
+ n = (int32_t)z;
+ z -= (double)n;
+ ih = 0;
+ if (q0 > 0) { /* need iq[jz-1] to determine n */
+ i = iq[jz-1]>>(24-q0); n += i;
+ iq[jz-1] -= i<<(24-q0);
+ ih = iq[jz-1]>>(23-q0);
+ }
+ else if (q0 == 0) ih = iq[jz-1]>>23;
+ else if (z >= 0.5) ih = 2;
+
+ if (ih > 0) { /* q > 0.5 */
+ n += 1; carry = 0;
+ for (i=0; i<jz; i++) { /* compute 1-q */
+ j = iq[i];
+ if (carry == 0) {
+ if (j != 0) {
+ carry = 1;
+ iq[i] = 0x1000000 - j;
+ }
+ } else
+ iq[i] = 0xffffff - j;
+ }
+ if (q0 > 0) { /* rare case: chance is 1 in 12 */
+ switch(q0) {
+ case 1:
+ iq[jz-1] &= 0x7fffff; break;
+ case 2:
+ iq[jz-1] &= 0x3fffff; break;
+ }
+ }
+ if (ih == 2) {
+ z = 1.0 - z;
+ if (carry != 0)
+ z -= scalbn(1.0,q0);
+ }
+ }
+
+ /* check if recomputation is needed */
+ if (z == 0.0) {
+ j = 0;
+ for (i=jz-1; i>=jk; i--) j |= iq[i];
+ if (j == 0) { /* need recomputation */
+ for (k=1; iq[jk-k]==0; k++); /* k = no. of terms needed */
+
+ for (i=jz+1; i<=jz+k; i++) { /* add q[jz+1] to q[jz+k] */
+ f[jx+i] = (double)ipio2[jv+i];
+ for (j=0,fw=0.0; j<=jx; j++)
+ fw += x[j]*f[jx+i-j];
+ q[i] = fw;
+ }
+ jz += k;
+ goto recompute;
+ }
+ }
+
+ /* chop off zero terms */
+ if (z == 0.0) {
+ jz -= 1;
+ q0 -= 24;
+ while (iq[jz] == 0) {
+ jz--;
+ q0 -= 24;
+ }
+ } else { /* break z into 24-bit if necessary */
+ z = scalbn(z,-q0);
+ if (z >= 0x1p24) {
+ fw = (double)(int32_t)(0x1p-24*z);
+ iq[jz] = (int32_t)(z - 0x1p24*fw);
+ jz += 1;
+ q0 += 24;
+ iq[jz] = (int32_t)fw;
+ } else
+ iq[jz] = (int32_t)z;
+ }
+
+ /* convert integer "bit" chunk to floating-point value */
+ fw = scalbn(1.0,q0);
+ for (i=jz; i>=0; i--) {
+ q[i] = fw*(double)iq[i];
+ fw *= 0x1p-24;
+ }
+
+ /* compute PIo2[0,...,jp]*q[jz,...,0] */
+ for(i=jz; i>=0; i--) {
+ for (fw=0.0,k=0; k<=jp && k<=jz-i; k++)
+ fw += PIo2[k]*q[i+k];
+ fq[jz-i] = fw;
+ }
+
+ /* compress fq[] into y[] */
+ switch(prec) {
+ case 0:
+ fw = 0.0;
+ for (i=jz; i>=0; i--)
+ fw += fq[i];
+ y[0] = ih==0 ? fw : -fw;
+ break;
+ case 1:
+ case 2:
+ fw = 0.0;
+ for (i=jz; i>=0; i--)
+ fw += fq[i];
+ // TODO: drop excess precision here once double_t is used
+ fw = (double)fw;
+ y[0] = ih==0 ? fw : -fw;
+ fw = fq[0]-fw;
+ for (i=1; i<=jz; i++)
+ fw += fq[i];
+ y[1] = ih==0 ? fw : -fw;
+ break;
+ case 3: /* painful */
+ for (i=jz; i>0; i--) {
+ fw = fq[i-1]+fq[i];
+ fq[i] += fq[i-1]-fw;
+ fq[i-1] = fw;
+ }
+ for (i=jz; i>1; i--) {
+ fw = fq[i-1]+fq[i];
+ fq[i] += fq[i-1]-fw;
+ fq[i-1] = fw;
+ }
+ for (fw=0.0,i=jz; i>=2; i--)
+ fw += fq[i];
+ if (ih==0) {
+ y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
+ } else {
+ y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
+ }
+ }
+ return n&7;
+}
+
+int __rem_pio2f(float x, double *y) {
+ /*
+ * invpio2: 53 bits of 2/pi
+ * pio2_1: first 25 bits of pi/2
+ * pio2_1t: pi/2 - pio2_1
+ */
+ static const double toint = 1.5/EPS,
+ invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+ pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
+ pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
+
+ union {float f; uint32_t i;} u = {x};
+ double tx[1],ty[1];
+ double fn;
+ uint32_t ix;
+ int n, sign, e0;
+
+ ix = u.i & 0x7fffffff;
+ /* 25+53 bit pi is good enough for medium size */
+ if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */
+ /* Use a specialized rint() to get fn. Assume round-to-nearest. */
+ fn = (double)x*invpio2 + toint - toint;
+ n = (int32_t)fn;
+ *y = x - fn*pio2_1 - fn*pio2_1t;
+ return n;
+ }
+ if(ix>=0x7f800000) { /* x is inf or NaN */
+ *y = x-x;
+ return 0;
+ }
+ /* scale x into [2^23, 2^24-1] */
+ sign = u.i>>31;
+ e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */
+ u.i = ix - (e0<<23);
+ tx[0] = u.f;
+ n = __rem_pio2_large(tx,ty,e0,1,0);
+ if (sign) {
+ *y = -ty[0];
+ return -n;
+ }
+ *y = ty[0];
+ return n;
+}
+
+double cos(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+// Taken from musl. See musl for the license/copyright!
+float cosf(float x) {
+ /* Small multiples of pi/2 rounded to double precision. */
+ static const double c1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
+ c2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
+ c3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
+ c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
+
+ double y;
+ uint32_t ix;
+ unsigned n, sign;
+
+ GET_FLOAT_WORD(ix, x);
+ sign = ix >> 31;
+ ix &= 0x7fffffff;
+
+ if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
+ if (ix < 0x39800000) { /* |x| < 2**-12 */
+ /* raise inexact if x != 0 */
+ FORCE_EVAL(x + 0x1p120f);
+ return 1.0f;
+ }
+ return __cosdf(x);
+ }
+ if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
+ if (ix > 0x4016cbe3) /* |x| ~> 3*pi/4 */
+ return -__cosdf(sign ? x+c2pio2 : x-c2pio2);
+ else {
+ if (sign)
+ return __sindf(x + c1pio2);
+ else
+ return __sindf(c1pio2 - x);
+ }
+ }
+ if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
+ if (ix > 0x40afeddf) /* |x| ~> 7*pi/4 */
+ return __cosdf(sign ? x+c4pio2 : x-c4pio2);
+ else {
+ if (sign)
+ return __sindf(-x - c3pio2);
+ else
+ return __sindf(x - c3pio2);
+ }
+ }
+
+ /* cos(Inf or NaN) is NaN */
+ if (ix >= 0x7f800000)
+ return x-x;
+
+ /* general argument reduction needed */
+ n = __rem_pio2f(x,&y);
+ switch (n&3) {
+ case 0: return __cosdf(y);
+ case 1: return __sindf(-y);
+ case 2: return -__cosdf(y);
+ default:
+ return __sindf(y);
+ }
+}
+long double cosl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double sin(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+// Taken from musl. See musl for the license/copyright!
+float sinf(float x) {
+ /* Small multiples of pi/2 rounded to double precision. */
+ static const double s1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
+ s2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
+ s3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
+ s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
+
+ double y;
+ uint32_t ix;
+ int n, sign;
+
+ GET_FLOAT_WORD(ix, x);
+ sign = ix >> 31;
+ ix &= 0x7fffffff;
+
+ if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
+ if (ix < 0x39800000) { /* |x| < 2**-12 */
+ /* raise inexact if x!=0 and underflow if subnormal */
+ FORCE_EVAL(ix < 0x00800000 ? x/0x1p120f : x+0x1p120f);
+ return x;
+ }
+ return __sindf(x);
+ }
+ if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
+ if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */
+ if (sign)
+ return -__cosdf(x + s1pio2);
+ else
+ return __cosdf(x - s1pio2);
+ }
+ return __sindf(sign ? -(x + s2pio2) : -(x - s2pio2));
+ }
+ if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
+ if (ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */
+ if (sign)
+ return __cosdf(x + s3pio2);
+ else
+ return -__cosdf(x - s3pio2);
+ }
+ return __sindf(sign ? x + s4pio2 : x - s4pio2);
+ }
+
+ /* sin(Inf or NaN) is NaN */
+ if (ix >= 0x7f800000)
+ return x - x;
+
+ /* general argument reduction needed */
+ n = __rem_pio2f(x, &y);
+ switch (n&3) {
+ case 0: return __sindf(y);
+ case 1: return __cosdf(y);
+ case 2: return __sindf(-y);
+ default:
+ return -__cosdf(y);
+ }
+}
+long double sinl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double tan(double x) {
+ mlibc::infoLogger() << "mlibc: tan() is not precise" << frg::endlog;
+ return tanf(x);
+}
+// Taken from musl. See musl for the license/copyright!
+float tanf(float x) {
+ /* Small multiples of pi/2 rounded to double precision. */
+ static const double t1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
+ t2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
+ t3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
+ t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
+
+ double y;
+ uint32_t ix;
+ unsigned n, sign;
+
+ GET_FLOAT_WORD(ix, x);
+ sign = ix >> 31;
+ ix &= 0x7fffffff;
+
+ if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
+ if (ix < 0x39800000) { /* |x| < 2**-12 */
+ /* raise inexact if x!=0 and underflow if subnormal */
+ FORCE_EVAL(ix < 0x00800000 ? x/0x1p120f : x+0x1p120f);
+ return x;
+ }
+ return __tandf(x, 0);
+ }
+ if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
+ if (ix <= 0x4016cbe3) /* |x| ~<= 3pi/4 */
+ return __tandf((sign ? x+t1pio2 : x-t1pio2), 1);
+ else
+ return __tandf((sign ? x+t2pio2 : x-t2pio2), 0);
+ }
+ if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
+ if (ix <= 0x40afeddf) /* |x| ~<= 7*pi/4 */
+ return __tandf((sign ? x+t3pio2 : x-t3pio2), 1);
+ else
+ return __tandf((sign ? x+t4pio2 : x-t4pio2), 0);
+ }
+
+ /* tan(Inf or NaN) is NaN */
+ if (ix >= 0x7f800000)
+ return x - x;
+
+ /* argument reduction */
+ n = __rem_pio2f(x, &y);
+ return __tandf(y, n&1);
+}
+long double tanl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double acosh(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float acoshf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double acoshl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double asinh(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float asinhf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double asinhl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double atanh(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float atanhf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double atanhl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double cosh(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float coshf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double coshl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double sinh(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float sinhf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double sinhl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double tanh(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float tanhf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double tanhl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double exp(double x) {
+ static const double half[2] = {0.5,-0.5},
+ ln2hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
+ ln2lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
+ invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
+ P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
+ P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
+ P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
+ P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
+ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
+
+ double hi, lo, c, xx, y;
+ int k, sign;
+ uint32_t hx;
+
+ GET_HIGH_WORD(hx, x);
+ sign = hx>>31;
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* special cases */
+ if (hx >= 0x4086232b) { /* if |x| >= 708.39... */
+ if (isnan(x))
+ return x;
+ if (x > 709.782712893383973096) {
+ /* overflow if x!=inf */
+ x *= 0x1p1023;
+ return x;
+ }
+ if (x < -708.39641853226410622) {
+ /* underflow if x!=-inf */
+ FORCE_EVAL((float)(-0x1p-149/x));
+ if (x < -745.13321910194110842)
+ return 0;
+ }
+ }
+
+ /* argument reduction */
+ if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if (hx >= 0x3ff0a2b2) /* if |x| >= 1.5 ln2 */
+ k = (int)(invln2*x + half[sign]);
+ else
+ k = 1 - sign - sign;
+ hi = x - k*ln2hi; /* k*ln2hi is exact here */
+ lo = k*ln2lo;
+ x = hi - lo;
+ } else if (hx > 0x3e300000) { /* if |x| > 2**-28 */
+ k = 0;
+ hi = x;
+ lo = 0;
+ } else {
+ /* inexact if x!=0 */
+ FORCE_EVAL(0x1p1023 + x);
+ return 1 + x;
+ }
+
+ /* x is now in primary range */
+ xx = x*x;
+ c = x - xx*(P1+xx*(P2+xx*(P3+xx*(P4+xx*P5))));
+ y = 1 + (x*c/(2-c) - lo + hi);
+ if (k == 0)
+ return y;
+ return scalbn(y, k);
+}
+float expf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double expl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double exp2(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+// Taken from musl. See musl for the license/copyright!
+float exp2f(float x) {
+ constexpr int TBLSIZE = 16;
+
+ constexpr float redux = 0x1.8p23f / TBLSIZE;
+ constexpr float P1 = 0x1.62e430p-1f;
+ constexpr float P2 = 0x1.ebfbe0p-3f;
+ constexpr float P3 = 0x1.c6b348p-5f;
+ constexpr float P4 = 0x1.3b2c9cp-7f;
+
+ constexpr double exp2ft[TBLSIZE] = {
+ 0x1.6a09e667f3bcdp-1,
+ 0x1.7a11473eb0187p-1,
+ 0x1.8ace5422aa0dbp-1,
+ 0x1.9c49182a3f090p-1,
+ 0x1.ae89f995ad3adp-1,
+ 0x1.c199bdd85529cp-1,
+ 0x1.d5818dcfba487p-1,
+ 0x1.ea4afa2a490dap-1,
+ 0x1.0000000000000p+0,
+ 0x1.0b5586cf9890fp+0,
+ 0x1.172b83c7d517bp+0,
+ 0x1.2387a6e756238p+0,
+ 0x1.306fe0a31b715p+0,
+ 0x1.3dea64c123422p+0,
+ 0x1.4bfdad5362a27p+0,
+ 0x1.5ab07dd485429p+0,
+ };
+
+ double t, r, z;
+ union {float f; uint32_t i;} u = {x};
+ union {double f; uint64_t i;} uk;
+ uint32_t ix, i0, k;
+
+ /* Filter out exceptional cases. */
+ ix = u.i & 0x7fffffff;
+ if (ix > 0x42fc0000) { /* |x| > 126 */
+ if (ix > 0x7f800000) /* NaN */
+ return x;
+ if (u.i >= 0x43000000 && u.i < 0x80000000) { /* x >= 128 */
+ x *= 0x1p127f;
+ return x;
+ }
+ if (u.i >= 0x80000000) { /* x < -126 */
+ if (u.i >= 0xc3160000 || (u.i & 0x0000ffff))
+ FORCE_EVAL(-0x1p-149f/x);
+ if (u.i >= 0xc3160000) /* x <= -150 */
+ return 0;
+ }
+ } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */
+ return 1.0f + x;
+ }
+
+ /* Reduce x, computing z, i0, and k. */
+ u.f = x + redux;
+ i0 = u.i;
+ i0 += TBLSIZE / 2;
+ k = i0 / TBLSIZE;
+ uk.i = (uint64_t)(0x3ff + k)<<52;
+ i0 &= TBLSIZE - 1;
+ u.f -= redux;
+ z = x - u.f;
+ /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
+ r = exp2ft[i0];
+ t = r * z;
+ r = r + t * (P1 + z * P2) + t * (z * z) * (P3 + z * P4);
+
+ /* Scale by 2**k */
+ return r * uk.f;
+}
+long double exp2l(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double expm1(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float expm1f(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double expm1l(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double frexp(double x, int *power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float frexpf(float x, int *power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double frexpl(long double x, int *power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double ilogb(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float ilogbf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double ilogbl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double ldexp(double x, int power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float ldexpf(float x, int power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double ldexpl(long double x, int power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double log(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float logf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double logl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double log10(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float log10f(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double log10l(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double log1p(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float log1pf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double log1pl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+// Taken from musl. See musl for the license/copyright!
+double log2(double x) {
+ static const double
+ ivln2hi = 1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */
+ ivln2lo = 1.67517131648865118353e-10, /* 0x3de705fc, 0x2eefa200 */
+ Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
+ Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
+ Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
+ Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
+ Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
+ Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
+ Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+ union {double f; uint64_t i;} u = {x};
+ double hfsq,f,s,z,R,w,t1,t2,y,hi,lo,val_hi,val_lo;
+ uint32_t hx;
+ int k;
+
+ hx = u.i>>32;
+ k = 0;
+ if (hx < 0x00100000 || hx>>31) {
+ if (u.i<<1 == 0)
+ return -1/(x*x); /* log(+-0)=-inf */
+ if (hx>>31)
+ return (x-x)/0.0; /* log(-#) = NaN */
+ /* subnormal number, scale x up */
+ k -= 54;
+ x *= 0x1p54;
+ u.f = x;
+ hx = u.i>>32;
+ } else if (hx >= 0x7ff00000) {
+ return x;
+ } else if (hx == 0x3ff00000 && u.i<<32 == 0)
+ return 0;
+
+ /* reduce x into [sqrt(2)/2, sqrt(2)] */
+ hx += 0x3ff00000 - 0x3fe6a09e;
+ k += (int)(hx>>20) - 0x3ff;
+ hx = (hx&0x000fffff) + 0x3fe6a09e;
+ u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
+ x = u.f;
+
+ f = x - 1.0;
+ hfsq = 0.5*f*f;
+ s = f/(2.0+f);
+ z = s*s;
+ w = z*z;
+ t1 = w*(Lg2+w*(Lg4+w*Lg6));
+ t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+ R = t2 + t1;
+
+ /*
+ * f-hfsq must (for args near 1) be evaluated in extra precision
+ * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
+ * This is fairly efficient since f-hfsq only depends on f, so can
+ * be evaluated in parallel with R. Not combining hfsq with R also
+ * keeps R small (though not as small as a true `lo' term would be),
+ * so that extra precision is not needed for terms involving R.
+ *
+ * Compiler bugs involving extra precision used to break Dekker's
+ * theorem for spitting f-hfsq as hi+lo, unless double_t was used
+ * or the multi-precision calculations were avoided when double_t
+ * has extra precision. These problems are now automatically
+ * avoided as a side effect of the optimization of combining the
+ * Dekker splitting step with the clear-low-bits step.
+ *
+ * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
+ * precision to avoid a very large cancellation when x is very near
+ * these values. Unlike the above cancellations, this problem is
+ * specific to base 2. It is strange that adding +-1 is so much
+ * harder than adding +-ln2 or +-log10_2.
+ *
+ * This uses Dekker's theorem to normalize y+val_hi, so the
+ * compiler bugs are back in some configurations, sigh. And I
+ * don't want to used double_t to avoid them, since that gives a
+ * pessimization and the support for avoiding the pessimization
+ * is not yet available.
+ *
+ * The multi-precision calculations for the multiplications are
+ * routine.
+ */
+
+ /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
+ hi = f - hfsq;
+ u.f = hi;
+ u.i &= (uint64_t)-1<<32;
+ hi = u.f;
+ lo = f - hi - hfsq + s*(hfsq+R);
+
+ val_hi = hi*ivln2hi;
+ val_lo = (lo+hi)*ivln2lo + lo*ivln2hi;
+
+ /* spadd(val_hi, val_lo, y), except for not using double_t: */
+ y = k;
+ w = y + val_hi;
+ val_lo += (y - w) + val_hi;
+ val_hi = w;
+
+ return val_lo + val_hi;
+}
+float log2f(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double log2l(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double logb(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float logbf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double logbl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double modf(double x, double *integral) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float modff(float x, float *integral) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double modfl(long double x, long double *integral) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double scalbn(double x, int n) {
+ union {double f; uint64_t i;} u;
+ double y = x;
+
+ if (n > 1023) {
+ y *= 0x1p1023;
+ n -= 1023;
+ if (n > 1023) {
+ y *= 0x1p1023;
+ n -= 1023;
+ if (n > 1023)
+ n = 1023;
+ }
+ } else if (n < -1022) {
+ /* make sure final n < -53 to avoid double
+ rounding in the subnormal range */
+ y *= 0x1p-1022 * 0x1p53;
+ n += 1022 - 53;
+ if (n < -1022) {
+ y *= 0x1p-1022 * 0x1p53;
+ n += 1022 - 53;
+ if (n < -1022)
+ n = -1022;
+ }
+ }
+ u.i = (uint64_t)(0x3ff+n)<<52;
+ x = y * u.f;
+ return x;
+}
+float scalbnf(float x, int power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double scalbnl(long double x, int power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double scalbln(double x, long power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float scalblnf(float x, long power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double scalblnl(long double x, long power) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double cbrt(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float cbrtf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double cbrtl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double fabs(double x) {
+ return signbit(x) ? -x : x;
+}
+float fabsf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double fabsl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double hypot(double x, double y) {
+ __ensure(isfinite(x));
+ __ensure(isfinite(y));
+ // TODO: fix exception handling
+ double u = fabs(x);
+ double v = fabs(y);
+ if(u > v)
+ return u * sqrt(1 + (v / u) * (v / u));
+ return v * sqrt(1 + (u / v) * (u / v));
+}
+float hypotf(float x, float y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double hypotl(long double x, long double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double pow(double x, double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float powf(float x, float y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double powl(long double x, long double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double sqrt(double x) {
+ auto sse_x = _mm_set_sd(x);
+ return _mm_cvtsd_f64(_mm_sqrt_sd(sse_x, sse_x));
+}
+float sqrtf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double sqrtl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double erf(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float erff(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double erfl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double erfc(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float erfcf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double erfcl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double lgamma(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float lgammaf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double lgammal(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double tgamma(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float tgammaf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double tgammal(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double ceil(double x) {
+ auto soft_x = ieee754::extractNative(x);
+ auto result = ieee754::ceil(soft_x);
+ return ieee754::compileNative(result);
+}
+float ceilf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double ceill(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double floor(double x) {
+ auto soft_x = ieee754::extractNative(x);
+ auto result = ieee754::floor(soft_x);
+ return ieee754::compileNative(result);
+}
+float floorf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double floorl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double nearbyint(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float nearbyintf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double nearbyintl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double rint(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float rintf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double rintl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+long lrint(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long lrintf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long lrintl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+long long llrint(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long long llrintf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long long llrintl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double round(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float roundf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double roundl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+long lround(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long lroundf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long lroundl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+long long llround(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long long llroundf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long long llroundl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double trunc(double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float truncf(float x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double truncl(long double x) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double fmod(double x, double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float fmodf(float x, float y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double fmodl(long double x, long double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double remainder(double x, double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float remainderf(float x, float y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double remainderl(long double x, long double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double remquo(double x, double y, int *quotient) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float remquof(float x, float y, int *quotient) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double remquol(long double x, long double y, int *quotient) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double copysign(double x, double sign) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float copysignf(float x, float sign) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double copysignl(long double x, long double sign) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double nan(const char *tag) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float nanf(const char *tag) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double nanl(const char *tag) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double nextafter(double x, double dir) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float nextafterf(float x, float dir) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double nextafterl(long double x, long double dir) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double nexttoward(double x, long double dir) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float nexttowardf(float x, long double dir) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double nexttowardl(long double x, long double dir) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double fdim(double x, double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+float fdimf(float x, float y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double fdiml(long double x, long double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double fmax(double x, double y) {
+ __ensure(isfinite(x) && isfinite(y));
+ return x < y ? y : x;
+}
+float fmaxf(float x, float y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double fmaxl(long double x, long double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+double fmin(double x, double y) {
+ __ensure(isfinite(x) && isfinite(y));
+ return x < y ? x : y;
+}
+float fminf(float x, float y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+long double fminl(long double x, long double y) {
+ __ensure(!"Not implemented");
+ __builtin_unreachable();
+}
+
+//gnu extension
+
+void sincos(double x, double *sx, double *cx) {
+ mlibc::infoLogger() << "mlibc: sincos() is not precise" << frg::endlog;
+ float sxf;
+ float cxf;
+ sincosf(x, &sxf, &cxf);
+ *sx = sxf;
+ *cx = cxf;
+}
+
+void sincosf(float x, float *sx, float *cx) {
+ // This is a lazy implementation.
+ __ensure(sx);
+ __ensure(cx);
+ *sx = sinf(x);
+ *cx = cosf(x);
+}
+void sincosl(long double, long double *, long double *) {
+ __ensure(!"sincosl() not implemented");
+ __builtin_unreachable();
+}
+
+double exp10(double) {
+ __ensure(!"exp10() not implemented");
+ __builtin_unreachable();
+}
+float exp10f(float) {
+ __ensure(!"exp10f() not implemented");
+ __builtin_unreachable();
+}
+long double exp10l(long double) {
+ __ensure(!"exp10l() not implemented");
+ __builtin_unreachable();
+}
+
+double pow10(double) {
+ __ensure(!"pow10() not implemented");
+ __builtin_unreachable();
+}
+float pow10f(float) {
+ __ensure(!"pow10f() not implemented");
+ __builtin_unreachable();
+}
+long double pow10l(long double) {
+ __ensure(!"pow10l() not implemented");
+ __builtin_unreachable();
+}
+
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-23 04:33:17 +0000